Emission of High-Density Tracer Molecules in Star Forming Regions

Transcription

1 Universitat de Barcelona Departament d Astronomia i Meteorologia Emission of High-Density Tracer Molecules in Star Forming Regions Òscar Morata Chirivella

2 UNIVERSITAT DE BARCELONA Departament d Astronomia i Meteorologia Emission of High-Density Tracer Molecules in Star Forming Regions Memòria presentada per Òscar Morata Chirivella per optar al grau de Doctor en Ciències Físiques Barcelona, setembre de 2001

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4 Programa de Doctorat d Astronomia i Meteorologia Bienni Memòria presentada per Òscar Morata Chirivella per optar al grau de Doctor en Ciències Físiques Directors de la tesi

5 Contents Resum de la tesi: Emissió de molècules traçadores d alta densitat en regions de formació estel lar vii 1 Introduction Molecular clouds General properties Constituents of molecular clouds Dense cores General properties Mass and virial balance Line width - size relations Ionization and magnetic support The formation and evolution of low mass stars Observations of star-forming regions Tracers of dense gas Line formation i

6 ii CONTENTS Differences between tracers of high density gas Goals and structure of this work CS observations of star-forming regions Introduction Observations Individual sources HH AFGL 6366S L W75S L General discussion CS emission Comparison with NH 3 results Conclusions Introduction to chemistry in molecular clouds Introduction Gas phase reactions Ion-molecule reactions Neutral-neutral reactions Radiative association reactions

7 CONTENTS iii Radiative recombination Dissociative recombination Charge transfer reactions Negative ion reactions Cosmic ray ionization Photochemistry Grain chemistry General properties of grains Interaction between gas and dust grains Initial gas phase reactions Modeling the chemistry in interstellar clouds Gas-phase models Modeling the gas dust interaction Setting up the equations Writing down the rate equations Choosing the reaction set Running the model The distribution of CS and NH 3 in star-forming regions Introduction Gas-phase chemistry of CS and NH Models of CS emission

8 iv CONTENTS 5.4 Chemical Model Discussion The distribution of molecules in star-forming regions Introduction Model Results and Chemistry Early-time molecules Late-time molecules Discussion Observability Chemistry Summary Multitransitional observations of the CS core of L Introduction Observations Results Morphology of the BIMA emission Kinematic structure Physical parameters Comparison with single-dish observations Discussion

9 CONTENTS v 7.5 Summary Conclusions 189

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11 Resum de la tesi: Emissió de molècules traçadores d alta densitat en regions de formació estel lar 1. Introducció El medi interstel lar constitueix una fracció significativa de la massa total de la Galàxia. La major part d aquest material es troba en forma de gas, principalment hidrogen, heli i traces d altres elements com carboni, oxigen, nitrogen i sofre. Els grans de pols, els raigs còsmics, els camps magnètics i la radiació són els altres components que formen amb el gas la complexa estructura del medi interstel lar, tots interaccionant a través d una varietat de processos físics i químics. La distribució del gas interstel lar és molt inhomogènia i s acostuma a diferenciar diverses components, segons les condicions de temperatura i densitat. Una d aquestes components, els núvols moleculars, és particularment important perquè és on es troben les regions de formació estel lar. Els núvols moleculars són els objectes més massius de la Galàxia, amb masses de fins a 10 6 M, i són el lloc de naixement de les estrelles. El seu constituent principal és l hidrogen molecular, H 2. Malgrat això, la molècula emprada per detectar i estudiar aquests objectes és la de CO, perquè la molècula de H 2 no té un moment dipolar permanent i la seva emissió es molt feble i difícil de detectar. Els mapes de núvols moleculars presenten generalment una forma irregular distribuïda de manera no uniforme, però molt estructurada, amb estructures allargades, condensacions vii

12 viii Resum de la tesi i nuclis densos, on es produeix la formació estel lar. Les regions més grans són conegudes com a núvols moleculars gegants, com Orion. Típicament tenen masses > 10 6 M, grandàries de pc, temperatures de 20 K, extinció visual 100 magnituds, amplades de línies d uns quants km s 1, i milers d estrelles en cúmuls densos, incloent nombroses estrelles OB. A l altre extrem, hi ha els complexos més petits com Taurus o Ophiucus, coneguts com a núvols foscos, que tenen grandàries 10 pc, temperatures 10 K, extinció visual d unes poques magnituds, amplades de línies 1 km s 1, i amb relativament poques estrelles, i cap massiva. Els núvols moleculars tenen una estructura molt poc uniforme, amb densitats que varien entre cm 3. Els núvols de gas amb densitats > 10 4 cm 3 són coneguts com nuclis densos i s ha trobat que estan molt relacionats amb la formació estel lar. Aquests objectes han estat estudiats extensivament mitjançant diverses línies moleculars, com CS (J=1 0), CS (J=2 1) o NH 3 (J, K)=(1,1), i s ha trobat que tenen masses típiques d una estrella de baixa massa, 1 M. A més, s ha trobat una associació molt estreta entre nuclis i estrelles, la qual cosa indicaria que hi ha una relació entre les propietats físiques del gas dels nuclis i la seva evolució fins que es forma una estrella. Per tant, sembla que és necessari el coneixement de les condicions físiques dels núvols que donen lloc a les estrelles i d aquells que envolten els objectes estel lars joves acabats de formar per poder inferir-ne els processos físics que tenen lloc durant la seva formació. Els nuclis densos en núvols foscos es caracteritzen per tenir grandàries pc, temperatures 10 K, amplades de línia km s 1, i massa M. Ha estat trobat també que aquests nuclis semblen estar molt a prop de la condició d equilibri virial, en la qual l energia potencial gravitatòria i l energia cinètica són aproximadament iguals. També s ha trobat una correlació entre la grandària del nucli i l amplada de la línia de les molècules que són habitualment emprades per estudiar aquests objectes, com NH 3, CO, 13 CO, C 18 O o CS, del tipus V R p, on p , depenent de la massa del nucli. La formació estel lar es produeix en els nuclis densos i freds dels núvols moleculars. Aquests nuclis són identificats observacionalment com nuclis pre-estel lars, els quals estan gravitacionalment lligats, però no existeix encara en el seu interior cap protoestrella central. L evolució inicial d un nucli constaria doncs de l acreció del material envoltant, amb el creixement de la condensació central, fins que es produiria el col lapse que formaria una protoestrella hidrostàtica central, la qual aniria

13 Resum de la tesi ix acumulant material, contraient-se i escalfant-se fins que s iniciés la fusió d hidrogen, i hagués nascut la nova estrella. Hi ha hagut un gran esforç teòric per descriure aquest procés. Es pot fer una divisió per etapes que relacionaria cada una d elles amb la classificació espectral dels objectes estel lars joves en diferents classes: i) Un nucli pre-estel lar en un núvol molecular, sense una font central de lluminositat i escalfat externament. ii) Fase d acreció principal, o etapa de Classe 0; una protoestrella hidrostàtica, envoltada d un disc progenitor i d un embolcall massiu, que estaria acumulant la majoria de la seva massa, a la vegada que crea un flux bipolar energètic i molt col limat. iii) Fase d acreció tardana, o etapa de Classe I; la protoestrella està envoltada per un embolcall remanent, i acumula la resta de la massa. El disc circumstel lar creix i el flux bipolar esdevé menys energètic i menys col limat. iv) Fase T Tauri clàssica, o etapa de Classe II; l objecte estel lar jove només té al seu voltant un disc òpticament gruixut que encara està acretant matèria. v) Fase T Tauri de línia feble, o etapa de Classe III; el disc és òpticament prim i la protoestrella completa la seva contracció fins a la seqüència principal. Les primeres tres etapes correspondrien a la fase embeguda on estrella està molt enfosquida i és invisible a longituds d ona visibles. Durant les darreres dues etapes l estrella és visible a longituds d ona del visible i de l infraroig proper. Com hem vist, en les primeres etapes de la formació estel lar les estrelles estan molt embegudes en núvols densos de gas i només poden ser estudiades a longituds d ona radio o infraroges. En aquestes condicions, l observació de l emissió i absorció de línies moleculars proporciona la informació sobre la densitat, temperatura i velocitat radial del gas. La majoria de les molècules detectades en aquestes condicions de temperatura són observades per les seves transicions rotacionals dins de l estat electronic i vibracional més baix. La sensibilitat dels telescopis moderns permet detectar línies febles i espècies químiques rares fins a abundàncies de respecte a l hidrogen. Malgrat això, algunes de les molècules més importants no poden ser observades, com és el cas de H 2, N 2 o CH 4. Per tant, CO és la molècula més emprada per traçar la distribució de H 2. Tanmateix, per estudiar regions denses, com els nuclis densos, l emissió de CO és òpticament gruixuda i es fan servir altres molècules. Aquestes molècules estan tan esteses com el CO, tot i que són tres o quatre ordres de magnitud menys abundants, i necessiten densitats molt més grans de H 2 abans que estiguin prou excitades per emetre. Aquestes molècules són conegudes com traçadores del gas dens perquè la seva emissió segueix la distribució de gas dens dins dels núvols moleculars. CS, NH 3 i HCO +

14 x Resum de la tesi són exemples típics de molècules àmpliament utilitzades en l estudi de regions de formació estel lar. Des de molt aviat es va veure que es podia aconseguir molta més informació dels nuclis densos si es feien observacions de múltiples transicions d una o més molècules, perquè cada transició revela tot sovint processos a diferents temperatures que poden tenir dinàmiques molt diferents. A més, mapes de la mateixa regió en diferents molècules poden mostrar diferències més o menys importants, atribuïbles a diferències d excitació, efectes de profunditat òptica, etc. Tanmateix, es va trobar que en alguns casos la distribució del gas que s obtenia d observacions de diferents traçadors de gas d alta densitat, com CS, NH 3, HC 3 N i HCO +, era molt diferent malgrat que tenien densitats crítiques molt similars. Comparacions sistemàtiques de CS i NH 3 fent servir resolucions angulars similars van confirmar que les diferències eren reals. Per explicar aquestes diferències es van proposar diversos mecanismes: variació d abundàncies químiques, el pas de xocs que augmentaria l abundància de molècules portadores de sofre, la dispersió de l emissió per material òpticament gruixut, etc. De totes maneres, alguns resultants eren sorprenents, com la més gran extensió de l emissió de CS respecte a NH 3, quan la densitat crítica de CS és més gran i s esperaria que tracés gas lleugerament més dens. Estudis en altres regions van trobar altres relacions de correlació i anticorrelació entre les molècules, en particular de correlació entre CCS i HC 3 N i d anticorrelació d aquestes amb NH 3 en la regió TMC 1, que podria ser explicada com un efecte de l evolució química del gas: molècules de cadenes de carboni podrien ser abundants en etapes primerenques de l evolució química, mentre que l NH 3 seria abundant en les etapes tardanes. L objectiu d aquest treball és doncs estendre la comparació sistemàtica començada per Pastor et al. (1991) per confirmar amb més regions els resultats preliminars obtinguts; i explicar les diferències en l emissió com a causades per canvis en les abundàncies químiques depenent de l etapa evolucionària de la condensació on s origina. Finalment, hem seleccionat una regió de la nostra mostra per fer-hi observacions en alta resolució angular que ens permetin comprovar la validesa del model químic que hem desenvolupat.

15 Resum de la tesi xi 2. Observacions en CS de regions de formació estel lar Es va continuar l estudi de comparació sistemàtica de l emissió de les molècules CS i NH 3, en condicions similars de resolució angular, per tal de trobar com està relacionada l emissió d aquestes dues molècules amb la distribució real del gas d alta densitat. Els objectius d aquest estudi són: clarificar les diferències intrínseques entre l emissió d aquests traçadors, donar un suport estadístic més ampli a la comparació de les emissions de CS i NH 3, i confirmar les conclusions del treball preliminar de Pastor et al. (1991). Es van seleccionar fonts pertanyents a un conjunt de regions de formació estel lar ja cartografiades amb la línia NH 3 (J, K)=(1,1) amb una resolució angular similar a la que faríem servir. Les regions van ser triades de manera que hi hagués una bona distribució en distància (entre 100 pc i uns pocs kpc), grandària de les condensacions de NH 3 ( pc) i en la lluminositat de les fonts excitadores. Amb l addició de les fonts estudiades en aquest capítol hem observat 11 regions amb un total de 14 condensacions. Vam fer observacions en la transició CS (J=1 0) de quatre regions de formació estel lar (HH 43, AFGL 6366S, L673 i L1251) amb el telescopi de 14 m del Centro Astronómico de Yebes (IGN). En posicions seleccionades de cada regió vam fer també observacions addicionals de C 34 S (J=1 0). Les posicions observades en CS estaven localitzades en la mateixa graella que les posicions de mapes de NH 3 obtinguts prèviament amb el telescopi de Haystack, per tal de fer una comparació més significativa entre els mapes de CS i NH 3 de la mateixa regió. Així mateix vam observar la regió W75S amb la transició CS (J=1 0) amb el telescopi de 37 m de Haystack. Vam detectar emissió de CS (J=1 0) en les cinc regions observades. Vam buscar emissió de C 34 S (J=1 0) als pics d emissió en quatre de les regions. Vam detectar emissió de C 34 S en AFGL 6366S, L673 i L1251. La relació mitjana entre les intensitats de l emissió de CS i C 34 S és 11. Vam cartografiar l emissió estesa de CS en totes les regions. Les condensacions van ser resoltes per a totes les fonts, excepte per a AFGL 6366S, que només es va resoldre en una direcció. La morfologia de les regions era generalment la d una emissió irregular elongada que s estenia per una àmplia àrea. L emissió de CS incloïa

16 xii Resum de la tesi i connectava altres traçadors de formació estel lar, prop dels quals l emissió de CS creixia. En particular, els pics d emissió de CS es van trobar sempre localitzats a distàncies < 0.3 pc de fonts IRAS. Les condensacions de CS observades tenien una grandària mitjana de 1.3 pc, i una profunditat òptica mitjana de 1.3. La temperatura d excitació calculada per a l emissió CS era sempre clarament inferior a la temperatura cinètica de la regió, mostrant que l emissió CS està lluny d estar termalitzada. Vam calcular la massa de les condensacions integrant la densitat columnar de H 2 calculada, i la vam comparar amb la massa virial estimada a partir de la l amplada de la linia mesurada al pic d emissió de CS i suposant una distribució de densitat homogènia. La majoria de les masses de virial de les condensacions concorden amb les masses calculades dins d un factor 3, suggerint que els nuclis es troben prop de l equilibri virial. Els resultats també indiquen que l abundància adoptada per al CS, [CS/NH 3 ]= , és adequada. Hem confirmat l existència d una correlació entre l amplada de la línia de CS i la grandària de la condensació. Hem comprovat que aquesta correlació no és una conseqüència d efectes de selecció de la nostra mostra. El millor ajust que obtenim per les nostres dades és log V = (0.50 ± 0.12) log l + (0.19 ± 0.04). Vam comparar l emissió de CS amb els mapes de NH 3. Vam confirmar que existeix una separació 0.2 pc entre els pics d emissió de CS i NH 3. Les regions traçades per CS són més extenses que les que ho són per NH 3. En general, l emissió de CS envolta i connecta els diferents nuclis de NH 3. Tanmateix, les nostres dades suggereixen que la relació de grandàries depen de la mida de la font. Per a condensacions de NH 3 més petites que 0.5 pc, la relació mitjana és de 3.2, mentre que per a condensacions de NH 3 més grans que 0.5 pc, la relació mitjana és 1.2. Vam observar que per a espectres amb una bona relació senyal soroll observats a la mateixa posició, les línies de CS eren 0.5 km s 1 més amples que les línies de NH 3. El millor ajust que vam obtenir estava descrit per: V CS = (1.0±0.3) V NH3 + (0.5 ± 0.1) km s 1. Aquesta diferència en l amplada de la línia l atribuïm a la grandària diferent de les regions traçades per les molècules de CS i NH 3. Per explicar les diferències observades entre l emissió de CS i NH 3, ens centrem en models basats en la variació de l abundància química causada per l evolució química i física. En el capítol 5 desenvolupem un model en el qual les condensa-

17 Resum de la tesi xiii cions d alta densitat estan formades per nuclis de < 0.1 pc de grandària, que no estarien resolts amb resolucions angulars moderades com les nostres. La majoria dels nuclis es dissoldrien abans que NH 3 arribés a nivells apreciables d abundància. Tanmateix, aquests nuclis contindrien quantitats substancials de CS i la seva emissió resultaria observable. Uns pocs nuclis, aquells prou vells o en un estat d evolució física i química més avançada perquè són més densos o més massius, formen un contingut significant de NH 3. Possiblement, aquests nuclis continuarien la seva evolució per formar finalment estrelles. Aquesta diferent evolució donaria compte de les diferències de grandària entre les condensacions de CS i NH 3. El model també prediu que per a les etapes tardanes, quan l adundància fraccional de NH 3 arriba al màxim, l abundància fraccional de CS decreix i, per tant, el pic d emissió de CS no té perquè coincidir amb el de NH 3. Per tant, les diferents etapes en l evolució dels nuclis d alta densitat sembla ser capaç d explicar algunes de les diferències millor establertes entre l emissió de CS i NH 3 : les diferències en grandària i la separació entre els pics d emissió. 3. Introducció a la química en els núvols moleculars Es creu que les molècules interstel lars es formen a partir de constituents més simples per un procés de síntesi, tot i que se sospita que molècules més grans, com els PAHs, es poden formar per la degradació de entitats més grans, com els grans interstel lars. Per tant, se suposa que una quantitat abundant d àtoms i d ions són convertits mitjançant reaccions químiques en molècules que poden prendre part en noves reaccions. Generalment se suposa que la química dels núvols moleculars comença amb un gas en el qual els diversos elements es troben en les proporcions de les seves abundàncies còsmiques relatives. Això vol dir que l hidrogen és l element més abundant, i que els elements químicament importants, i dels quals es preocupa la química interstel lar, com carboni, nitrogen, oxigen, i sofre només constitueixen 0.1% de l hidrogen. Les condicions físiques de les regions que es tenen en compte, els núvols moleculars que és on es troben les molècules interstel lars, estan caracteritzades per temperatures baixes 10 < T < 100 K, i densitats de H 2 de 10 3 < n < 10 6 cm 3. El tipus general de reacció que es considera suposa dues espècies A i B, que poden

18 xiv Resum de la tesi Taula 1: Alguns processos químics bàsics Procés A + + BC AB + + C A + B AB + hν A + BC AB + C A + + e A + hν AB + + e A + B A + + B A + B + A + e A + hν A + raig còsmic A + + e AB + hν A + B A + hν A + + e A + B:gra AB + gra Nom Reacció ió molècula Associació radiativa Reacció neutre neutre Recombinació radiativa Recombinació dissociativa Reacció de transferència de càrrega Reacció d ions negatius Ionització per raigs còsmics Fotodissociació Fotoionització Formació a la superfície de grans ser neutres, ions, radicals o molècules, que reaccionen, per donar lloc als productes M i N. El ritme de cada reacció s acostuma a escriure en funció de les concentracions dels reactants i d un coeficient de reacció. L equació que controla l abundància de M ve donada per d[n(m)]/dt = k n(a) n(b). En les condicions de densitat que hi ha als núvols moleculars, es pot considerar que no es produeixen reaccions de tres cossos i que la química del gas interstel lar està basada en reaccions binàries, a menys que el tercer cos sigui un gra de pols. Les baixes temperatures cinètiques dels núvols moleculars fan que les reaccions endotèrmiques no es produeixin de manera significativa, i que només les exotèrmiques s arribin a produir, malgrat que moltes d aquestes reaccions de la fase gasosa tinguin barreres d energia d activació. En aquests casos, la secció eficaç de la reacció serà zero a menys que l energia dels reactants superi el valor de l energia d activació. Les reaccions ió molècula exotèrmiques no tenen, en general, barreres d activació, per la qual cosa dominen la química de la fase gasosa perquè es produeixen amb ritmes ràpids. És possible establir una classificació de les reaccions que es produeixen en la fase gasosa del medi interstel lar d acord amb les espècies participants, els ritmes de reacció i la dependència de la densitat i de la temperatura. A la taula 1 n indiquem les més importants. Com hem mencionat, les reaccions ió molècula dominen la química interstel lar. A més, es caracteritzen per no tenir una dependència exponencial del coeficient de reacció amb la temperatura, i els ritmes de reacció acostumen a ser

19 Resum de la tesi xv grans i prop de 10 9 cm 3 s 1. Això ha fet possible fer una estimació dels valors dels coeficients desconeguts i que es pogués modelar la química interstel lar basada en reaccions ió molècula. Fins fa poc temps, es considerava que les reaccions neutre neutre no es produien a ritmes significatius a les temperatures dels núvols molèculars. A més, hi havia una gran incertesa en la determinació dels seus ritmes de reacció, perquè era difícil predir si les reaccions neutre neutre tenien energia d activació, o quina era la forma de la seva dependència de la temperatura. Amb els anys s han anat mesurant els coeficients de reacció per cada cop més espècies a temperatures més baixes i es comença a veure que un nombre sorprenent de reaccions són ràpides, i que les reaccions neutre neutre poden jugar un paper molt més important del que es pensava. Altres tipus de reaccions interessants són les reaccions d associació radiativa que es pensa que són fonamentals en la formació de molècules complexes en la fase gasosa de núvols interstel lars densos i difusos; o la recombinació radiativa i la recombinació dissociativa que controlen el nivell d ionització del gas i, per tant, el ritme de reaccions químiques en els núvols, perquè controlen l abundància d alguns ions crítics per a la química, com H + 3. La ionització per raigs còsmics té una important influència sobre els núvols interstel lars. Primer, perquè lliga el núvol al camp magnètic galàctic, la qual cosa té un paper important en la formació estel lar; i segon, els raigs còsmics són responsables del primer pas en la química ió molècula, en produir la ionització dels àtoms i molècules d hidrogen. En cert sentit, doncs, es pot dir que la química ió molècules comença amb la ionització de les espècies neutres pels raigs còsmics. Els fotoprocessos, que es divideixen principalment en fotodissociació i fotoionització, resulten ser els agents primaris de destrucció de molècules en condicions de baixa densitat del gas. Això fa que els núvols interstel lars siguin dividits en regions difuses de baixa extinció visual on els fotons penetren apreciablement i els fenòmens fotodestructius afecten la química, o els núvols densos on la extinció visual és prou alta com perquè els efectes fotodestructius no es tinguin en compte o no siguin comparables als processos de la fase gasosa que competeixen amb ells. Tanmateix, els efectes dels fotoprocessos induïts per raigs còsmics sí que poden afectar de manera significativa algunes espècies en l interior dels núvols densos. Els grans de pols constitueixen una petita part de la massa de la Galàxia, i 1% de la massa del medi interstel lar, però el seu estudi és molt important per entendre les propietats dinàmiques, tèrmiques i químiques de les fases denses del medi interstel lar, ja que tenen una forta interacció amb el gas i les estrelles. Els grans

20 xvi Resum de la tesi de pols juguen diversos papers importants: dominen l escalfament i el refredament dels núvols a partir de fotoelectrons energètics i col lisions gas-grans; són la font dominant d opacitat i modifiquen les propietats òptiques de la llum de les estrelles; també determinen els espectres dels objectes envoltats per pols, els quals es fan servir per detectar aquests objectes; també poden ser portadors d una fracció substancial de la càrrega elèctrica. Els grans tenen una influència crucial sobre la química interstel lar. Primer, regulen la penetració de fotons de l UV llunyà, que destrueixen i ionitzen molècules. Per tant, els grans permeten que es desenvolupi una química complexa i influeixen en la composició del gas. Segon, les seves superfícies poden servir per a la formació de molècules que després tornen a la fase gasosa, com és el cas de l hidrogen molecular. Finalment, els grans poden aportar o fer desaparèixer molècules de la fase gasosa, a partir de l absorció d elements i molècules de la fase gasosa, reaccions en la fase sòlida i la posterior expulsió per causa de la destrucció de l embolcall o del gra. Aquests processos modifiquen la composició molecular dels núvols i el comportament de la química. A les temperatures trobades generalment en els núvols moleculars, les col lisions entre la component neutra del gas i la pols porta a la retenció de les partícules de la fase gasosa en la superfície dels grans, amb una gran eficiència, com demostra la detecció generalitzada d embolcalls moleculars en els grans de pols. Es calcula que per a les densitat típiques d un núvol dens, 10 4 cm 3, totes les molècules que poden ser adsorbides pels grans desapareixerien del gas en menys de 10 6 anys, un temps més curt que les vides dels nuclis densos o dels núvols moleculars. Per tant, com que encara es detecten molècules en aquestes regions, han d existeir mecanismes d expulsió que retornin aquestes molècules al gas. Els mecanismes proposats per limitar el creixement dels embolcalls dels grans s agrupen en dos grans grups: l expulsió intermitent, o esporàdica, i l expulsió contínua. Els primers agrupen principalment els efectes que la radiació procedent d una estrella acabada de formar pot tenir sobre els grans, destruint-los o evaporant-ne els embolcalls. El resultat és la creació de poblacions de molècules molt diferents de les que es troben habitualment als núvols freds. Els segons, intenten explicar l existència de molècules complexes en nuclis on no hi ha formació estel lar i que poden tenir una vida llarga. Aquests proposen mecanismes continus d expulsió dels components dels embolcalls, com els causats pel pas de raigs còsmics pesants, per la radiació UV

21 Resum de la tesi xvii induïda per la ionització per raigs còsmics de H 2, reaccions exotèrmiques a l embolcall, com la formació d H 2, que poden escalfar més o menys punts de l embolcall i produir l alliberament de les molècules contingudes. Altres mecanismes proposats són mitjançant col lisions entre grans o per efectes de xocs. La síntesi de les espècies moleculars en els núvols densos interstel lars comença amb la ionització per raigs còsmics de l abundant molècula H 2, per acabar formant la molècula H + 3, la qual és una molècula reactiva, tot i que estable, de gran importància en la química dels núvols densos perquè pot reaccionar amb moltes de les espècies atòmiques que es creu que es troben en les primeres etapes químiques. Així la reacció de H + 3 amb O dona una via d entrada a la química de l oxigen que porta a la formació de H 3 O +, OH, H 2 O i O 2. La reacció del radical OH amb C + és una entrada per a la formació de CO, CO 2 i de l important ió HCO +. La reacció de C amb H + 3 dóna entrada a la producció d hidrocarburs: CH, CH 2, CH 3, CH 4, i amb reaccions amb CO una altra via de formació de HCO +. Els ions d heli proporcionen l entrada a la química del nitrogen i produeixen la formació de NH 3, NH 2 i NH. La reacció d àtoms de nitrogen amb NH + i NH + 2 és una via de formació dels enllaços N N per formar N 2, N 2 H +. Reaccions neutres de N, NH, NH + 2 i NH + 3 amb OH o O formen NO i HNO +. La formació de lligams C N insertant nitrogen atòmic en la cadena que forma CH 2 i CH 3 permet formar CN +, HCN +, CN i HCN. Finalment, a partir de la formació d hidrocarburs es poden formar molècules orgàniques molt més complexes. 4. Modelització de la química en els núvols moleculars La modelització de la química dels núvols interstel lars, i dels núvols moleculars en particular, busca identificar les espècies que poden existir en el medi interstel lar, les rutes químiques que es veuen involucrades en la formació i la destrucció d aquestes espècies, i els processos que són significatius en els règims que són descrits, per tal d obtenir informació sobre les condicions físiques de les regions on existeixen aquestes espècies. La modelització es troba amb una sèrie de dificultats inicials. En primer lloc, cal triar d entre els processos que es produeixen en el medi interstel lar aquells que són significatius per al règim que pretenem descriure. A continuació, cal triar les reaccions químiques que cal incloure en el model. Tot i que la química inicial

22 xviii Resum de la tesi pot estar clara, hi ha incerteses associades a molts coeficients de reacció, o fins i tot incerteses sobre quins són els productes de certes reaccions, o la dinàmica de la seva formació. Finalment, la interacció entre el gas i la pols es un tema força desconegut, malgrat que pot jugar un paper clau en la interpretació de dades observacionals i en la comprensió de les condicions físiques. Aquest fet fa que l estudi de les reaccions superficials i de processos en l estat sòlid hagin adquirit una gran importància. El càlcul de les abundàncies en regions de formació estel lar requereix establir un model físic que especifiqui les variables físiques com temperatura, densitat, etc., com a funcions de l espai i/o el temps. En la seva forma bàsica, s acostumen a considerar dues menes de model: models estacionaris, en els quals les abundàncies de les molècules no canvien amb el temps, i són funció de la profunditat dins de la regió; i models depenents del temps, en els quals les abundàncies són calculades com a funcions del temps en una única posició dins del núvol. La modelització de la interacció entre el gas i la pols s ha trobat amb una sèrie de limitacions importants: una comprensió incompleta de la natura exacta de les superfícies dels grans, limitacions en el coneixement de la química superficial a baixes temperatures, i problemes amb la modelització de la química dels grans depenent del temps. Hi ha dos aproximacions a la modelització de la química dels grans: el règim limitat per acreció, que és, en general, teòricament més precís, on la química està limitada pel ritme amb el qual les espècies reactives són transportades a la superfície; i el règim limitat per reacció, que està limitat pels ritmes de reacció superficial un cop les espècies han estat adsorbides als grans. La majoria dels models químics que incorporen interaccions entre grans i gas han estat formulats en el règim limitat per reacció perquè es fàcilment incorporable als models químics depenents del temps. Un cop ha estat triat el model físic que millor descriu les condicions de la regió que volem estudiar, hem de triar el conjunt d espècies, és a dir molècules, àtoms i ions, que cal incloure per explicar la química de la regió; tant aquelles per a les quals hi ha proves de la seva existència, com aquelles que, malgrat no haver estat detectades, hi són presents probablement perquè estan estretament relacionades amb les anteriors o amb les reaccions que les inclouen. El resultat de la selecció d espècies del model ens porta generalment a establir una extensa i complexa xarxa de reaccions químiques que governa les abundàncies de les espècies del nostre model. Per a cada una de les N S espècies del nostre model, definim una equació de variació de l abundància resultat de la suma de totes les reaccions que produeixen l espècie

23 Resum de la tesi xix menys les reaccions que la destrueixen. A més, generalment cal incloure una equació de conservació del número total d àtoms de cada element particular per unitat de volum, i la conservació de la càrrega total. Les reaccions que es faran servir es trien a partir dels conjunts de reaccions que han estat publicades dins de les bases de dades de reaccions per a astroquímica. Aquestes bases de dades especifiquen els reactants i productes de cada reacció i els valors de tres coeficients (α, β, γ) a partir dels quals es pot calcular el ritme de reacció depenent de si la reacció és de dos cosos, ionització per raigs còsmics, fotoreaccions o fotoreaccions induïdes per raigs còsmics. Aquests coeficients tenen a veure amb dependències de la temperatura (β), o amb l existència de barreres de reacció (γ), la qual cosa pot fer que algunes reaccions no calgui incloure-les en el model que es faci servir. De totes maneres, la condició bàsica per a la xarxa de reaccions és que sigui químicament tancada. És a dir, cada molècula formada ha de poder ser destruïda. Per començar a calcular el model, cal donar un conjunt de condicions inicials del núvol, com densitat, extinció visual, abundàncies elementals i/o moleculars, i ritmes d ionització, a partir dels quals el programa detemina els valors adients dels mecanismes químics de producció i destrucció, i inicia la solució depenent del temps. Cal fer notar que les abundàncies elementals inicials poden tenir una gran influència en el valors de les solucions finals, com per exemple es demostra en el cas del sofre. Apart de les equacions descrites per a cada espècie, altres magnituds que han d incloure s per tal d explicar la química als núvols moleculars són la densitat, que si hi ha un col lapse del material ha de variar en funció del temps, generalment accelerant el ritme d evolució química; l extinció visual, que ve directament afectada per la variació de la densitat; i el grau de deposició de molècules en els grans de pols, que governa l evolució química del núvol en determinar la quantitat de material que resta disponible en la fase gasosa. 5. La distribució de CS i NH 3 en regions de formació estel lar Hem investigat si les diferents distribucions espacials observades de les molècules de CS i NH 3 poden ser explicades a partir de les diferents dependències temporals de

24 xx Resum de la tesi les químiques de CS i NH 3. Les molècules de CS i NH 3 es formen de manera molt diferent. Per a la majoria de les circumstàncies, el CS és format a partir de la reacció del seu ió amb H 2, i la posteriór recombinació. El CS + es pot formar a partir de sofre neutre o ionitzat. Es poden formar grans abundàncies de CS, donat que no té vies de destrucció de reaccions neutres a través d O i C, i moltes reaccions amb ions només el reciclen. La destrucció primària de CS és produeix mitjançant un intercanvi dissociatiu de càrrega amb ions d He. L NH 3 es forma a través de successives reaccions d abstracció d hidrogen seguides per recombinació, i és destruït per intercanvi de càrrega amb ions i per la fotodestrucció induïda per raigs còsmics. La relació entre les temperatures d antena de les transicions (J=1 0) de C 32 S i de C 34 S a la regió L1524 és molt inferior a la relació d abundàncies terrestres entre els dos isòtops. Això pot indicar que l emissió detectada es subtèrmica o que pateix de dilució pel feix. La possibilitat de subtermalitat ha estat investigada construint un model de capa homogènia, per tal d examinar l excitació i el transport radiatiu. Hem calculat la intensitat emergent del núvol per a diversos valors de la densitat d H 2 i de la densitat columnar de CS fent servir l aproximació de probabilitat d escapament microturbulent. Els resultats donen una fracció de CS de 10 8, consistent amb models de núvols foscos. Tanmateix, la profunditat òptica de la línia, 6, hauria de mostrar-nos perfils de línia amb autoabsorció, que no són trobats. Per tant, considerem que la subtermalitat en CS és inconsistent amb les observacions. Una altra possibilitat per explicar les observacions és que existeixi un embolcall de baixa densitat al voltant del nucli dens. Si la transició és òpticament gruixuda, l embolcall pot dispersar l emissió del nucli donant la impressió que hi hagi una àrea d emissió més ampla. L autoabsorció estarà reduïda si el nucli té una amplada de la línia menor que l embolcall, seguint les relacions conegudes entre la grandària del núvol i l amplada de la línia. Aquest efecte només seria observable per al CS. Vam obtenir abundàncies per a un model nucli-embolcall a dos temps diferents ( primerencs i tardans ). En els dos casos, l NH 3 té una abundància molt més petita en l embolcall, mentre que el CS és encara prou abundant. No està clar si la combinació d una temperatura d antena baixa i una àrea d emissió del CS cinc cops més gran poden ser explicades per aquest model. Una tercera possibilitat és que existeixin en el feix condensacions sense resoldre que emetin preferentment en CS. Aquest model és favorable perquè permet expli-

25 Resum de la tesi xxi car la manca de coincidència entre els pics d emissió de les dues molècules i també l amplada de línia més gran de CS. També permet continuar explicant les observacions inclús quan les línies de CS són òpticament primes, com és gairebé el cas en L43. Considerem que la diferència d emissió entre CS i NH 3 és causada per l evolució relativa de les condensacions que proposem que es troben en el medi observat. Aquesta evolució és a la vegada física i química causada per diferències en la densitat o en l etapa de col lapse. El col lapse pot produir-se des de condicions relativament difuses. Fem servir la química de les molècules de CS i NH 3, tenint en compte els efectes del canvi de densitat i de congelació de les molècules en els grans de pols. El model és un càlcul en un punt, és a dir, només reflecteix les condicions al centre d un fragment en col lapse. El model de col lapse que seguim considera que el gas dels núvols es contrau fins a un estat d equilibri seguint les línies de camp magnètic. A mesura que es perd flux magnètic per difusió ambipolar es va produint una evolució lenta del núvol. Quan es completa aquest procés, el col lapse dinàmic del nucli cap a un objecte protoestel lar pot començar. Per tant, fem augmentar la densitat del gas fins que l aturem a un valor arbitrari que dependria de l equilibri de forces. Per la deposició en els grans, suposem que totes les espècies neutres poden dipositar-se sobre els grans amb la mateixa eficiència i que les espècies iòniques s enganxen com una contrapartida neutra. Fem servir la fórmula de Rawlings et al. (1992) per calcular el ritme de deposició, que ve controlat per un únic paràmetre, F R. No hem tingut en compte processos de desabsorció, que poden afectar significativament el ritme d acreixement, la qual cosa indicaria un valor efectiu de F R més petit. Mostrem els resultats per a un col lapse amb densitat inicial 1000 cm 3 i extinció visual 0.5 (de la vora al centre), i densitat final cm 3. El factor de col lapse és B = 1, i hem fet servir diversos valors de F R. Per a F R = 0.01, CS i NH 3 arriben a abundàncies altes, l NH 3 ho fa més tard que el CS, anys. A F R = 0.1 la congelació afecta especialment el CS, mentre que l NH 3 encara arriba a la seva abundància màxima abans de caure com la resta de les espècies. A valors més alts de F R cap espècie arriba a abundàncies altes. Si l abundància de NH 3 en el pic de l abundància de CS és tal que la seva emissió no és observable, és raonable associar l extensió relativament més gran de CS a nuclis no resolts que han existit en escales de temps de 2 milions d anys o menys. Si la

26 xxii Resum de la tesi densitat del nucli no resolt va creixent lentament amb el temps, la densitat columnar d amoníac augmentarà fins a fer-se observable. Aquest augment de densitat implica una disminució en el temps de la columna de CS per causa de la química, i per tant els pics de CS i NH 3 no tenen perquè coincidir. Per tant, és possible que la majoria dels nuclis que han format CS és dispersin abans de poder ser magnèticament supercrítics i evolucionar més. En canvi, només aquells nuclis més densos o més massius arriben a formar NH 3, perquè tenen una evolució accelerada. Potser aquests nuclis són els que es veuen involucrats en la formació estel lar. Un altre resultat observacional pot ser explicat pel model. Com hem mencionat, s ha trobat que les línies de CS són sistemàticament més amples que les de NH 3. Un conjunt de condensacions movent-se a l atzar tendiran naturalment a tenir amplades de línia més amples que l emissió intrínseca d una única condensació. A la vegada els perfils d abundàncies que es poden extreure del model poden permetre comprovar la seva validesa, si les molècules que tenen perfils similar als de CS i NH 3 són observades correlades amb una o altra espècie. El model també suggereix que el valor de F R és molt petit, la qual cosa indicaria que estan tenint lloc processos de desabsorció, els quals endarreririen en certa mesura la congelació. Per concloure, proposem que la diferència entre CS i NH 3 prové de la natura no homogènia dels núvols moleculars. Dins del feix de baixa resolució angular es trobarien condensacions de < 0.1 pc de grandària, probablement suportades magnèticament. La majoria de les condensacions es dissiparien abans que les abundàncies de NH 3 arribin a nivells substancials, però contenen prou CS. Unes poques condensacions, possiblement una mica més denses o més massives, viuen prou temps com per formar abundàncies altes de NH 3. Aquestes condensacions poden ser el nuclis que continuïn col lapsant per formar estrelles. 6. La distribució de molècules en regions de formació estel lar En aquest capítol ampliem el treball del capítol anterior per examinar si hi ha altres molècules potencialment observables que mostrin emissió extesa com el CS, o més compacta com l NH 3, si el model de la condensació no resolta és correcte. Es-

27 Resum de la tesi xxiii tem interesats en molecules que no continguin sofre, malgrat que algunes molècules que contenen sofre són de les més útils quan cal observar aquestes regions, però la seva modelització es veu dificultada per la manca d informació sobre el valor de l abundància elemental de sofre. En les nostres figures veiem que quan el gas arriba a la seva densitat final es produeix la transició que converteix el carboni lliure en CO. Això passa mentre diverses molècules basades en carboni arriben a la màxima abundància, amb pics més pronunciats que el de CS. Aquestes són molecules primerenques, que tenen els pics cap a t anys. Altres molècules arriben a la seva màxima abundància (normalment la seva abundància química d equilibri) al menys anys després. Aquestes són molècules tardanes. Les molècules primerenques es formen immediatàment que el gas és dens i opac; es podrir dir que són dirigides dinàmicament, mentre que les espècies tardanes apareixen en un temps posterior dictat per l escala de temps química. Molècules que es formen en etapes primerenques, a part de CS, són H 2 CO, CN, HCN, H 2 CS o HC 3 N. En etapes tardanes, a part de NH 3 es formen: OH, OCN, NO, SO o HCO +. A l hora de discutir l observabilitat de les molècules no n hi ha prou amb argumentar que les molècules de la família de NH 3 ocuparan regions més petites del cel que les molècules de la família del CS. El que sí que es pot dir és que per a una resolució angular similar les molècules de la família de l NH 3 haurien de mostrar una disminució més marcada de la intensitat del màxim. A la vegada, les condicions d excitació de cada transició particular són importants. Així per exemple, un membre de la família del CS pot no aparèixer molt estés comparat amb l NH 3 si la densitat crítica de termalització de la transició és tan alta que només està excitat significativament en els nuclis més densos. A continuació, ens preocuparem de la observabilitat potencial de cada molècula. Molècules primerenques. HCN és fàcilment observable en fonts de baixa massa, i ha estat cartografiat en dos nuclis de regions de formació estel lar d alta massa, on s ha trobat que segueix la distribució espacial de CS. Esperem que CN segueixi la mateixa distribució. H 2 CO i H 2 CS també han estat àmpliament observats. Prediem també que una sèrie de cadenes de carboni siguin membres també de la família del CS, especialment C 3 N, HC 3 N i C 3 H. Les molècules CCS i HC 5 N, tot i que no estan incloses en el nostre model haurien de seguir el comportament del CS i han estat observades. Els models prediuen que CCN pertany a la família de CS, però no ha

28 xxiv Resum de la tesi estat encara observat. Molècules tardanes. Esperem que HCO + segueixi el comportament de l NH 3. En algunes fonts observades es troba que aquesta molecula està més a prop de l amoníac que del CS. La molècula SO també ha estat observada en una sèrie de fonts que van de baixa massa a massa intermèdia, amb emissió força compacta. Una comparació amb CS seria força interessant. NO i OCN també haurien de pertànyer a aquesta categoria, encara que hi ha pocs mapes de la primera, mentre que la segona no ha estat observada encara. Diverses molècules tardanes, com O 2, N 2 o C 2 H 2 no són observables per causa de la seva manca de moment dipolar. L estudi de les equacions químiques del nostre model confirmen que les reaccions neutre-neutre són sorprenentment importants, malgrat que la majoria de la química interstel lar està basada en la química ió-molècula. Un punt clau és confirmar que aquestes reaccions neutre-neutre ocorren a 10 K, perquè la majoria només han estat estudiades a temperatura ambient, o no han estat ni tan sols estudiades. En particular, la química de la família del CS depèn de reaccions neutre-neutre eficients. L eliminació d aquestes rutes significaria per a les molècules pertanyents a la família del NH 3 que la seva formació seria encara més lenta. Les condicions inicials del gas que hem adoptat ha estat la típica de material interstel lar força difús, i a més hem suposat que la majoria del carboni està en forma de C +. Tanmateix, hem estudiat el cas que la majoria del carboni comencés en forma de CO. Els resultats no varien gaire dels ja obtinguts, perquè la fotodissociació del CO abans que domini el col lapse assegura prou carboni lliure per fer funcionar la química del carboni. Les condicions inicials donen també una abundància de sofre 1% del seu valor còsmic. Això és incorrecte perquè en condicions difuses s ha observat que l abundància de sofre es troba molt propera al valor còsmic. Tanmateix, si fem els càlculs amb valors més grans de sofre obtenim abundàncies molt altes de les molècules portadores de sofre quan els comparem amb les observades. Per tant, això ens diu que el sofre és retirat intensament del gas durant el procés de col lapse, tot i que el mecanisme físic que ho provoca no és conegut encara. Com hem mencionat abans, les escales de temps dinàmiques i químiques controlen l aparició de les molècules primerenques i tardanes. Si modifiquem el paràmetre d escalat dinàmic B, que ha estat igual a 1 en els càlculs realitzats, i el fem B = 0.1

29 Resum de la tesi xxv per explorar les conseqüències d un col lapse lent, veiem que els pics d abundància primerencs desapareixen. Aquests pics són conseqüència del fet que el núvol ha arribat a altes densitats abans que el gas hagi pogut respondre químicament. Si el col lapse és més lent, l escala de temps química és més curta que la dinàmica i els pics se suavitzen fins a desaparèixer. 7. Observacions multitransicionals del nucli dens de CS de L673 Per comprovar les prediccions del model químic que hem desenvolupat, hem triat la condensació d alta densitat que vam detectar en la regió L673 mitjançant observacions de la transició CS (J=1 0), per observar-la amb resolució angular més alta en diverses transicions de molècules pertanyents als dos tipus de famílies de molècules que vam obtenir en el model químic. Aquesta condensació s adiu amb els nostres propòsits per diverses raons. Una condensació d alta densitat ha estat detectada molt a prop en la transició NH 3 (J, K)=(1,1) per Sepúlveda et al. (2001), que mostra el mateix comportament que vam trobar en altres fonts de la nostra mostra: una separació del pic d emissió de CS de 0.2 pc, i una grandària en NH 3 clarament més petita que en CS. A més, la regió es troba situada a poca distància, 300 pc, que ens pot ajudar en l estudi de l estructura més petita del núvol. Finalment, les condensacions detectades en CS i NH 3 no mostren signes d altres traçadors de formació estel lar, la qual cosa indica que probablement sigui un nucli quiescent, potser en els primers passos del col lapse, com eren les condicions del model químic. Vam observar la regió L673 amb l interferòmetre de 10 elements de BIMA. Per tal d incloure les posicions dels màxims de CS (J=1 0) i NH 3 (J, K)=(1,1) observats amb una sola antena, vam fer un mosaic de dos punts amb un dels camps centrat aproximadament en la posició d un dels dos pics. Vam observar les següents transicions: HCO + (1 0), C 3 S (16 15), N 2 H + (1 0), C 2 S ( ), OCS (8 7), CS (2 1), C 2 S ( ), HNCS (9 1,8 8 1,7 ), HC 3 N (12 11), SO ( ) i OCS (9 8). Vam detectar emissió en les transicions CS (J=2 1), N 2 H + (J=1 0) i HCO + (J=1 0), i marginalment, a un nivell 2σ, la transició SO ( ). Comparant els mapes de la intensitat integrada per a les tres molècules detectades observem que l emissió de N 2 H + és més concentrada que les de CS i HCO +,

30 xxvi Resum de la tesi les quals es troben més distribuïdes per tota la regió. L emissió de CS (J=2 1) en la regió sud coincideix amb la condensació nord de l emissió de N 2 H +, el pic de la qual es troba situat entre els dos màxims locals de CS (J=2 1). En la regió nord, les emissions de CS (J=2 1) i HCO + (J=1 0) són molt coincidents, especialment al voltant de la posició del pic de CS (J=1 0). Pel contrari, l emissió de N 2 H + i HCO + coincideixen en general marginalment. També vam detectar marginalment una condensació en SO, molt a prop de la condensació nord de N 2 H +. Per tal de comparar els paràmetres físics del gas traçat per cada molècula, vam triar quatre posicions en la regió cartografiada. Vam etiquetar aquestes posicions com S, E, W i N, les quals corresponen amb les condensacions d alta resolució més prominents: la posició del pic sud del mapa de N 2 H +, el màxim local est de l emissió de CS, el màxim oest de CS i la condensació nord de HCO + prop del pic d emissió de CS (J=1 0), respectivament. Els espectres obtinguts en aquestes quatre posicions mostren que l emissió de CS és detectada en totes quatre posicions, mentre que l emissió de HCO + només és detectada a les posicions N i W, i l emissió de N 2 H + a les posicions S i E. Tanmateix, les velocitats centrals de les línies en les posicions on es pot obtenir un ajust ben determinat mostren que són compatibles amb ser originades en el mateix gas. Les nostres observacions indiquen que hem de corregir la freqüència que vam fer servir per a les observacions de N 2 H +. El diagrama posició velocitat obtingut per a la línia CS (J=2 1) al voltant de la posició del pic d emissió oest al llarg de la direcció NE-SO (P.A. 73 ) mostra marginalment una estructura el líptica, aproximadament simètrica al voltant de V LSR 6.9 km s 1, amb una ala blava més intensa i una ala vermella més feble. Aquesta estructura es pot explicar per moviments de caiguda dins de la condensació. Vam aplicar un model d un anell prim vist de costat, incloent efectes de caiguda i rotació. El millor ajust al nostre diagrama posició velocitat obté radi interior, R inn = 4200 UA, radi exterior R out = 6000 UA, velocitat de caiguda, V infall = 0.45 km s 1, velocitat de rotació V rot = 0 km s 1, i amplada intrínseca de la línia V core = 0.65 km s 1. Vam comparar les emissions interferomètriques de CS (J=2 1) i les obtingudes amb una sola antena de CS (J=1 0). Vam trobar que l interferòmetre de BIMA detecta 10% del flux, la qual cosa indica que 90% del flux de CS obtingut amb una única antena es troba en components extenses. També vam comparar la distribució de CS (J=1 0) i NH 3 (J, K)=(1,1) obtinguts amb una sola antena amb

31 Resum de la tesi xxvii els mapes de les observacions interferomètriques. Vam trobar que la major part de l emissió més intensa de CS (J=2 1) i tota l emissó de N 2 H + es troba dins dels contorns més intensos del mapa de NH 3, localitzats en la regió sud. En la regió nord, vam trobar que l emissió de CS i HCO + es troben incloses dins del feix de les observacions amb una antena de CS. Observem, per tant, que les observacions interferomètriques a alta resolució angular, 13 revelen un medi molt més inhomogeni que les observacions a baixa resolució angular, 1. 5, amb una sola antena. Trobem diverses condensacions de grandària < 0.08 pc per a cada línia, distribuïdes per tota la regió on fou trobada emissió amb una sola antena. Aquest fet vindria a donar suport a la idea proposada pel nostre model que l emissió de baixa resolució estaria originada en condensacions no resoltes de < 0.1 pc. Vam trobar que cada transició molecular traçava d una manera diferent la distribució de les condensacions, tot i que en alguns casos les condensacions detectades coincidien. El fet que l emissió de N 2 H + es trobi totalment inclosa dins de l emissió màxima de NH 3 observada amb una sola antena, i que ambdues emissions siguin molt compactes i compatibles amb haver estat originades en el mateix gas, dóna suport a la predicció del model químic que com les dues molècules es formen en temps tardans haurien de trobar-se en la mateixa regió. Interpretem que aquests resultats estant causats per una diferenciació química entre les condensacions de gas depenent de la seva densitat local i/o edat, la qual podria ser emprada per determinar l estat d evolució química de cada condensació. Vam calcular les relacions d abundància [N 2 H + /CS] i [HCO + /CS] en les quatre posicions que havíem seleccionat previament, per tal de comparar-les amb els valors que prediu el model químic. Vam trobar que en les posicions N i W hi havia una abundància alta de HCO + respecte de CS i una abundància baixa de N 2 H +, mentre que en les posicions S i E es produïa el cas invers. El model químic era capaç d explicar les abundàncies relatives de [HCO + /CS] allà on l HCO + havia estat detectat, posicions N i W. El millor ajust l hem trobat per a un model on la densitat a la qual s atura el col lapse és n f = cm 3. Per a aquest cas vam trobar que les abundàncies predites de [N 2 H + /CS] estaven més d acord amb les observacions. Una abundància alta de HCO +, pero baixa de N 2 H +, representaria una fase primerenca, on podrien trobar-se les posicions W i N. Les posicions S i N estarien en unes fases d evolució química posteriors donada

32 xxviii Resum de la tesi l abundància més alta de N 2 H +. Tanmateix és difícil de fer una diferenciació més precisa. 8. Conclusions En aquest treball hem estés la comparació sistemàtica de les emissions de les molècules de CS i NH 3 en regions de formació estel lar iniciada per Pastor et al. Hem confirmat els resultats preliminars. En particular, que existeix una separació entre els màxims d emissió de CS i NH 3 de 0.2 pc; l emissió de les regions traçades per CS és més extensa que les traçades per NH 3, tot i que troben que la relació de grandàries depèn de la grandària de la font; les línies de CS són 0.5 km s 1 més amples que les de NH 3. Les diferències en la distribució espacial de CS i NH 3 les atribuim a diferències en l abundància química causades per l evolució química i física del gas. Vam modelitzar la química dels nuclis densos dels núvols moleculars i vam investigar si les diferents dependències del temps de les químiques de CS i NH 3 eren capaces d explicar les diferents distribucions espacials observades per a aquestes dues molècules. Proposem que la diferència entre els mapes de CS i NH 3 neixen de la natura inhomogènia dels núvols moleculars. Considerem que hi ha un nombre de condensacions no resoltes, probablement suportades magnèticament, en el nostre feix. La majoria de les condensacions es dissiparien abans que les abundàncies de NH 3 arribessin a nivells significatius, però contindrien quantitats substancials de CS. Unes poques condensacions, possiblement una mica més denses o més massives, viuen prou temps per permetre que l abundància de NH 3 augmentés. Aquests nuclis continuarien el col lapse per formar estrelles. També vam investigar si hi hauria altres molècules potencialment observables que fossin capaces de comprovar la validesa del model, donat que aquest prediu que hi hauria dues grans famílies de molècules: les que es formarien aviat com el CS, i les que es formarien tard com l NH 3. HCN, H 2 CO, H 2 CS, C 3 N, HC 3 N i C 3 H pertanyerien a la família del CS, mentre que HCO +, SO, NO, OH, N 2 H + i OCN es trobarien en la família del NH 3. Finalment, vam fer un estudi multitransicional amb l interferòmetre de BIMA en el nucli sense estrelles trobat en la regió L673 amb les observacions amb una sola

33 Resum de la tesi xxix antena de CS (J=1 0) per tal de comprovar les prediccions del model químic. Vam detectar emissió en les transicions CS (J=2 1), N 2 H + (J=1 0) i HCO + (J=1 0). Les observacions en alta resolució angular han trobat que l emissió sembla estar originada en condensacions de < 0.1 pc, les quals són detectades de manera diferent per cada molècula. Hem trobat que el model és capaç d explicar les les observacions interferomètriques, tenint en compte la probable autoabsorció de l HCO +. En particular, la diferenciació química de les condensacions detectades i la coincidència de les emissions de NH 3 i N 2 H +. El model també ens ha permés explicar les emissions d HCO + i N 2 H +, i proposar una classificació de les condensacions estudiades d acord amb l estat d evolució química indicat per les abundàncies moleculars.

34 xxx Resum de la tesi

35 Agraïments and to all those opposed hmm... well - W.A.R. Després de tants anys, tants dies i tantes nits, tants esforços, penes i alegries, la tasca de recordar la gent que d una manera o una altra ha estat al meu costat es fa llarga, però espero que no es faci pesada ni tampoc deixar-me ningú que mereixeria ser-hi: En primer lloc he d agrair el poder haver fet aquesta tesi als meus directors: al Dr. Robert Estalella, per haver-me introduït en el tema de la formació estel lar i haver-me donat la possibilitat d estar durant tant de temps corrent pel Departament d Astronomia i Meteorologia de la Universitat de Barcelona, i al Prof. David A. Williams, al qual dec el més profund agraïment i la més sentida admiració, que em va iniciar en el tema de la astroquímica, i va aconseguir que la meva estada al UCL fos extremadament profitosa i encoratjadora. També he d agrair l ajuda i direcció rebuda en diferents èpoques al Dr. Guillem Anglada, a la Dra. Rosario López i al Dr. Josep Miquel Girart. També vull reconèixer les experiències realment i luminadores que he rebut dels components del Departament d Astronomia i Meteorologia de la Universitat de Barcelona. Apart d ells, he d agrair molt especialment l ajuda rebuda per part del Josep Ramon Rodríguez, per la seva gran amabilitat i extrema eficiència en tots els (molts) tràmits que ha calgut fer durant aquest temps, i al Jaume Soley per l ajut (mutu?) informàtic. També vull agrair al Dr. Steven D. Taylor, al Dr. Jonathan C.M. Rawlings i als seus estudiants de l any 1996, per la seva gran hospitalitat, amabilitat, ensenyaments xxxi

36 xxxii Agraïments i encoratjaments que no podré oblidar mai. De fet, si no hagués estat per tots ells, aquesta tesi no existiria a hores d ara. Així mateix, el bon acolliment que em van donar els membres del Department of Astronomy and Astrophysics del University College London. Seguint en la llarga llista, vull tenir un record per als meus veïns de despatx del Departament d Astronomia i als companys amb qui vaig compartir, ja farà temps o no tant, xerrades i interessos: Albert Prades, David Lario, Josefa López, Carlos Pérez, Eduard Masana, Eva Villuendas, Marc Ribó, Octavi Fors, Maite Beltrán, Francesc Blasi, Marc Mars i Mercè Martin. També vull fer-ho amb tants d altres que han passat per la facultat i han estat més o menys a prop en un moment o l altre, és a dir els agraïments del disc : Javier Sanz, Santiago Serrano, Sergi R. Massanés, Miguel Rodríguez, Sito, José Martínez, José Alberto Garcia, Sandra Hereter, Toni Jofre, Alba de Lamo, Javier García; a tota la colla dels globus que van estar allà dalt, de manera atrevida, triomfant i íntegra; als que segur que em deixo perquè fa massa temps que no els veig i a les ànimes estimulants. Recordant la meva llarga estada a la Sala d Informàtica de la Facultat de Física, he d agrair al Dr. Atilà l Atilíssim Herms, amb control remot inactiu, que m anés renovant... o no. També vull recordar a tota la colla de monitors que van servir amb mi. Especialment: Elena Álvarez, Rosa Soler, Francisco Frechilla, Quico, Jordi Vilar, els darrers novatos Sandra Aguilar i Roger Torrents, i tota la resta. Invisibles imprescindibles, anys inoblidables i plens d anècdotes. Dies, nits, més dies i més nits, amb tot el que acompanyen, m obliguen a agrair el suport moral, segurament inconscient però invaluable, de tota la tropa de Pink- 7 Ummagumma i Pere Vila, especialment: Enrique López, Juan Enrique Sánchez Aretio, Pedro Domínguez, Enrique Sánchez Zapata, José, Santiago i Mariano Royo, Albert Casas, Héctor Garrido, Jordi Maldonado, Pedro García del Río, Chicho i Yolanda Núñez. Evidentment, tinc molt per agrair als altres membres del 3sm: a l Antoni Garcia Santiago per tot el temps, converses i ànims, interessos i milers de coses més, and let the music do the talking; i al Pau Gorostiza, més temps, converses i invents, que d una manera o d una altra no va deixar que em rendís, i em va recordar què feia aquí. Molt especialment, vull agrair haver tingut el privilegi d haver conegut el Juan Luis Ruiz i l Ignasi Garcia, segons d abord, el David sempre ens quedaran BCN... i indies Fernández Guevara i la Meritxell Torres, aiaiai: gràcies per tot!. També

37 Agraïments xxxiii dec moltíssim al Josep Urdi Reche, que sempre ha cregut en mi, malgrat jo mateix, i al qual no he pogut decebre (espero, perquè és un dels primers culpables que em fiqués en aquestes coses). Ara que això arriba, afortunadament, al seu fi, he d agrair a la meva família, sobretot als meus pares i germans, que m hagin suportat durant tant de temps, especialment en els moments dolents. També vull tenir un record pels que ja han marxat i que trobem a faltar. Ja no hi són, però em van deixar molt més que records. Com és de justícia, vull agrair infinitament a aquells que poden arribar a saber què ha estat això: Inmaculada Sepúlveda (també trobada dins de Sepúlveda et al. i algun altre et al.), la companya de fatigues, cerveses, hores i més hores, xerrades i més xerrades, i un exemple alliçonador; i al meu germà Virgili, per estar allà sempre, o gairebé, que el vaig necessitar després d algun dia, mes o any especialment dolent. Només ell pot arribar a saber què ha estat això. Fi del segon plan quinquenal

38

39 fourteen seconds until sunrise tired but wiser for the time lightning 30 miles away three thousand more in two days - Chris & Rich Robinson Wiser Time

40

41 Chapter 1 Introduction Since the beginning of Astronomy thousands of years ago, stars have been the main objects of study of the astronomical universe. Therefore, a great amount of knowledge has been accumulated about their positions, movements, structure and evolution. Yet, despite all the years of stellar observations and much speculation about their origin, star formation is a phenomenon that has only begun to be understood in the last 30 years. It is not surprising then that one of the most interesting and fundamental problems of modern astrophysics is the understanding of the origin of stars. Several reasons explain the persistence of this problem waiting to be solved. First, it has been discovered that although star formation takes a relatively short time in astronomical timescales, years, it is by no means observable in human timescales. Thus, the study of star formation has consisted in observing young stellar objects at different evolutionary stages in order to determine the phases that a star undergoes from its beginning until it enters the main sequence phase. A second difficulty is to find where stars are born, because stars are not forming randomly all over the Galaxy. On the contrary, it has been found that star formation takes place in certain very particular regions of our galaxy, called accordingly starforming regions, which need to be found first and then have to be studied. Third, it was not known until recent times neither what was the origin of the material from which stars are made, nor how this material aggregated to become a young stellar object. Fourth, the discovery of the nature of stars as natural thermonuclear reactors was not known until the twentieth century. Although the theory of stellar structure and evolution neither accounts nor predicts the formation of stars, it provides the 1

42 2 Chapter 1. Introduction mechanism that explains their energy source, their evolution and subsequent death, and a physical basis to the nature of the stars, which any star formation theory will have to explain. Finally, the process of star formation has never been observed with the telescope at visual wavelengths. The gas and dust that ends up forming stars and the physical processes that are involved in star formation take place under very extreme physical conditions of temperature and density. These processes can only be observed at wavelenghts longer than those of visible light, the detection of which has required, in most cases, the development and refinement of new technologies, telescopes, and observational techniques that have only been available in recent times. All these difficulties notwithstanding, a lot of effort has been applied from the physical, and more lately from the chemical, sciences to the study of the star-forming processes, because they may provide us with important information related to our basic knowledge of the Universe: about physical mechanisms that take place in the dense interiors of stars or in the almost empty interstellar clouds; about how do stars form and, by extension how did our Sun form; and how our planetary system, and the Earth was born. Even the ongoing discussion of the beginning of life on Earth, or in other places, can be affected by the study of the formation of stars, because, as we will see, complex organic molecules are being found in star forming regions, and even molecules more complicated and more intimately related to life formation, such as aminoacids or DNA bases (e.g. Chakrabarti and Chakrabarti 2000), are postulated to exist in disks and envelopes that can be found around very young stars. Earth is thought to have been formed from a similar disk, and maybe these molecules could have contaminated the earth since the beginning. 1.1 Molecular clouds A significant fraction of the mass of the Galaxy, whose main component is stars accounting for M, is found in the vast region of interstellar space, constituting the interstellar medium. Most of this material is found as a gas, mainly hydrogen, the most abundant element in the Universe, either in atomic, molecular or ionized form. The gas also contains helium and traces of other elements, such as carbon, oxygen, nitrogen, and sulphur. Dust grains, cosmic rays, magnetic fields, and radiation are the other components that with the gas conform the complex structure of

43 1.1. Molecular clouds 3 the interstellar medium, all interacting through a variety of physical and chemical processes. The outflow of energy from stars through the interstellar medium to the intergalactic medium, in the form of radiation, winds, and shocks from supernova explosions, rules the structure and overall energetics of the interstellar medium. The distribution of interstellar gas is highly inhomogeneous. Maps made in the 21 cm line of hydrogen and in a variety of molecular lines show that much of the interstellar matter is concentrated in clouds, clumps, filaments, sheets and other contorted structures, which occupy a small fraction of the volume, and under very different conditions of temperature and density, whereas much of the volume is filled with warmer intercloud gas (McKee 1990). Following observational criteria, the interstellar medium is usually divided into several major components (Heiles and Kulkarni 1987, McKee 1990). Molecular clouds are one of these components, which play a crucial role in astrophysics because they contain the regions where star formation takes place General properties Molecular clouds are the birthplaces of stars. Their main constituent is hydrogen, primarily in molecular form, H 2, while the atomic hydrogen component is less abundant by a factor 10 3 (Myers 1999). Yet, the molecule used to detect and map these objects is not H 2, but the CO molecule, despite its relatively low abundance with respect to H 2 of 10 4, because the H 2 molecule has no permanent dipole moment, and its emission is very weak and difficult to detect. The most used line is the brightest line of CO, the (J=1 0) rotational transition at a wavelength of 2.6 mm. Almost all known molecular clouds in the Galaxy are detectable in CO (Blitz and Williams 1999). The overall extent of CO maps of nearby molecular cloud complexes, such as Taurus, Orion, Perseus, Ophiucus, is typically pc, and the mass enclosed is M (Blitz and Williams 1999). The largest regions are called giant molecular clouds (GMCs), and represent the most massive non-stellar baryonic objects in the Galaxy, with masses often exceeding 10 6 M (see Fig. 1.1). The properties of molecular clouds vary in numerous ways from region to region, mainly as size decreases. The largest GMCs, such as Orion, have extents pc, visual extinction of 100 magnitudes, turbulent line widths of several km s 1, typical gas temperatures of 20 K, and thousands of stars in dense clusters, including numerous

44 4 Chapter 1. Introduction Figure 1.1: CO line emission from the Orion A and B giant molecular cloud complexes (Blaauw 1991). The overall extent of each complex is about 60 pc OB stars (Lada 1999). At the other end, the smaller complexes, such as in Taurus, Ophiucus, and Chamaeleon, which are usually called dark clouds (see Fig. 1.2) because of their obscuration of background starlight, have lengths 10 pc, maximum visual extinction of a few magnitudes, turbulent line widths of 1 km s 1, gas temperatures of 10 K, relatively few stars, no massive stars, and no clusters (Myers 1999). Cold dark clouds are formation sites for low-mass stars and planetary systems. Most of the star formation in the Galaxy occurs in GMCs, where the birthplaces of massive stars and rich star clusters are found, even though lower mass clouds are more numerous. Table 1.1 shows some typical values for GMCs and dark clouds. Molecular cloud structure can be mapped via radio spectroscopy of molecular lines (e.g., Bally et al. 1987), continuum emission from dust (e.g., Wood, Myers, and Daugherty 1994), or stellar absorption by dust (Lada et al. 1994). The resulting density structure of molecular clouds is highly nonuniform, with densities ranging

45 1.1. Molecular clouds 5 Figure 1.2: 13 CO (J=1 0) line emission from the Taurus molecular cloud complex (Mizuno et al. 1995). The longest dimension is about 25 pc, substantially less than in Orion from a few hundreds to a few million hydrogen molecules per cubic centimeter. The mean density over a GMC complex is roughly 10 2 cm 3, averaged over a scale of 10 pc. In fact, most of the material (80 90%) is at densities between cm 3 (Lada 1999). Molecular clouds are collections of clumps of gas embedded in a more tenuous background of neutral gas. The number density, n H, of hydrogen nuclei in these clumps is n H < 10 3 cm 3, averaged over a scale 1 pc (Myers 1999). Within a clump several clusters of cores may exist, with n H 10 5 cm 3, over a scale 0.1 pc (Mundy 1994). It is thought that from dense cores protostars may form. Dense gas is traced by molecular transitions whose excited states require high densities to be collisionally populated and which are optically thin. Thus, different transitions will trace different densities. Lines of CO, 13 CO or C 18 O trace lower density gas, n H cm 3, while lines of CS, NH 3, HCO + or N 2 H + trace densities 10 4 cm 3. The diversity of density implies that, regardless of the spatial

46 6 Chapter 1. Introduction Table 1.1: Physical properties of molecular clouds (from Cernicharo 1991; Lada 1999) Property GMCs Dark clouds Mass M M Maximum linear extent pc 6 20 pc Mean density, n(h 2 ) cm cm 3 Typical line width 6 15 km s km s 1 Kinetic temperature 20 K 10 K resolution used, no single observable tracer can completely represent its structure. Moreover, the spatial structure inferred from observation requires caution and discrepancies between tracers have to be treated with great care Constituents of molecular clouds The main constituents of molecular clouds are molecules, dust grains, and ions, each one playing a very distinct role in the physics of molecular clouds. We give a deeper review of interstellar molecules, dust grains and ions, in chapter 3, mainly from a chemical point of view. However, it is important to note some important physical effects of these components. The radiation emitted from the rotational lines of interstellar molecules, especially the molecular species CO and H 2 O, is the main coolant for nearly all the gas in molecular clouds, balancing the heating, produced mainly by cosmic rays and external UV photons, and maintaining an equilibrium temperature of 10 K. If this was not the case, molecular clouds would be substantially warmer, approaching the temperatures of diffuse clouds, 100 K (Myers 1999). Dust grains are the main site of formation of H 2 from H; they are also thought to be the main coolant in molecular clouds when the gas density exceeds 10 5 cm 3, and act as reservoir of molecular material, since in dense cores grains accrete mantles or layers of molecules sufficiently polar that upon colliding with the grain are bond to the surface (see chapter 3).

47 1.2. Dense cores 7 Although molecular clouds have a low level of ionization, with an electron fraction x e < 10 5 (Myers 1999), caused by cosmic rays ionization and photoionization by ultraviolet photons from distant OB stars, the ionization level of the gas affects the clouds both chemically, because gas-phase chemical reactions in the molecular clouds are driven primarily by ionized species in ion-molecule reactions (see chapter 3), and physically, because ion-neutral collisions are capable to couple the motions of the magnetic field to those of neutral gas, allowing the propagation of magnetohydrodynamic (MHD) waves and turbulence. As a consequence, the magnetic field and the neutral gas move together as a single fluid (e.g. Myers and Goodman 1988). These MHD motions have been proposed to help support molecular clouds against the inward pull of their self-gravity (e.g. Mouschovias 1987; Shu et al. 1987). Finally, as we have mentioned, molecular clouds also host young stellar objects (YSOs) existing in a wide range of evolutionary stages, from the youngest Class 0 protostars, some 10 4 yr old, which derive most of their luminosity from gravitational infall (André et al. 1993), to T Tauri stars a few 10 6 yr old, deriving their luminosity from quasi-static contraction (Walter 1987). The masses of stars in molecular clouds also cover nearly all the range of known stellar masses, from about 0.1 to 30 M (Myers 1999). The spatial distribution of stars inside molecular clouds may range from isolated stars with no known neighbors within a few pc, such as in Taurus, to rich star clusters having more than 1000 stars within a few pc, such as in Orion (Lada 1999). The winds and outflows originating in embedded stars contribute a major part of the turbulent kinetic energy in molecular clouds. Also, the winds, outflows and radiation from the most massive stars are probably able to unbind and disperse the gas, and thus destroy molecular clouds. 1.2 Dense cores Molecular clouds contain denser aggregates of gas with densities > 10 3 cm 3. These denser clouds have been usually classified according to some observational definition (i.e. minimum column density defining the cloud, optical aspect, mean density,...), which separated them into categories such as cores, clumps, etc (see Cernicharo 1991). This division does not imply that these clouds are clearly different objects, but it has been used as a practical tool to study them, because some of these clouds

48 8 Chapter 1. Introduction are contained within others. It must be noted that the objects found in massive clouds, associated to high mass stars, are larger, denser, more massive, and hotter than those found in dark clouds, associated with low mass stars, which are the subject of our study. These denser objects are usually identified as coherent regions in position and velocity (l-b-v) when observed in the emission lines of high-density tracers such as 13 CO, C 18 O, NH 3, CS (Bertoldi and McKee 1992). Clouds of gas with densities > 10 4 cm 3, also known as dense cores, which have been extensively studied by several molecular lines, such as the CS (J=1 0), CS (J=2 1), or the NH 3 (J, K)=(1,1) lines, have been found to be very much related to star-formation. Observations with these lines in Taurus and other nearby complexes have shown that dense cores have generally masses of 1 M (Myers and Benson 1983, Benson and Myers 1989), which is typical of a low-mass star. Moreover, observations in the far- (Beichman et al. 1986) and near-infrared (Myers et al. 1987) have shown a close association between such cores and stars, which seems to indicate that there is a link between the physical properties of the core gas and its evolution until a star is formed. This observational information is widely used to support the models of isolated, low-mass star formation, (e.g. Shu et al. 1987; Mouschovias 1987, etc). Finally, it has also been found that groups and clusters of young stars in regions of massive star formation are often associated with cores detected with lines of CS and NH 3 (Lada et al. 1991; Harju et al. 1993) General properties Consequently, the knowledge of the physical conditions in the clouds that give birth to stars and of those that surround the newly born young stellar objects appears to be a necessary step to study and to infer the physical processes that occur during their formation. Table 1.2 shows typical values of parameters that characterize the physical conditions in cloud cores, such as temperature, volume density, mass, velocity field, or cloud size. The shape of a molecular cloud dense core contains information on the recent history of the core s internal and external forces and motions. The analysis of core shapes might give some clues to identify the initial conditions for star formation, and additionally to describe the physical processes that form, maintain and destroy dense cores. Low angular resolution observations of the emission of high density

49 1.2. Dense cores 9 Table 1.2: Physical properties of dense cores (from Cernicharo 1991, Mundy 1994) Property Dark cloud GMC Size pc pc Average density, n(h 2 ) cm cm 3 Mass M M Line width, V km s km s 1 Temperature 10 K K tracing molecules, such as the CS (J=2 1) transition, in regions where bright CO emission had been found have shown that the distribution of the high density gas is very clumpy, and is usually dominated by a few very large clumps or cores (Snell et al. 1982; Stutzki and Güsten 1990; Langer et al. 1995). These cores were found to have radii which ranged from < 0.05 pc to 0.5 pc (Mundy 1994). The motions of the gas in dense cores are traced by the width of spectral lines, which is related to the velocity dispersion along the line of sight. The line width of emission lines in a core is a result of both thermal Doppler broadening and nonthermal, or turbulent, motions in the gas. Considering V tot as the FWHM of the observed line profile, corrected for optical depth and resolution effects, we may write ( V tot ) 2 = ( V th ) 2 + ( V nth ) 2 (1.1) or expressing the thermal line width in terms of the kinetic temperature ( V tot ) 2 = 8ln2kT m obs + ( V nth ) 2 (1.2) where k is the Boltzmann s constant, T is the kinetic temperature of the gas, and m obs if the mass of the observed molecule. The nonthermal portion of the line width, V nth, may arise from such phenomena as rotation, gravitational collapse, turbulence, or other large scale motions within the core (see e.g. Wolkovitch et al. 1997). Nonthermal line widths in dense cores range from from subsonic by a factor 4 in small quiescent cores, such as L1512 (Fuller and Myers 1993), to supersonic by a factor greater than 10 in large turbulent cores associated with compact H II regions (Ho and Townes 1983). In the next three subsections we describe three properties of dense cores that we

50 10 Chapter 1. Introduction will revisit in later chapters (see chapters 2 and 5). Two of them involve spectral line widths, which can be used to estimate the core mass from the virial theorem, and have also been found to be related to the core size. Finally, we will make some comments about the ionization level of cores, which is closely related the gas core chemistry Mass and virial balance A commonly used method for deriving molecular cloud masses applies the virial theorem to measurements of emission lines of molecules, in order to estimate the mass of H 2 in molecular clouds. The popularity of this technique has been largely due to its apparent simplicity, although in practice, great care has to be taken because due to its implicit assumptions and the limited range of applicability uncertainties can easily lead to systematic errors in the mass. The simplest expression of the virial theorem, if we do not take into account cloud magnetic fields or internal energy sources, leads to an expression for the total mass of a simple spherical system of M vir = k 1σ 2 R G (1.3) where σ is the full three-dimensional velocity dispersion averaged over the whole system, R is the cloud radius, and k 1 is a constant whose exact value depends on the form of the density distribution as a function of distance from the cloud center, ρ(r) (MacLaren, Richardson and Wolfendale 1988). For ρ(r) r n, where n < 3, k 1 = 5 2n 3 n (1.4) If we assume a gaussian velocity distribution, equation (1.3) can be expressed in practical units as [ Mvir M ] [ ] [ ] 2 R V = k 2 (1.5) pc km s 1 where M is the cloud mass in M, R the radius in parsecs, and V is the FWHM intensity in km s 1. Table 1.3 gives some values for the virial coefficients depending on the density distribution. Core surveys based on molecular line tracers provide measurements of core radii and velocity dispersion, and hence an estimate of M vir. With an assumption for the

51 1.2. Dense cores 11 Table 1.3: Virial theorem coefficients Density distribution k 1 k 2 ρ constant 5/3 210 ρ r 1 3/2 190 ρ r fractional abundance of the tracer molecule, the mass can be estimated separately from the LTE molecular column density and core size. Observationally, the velocity dispersion within a cloud is estimated by measuring the line width. As we have previously mentioned, the line width arises as a consequence of both thermal and dynamical broadening, and is probably modified by optical depth effects. If the thermal line width is considerably narrower than the observed line width, which is often the case, the observed line width is presumed to be representative of the cloud s velocity structure. The estimated virial masses of dense cores is found to range between M (Loren 1989; Lada, Bally and Stark 1991; Williams et al. 1994). Most cores have masses less than 100 M, and the number of cores increases with decreasing mass for M > 20 M. A turnover in the mass spectrum can be seen for lower masses, which although difficult to determine, could be due to incomplete sensitivity to lowmass cores. The mass spectrum for cores with M > 20 M, can be characterized by a power-law with an index of 1.6 (Lada, Bally and Stark 1991), which implies that a significant amount of the mass of the dense gas is contained in the most massive cores. Williams et al. (1994) also find that, in general, cores with masses greater than 100 M have mass near M vir, whereas lower mass cores often have masses significantly less than M vir, even as little as 0.1 to 0.01 of M vir. Not being in gravitational virial equilibrium does not necessarily mean that a core is not gravitationally bound, because it may be bound by a combination of gravity and magnetic, turbulent, or thermal pressure of the surrounding cloud (Bertoldi and McKee 1992; Mundy 1994). However, at this point we have to consider the question as to whether or not molecular cloud cores are in fact in or near virial equilibrium, taking into account the possible influence of young stars or other sources of energy input over the measured

52 12 Chapter 1. Introduction average gas velocities, and secondly, how this simplistic model is affected by the presence of magnetic fields. Work by several authors (Myers et al. 1991; Harju, Walmsley and Wouterloot 1993) has shown that cores have line widths, column densities, and map sizes which appear close to the condition of virial balance, in which the gravitational potential energy and kinetic energy are approximately equal Line width - size relations It has long been known that V obs, the FWHM velocity width of a line, such as NH 3 12 CO, C 18 O and 13 CO, which are sensitive to a wide range in density, observed in a particular cloud, and R, the size of the half-maximum contour map of the intensity of the same line, have two types of relation of the form V obs R p. Observations of tens to hundreds of clouds in the same line indicate a cloud-to-cloud correlation with p 0.5 (Dame et al. 1986; Solomon et al. 1987; Leung, Kutner and Mead 1982; Torrelles et al. 1983). At the same time, observations in several lines of one or several clouds show a line-to-line correlation with 0.25 < p < 0.7 (Ho et al. 1977; Larson 1981; Martin and Barrett 1978; Myers et al. 1978; Snell 1981). Several authors have combined these two types of correlation, by considering V obs versus R for many tens of clouds, in more than one line, which increases the range of V obs and R, yielding correlations of increased significance, with a similar result of p 0.5 (Larson 1981; Myers 1983; Falgarone and Perault 1987; Myers and Goodman 1988). However, the physical basis of the relationship is still poorly understood, although the line broadening is probably magnetic in origin (Myers and Goodman 1988; Goodman et al. 1989). In the case when the observed lines are primarily nonthermal, and when p = 0.5, the cloud-to-cloud relations are consistent with virial equilibrium, combined with a relative variation from cloud to cloud in the column density or the internal pressure, which is smaller than the relative variation from cloud to cloud in the cloud size (Fuller and Myers, 1992). There are several possible reasons that give account of these variations: from a combination of sensitivity and selection (Larson 1981; Kegel 1989); cloud stability (Chièze 1987); equipartition between magnetic and kinetic energy (Myers and Goodman 1988); external pressure (Fleck 1988; Elmegreen 1989); or the effects of star formation (McKee 1989). The cloud-to-cloud relations have also been alternatively interpreted as indicating a turbulent cascade of energy from large to small scales (Larson 1981; Myers 1983).

53 1.2. Dense cores 13 Figure 1.3: Line width-size relation in (a) massive cores in Orion, and (b) low-mass cores in Perseus, Taurus, Orion, Ophiuchus, and Cepheus. Dashed lines labeled V T represent the thermal part of the line width of the molecule of mean mass m assuming a temperature of 18 K (massive cores), or 10 K (low-mass cores). Taken from Caselli and Myers (1995). On the other hand, the line-to-line relations in a cloud are dependent on the spatial structure of the cloud motions, and the density structure of the cloud. The use of several lines, sensitive to a wider range of densities, increases the range of column density to which the observations are sensitive. Fuller and Myers (1992) observed 14 low-mass cores (six starless cores and eight with associated stars) in lines of NH 3, CS and C 18 O. They found that the slope of the line width-size relation, p 0.4, was independent of the presence of associated stars. Thus, it can be considered that the physical conditions underlying this relation are part of the initial conditions of the star formation process. Caselli and Myers (1995) carried out a study of the line width-size relation in a sample of massive cores in Orion A and Orion B, which had been previously mapped in at least three different molecular lines of NH 3, CS, and 13 CO. They found that the nonthermal component of the

54 14 Chapter 1. Introduction line width ( v NT ) followed the trend v NT R p, where p = 0.21 ± 0.03 (see Figure 1.3a), while the value they found for observations made by other authors in low-mass cores in Perseus, Taurus, Orion, Ophiuchus and Cepheus was significantly lower p = 0.53 ± 0.07 (see Figure 1.3b). They also found that, for massive cores, the estimated value of the radius at which the thermal and nonthermal components of the line widths are equal is 15 times smaller than in low-mass cores; and that nonthermal motions dominate thermal motions at all observed size scales, and, in particular, at the size scales 0.1 pc traced by low-resolution NH 3 maps, where low-mass cores are primarily thermal Ionization and magnetic support Magnetic fields play an important part in supporting dense cores against gravity (Mouschovias 1976). The fields are coupled to the gas through the ions and electrons which are constrained to move with the field because the period of ion gyration around the field is much shorter than ion-neutral collision times (Myers 1999). Collisions between ions and neutrals causes a friction which limits the speed of movement between the field and the neutral gas. Ambipolar diffusion, the ion-neutral relative motion, is controlled by this friction, and the ambipolar diffusion time, t D, is a measure of the period for which magnetic support may be significant (Williams 1991). The field and the neutral gas can move together as a single-fluid system if the ions have time to transmit their motion to the neutrals, i.e. the period of fluctuation of the field is long enough for an ion to hit a neutral. If not, the decoupling can limit the cloud s ability to adjust its structure on small scales. The ionization level x i = n i /n, where n i is the number density of ions, inside cores determines the ambipolar diffusion time, since it can be shown that, approximately [ ] td [ 10 6 xi ] years 10 8 (1.6) (Mouschovias 1979; Hartquist and Williams 1989). As we will see in chapter 3, the ionization is controlled by the chemistry. External UV photons determine the ionization structure of molecular clouds up to a visual extinction of about magnitudes (McKee 1989; Bertoldi and McKee 1992). At higher extinctions, the ionization becomes dominated by cosmic rays because the flux of UV photons is attenuated. The dominant ion is expected to be HCO +, arising from the transfer of a proton from H + 3

55 1.3. The formation and evolution of low mass stars 15 to CO; the H + 3 ion formed from H + 2, which itself is a result of cosmic ray ionization of H 2 (see chapter 3). Fast recombinations of HCO + ions with electrons maintain the level of ionization at relatively low values, x i (Williams 1991). If, however, CO is strongly depleted from the gas, then recombination will be slower and the level of ionization will increase, with a consequent increase in t D. 1.3 The formation and evolution of low mass stars Star formation takes place in cold, dense cores in molecular clouds. These cores have been identified observationally as pre-stellar, or pre-protostellar, cores. The pre-stellar stage can be defined as the phase in which a gravitationally bound core has formed in a molecular cloud, but no central protostar exists yet within the core. The initial evolution of a pre-stellar core would consist in the aggregation of the surrounding material achieving higher degrees of central condensation, which eventually would lead to collapse, and to the formation of a central hydrostatic protostar. The timescale for the gravitational collapse of a cloud core, a quantity also known as the free-fall time, is largely determined by the density of the cloud, ρ 3π τ ff = (1.7) 32Gρ The free-fall time is about years for the typical mean density of a cloud core, n 10 4 cm 3. However, once a stellar object of mass M forms at the center of a collapsing cloud, it continues to slowly accrete material, contract and heat up. The slow contraction continues until the center becomes hot enough to fuse hydrogen. The timescale for its (pre-hydrogen burning) evolution is initially given by the Kelvin-Helmholtz time: τ KH GM 2 R L (1.8) This time is very short for a high mass star, 10 4 years for M = 50 M, and relatively slow for a low mass star, years for M = 1 M. This implies that high mass stars, where τ KH < τ ff, begin burning hydrogen and reach the main sequence before the end of the infall phase of protostellar evolution, while low mass stars, where τ KH > τ ff, do have an observable pre-main sequence stage of stellar evolution. This is the main reason why regions of low mass star formation are used for star formation research. Additionally, low mass stars are considerably less destructive

56 16 Chapter 1. Introduction Figure 1.4: The empirical classification scheme for YSO spectral energy distributions. The vertical line is placed at wavelength of 2.2µm in each panel. (Taken from Lada 1999). to their native environments than high mass stars, which can quickly disrupt dense molecular gas, or modify the process of collapse of the surrounding interstellar material by hindering its fall or even blowing it away (Lada 1991). A final advantage of low mass stars is that they can form in relative isolation so that their immediate circumstellar environment is not influenced by the disruptive presence of nearby stars. High mass stars, on the other hand, rarely form in isolation and their environments are nearly always confused by the effects of other recently formed nearby stars. Since the works of Lada and Wilking (1984) and Adams et al. (1987), the vast majority of known low mass young stellar objects were classified based on the nearinfrared spectral index of their spectral energy distributions into three broad classes,

57 1.3. The formation and evolution of low mass stars 17 designated I, II and III. André et al. (1993) identified in the submillimeter the youngest protostars to have been observed and classified them as Class 0 objects to indicate their extreme youth. Figure 1.4 shows the spectral energy distributions that characterize each of these classes. The variation in the spectral energy distribution shape can be explained by an evolutionary sequence from protostar to main sequence star, corresponding to the gradual dissipation of gas and dust envelopes around newly formed stars. The spectral energy distributions of class 0 and I sources peak at sub-millimeter and far-infrared wavelengths, which indicates that the spectral energy distributions are dominated by emission from cold dust. These objects are thought to be the least evolved of YSOs because they are the most deeply embedded of the YSOs and protostellar in nature (Adams et al. 1987, André et al. 1993). Class II and III sources are much less reddened. They have energy distributions that peak at optical and near-infrared wavelenghts where emission from stellar photospheres is expected to dominate. These objects correspond to the more evolved pre-main sequence stars. However, the physical characteristics of a young stellar object are not only characterized by their spectral energy distribution. The interaction of the YSO with the ambient gas associates them, in varying degrees, to a range of astrophysical phenomena, such as jets, bipolar outflows, Herbig-Haro objects, masers, optical/infrared emission lines, and variability. Thus, the understanding of the physical nature of the young stellar objects seems to require precise knowledge of their relation to these various phenomena, which are also used as tracers of star forming regions and help in the identification of cores that are undergoing star formation. A great deal of effort has been put into modeling and describing the evolution from a dense core to the formation of a star (e.g. Larson 1981; Shu et al. 1987; Ciolek and Mouschovias 1993). The evolution of a young stellar object from pre-stellar core to main-sequence star can be then divided into five stages (Ward-Thompson, 1996), corresponding roughly to each of the spectral classes of young stellar objects we discussed above plus an initial pre-stellar stage (Fig. 1.5): i) A pre-stellar core in a molecular cloud. It has no central luminosity source, and hence is externally heated. Its radial density profile suggests pressureconfinement and evolution through ambipolar diffusion. It has to be noted that an alternative view (Evans et al. 2001) proposes that some cores have density structures like those of Bonnor Ebert spheres, suggesting that the magnetic

58 18 Chapter 1. Introduction B Pre stellar Class 0 Class I (main infall) (late infall) i) ii) iii) Class II Class III iv) v) Figure 1.5: Sketch sumarising the five stages of young stellar object evolution from pre-stellar core to main-sequence star field may have a minor role in supporting dense cores. ii) The main accretion phase, or Class 0 stage. A hydrostatic protostar, surrounded by a progenitor disc, and massive envelope, is in the process of accumulating the majority of its mass, while simultaneously driving a highly collimated, energetic bipolar outflow. iii) The late accretion phase, or Class I stage. The protostar, surrounded by a remnant envelope, is accumulating the remainder of its mass. The circumstellar disc grows, and the bipolar outflow becomes less energetic and less well collimated. iv) The classical T Tauri phase, or Class II stage. The YSO has effectively no remaining envelope, but an optically thick disk, which is still accreting onto the YSO. v) The weak-line T Tauri phase, or Class III stage. The disc is now optically thin, and the YSO completes its Kelvin-Helmholtz contraction onto the main sequence.

59 1.4. Observations of star-forming regions 19 The first three stages would correspond to the embedded phase during which protostellar evolution takes place, and the initial stellar core acquires the bulk of its mass. Throughout most of this phase, the embryonic star is heavily obscured and invisible to optical wavelengths. The later two stages correspond to the revealed phase, once the young stellar object has acquired most of its final mass, when the star becomes visible to optical and near-infrared wavelengths. In low mass stars, this corresponds to the pre-main sequence evolution phase. 1.4 Observations of star-forming regions Tracers of dense gas In the earliest stages of star formation, stars are deeply embedded in dense clouds of gas and can only be studied at infrared or radio wavelengths. Under these conditions, the observation of molecular emission and absorption provides important information about the density, temperature, and the radial velocity of the gas. Given the temperature conditions inside molecular clouds, most of the molecules detected until now are observed by their rotational transitions within the ground electronic and vibrational state. Weak lines and rare chemical species and isotopes down to abundances of with respect to hydrogen have been detected with the more sensitive single-dish (sub-)millimeter telescopes (van Dishoeck and Hogerheijde 1999). However, some of the more important molecules can not be observed by this method, especially the molecule more abundant of all, H 2, because symmetric molecules lack the permanent dipole moment required for rotational emission lines. Other symmetric molecules unobservable in this way are N 2, CH 4 and C 2 H 2. Additionally, the Earth s atmosphere prevents ground-based observations of some transitions of O 2, CO 2 and H 2 O. Therefore, the CO molecule has been used as the foremost tool to trace H 2, with which to detect and map the giant molecular clouds in the Galaxy and their inner structure, for three main reasons: CO is chemically stable; it is widely distributed throughout the Galaxy; and its emission is excited by collisions with gas at densities of only a few 10 2 hydrogen molecules per cm 3. However, for studies of denser regions, such as dense cores, CO emission is usually optically thick and other

60 20 Chapter 1. Introduction molecules are used to trace H 2. These molecules are as ubiquitous as CO, although three or more orders of magnitude less abundant, and require much higher densities of surrounding H 2 before they are significantly excited into emission. These molecules are usually known as tracers of dense gas, because their emission follows the distribution of the dense gas inside molecular clouds. CS, NH 3, and HCO + are typical examples of tracers of dense molecular gas used extensively in the study of star-forming regions. In summary, observations of different rotational lines have proved to be very useful probes of the molecular gas, because they are collisionally excited by H 2 for densities cm 3 and temperatures of K (Evans 1980; Walmsley 1987; Genzel 1991). The identification of dense cores is the first step in the study of the denser phases of molecular clouds. Tracers of dense gas are used following two different approaches. One method is to make complete surveys of clouds or regions, such as the mapping of CS in Orion A and B (Lada et al. 1991; Tatematsu et al. 1993), or the 13 CO and C 18 O mappings of Taurus (Fukui et al. 1994). This approach has the advantage that it is unbiased and can address questions such as what fraction of gas in a cloud is found above a certain density. However, it is relatively inefficient at finding cores, as the cores occupy a small fraction of the volume of a typical cloud (Fuller 1994). Another method is to search towards some target where dense gas is expected. The targets used are usually marked by extinction peaks, young stars identified by IRAS point sources, or other tracers of star formation such as Herbig-Haro objects. This method is more efficient at finding cores but it is biased. Examples are the surveys in NH 3 made by Torrelles et al. (1983), Anglada et al. (1997), or Sepúlveda et al. (2001). It was early evident that a lot more information can be gathered from dense cores in molecular clouds if they are observed in multiple transitions of one or more molecules, e.g. Welch (1989). Studies of different transitions of a given molecule often reveal processes at different temperatures which may have different dynamics: i.e., the lower rotational transition may trace cool and quiescent gas, while the higher rotational transition is associated with warmer gas in a bipolar outflow. Moreover, maps of particular regions in different molecules may show striking differences from one another (Fuller and Myers 1987). The differences may be due to excitation, because each line traces a different mean density of collision partners (mainly H 2 molecules and He atoms), to optical depth effects, or to real abundance differences. This latter case implies a clear understanding of the chemistry.

61 1.4. Observations of star-forming regions 21 The interpretation of the results obtained from the observation of molecular lines in molecular clouds faces another source of uncertainty. Maps of clouds obtained with single-dish telescopes have angular resolutions between 10 and a few arcminutes. However, even in the nearest star-forming regions, the beam may encompass regions of very different physical or chemical characteristics, as circumstellar disks, or bipolar outflows, envelopes, etc. Therefore, the derivation of molecular abundaces becomes a complicated matter. Interferometers can obtain much higher angular resolution, 1, but their sensitivity is significantly lower than that of single-dish telescopes. The interpretation of interferomeric observations is further complicated because they filter out all emission on extended scales defined by the shortest baselines. Some help to this problem comes from the fact that heterodyne (sub-)millimeter spectroscopy has attained very high spectral resolution, typically better than a few tenths of a km s 1, and covers the full extent of the lines up to a few hundred km s 1. Thus, regions with different physical conditions within one beam can be separated if they have different velocities or line profiles, although multitransitional observations have the disadvantage that the frequency separation between different rotational transitions of the same molecule is usually so large that multiple observations are needed to constrain the excitation, often involving different telescopes and/or beam sizes Line formation The analysis of the lines obtained with telescopes requires an understanding of the line formation mechanism. That is, how the observed molecular levels are excited and de-excited. For conditions in typical interstellar clouds, the populations of the rotational levels, n i, of molecules are controlled by radiative transitions among levels and by collisional processes with the dominant neutral species, H 2 and He. If we balance the processes leading to the loss of population of level i, with the ones leading to the gain of population, the statistical equilibrium equations can be written (Spitzer, 1978) as n i A ij + n i (B ij U ν + γ ij n col ) = n j A ji + n j (B ji U ν + γ ji n col ) (1.9) j<i j j>i j where A ij, A ji, and B ij are the Einstein coefficients for spontaneous and stimulated emission and absorption, U ν is the intensity of the radiation field averaged over all

62 22 Chapter 1. Introduction directions and integrated over the line profile, γ ij and γ ji are the collisional rate coefficients between levels i and j, and n col is the density of collision partners. The upward and downward collisional rate coefficients are related by where g i is the statistical weight of level i. γ ji γ ij = g i g j e hν/kt (1.10) The radiative rates are related to the permanent dipole moment of the molecule, and are generally well known experimentally. On the contrary, collisional rates have been more difficult to obtain in the laboratory. The values of γ ij for collisions of different molecules with H 2 (J = 0) have largely been derived from detailed quantum mechanical calculations (Green, 1975; Green and Thaddeus, 1976), and are one of the largest uncertainties in analyzing molecular excitation. Furthermore, collisional rates depend on kinetic temperature, and it has been often difficult to obtain even averaged rates at the low temperatures of molecular clouds (Green and Chapman, 1978). There is little information on collisional rate coefficients at high temperatures > 200 K, and collisions with H 2 (J = 1) or higher are generally not taken into account explicitly (van Dishoeck and Hogerheijde 1999). The critical density for a given transition is the density at which the rates for collisional processes become comparable to those for radiative processes, resulting in substantial population of level i n i crit = A ij γ ij (1.11) In this case, the line is thermalized, i.e. the excitation temperature of the transition will be very close to the kinetic temperature of the cloud. If the transition becomes optically thick, part of the emitted photons are re-absorbed and the critical density is lowered by 1/τ, where τ is the optical depth of the line (van Dishoeck and Hogerheijde 1999). Since A ij ν 3 µ 2, where ν is the line frequency and µ the molecular dipole moment, higher frequency transitions and molecules with large dipole moments have higher critical densities. Therefore, a large range of densities can be probed just by carefully choosing the appropriate molecule and transitions more sensitive to the physical conditions of the cloud. Figure 1.6 shows molecules and transitions that cover the range of densities and temperatures found in dense cores of molecular clouds.

63 1.4. Observations of star-forming regions 23 Figure 1.6: Molecular lines as probes of physical conditions in molecular clouds (from Genzel 1991) Differences between tracers of high density gas The use of different molecular tracers of high-density gas soon showed that, in some cases, the distribution of gas that emerged from the observations was clearly different depending on the particular molecular tracer or transition that had been used and indicated abundance variations of different molecular species (e.g. Goldsmith 1991 and references therein). CS, NH 3, HC 3 N, and HCO + were some of the most commonly used high-density gas tracers, having very similar critical densities > 10 4 cm 3. Yet, maps obtained in several regions, such as in L134N (Ungerechts et al. 1980; Snell et al. 1982; Swade 1989a, 1989b), or TMC-1 (Little 1979, Olano et al. 1988) showed discrepancies, such as very different shapes, or different position of the emission peaks. Systematic comparisons of the emission of CS and NH 3 were made by Zhou et al. (1989), and Myers et al. (1991), using different angular resolutions, and by Pastor et al. (1991) using the same angular resolution for observation of both

64 24 Chapter 1. Introduction molecules, which avoided morphological differences due to instrumental effects. All these studies confirmed the discrepancies, and showed that cloud structure may appear to be very different depending on which tracer is used, even when effects of excitation and radiative transfer are accounted for. To explain the differences in the emission, several mechanisms were proposed: variations of chemical abundances (Cernicharo et al. 1984; Olano et al. 1988); the passing of shocks, which could enhance the abundance of sulphur-bearing molecules (Hartquist et al. 1980; Mitchell 1984) while leaving NH 3 abundance unchanged (Iglesias and Silk 1978); spatial variation of total particle density (Bujarrabal et al. 1981); or scattering of the emission by optically thick surrounding material (Fuller and Myers 1987). However, some results were puzzling. For instance, the extension of CS emission in all the surveys was usually much larger than that of NH 3, yet NH 3 critical density is slightly lower than CS, and one would expect the emission of CS being found in more confined regions, where gas was denser. In other cases, such as in NGC 2071N (Goldsmith et al. 1992) the distribution of the emission of several molecules, such as C 18 O, NH 3, CS, or HCO +, was so different that suggested that chemical evolution in different clumps was at different phases, and that there was a time dependence of the abundance of different species. Studies made by Hirahara et al. (1992) and Suzuki et al. (1992) in the TMC-1 cloud, comparing the emission of the molecules CCS, HC 3 N, and NH 3 also confirmed the differences in the distribution of the emission and in the position of the emission peaks. However, in this region, these authors found an anticorrelation between the emission of CCS and HC 3 N, and that of NH 3. They attributed the differences to an effect of chemical evolution of dark clouds; carbon-chain molecules, including CCS, would be abundant in the early stages of chemical evolution, whereas NH 3 is abundant in the later stages. The observed dense cores would be at different stages of chemical evolution and/or would have different physical conditions of density or visual extinction, which would explain the observed structure. Therefore, the study of the structure of dense clouds has to face the issue of variations of molecular abundance, in order to distinguish between density inhomogeneities and nonuniformities in the abundance of trace molecules. Serious errors in the perception of the structure of a cloud can be made if studies are limited to a single, or very few, molecular species, no matter how good tracers of molecular material they may be, because they are subjected to significant abundance variations within individual clouds. However, as we will see, this apparent complication

65 1.5. Goals and structure of this work 25 of molecular abundance variations may be a valuable source of information about the structure and evolutionary state of dense cores in molecular clouds. 1.5 Goals and structure of this work This work has two main goals: to extend the systematic comparison begun by Pastor et al. (1991), in order to confirm their results; and to explain the differences in emission as caused by changes in chemical abundances depending on the evolutionary stage of the cloud. Finally, a higher resolution study of a selected region of the survey was made to test the predictions of the chemical model. Accordingly, the structure of this work is the following: In chapter 2 we present the systematic study comparing the emission of the CS (J=1 0) and NH 3 (J, K)=(1,1) transitions in several star-forming regions under similar conditions of angular resolution that we made in order to find how their transitions relate to the actual distribution of the high-density gas. The explanation of the observed differences involved the modeling of the chemistry of dense clouds. Therefore, we first make an introduction to astrochemistry in chapter 3. We describe the most relevant chemical processes ocurrying in the gas phase of the interstellar medium and in dust grains. Next, in chapter 4, we explain how the modeling of the interstellar chemistry is made, and in particular how we built the models that we present later in the work. Chapters 5 and 6 discuss the model we made to explain our observations, which are their predictions, and discuss the observability of several molecules and transitions which could be used to test the validity of the model. In chapter 7, we show the results of a multitransitional study we made in the L673 region, previously observed at 1. 5 resolution in the CS (J=1 0) and NH 3 (J, K)=(1,1) transitions, using the BIMA interferometer, in order to test the predictions of the model.

66 26 Chapter 1. Introduction

67 Bibliography Adams F. C., Lada C. J., Shu F. H., 1987, The Astrophysical Journal, 312, 788 André P., Ward-Thompson D., Barsony M., 1993, The Astrophysical Journal, 406, 122 Anglada G., Sepúlveda I., Gómez J. F.,1997, Astronomy and Astrophysics Supplement Series, 121, 255 Bally J., Stark A. A., Wilson R. W., Langer W. D., 1987, The Astrophysical Journal, 312, L45 Beichman C. A., Myers P. C., Emerson J. P., et al., 1986, The Astrophysical Journal, 307, 337 Benson P. J., Myers P. C., 1989, The Astrophysical Journal Supplement Series, 71, 89 Bertoldi F., McKee C. F., 1992, The Astrophysical Journal, 395, 140 Blaauw A., 1991, in Lada C. J. and Kylafis N. D., eds., The Physics of Star Formation and Early Stellar Evolution. Kluwer Academic Publishers, p. 125 Blitz L., Williams J. P., 1999, in Lada C. J. and Kylafis N. D., eds., The Origin of Stars and Planetary Systems. Kluwer Academic Publishers, p. 3 Bujarrabal V., Guélin M., Morris M., Thaddeus P., 1981, Astronomy and Astrophysics, 99, 239 Caselli P., Myers P. C., 1995, The Astrophysical Journal, 446, 665 Cernicharo J., 1991, in Lada C. J. and Kylafis N. D., eds., The Physics of Star Formation and Early Stellar Evolution. Kluwer Academic Publishers, p

68 28 BIBLIOGRAPHY Cernicharo J., Guélin M., Askne J., 1984, Astronomy and Astrophysics, 138, 371 Chakrabarti S., Chakrabarti S. K., 2000, Astronomy and Astrophysics, 354, L6 Chièze J. P., 1987, Astronomy and Astrophysics, 171, 225 Ciolek G. E., Mouschovias T. Ch., 1993, The Astrophysical Journal, 418, 774 Dame T. M., Elmegreen B. G., Cohen R. S., Thaddeus P., 1986, The Astrophysical Journal, 305, 892 Elmegreen B. G., 1989, The Astrophysical Journal, 338, 178 Evans N. J., 1980, in Andrew B. H., ed., Interstellar Molecules. Reidel, Dordrecht, p. 1 Evans, N. J., Rawlings, J. M. C., Shirley, Y. L., Mundy, L. G. 2001, The Astrophysical Journal, 557, 193 Falgarone E., Perault M., 1987, in Morfill G. and Scholer M. S., eds., Physical Processes in Interstellar Clouds. Reidel, Dordrecht, p. 59 Fleck R. C., 1988, The Astrophysical Journal, 328, 299 Fukui Y., Mizuno A., Ogawa H., et al., 1994, in Montmerle Th., Lada Ch. J., Mirabel I. F., and Trân Thanh Vân J., eds., The Cold Universe. Editions Frontières, Gifsur-Yvette, p. 157 Fuller G. A., 1994, in Clemens D. P. and Barvainis R., eds., Clouds cores and low mass stars. ASP Conf. Ser., 65, San Francisco, p. 3 Fuller G. A., Myers P. C., 1987, in Morfill G. and Scholer M. S., eds., Physical Processes in Interstellar Clouds. Reidel, Dordrecht, p. 137 Fuller G. A., Myers P. C., 1992, The Astrophysical Journal, 384, 523 Fuller G. A., Myers P. C., 1993, The Astrophysical Journal, 418, 273 Genzel R., 1991, in Lada C. J. and Kylafis N. D., eds., The Physics of Star Formation and Early Stellar Evolution. Kluwer Academic Publishers, p. 155 Goldsmith P. F. 1991, in Falgarone E., Boulanger F., and Duvert G., eds., Fragmentation of Molecular Clouds and Star Formation. Kluwer, Dordrecht, p. 177

69 BIBLIOGRAPHY 29 Goldsmith P. F., Margulis M., Snell R. L., Fukui Y., 1992, The Astrophysical Journal, 385, 522 Goodman A. A., Crutcher R. M., Heiles C., Myers P. C., Troland T. H., 1989, The Astrophysical Journal, 338, L61 Green S., 1975, The Astrophysical Journal, 201, 366 Green S., Chapman S., 1978, The Astrophysical Journal Supplement Series, 37, 169 Green S., Thaddeus P., 1976, The Astrophysical Journal, 205, 766 Harju J., Walmsley C. M., Wouterloot J. G. A., 1993, Astronomy and Astrophysics Supplement Series, 98, 51 Hartquist T. W., Oppenheimer M., Dalgarno A., 1980, The Astrophysical Journal, 236, 182 Hartquist T. W., Williams D. A., 1989, Monthly Notices of the Royal Astronomical Society, 241, 417 Heiles C., Kulkarni S. R., 1987, in Morfill G. E. and Scholer M., eds., Physical Processes in Interstellar Clouds. Reidel, Dordrecht, p. 13 Hirahara Y., Suzuki H., Yamamoto S., et al., 1992, The Astrophysical Journal, 394, 539 Ho P. T. P., Martin R. N., Myers P. C., Barrett A. H., 1977, The Astrophysical Journal, 215, L29 Ho P. T. P., Townes C. H., 1983, Annual Review of Astronomy and Astrophysics, 21, 239 Iglesias E. R., Silk J., 1978, The Astrophysical Journal, 226, 851 Kegel W. H., 1989, Astronomy and Astrophysics, 225, 517 Lada C. J., 1991, in Lada C. J. and Kylafis N. D., eds., The Physics of Star Formation and Early Stellar Evolution. Kluwer Academic Publishers, p. 329 Lada C. J., 1999, in Lada C. J. and Kylafis N. D., eds., The Origin of Stars and Planetary Systems. Kluwer Academic Publishers, p. 143 Lada E. A., Bally J., Stark A. A., 1991, The Astrophysical Journal, 368, 432

70 30 BIBLIOGRAPHY Lada C. J., Lada E. A., Clemens D. P., Bally J., 1994, The Astrophysical Journal, 429, 694 Lada C. J., Wilking B. A., 1984, The Astrophysical Journal, 287, 610 Langer W. D., Velusamy T., Kuiper T. B. H., et al., 1995, The Astrophysical Journal, 453, 293 Larson R. B., 1981, Monthly Notices of the Royal Astronomical Society, 194, 809 Leung C. M., Kutner M. L., Mead K. N., 1982, The Astrophysical Journal, 262, 583 Little L. T., MacDonald G. H., Riley P. W., Matheson D. N., 1979, Monthly Notices of the Royal Astronomical Society, 189, 539 Loren R. B., 1989, The Astrophysical Journal, 338, 902 MacLaren I., Richardson K. M., Wolfendale A. W., 1988, The Astrophysical Journal, 333, 821 Martin R. N., Barrett A. H., 1978, The Astrophysical Journal Supplement Series, 36, 1 McKee C. F., 1989, The Astrophysical Journal, 345, 782 McKee C. F., 1990, in Blitz L., ed., The Evolution of the Interstellar Medium. ASP Conf. Ser., 12, San Francisco, p. 3 Mitchell G. F., 1984, The Astrophysical Journal, 287, 665 Mizuno A., Onishi T., Yonekura Y., et al., 1995, The Astrophysical Journal, 445, L161 Mouschovias T. Ch., 1976, The Astrophysical Journal, 207, 141 Mouschovias T. Ch., 1979, The Astrophysical Journal, 228, 475 Mouschovias T. Ch., 1987, in Morfill G. E. and Scholer M., eds., Physical Processes in Interstellar Clouds. Dordrecht, Reidel, p. 453 Mundy L. G., 1994, in Clemens D. P. and Barvainis R., eds., Clouds, cores and low mass stars. ASP Conf. Ser. 65, San Francisco, p. 35 Myers P. C., 1983, The Astrophysical Journal, 270, 105

71 BIBLIOGRAPHY 31 Myers P. C., 1999, in Lada C. J. and Kylafis N. D., eds., The Origin of Stars and Planetary Systems. Kluwer Academic Publishers, p. 67 Myers P. C., Benson P. J., 1983, The Astrophysical Journal, 266, 309 Myers P. C., Fuller G. A., Goodman A. A., Benson P. J., 1991, The Astrophysical Journal, 376, 561 Myers P. C., Fuller G. A., Mathieu R. D., et al., 1987, The Astrophysical Journal, 319, 340 Myers P. C., Goodman A. A., 1988, The Astrophysical Journal, 329, 392 Myers P. C., Ho P. T. P., Schneps M. H., et al., 1978, The Astrophysical Journal, 220, 864 Myers P. C., Ladd E. F., Fuller G. A., 1991, The Astrophysical Journal, 372, L95 Norman C., Silk J., 1980, The Astrophysical Journal, 238, 158 Olano C. A., Walmsley C. M., Wilson T. L., 1988, Astronomy and Astrophysics, 196, 194 Pastor J., Estalella R., López R., et al., 1991, Astronomy and Astrophysics, 252, 320 Sepúlveda et al., 2001, in preparation Shu F. H., Adams F. C., Lizano S., 1987, Annual Review of Astronomy and Astrophysics, 25, 23 Snell R. L., 1981, The Astrophysical Journal Supplement Series, 45, 121 Snell R. L., Langer W. D., Frerking M. A., 1982, The Astrophysical Journal, 255, 149 Solomon P. M., Rivolo A. R., Barrett J., Yahil A., 1987, The Astrophysical Journal, 319, 730 Spitzer L., 1978, Physical Processes in the Interstellar Medium. New York, Wiley- Interscience Stutzki J., Güsten, R., 1990, The Astrophysical Journal, 356, 513

72 32 BIBLIOGRAPHY Suzuki H., Yamamoto S., Ohishi M., et al., 1992, The Astrophysical Journal, 392, 551 Swade D. A., 1989a, The Astrophysical Journal, 345, 828 Swade D. A., 1989b, The Astrophysical Journal Supplement Series, 71, 219 Tatematsu K., Umemoto T., Kameya O., et al., 1993, The Astrophysical Journal, 404, 643 Torrelles J. M., Rodríguez L. F., Cantó J., et al., 1983, The Astrophysical Journal, 274, 214 Ungerechts H., Walmsley C. M., Winnewisser G., 1980, Astronomy and Astrophysics, 88, 259 van Dishoeck E. F., Hogerheijde, M. R., 1999, in Lada C. J. and Kylafis N. D., eds., The Origin of Stars and Planetary Systems. Kluwer Academic Publishers, p. 97 Walmsley C. M., 1987, in Morfill G. and Scholer M. S., eds., Physical Processes in Interstellar Clouds. Reidel, Dordrecht, p. 161 Walter F., 1987, Publications of the Astronomical Society of the Pacific, 99, 31 Ward-Thomson D., 1996, Astrophysics and Space Science, 239, 151 Welch W. J., 1989, in Winnewisser G. and Armstrong J. T., eds., The Physics and Chemistry of Interstellar Molecular Clouds. Springer Verlag, Berlin Heidelberg, p. 5 Williams D. A., 1991, in James R. A. and Millar T. J., eds., Molecular Clouds. Cambridge University Press, Cambridge, p. 295 Williams J. P., de Geus E. J., Blitz L., 1994, The Astrophysical Journal, 428, 693 Wolkovitch D., Langer W. D., Goldsmith P. F., Heyer M., 1997, The Astrophysical Journal, 477, 241 Wood D. O. S., Myers P. C., Daugherty D. A., 1994, The Astrophysical Journal Supplement Series, 95, 457 Zhou S., Wu Y., Evans N. J., Fuller G. A., Myers P. C., 1989, The Astrophysical Journal, 346, 168

73 Chapter 2 CS observations of star-forming regions Introduction The study of dense cores in molecular clouds may provide us with information about the phenomena associated with the first stages of stellar evolution. The emission of several molecules that are good tracers of high density molecular gas has been used for studying these dense cores; in particular, the CS and NH 3 molecules, which have significant emission for densities > 10 4 cm 3. However, large discrepancies between the observed emission of these two molecules have been found (see e.g., Zhou et al. 1989; Myers et al. 1991). These observations showed that, in general, CS emission regions are larger than NH 3 regions, and that in some cores, the shapes of the regions traced by the CS emission are also different from those traced by the NH 3 emission. A systematic comparison, under similar conditions of angular resolution, between the emission of the CS and NH 3 molecules was begun by Pastor et al. (1991). The aim of the study was to find how the emission of these two molecules is related to the actual distribution of the high density gas. The sources to be observed were selected from a set of star-forming regions already mapped in the NH 3 (J, K) = (1, 1) line with a similar angular resolution as the one we used (see Anglada et al. 1989, 1997; Verdes-Montenegro et al. 1989; and Wilson and Mauersberger 1990). As our intent 1 Published in Morata O., Estalella R., López R., Planesas P., 1997, Monthly Notices of the Royal Astronomical Society, 292,

74 34 Chapter 2. CS observations of star-forming regions was to find general relationships between the CS and NH 3 emissions valid for a wide range of physical parameters of the regions, we selected our sources so as to have a global sample with a good distribution in distance, size of the NH 3 condensations and luminosity of the exciting sources. In particular, the sources of our sample cover fairly well the range of distances between 100 pc and a few kpc, with several sources located at short, medium and long distances. Similarly, the distribution of sizes of the NH 3 condensations ranges from compact sources, 0.1 pc, to rather extended ones ( 2 pc). Six star-forming regions were already observed in Pastor et al. (1991). With the addition of the regions presented in this chapter (see Table 2.1 and Fig. 2.1), we have almost doubled the number of regions observed up to 11 regions, for a total of 14 condensations. Thus, the work shown in this chapter is a continuation of this study, in order to clarify the intrinsic differences between the emission of these tracers, to give a wider statistical support to the comparison between the CS and NH 3 emission, and to confirm the conclusions reached in the preliminary work presented in Pastor et al. (1991). Table 2.1: Regions observed Region Distance Ref. Outflow Exciting source Luminosity Ref. l NH3 b (pc) type a (L ) (pc) Ref. HH HH IRAS C AFGL 6366S CO, H 2 O IRAS L CO IRAS W75S H 2 O DR 21(OH) L1251 IRAS CO, HH IRAS IRAS CO, HH IRAS a CO CO outflow; HH Herbig-Haro object; H 2 O H 2 O maser. b Geometric mean of the major and minor axes of the half-power contour of the map, from NH 3 observations made with the Haystack telescope (1. 4 resolution) for HH 43, AFGL 6366S, L673 and L1251; and the Effelsberg telescope (40 resolution) for W75S. References: (1) Genzel et al. 1981; (2) Cohen 1990; (3) Anglada et al. 1989; (4) Snell et al. 1988; (5) Verdes- Montenegro et al. 1989; (6) Herbig and Jones 1983; (7) Armstrong and Winnewiser 1989; (8) Anglada et al. 1997b; (9) Wilson and Mauersberger 1990; (10) Chandler et al. 1993; (11) Kun and Prusti 1993; (12) Sato and Fukui 1989.

75 2.2. Observations 35 Figure 2.1: Spectra of the CS (J=1 0) rotational transition at selected positions of the observed sources. Declination and right ascension coordinates are referred to the 1950 equinox 2.2 Observations We carried out CS (J=1 0) observations of four star-forming regions (HH 43, AFGL 6366S, L673 and L1251) during several observing sessions on 1990 January; 1992 May, July, September, and October; and 1993 August with the 14-m telescope at the Centro Astronómico de Yebes 2 (Spain). Additional C 34 S (J=1 0) observations at selected positions of each source were made during 1992 July and 1993 August. At 49 GHz, the frequency of the observations, the half-power beam width and the Moon coupling coefficient of the Yebes telescope, determined from observations of Jupiter and the Moon, were 1. 9 and 0.55, respectively. We used a cooled Schottky diode mixer receiver with an average DSB noise temperature of 75 K. The spectrometer was a 256 channel filter bank with 50 khz of spectral resolution. At 49 GHz, the velocity resolution is 0.31 km s 1, giving a velocity coverage of 39 km s 1 when used in frequency switching mode. The data were calibrated using a chopper wheel to switch alternately from the sky to an ambient temperature load. Pointing was checked to be better than 15 by observing continuum unresolved sources. The central position of each source was observed frequently during each observing 2 The Centro Astronómico de Yebes is operated by the Instituto Geográfico Nacional of Spain

76 36 Chapter 2. CS observations of star-forming regions Table 2.2: CS line parameters (a) CS C 34 S Position T b c A VLSR V d T b A T A (CS) Region α(1950) δ(1950) (K) (km s 1 ) (km s 1 ) (K) T A (C 34 S) HH h 35 m 42 ṣ e 17 AFGL 6366S 06 h 05 m 40 ṣ L h 18 m 30 ṣ W75S 20 h 37 m 13 ṣ L1251 IRAS h 34 m 22 ṣ IRAS h 37 m 40 ṣ a Obtained from Gaussian fits to the observed spectra at the peak position of each source. b Antenna temperature corrected for atmospheric attenuation, antenna coupling to the sky, and elevation-dependent gain variations c Line center velocity d Line width at half height e Upper limit taken as 5σ δv V, where σ is the sensitivity per channel, δv the spectral resolution and V the CS line width. session to check the relative calibration of the maps. We also observed the central position of the bright source NGC 2264G, which has a line intensity of 1.3 K, in each session in order to monitor long term changes in gain. The positions observed in CS were located on the same grid as the positions of the NH 3 maps previously obtained with the Haystack radio telescope, in order to make more meaningful the comparison between the CS and NH 3 maps of the same source. The W75S region was observed in the CS (J=1 0) transition with the 37-m telescope at the Haystack Observatory 3 during 1987 August. At 49 GHz, the half-power beam width was 41 and the beam efficiency at an elevation of 45 was 0.1. The calibration of the antenna response to extended sources is uncertain (Barvainis et al. 1993), so we used the CS (J=1 0) observations of the same source made with the Nobeyama Radio Observatory 45-m telescope by Chandler et al. (1993) to estimate the antenna response to extended sources. We estimated a value of the coupling coefficient η c = Observations were carried out using the position switching mode. We used a cooled Q band maser receiver and a 1024-lag digital autocorrelation spectrometer with an effective bandwidth of 13.3 MHz, covering a 3 Radio Astronomy at Haystack Observatory of the Northeast Radio Observatory Corporation is supported by the National Science Foundation

77 2.3. Individual sources 37 velocity range of 82 km s 1, and giving a spectral resolution of 0.4 km s 1 after Hanning-smoothing. System temperatures were in the range K. Calibrations were made with the standard noise-tube method. All the spectra were corrected for elevation-dependent gain variations and for atmospheric attenuation. The rms pointing error of the telescope was checked to be better than 15. The CLASS and GRAPHIC packages of IRAM were used to reduce, analyze and display the CS data. We detected CS (J=1 0) emission in all the observed sources. In Fig. 2.1 we show CS spectra at selected positions of the sources of our survey. In Figs. 2.2, and 2.5 to 2.8 we present our maps of the sources. In Table 2.2 we give the line parameters at the emission peak position of each observed source. 2.3 Individual sources HH 43 This region is located in the L1641 dark cloud complex in Orion. The Herbig- Haro objects 38 and 43 are aligned with the infrared source IRAS (see Fig. 2.2) and have possibly proper motions away from the IRAS source (B. F. Jones unpublished, as cited by Schwartz et al. 1985). Cohen and Schwartz (1987) proposed this IRAS source as their exciting source. Anglada et al. (1989) found a high-density condensation with its emission peak half-way between IRAS and HH 64, and proposed that the exciting source of the three Herbig-Haro objects might be an embedded object near the position of the NH 3 peak. Cohen (1990) found a COADDed IRAS source, IRAS C, coincident with the NH 3 peak, and proposed it as the possible driving source for HH 64. Thus, at present, it is unclear if the three HH objects belong to the same bipolar HH system, and which infrared object is the exciting source. Edwards and Snell (1984) could not find evidence for CO molecular outflows associated with these objects. We mapped in CS a region centered at the position of the source IRAS (Fig. 2.2). We found a strip of CS emission elongated in the northwest-southeast direction, with a secondary branch in the east-west direction. This distribution corresponds to that of two velocity components in the region, as can be seen in the maps of the integrated line intensity for velocities lower

78 38 Chapter 2. CS observations of star-forming regions Figure 2.2: Contour map of the integrated line intensity of the CS (J=1 0) transition for HH 43 (solid line). The lowest contour level is K km s 1, and the increment is K km s 1 (the thick line indicates the half-power contour). The observed positions are indicated with small crosses and the half-power contour of the beam is indicated as a circle. The half-power contour of the NH 3 emission (Anglada et al. 1989) is also shown (dashed line). NH 3 observations cover the regions with significant CS emission west of 5 h 36 m and north of The HH objects are, in order of increasing right ascension, HH 64, HH 43 and HH 38. The IRAS sources located between HH 64 and HH 43 are, from west to east, IRAS C, IRAS and greater than 5.5 km s 1 (Fig. 2.3). The high-velocity component, centered at 6.5 km s 1, is elongated in the northwest-southeast direction and encloses the two IRAS sources and the three Herbig-Haro objects. The low-velocity component, centered at 4.9 km s 1, appears only at the eastern part of the map. The two velocity components overlap at the central regions of the map, where we find double-peaked line profiles in some spectra (see Fig. 2.4). We found several CS emission enhancements in our integrated line intensity map. The emission peak is located between the sources IRAS C and IRAS , and strong CS emission is found in the region where HH 38 and

79 2.3. Individual sources 39 Figure 2.3: a) Contour map of the integrated line intensity for velocities less than 5.5 km s 1 for HH 43. b) Same as (a) for velocities greater than 5.5 km s 1. The lowest contour level is 0.3 K km s 1, and the increment is 0.1 K km s 1 Figure 2.4: Average of 30 spectra around the position α(1950) = 5 h 35 m 59 ṣ 0, δ(1950) = , of the CS (J=1 0) transition for HH 43

80 40 Chapter 2. CS observations of star-forming regions HH 43 are located. HH 64 lies outside our CS emission half-maximum contour, which suggests that it might be located outside the densest molecular gas. Tatematsu et al. (1993a) found several cloud cores through velocity-channel maps in a CS (J=1 0) high-resolution (HPBW 36 ) survey. Our signal-to-noise ratio per channel does not allow us to make a similar data analysis. However, all the cloud cores of Tatematsu et al. (1993a) are enclosed inside our half-maximum contour, and all are located near the CS emission enhancements found in our map. The CS emission half-maximum contour encloses the half-maximum contour of the NH 3 emission mapped by Anglada et al. (1989) (see Fig. 2.2). The CS emission peak is displaced 2. 5 ( 0.3 pc) southeast of the NH 3 emission peak. The region mapped in CS ( ) is much larger than that mapped in NH 3 ( ). However, the low-intensity contours of the NH 3 map are elongated in the same direction, northwest-southeast, as the CS emission. The region mapped in CS extends to the south very near the Haro 4-255FIR NH 3 clump mapped by Anglada et al. (1989), where Tatematsu et al. (1993b) identified an intense CS outflow AFGL 6366S The infrared source AFGL 6366S is located in a complex of molecular clouds (Huang and Thaddeus 1986) associated with the H II regions S247/S252. Verdes-Montenegro et al. (1989) detected an NH 3 condensation highly elongated in the southwestnortheast direction, not resolved in the perpendicular direction. The NH 3 emission peak is coincident with the infrared source IRAS (see Fig. 2.5). The CS (2 1) emission mapped by Carpenter et al. (1995) is similar to that of NH 3. Snell et al. (1988) detected a CO bipolar outflow with a low degree of collimation. Our CS map is shown in Fig We found a distribution of CS emission highly elongated in the southwest-northeast direction, which continues to the northeast, outside the mapped region. The shape of the CS condensation is extremely similar to that of NH 3, although the CS emission is slightly more extended than that of NH 3. The CS emission peak is nearly coincident, within our beam resolution, with the positions of both the NH 3 emission peak and the IRAS source. Line widths of the spectra obtained in this region range from 1.5 to 2.5 km s 1. We found line central velocities 0.6 km s 1 higher at the northeastern and south-

81 2.3. Individual sources 41 Figure 2.5: Same as Fig. 2.2, for AFGL 6366S. The lowest contour level is 0.3 K km s 1, and the increment is K km s 1. NH 3 emission (Verdes-Montenegro et al. (1989) has been searched over the same region as CS emission. The infrared source is IRAS The H 2 O maser was detected by Kömpe et al. (1989). The 6-cm radio continuum source was detected by Carpenter et al. (1990) western edges of the condensation than at the central positions L673 L673 is a small condensation ( 3 5 ), catalogued by Lynds (1962), located roughly at the center of a filamentary dark cloud. Armstrong and Winnewiser (1989) detected a CO molecular outflow with a large angular extent, They proposed the source IRAS , which coincides with RNO 109 (Cohen 1980) and has colors characteristic of an embedded star, as the most likely candidate for the driving source of the outflow. The T Tauri star AS 353A is probably the exciting source of the object HH 32 (Herbig 1974; Mundt et al. 1983; Herbig and Jones

82 42 Chapter 2. CS observations of star-forming regions Figure 2.6: Same as Fig. 2.2 for L673. The lowest contour level is 0.18 K km s 1, and the increment is 0.1 K km s 1. NH 3 observations (Anglada et al. 1997) cover the region with significant CS emission west of 19 h 18 m 20 s. The three IRAS sources near the NH 3 core are, in order of increasing right ascension, IRAS , IRAS , and IRAS To the south of the region we find the T Tauri star AS 353A, the infrared source IRAS , the Herbig-Haro object HH 32, and several cm radio continuum sources (Cohen and Bieging 1986; Anglada et al. 1992) 1983), which is tracing a well-collimated high-velocity bipolar optical outflow. Edwards and Snell (1982) detected a CO molecular outflow centered on the position of AS 353A. The NH 3 map obtained by Anglada et al. (1997) showed a condensation that enclosed the three western IRAS sources of the region (see Figure 2.6). An NH 3 emission enhancement was found near the position of each IRAS source. Torrelles et al. (1983) and Anglada et al. (1989) did not detect NH 3 emission at the position of AS 353A. The CS emission (Fig. 2.6) shows an elongated shape and extends from 7 north

83 2.3. Individual sources 43 of IRAS to 14 to the southeast. The three western IRAS sources and the CO bipolar outflow are roughly enclosed within our CS half-maximum contour. To the south, a faint emission continues toward the AS 353A region, where we find a CS emission enhancement peaking 1 to the east of the star. We found several emission enhancements in our CS map. The CS emission peak is located 9. 5 to the southeast of IRAS A fainter and more extended CS emission enhancement stretches along the three western IRAS sources with two local maxima, one coinciding with IRAS and the other, slightly more intense, coinciding with IRAS This extended emission encompasses the NH 3 condensation, which is enclosed in our CS half-maximum contour. The NH 3 emission peaks near IRAS , very close to the CS half-maximum contour. The line widths of our spectra are typically smaller than 1.2 km s 1. We found in our data an increase of the line central velocity from north to south, corresponding to a velocity gradient of 0.5 km s 1 pc W75S The region W75S, also referred to as DR21(OH), is located in the DR21/W75S molecular cloud, in the north-eastern part of the Cygnus X giant H II region complex. This region contains several far-infrared and radio continuum sources, as well as other tracers of star formation (for a more detailed description see e.g., Richardson et al. 1986, and Wilson and Mauersberger 1990 and references therein). W75S is a prominent OH, H 2 O and methanol maser source (Cato et al. 1976; Genzel and Downes 1977; Batrla and Menten 1988). The intensities of W75S and the compact H II region DR21 ( 3 to the south) are comparable in the far-ir. High-resolution line and continuum observations show that W75S contains several dense cores (see Chandler et al and references therein). Molecular line observations made with 1 2 angular resolution in CO (Dickel et al. 1978), HCN and CS (Morris et al. 1974), and H 2 CO (Bieging et al. 1982), as well as 1-mm continuum observations by Werner et al. (1975), show a narrow emission strip elongated in the north-south direction, from W75S to DR21. Molecular emission extends 20 farther to the north in the direction of the nearby W75N region.

84 44 Chapter 2. CS observations of star-forming regions Figure 2.7: Same as Fig. 2.2, for W75S. The lowest contour level is 1.5 K km s 1, and the increment is 1.0 K km s 1. NH 3 emission (Wilson and Mauersberger 1990) has been searched over the same region as CS emission The velocities of the molecular gas in the W75 region indicate that there is a system of at least two interacting giant clouds (Dickel et al. 1978). The component with V LSR 3 km s 1 is mainly found near W75S, although a small amount of molecular gas has a V LSR of +9 km s 1. NH 3 observations made by Wilson and Mauersberger (1990) around the position of W75S detected molecular emission elongated in the north-south direction. Chandler et al. (1993) mapped the CS (J=2 1) emission near the W75S maser source with a 18 angular resolution. They also found the emission elongated in the north-south direction, corresponding closely to the dust continuum emission.

85 2.3. Individual sources 45 Our CS map is shown in Fig The CS emission has an elongated shape in the north-south direction. The CS emission peak is located at the position of W75S. CS emission extends to the north of W75S, and a local enhancement of the CS emission is found near the position of a northern H 2 O maser. To the south, there is also a fainter local emission enhancement at the position of the compact H II region DR21. The shape and size of the CS emission are very similar to that of NH 3 (Wilson and Mauersberger 1990). Emission peaks corresponding to each molecule are also coincident, within our beam resolution (< 20, < 0.3 pc). The northern and southern CS emission enhancements are also found in NH 3. CS lines are very wide, with line widths ranging from 3.5 to 4 km s 1 around the positions of W75S and the northern H 2 O maser, and 2.5 km s 1 around DR L1251 L1251 is a small elongated cloud located at Cepheus and catalogued by Lynds (1962). Several IRAS point sources and Hα emission stars are found in the cloud (Kun and Prusti 1993). Two deeply embedded sources, IRAS to the east, and IRAS to the west, are the most luminous, and with no optical counterpart. The western luminous IRAS source (Rosvick and Davidge 1995) is in an early stage of pre-main-sequence evolution. The other IRAS sources are much fainter and have not been detected at all four IRAS wavelengths, but their colors indicate that they are most probably T Tauri stars (Kun and Prusti 1993). Sato et al. (1994) found several C 18 O cores in the cloud, two of which encompassed the two luminous IRAS sources. Schwartz et al. (1988) detected an extended CO bipolar molecular outflow associated with IRAS , the proposed exciting source of the outflow. Near this source, Wilking et al. (1994) detected a H 2 O maser. Sato and Fukui (1989) detected a well-collimated compact molecular outflow near the position of IRAS , the proposed exciting source of the outflow. Eiroa et al. (1994) proposed a nebulous star aligned with HH 189 as a candidate for powering the HH emission, although it cannot be excluded that the IRAS source is the exciting source. Tóth and Walmsley (1996), at high resolution, and Anglada et al. (1997), at lower resolution, mapped in NH 3 the regions near both luminous IRAS sources.

86 46 Chapter 2. CS observations of star-forming regions Figure 2.8: Same as Fig. 2.2, for L1251. The lowest contour level is 0.3 K km s 1, and the increment is 0.1 K km s 1. NH 3 emission observations (Anglada et al. 1997) around IRAS cover the region east of 22 h 34 m, and around IRAS cover the region with significant CS emission south of The HH objects associated with these IRAS sources are, in order of increasing right ascension, HH 149 (Balázs et al. 1992; Reipurth 1994) and the complex HH 189 (Eiroa et al. 1994). The remaining HH objects have been recently discovered by Alten et al. (1997).The cm radio continuum sources were detected by Anglada et al. (2001) Both sets of observations agree very well. Anglada et al. (1997) detected a compact clump north-east of the western IRAS source, coincident with the N clump of Tóth and Walmsley (1996), elongated in the north-south direction, and with no IR source embedded within. In the second region, they detected emission extended in the eastwest direction, enclosing the H1, H2 and H3 clumps of Toth and Walmsley (1997), with its peak located to the east of the IRAS source, similar to the distribution found in H 13 CO + by Sato et al. (1994). We mapped in CS the regions near both IRAS luminous sources (Fig. 2.8). The CS emission is elongated in the east-west direction and correlates very well with a high visual extinction region found in the Palomar Sky Survey plates and with the

87 2.4. General discussion CO map of Sato and Fukui (1989). Our map covers partially the region where the extended outflow is found, and also encloses completely the compact outflow. The CS emission in the region near the source IRAS appears as a background emission without any remarkable emission peak. However, we find a CS emission enhancement elongated in the east-west direction containing two local emission maxima which are located very close to the luminous IRAS source ( 0. 5, 0.05 pc), and to IRAS ( 1, 0.1 pc). The NH 3 clump is located outside the main CS emission region. The CS emission is stronger in the region near IRAS The shape of the emission is elongated in the southeast-northwest direction. The CS emission peak is found 2. 8 north of the IRAS source. The southern half of this CS condensation is coincident with the NH 3 clump. The CS emission maximum is located 3. 2 ( 0.28 pc) to the northwest of the NH 3 peak. Line widths of our CS spectra are similar in all the region, with a median value of 1.3 km s 1. The line central velocity in the western region is V LSR 4.7 km s 1, while in the eastern region is V LSR 3.9 km s 1. In the eastern region, we find a velocity gradient of 1 km s 1 pc 1 in the northeast-southwest direction. Sato and Fukui (1989) in C 18 O, and Goodman et al. (1993) and Anglada et al. (1997) in NH 3, also detected velocity gradients in this region in the northeast-southwest direction, with values similar to the CS velocity gradient. 2.4 General discussion CS emission We detected CS (J=1 0) emission in the five sources observed. We also searched for C 34 S (J=1 0) emission at the position of the CS emission peaks in four of the sources. We detected C 34 S emission in AFGL 6366S, L673 and L1251. The median ratio between the intensities of the CS and C 34 S emission was 11. We compared the CS (J=1 0) emission with the line parameters of the J=2 1 emission given by Bronfman et al. (1996) for AFGL 6366S, obtained with an angular resolution of 50. The intensity ratio of the J=2 1 to J=1 0 lines is 6. This value, higher

88 48 Chapter 2. CS observations of star-forming regions Table 2.3: Parameters of the CS condensations Region Dimensions a l b CS τ c T d ex T e k Ref. N CS f M g M h vir (arcmin) (pc) (K) (K) (10 13 cm 2 ) (M ) (M ) HH i AFGL 6366S L W75S j j L1251 IRAS IRAS a FWHM of the CS emission. b Geometric mean of the major and minor axes of the half-power contour of the map. c CS optical depth obtained from T A CS T A C34 S given in Table 2.2 and adopting an abundance ratio [CS/C 34 S]=20 (terrestrial abundance). d Derived from the transfer equation. e Estimated from the rotational temperature of NH 3. f CS column density at the positions given in Table 2.2, calculated as N CS cm T ex 0 39 τ η c e 2 35 T ex e 1 τ Q τ T A dv 1 K km s where τ and T ex are given in columns 2 and 3, η c 0 55 (Moon coupling coefficient for the sources observed at Yebes), and Q τ is the line width correction for opacity broadening (Phillips et al. 1979). For W75S we used η c 0 27 (see text). g Mass obtained from integration of the H 2 column density inside the half-power contour of the map. We adopted a CS abundance X CS (Irvine et al. 1987). h Virial mass obtained from our CS data using M vir M =210 l CS 2 pc V km s 1 2, where l CS is given in column 3 and V is given in Table 2.2. i Estimated from CO observations. j τ 1 is assumed. References: (1) Edwards and Snell 1984; (2) Verdes-Montenegro et al. 1989; (3) Anglada et al. 1997b; (4) Wilson and Mauersberger than the upper limit of 4 obtained for optically thin emission assuming the same filling factor and excitation temperature, is probably due to the beam dilution of the lower angular resolution J=1 0 observations. We mapped the extended CS emission in all the sources. The parameters of the CS condensations are shown in Table 2.3. The condensations were angularly resolved for all the sources, except for AFGL 6366S, resolved in only one direction. The morphological appearance of the condensations was generally that of an elongated irregular emission which extended over a large area. The CS emission included and connected tracers of star formation, near which the CS emission was enhanced. In particular, CS emission peaks were always located at distances < 0.3 pc from

89 2.4. General discussion 49 IRAS point sources. The sizes of the CS condensations ranged from 0.4 pc for IRAS to 2.4 pc for W75S. The median size of the CS condensations was 1.3 pc. At the CS emission peak of each region we were able to calculate the excitation temperature and the optical depth of the CS (J=1 0) transition. We found that the excitation temperature for the CS emission was always clearly lower than the kinetic temperature of the region (see Table 2.3), showing that the CS emission is far from being fully thermalized, which is the expected behavior for a high density tracer molecule like CS. The optical depth of the sources of our survey ranges from the optically thin case (τ < 0.3) for HH 43, to the optically thick (τ = 4.5) for AFGL 6366S. The median value of the optical depth is 1.3. In order to test variations in the CS abundance, we compared the CS column density obtained at the emission peak of each region (Table 2.3) with the H 2 column density obtained from observations of 13 CO and C 18 O for AFGL 6366S (Kömpe et al. 1989), L673 (Kislyakov and Gordon 1983), W75S (Wilson and Mauersberger 1990), and L1251 (Sato et al. 1994). The ratio N(CS)/N(H 2 ) was in the range , except for AFGL 6366S, where it was around Thus, we do not detect significant variations in the CS abundance from source to source. The median value obtained is near the adopted value of [CS/H 2 ] = In Table 2.3 we also show the mass of the condensations, calculated by integrating the H 2 column density, and the virial mass estimated from the line width measured at the CS emission peak and assuming a homogeneous density distribution. Most of the virial masses of the condensations agree with the calculated masses within a factor of 3. Thus, our data suggest that the cores are, in general, near virial equilibrium, and that the assumed CS abundance, [CS/H 2 ] = , is adequate. Observations of several molecular lines such as CO, NH 3 and CS in molecular clouds reveal correlations between the line width and the size of a cloud. These correlations have been found for the same line from cloud to cloud, and for one or a few clouds from line to line (Larson 1981; Fuller and Myers 1992 and references therein). The physical basis of these relation it is not well established yet, but it seems related to the support of clouds by their internal motions. According to the evidence available, the line width-size correlation for the non-thermal component of the line width goes as V NT l q,

90 50 Chapter 2. CS observations of star-forming regions 10 log [ V (km s 1 )] 1 This work Pastor et al. (1991) log [l (pc)] Figure 2.9: Plot of the CS line width versus the cloud size traced by CS emission. The solid line is the best linear fit to the data. Filled symbols are from the observations of this chapter. CS line width data are from Table 2.2. Cloud size data are from Table 2.3. Non-filled symbols are from Pastor et al. (1991) with q 0.5 for low-mass cores, and q 0.2 for high-mass cores (Caselli and Myers 1995). In figure 2.9 we show line width and size data from Tables 2.2 and 2.3, and from Pastor et al. (1991). The best linear fit to the data gives log V = (0.50 ± 0.12) log l + (0.19 ± 0.04), (2.1) with a correlation coefficient r = 0.8. It must be noted that our sample includes high-mass and low-mass star forming regions, but the fit for the CS observations coincides with the value of q given by Caselli and Myers (1995) for low-mass cores obtained from CO observations. We analyzed whether the correlation found between line width and cloud size might be a result of selection effects. As can be seen in Tables 2.1 to 2.3, cloud size tends to increase with distance, due to the difficulty of detecting small sources at large distances, and line width also tends to increase with distance, which could be attributed to the averaging of velocity gradients inside the area covered by the beam. The combination of these two effects could cause an apparent correlation between line width and size. In order to check this possibility, we averaged the spectra of each source for the same physical size ( 0.8 pc) but did not find any significant line broadening in any source. Thus, we can discard this effect and confirm that the

91 2.4. General discussion 51 Table 2.4: Column densities of CS and NH 3 Region N CS a N NH 3 Ref. CS NH 3 (10 13 cm 2 ) (10 14 cm 2 ) L AFGL AFGL HH NGC AFGL 6366S L L W75S HHL 73 (IRS 1) (IRS 2) (IRS 3) L1251 IRAS IRAS a See Table 2.3 and Table 2 of Pastor et al. (1991). References: (1) Anglada et al. 1989; (2) Verdes-Montenegro et al. 1989; (3) Matthews and Little 1983; (4) Anglada et al. 1997b; (5) Wilson and Mauersberger 1990 correlation between line width and cloud size is real Comparison with NH 3 results As all the sources detected in our survey had been mapped earlier in NH 3 with a similar angular resolution, we were able to make a comparative study between both emissions. A clear difference found in our maps was that the CS and NH 3 emission peaks did not coincide spatially. The separation ranged from 0.2 pc to 0.3 pc in the condensations well resolved by our beam, while in AFGL 6366S and W75S, where both emission peaks apparently coincided, the angular resolution set an upper limit

92 52 Chapter 2. CS observations of star-forming regions 2.0 V CS (km s 1 ) 1.0 HH 43 AFGL 6366S L673 IRAS IRAS V NH3 (km s 1 ) Figure 2.10: Plot of the CS line width vs. the NH 3 line width, for pairs of spectra of CS (corrected for spectral channel width and opacity broadening) and NH 3 (corrected for spectral channel width and hyperfine broadening), observed at the same position and with signal-to-noise ratio SNR > 10 for both molecules, where SNR = (TA /σ)( V/δV )1/2, T A is the line intensity, σ is the sensitivity per channel of the spectra, V is the spectral line width and δv is the spectral resolution. The solid line is the best linear fit to the data considering the same error in both axes. NH 3 data are from Anglada et al. (1989, 1997), and Verdes-Montenegro et al. (1989) for the separation of 0.3 pc. So, our data confirm the result obtained in Pastor et al. (1991) that, in general, there is a separation between the CS and NH 3 emission peaks of 0.2 pc. This separation should be taken into account by any model intending to explain the emission of these two molecules. The shape of the emission traced by the CS and NH 3 molecules also shows clear differences. In general, the CS emission encompasses and connects different NH 3 clumps. Although the NH 3 observations do not cover all the region with significant CS emission for some sources (see Figs. 2.2, 2.6, and 2.8), it seems clear that the CS emission is more extended than the NH 3 emission for the nearest sources, while the sizes of both emissions are comparable for the most distant sources (Figs. 2.5 and 2.7). More quantitatively, the median size ratio between the CS and NH 3 condensations is 2, and ranges from 1 for AFGL 6366S, to 5 for HH 43. In order to test variations in the CS to NH 3 abundance ratio, we compared, for

93 2.4. General discussion 53 the sources of our sample, the NH 3 column density with the CS column density found in this paper and Pastor et al. (1991) (see Table 2.4). The median value of the ratio of CS and NH 3 abundances is 0.14, while half of the sources have abundance ratios between 0.09 and We only find two sources (AFGL 5157 and AFGL 6366S) with higher ratios, 0.5. From our data we find no clear evidence of variations of the CS and NH 3 abundance ratio, and no relationship between the value of the abundance ratio and source size or distance. From our data we found that CS lines are, in general, broader than NH 3 lines, as had been previously reported by Zhou et al. (1989), Pastor et al. (1991), Myers et al. (1991). In Fig we compare the CS and NH 3 line widths of good signal-to-noise ratio spectra observed at the same spatial position. As the errors in the CS and NH 3 line widths were similar, we performed a linear fit to the data considering the same error in both axes. The best linear fit to our data is V CS = (1.0 ± 0.3) V NH3 + (0.5 ± 0.1) km s 1, (2.2) with a correlation coefficient r = 0.6, and a mean square residual of 0.16 km s 1. In a previous study, Zhou et al. (1989) found that the CS (3 2) and (2 1) line widths were a factor of 2 larger than that of the NH 3 (1, 1). These authors analyzed their data by fitting only one parameter, i.e. the average ratio of the CS line width to the NH 3 line width. If we perform such a fit to our data, the mean square residual of our data increases a 25%. Thus, our data are better described by the 2- parameter fit. Pastor et al. (1991) performed a fit with two independent parameters, and found that the relationship between the CS line width and the intrinsic NH 3 line width was better described as an additive term of 0.4 km s 1. Anglada et al. (1996), in a survey of H 2 O masers observed in CS and NH 3 spanning a large range of line widths up to 12 km s 1, also found an additive term of 0.3 km s 1. Our result confirms in an independent way that the difference between the CS and NH 3 line widths is better described as an additive term than as a multiplicative factor. The difference in line widths between the CS and NH 3 lines might be explained if CS traced hotter regions than NH 3. However, if the line width difference of 0.5 km s 1 was to be accounted for by thermal broadening of the lines, it would be necessary that the material traced by the CS had a kinetic temperature of 10 2 K greater than that traced by the NH 3, which does not seem reasonable. Alternatively, the difference in line widths between the CS and NH 3 lines might be attributed to the different size of the region traced by each molecule. As the

94 54 Chapter 2. CS observations of star-forming regions condensations traced by the CS emission are larger than those traced by NH 3, the well known relationship between cloud size and line width, confirmed by our data, would imply that the CS lines should be broader than those of NH 3. From Eq. (2.1), a size ratio between the CS and NH 3 condensations of 2 gives a line width ratio of 1.5. However, our data suggest that the difference between the CS and NH 3 line widths is an additive term of 0.5 km s 1. If this is a consequence of the line width-size relationship, the CS and NH 3 size ratio should depend on the source size, as was first noted by Anglada et al. (1996) and we show in the following. In general, for a linear relationship between the CS and NH 3 line widths, and the line width being related to the cloud size by V CS = a V NH3 + b, (2.3) V = Kl q, (2.4) the size ratio between the CS and NH 3 condensations can be expressed as l CS /l NH3 = [a + (L/l NH3 ) q ] 1/q, (2.5) where L = (b/k) 1/q. Thus, if L 0, the CS and NH 3 size ratio should be higher for smaller sources. From our fits (Eqs. 2.1 and 2.2), a 1.0, b 0.5 km s 1, q 0.5, and L 0.1 pc. The predicted size ratio for NH 3 condensations of the order of 0.1 pc is 4, while for NH 3 condensations of the order of 1 pc is 2. In Fig we have plotted the size ratio between the CS and NH 3 condensations vs. the NH 3 cloud size. We added the sources from Pastor et al. (1991) to our data, in order to achieve a higher statistical significance. We have also plotted the line corresponding to Eq. (2.5) for the values of the parameters obtained from our fits. As can be seen in the figure, our data suggest that smaller sources have a higher size ratio. We find that for NH 3 condensations smaller than 0.5 pc the median size ratio is 3.2, while for condensations larger than 0.5 pc the median size ratio is 1.2. Moreover, we did not found any correlation between the size ratio and the angular size of the condensations. Thus, our data suggest that there is a real dependence of CS and NH 3 cloud size ratio on source size, and that the difference in line width can be attributed to the different size of the regions traced by the CS and NH 3 molecules. Any model of the emission of these molecules should try to explain why the size ratio between the CS and NH 3 condensations is higher for the smallest sources. In order to explain the observed differences between the emission of CS and NH 3, several mechanisms were discussed in Pastor et al. (1991). Here, we will focus our

95 2.4. General discussion l CS /l NH This work Pastor et al. (1991) l NH3 (pc) Figure 2.11: Plot of the size ratio of the CS and NH 3 condensations vs. the NH 3 cloud size. The data suggest that smaller sources have a higher size ratio. The solid line is l CS /l NH3 = [1.0 + (0.1/l NH3 ) 0.5 ] 2.0 (see text) attention on models based on variations in the chemical abundance due to chemical and physical evolution. The observations of Hirahara et al. (1992) toward the dark cloud TMC1 show a clear anticorrelation between the emission peaks of NH 3 and those of sulfur-containing carbon-chain molecules, such as CS or CCS. Chemical models of the collapse of such cores show that CS is likely to be associated with cores in earlier stages of collapse than NH 3, which would be more abundant in more evolved cores. In chapter 5 (Taylor et al. 1996), we consider a model in which high density condensations are formed by clumps < 0.1 pc in size, which would be unresolved in moderate angular resolution observations like ours. Most clumps disperse before NH 3 abundances build up to significant levels. However, these clumps would be observable in CS because they contain a substantial abundance of CS, up to a maximum abundance of the order of X(CS) A few clumps, sufficiently long lived, or in a more advanced stage of physical and chemical evolution because of being denser or more massive, form a significant content of NH 3, with a typical NH 3 abundance of X(NH 3 ) Possibly, these clumps would continue their evolution to eventually form stars. This would account for the difference in size between CS and NH 3 condensations. Furthermore, this model also predicts that for the later stages, when the NH 3 fractional abundance peak is reached, CS fractional abundance decreases, and therefore, the peak in CS emission need not coincide with that of NH 3. Thus, the different stage in the evolution of high density clumps seems

96 56 Chapter 2. CS observations of star-forming regions to be able to account for some of the better established differences between the CS and NH 3 emission: difference in size and separation between emission peaks. 2.5 Conclusions We have detected and mapped the CS (J=1 0) emission in five sources previously mapped with a similar angular resolution in the NH 3 (J, K) = (1, 1) line. Our main conclusions can be summarized as follows: 1. The median size of the CS condensations mapped was 1.3 pc. The CS emission peaks were always located near IRAS point sources. 2. The masses of the condensations agree with the virial masses, suggesting that the cores are near virial equilibrium and that the CS abundance adopted, [CS/H 2 ] = , is adequate. 3. Our data confirm the correlation between line width and the size of the cloud. This correlation is not a consequence of selection effects in our sample. The best fit to our data gives V l We confirm that, in general, there is a separation between the CS and NH 3 emission peaks of 0.2 pc. 5. Regions traced by CS are larger than those traced by NH 3. However, our data suggest that the size ratio depends on the size of the source. For NH 3 sources smaller than 0.5 pc the median size ratio is 3.2, while for NH 3 condensations larger than 0.5 pc the median size ratio is For good signal-to-noise spectra observed at the same position, the CS lines are 0.5 km s 1 wider than those of NH 3. If this is attributed to the different size of the region traced by each molecule, the CS and NH 3 size ratio should depend on the source size, in accordance with our data. 7. The differences in the spatial distribution of the emission of the CS and NH 3 molecules could be attributed to differences in the chemical abundance due to chemical and physical evolution.

97 Bibliography Alten V. P., Bally J., Devine D., Miller G. J., 1997, in Malbet F. and Castets A., eds., Poster Proc. IAU Symp. No. 182, Low Mass Star Formation from Infall to Outflow, p. 51 Anglada G., et al., 2001, in preparation Anglada G., Estalella R., Pastor J., Rodríguez L. F., Haschick A. D., 1996, The Astrophysical Journal, 463, 205 Anglada G., Rodríguez L. F., Cantó J., Estalella R., Torrelles J. M., 1992, The Astrophysical Journal, 395, 494 Anglada G., Rodríguez L. F., Torrelles J. M., et al., 1989, The Astrophysical Journal, 341, 208 Anglada G., Sepúlveda, I., Gómez, J. F., 1997, Astronomy and Astrophysics Supplement Series, 121, 255 Armstrong J. T., Winnewisser G., 1989, Astronomy and Astrophysics, 210, 373 Balázs L. G., Eislöffel J., Holl A., Keleman J., Kun M., 1992, Astronomy and Astrophysics, 255, 281 Barvainis R., Ball J. A., Ingalls R. P., Salah J. E., 1993, Publications of the Astronomical Society of the Pacific, 105, 1334 Batrla W., Menten K. M., 1988, The Astrophysical Journal, 329, L117 Bieging J. H., Wilson T. L., Downes D., 1982, Astronomy and Astrophysics Supplement Series, 49,

98 58 BIBLIOGRAPHY Bronfman L., Nyman L.-A., May J., 1996, Astronomy and Astrophysics Supplement Series, 115, 81 Carpenter J. M., Snell R. L., Schloerb F. P., 1990, The Astrophysical Journal, 362, 147 Carpenter J. M., Snell R. L., Schloerb F. P., 1995, The Astrophysical Journal, 450, 201 Caselli P., Myers P. C., 1995, The Astrophysical Journal, 446, 665 Cato B. T., Rönnäng B. O., Rydbeck O. E. H., Lewin P. T., et al., 1976, The Astrophysical Journal, 208, 87 Chandler C. J., Moore T. J. T., Mountain C. M., Yamashita T., 1993, Monthly Notices of the Royal Astronomical Society, 261, 694 Cohen M., 1980, The Astronomical Journal, 85, 29 Cohen M., 1990, The Astrophysical Journal, 354, 701 Cohen M., Bieging J. H., 1986, The Astronomical Journal, 92, 1396 Cohen M., Schwartz R. D., 1987, The Astrophysical Journal, 316, 311 Dickel J. R., Dickel H. R., Wilson W. J., 1978, The Astrophysical Journal, 223, 840 Edwards S., Snell R. L., 1982, The Astrophysical Journal, 261, 151 Edwards S., Snell R. L., 1984, The Astrophysical Journal, 281, 237 Eiroa C., Torrelles J. M., Miranda L. F., Anglada G., Estalella R., 1994, Astronomy and Astrophysics Supplement Series, 108, 73 Fuller G. A., Myers P. C., 1992, The Astrophysical Journal, 384, 523 Genzel R., Downes D., 1977, Astronomy and Astrophysics Supplement Series, 30, 145 Genzel R., Reid M. J., Moran J. M., Downes D., 1981, The Astrophysical Journal, 244, 884 Goodman A. A., Benson P. J., Fuller G. A., Myers P. C., 1993, The Astrophysical Journal, 406, 528

99 BIBLIOGRAPHY 59 Herbig G. H, 1974, Lick Obs. Bull., No. 658 Herbig G. H., Jones B. F., 1983, The Astronomical Journal, 88, 1040 Hirahara Y., Suzuki H., Yamamoto S., et al., 1992, The Astrophysical Journal, 394, 539 Huang Y.-L., Thaddeus P., 1986, The Astrophysical Journal, 309, 804 Irvine W. M., Goldsmith P. F., Hjalmarson A., 1987, in Hollenbach D. J. and Thronson H. A., eds., Interstellar Processes. Reidel, Dordrecht, p. 561 Kislyakov A. G., Gordon M. A., 1983, The Astrophysical Journal, 265, 766 Kömpe C., Joncas G., Baudry A., Wouterloot J. G. A., 1989, Astronomy and Astrophysics, 221, 295 Kun M., Prusti T., 1993, Astronomy and Astrophysics, 272, 235 Larson R. B., 1981, Monthly Notices of the Royal Astronomical Society, 194, 809 Lynds B. T., 1962, The Astrophysical Journal Supplement Series, 7, 1 Matthews N., Little L. T., 1983, Monthly Notices of the Royal Astronomical Society, 205, 123 Morris M., Palmer P., Turner B. E., Zuckerman B., 1974, The Astrophysical Journal, 191, 349 Mundt R., Stocke J., Stockman H., 1983, The Astrophysical Journal, 265, L71 Myers P. C., Fuller G. A., Goodman A. A., Benson P. J., 1991, The Astrophysical Journal, 376, 561 Pastor J., Estalella R., López R., et al., 1991, Astronomy and Astrophysics, 252, 320 Phillips T. G., Huggins P. J., Wannier P. G., Scoville N. Z., 1979, The Astrophysical Journal, 231, 720 Reipurth B., 1994, A general catalogue of Herbig-Haro objects. electronically published via anon. ftp to ftp.hq.eso.org, directory /pub/catalogs/herbig-haro Richardson K. J., White G. J., Phillips J. P., Avery L. W., 1986, Monthly Notices of the Royal Astronomical Society, 219, 167

100 60 BIBLIOGRAPHY Rosvick J. M., Davidge T. J., 1995, Publications of the Astronomical Society of the Pacific, 107, 49 Sato F., Fukui Y., 1989, The Astrophysical Journal, 343, 773 Sato F., Mizuno A., Nagahama T., et al., 1994, The Astrophysical Journal, 435, 279 Schwartz R. D., Dopita M. A., Cohen M., 1985, The Astronomical Journal, 90, 1820 Schwartz P. R., Gee G., Huang Y.-L., 1988, The Astrophysical Journal, 327, 350 Snell R. L., Huang Y.-L., Dickman R. L., Claussen M. J., 1988, The Astrophysical Journal, 325, 853 Tatematsu K., Umemoto T., Kameya O., et al., 1993a, The Astrophysical Journal, 404, 643 Tatematsu K., Umemoto T., Murata Y., et al., 1993b, The Astrophysical Journal, 419, 746 Taylor S. D., Morata O., Williams D. A., 1996, Astronomy and Astrophysics, 313, 269 Torrelles J. M., Rodríguez L. F., Cantó J., et al., 1983, The Astrophysical Journal, 274, 214 Tóth L. V., Walmsley C. M., 1996, Astronomy and Astrophysics, 311, 981 Verdes-Montenegro L., Torrelles J. M., Rodríguez L. F., et al., 1989, The Astrophysical Journal, 346, 193 Werner M. W., Elias J. H., Gezari D. Y., Hauser M. G., Westbrook W. E., 1975, The Astrophysical Journal, 199, L185 Wilking B. A., Claussen M. J., Benson P. J., et al., 1994, The Astrophysical Journal, 431, L119 Wilson T. L., Mauersberger R., 1990, Astronomy and Astrophysics, 239, 305 Zhou S., Wu Y., Evans N. J., Fuller G. A., Myers P. C., 1989, The Astrophysical Journal, 346, 168

101 Chapter 3 Introduction to chemistry in molecular clouds 3.1 Introduction Interstellar chemistry has been an active field of research for more than 60 years, ever since the detection of the first molecules at the end of the 1930s decade. Nearly 120 different gas species have been found, not including isotopic varieties, with abundances down to with respect to H 2. In Table 3.1 we show the species identified to this date. Most of the species have been detected through their rotational transitions at millimeter wavelengths, at scales that range from the gas surrounding dark cloud cores ( 1 pc) to the dense envelopes around YSOs ( 100 AU). Although most of the observing effort had been initially focused on gas-phase chemistry, water ice was identified already in 1973 through its vibrational absorption toward bright infrared sources. The enormous advances in infrared instrumentation in the last decade, both from the ground and from the space with the Infrared Space Observatory (ISO), have resulted in the detection of several other solid-state species and allow a complete inventory to be made (Tielens and Whittet 1997). The most apparent consequence has been the realization that the development of realistic models which include both gas-phase and grain-surface chemistry provides a new challenge to theorists. It is generally believed that interstellar molecules are formed from simpler con- 61

102 62 Chapter 3. Introduction to chemistry in molecular clouds Table 3.1: Identified interstellar and circumstellar molecules Simple Hydrides, Oxides, Sulfides, Halogens and related molecules H 2 (IR) CO NH 3 CS NaCl HCl SiO SiH 4 (IR) SiS AlCl H 2 O SO 2 C 2 (IR) H 2 S KCl N 2 O OCS CH 4 (IR) PN AlF HF Nitriles and Acetylene derivatives C 3 (IR,UV) HCN CH 3 CN HNC C 2 H 4 (IR) C 5 (IR) HC 3 N CH 3 C 3 N HNCO C 2 H 2 (IR) C 3 O HC 5 N CH 3 C 5 N? HNCS C 3 S HC 7 N CH 3 C 2 H HNCCC C 4 Si HC 9 N CH 3 C 4 H CH 3 NC HC 11 N CH 3 CH 2 CN HCCNC HC 2 CHO CH 2 CHCN Aldehydes, Alcohols, Ethers, Ketones, Amides and related molecules H 2 CO CH 3 OH HCOOH CH 2 NH CH 2 CC H 2 CS CH 3 CH 2 OH HCOOCH 3 CH 3 NH 2 CH 2 CCC CH 3 CHO CH 3 SH (CH 3 ) 2 O NH 2 CN NH 2 CHO (CH 3 ) 2 CO H 2 CCO CH 3 COOH Cyclic Molecules C 3 H 2 SiC 2 c-c 3 H CH 2 OCH 2 Molecular Ions CH (VIS) HCO HCNH H 3 O HN 2 HCS HOCO HC 3 NH HOC H 3 (IR) CO H 2 COH SO Radicals OH C 2 H CN C 2 O C 2 S CH C 3 H C 3 N NO NS CH 2 C 4 H HCCN SO SiC NH (UV) C 5 H CH 2 CN HCO SiN NH 2 C 6 H CH 2 N MgNC CP HNO C 7 H NaCN MgCN C 6 H 2 C 8 H C 5 N From Ohishi (1997) and van Dishoeck and Hogerheijde (1999). Species denoted with a * have only been detected in the circumstellar envelope of carbon-rich stars. Most molecules have been detected at radio and millimeter wavelengths, unless otherwise indicated (IR, VIS or UV)

103 3.1. Introduction 63 stituents by a process of synthesis, but larger molecules, such as the PAHs that are suspected to be present may arise from the degradation of larger entities, the interstellar grains. It is thus presumed that abundant atoms and ions are converted by chemical reactions into molecules which themselves may take part in further reactions. The main aims of this chapter are to review the most relevant chemical processes that take place in the interstellar gas, especially the gas phase chemistry in molecular clouds; and to make an introduction to the grain chemistry and the effect of dust grains on the chemistry. In chapter 4 we will describe briefly how is performed the modeling of the chemical processes that happen in molecular clouds. It is generally assumed that the chemistry of molecular clouds begins with a gas in which the various elements are present in the proportions of their relative cosmic abundances. This means that hydrogen is the most abundant element, and the chemically important elements carbon, nitrogen, oxygen, and sulphur amount by number to about 0.1 % of hydrogen (Duley and Williams 1984). But, it is with this small fraction that interstellar chemistry is concerned. The physical conditions of the regions that we will consider, molecular clouds where interstellar molecules are found, are usually constrained to low gas temperatures, 10 K < T < 100 K, and H 2 densities of 10 3 < n < 10 6 cm 3. We can begin by considering a reaction between species A and B to form products M and N A + B M + N (3.1) where A and B can be neutrals, ions, atoms, radicals or molecules. The rate of such a reaction is normally written in terms of the concentration of the reactants and a rate coefficient k, in units of cm 3 s 1, given by the expression k =< σv > (3.2) where σ is the total cross section, v is the relative velocity between reactants, and the averaging is performed over the thermal distribution. The rate equation controlling the abundance of M is thus given by d [n(m)] = kn(a)n(b). (3.3) dt The physical conditions of the clouds where molecules form constrain the type of chemistry that exists inside these clouds and the rate coefficients at which these reactions proceed. The gas densities in the interstellar gas that we consider are

104 64 Chapter 3. Introduction to chemistry in molecular clouds sufficiently low, except in the immediate vicinity of protostars, to preclude the possibility of three-body reactions playing a significant role in the gas phase chemistry (Herbst and Klemperer 1973). In the most elementary chemical reaction, A + B AB (3.4) an atom A collides with another atom or atomic ion B to form a complex, labeled AB, with internal energy. The complex can last for times between s and s, depending on its energy, size, structure and potential well (Herbst 1985; Herbst 1987). However, the complex will dissociate and no molecule will be formed unless some energy, greater than the kinetic energy relative to the center of mass of A and B, can be removed from the system. The collision with a third body, C, could stabilize the system. However, the estimated time interval between collisions in an interstellar cloud is far longer than a millisecond, so that the probability of the complex lasting until a third body collides with it is quite small. In a favorable situation, the formation rate of a molecule as a result of these reactions can be estimated to be n 3 cm 3 s 1 (Duley and Williams 1984), where n is the total number of hydrogen nuclei per unit volume, while the production rate required to maintain molecular abundances in the interstellar clouds is about a few n cm 3 s 1 (Iglesias 1977). Thus, it is safe to say that the chemistry in the interstellar gas is based in binary reactions, unless the third body is a grain. In this case, there is enough time for these reactions to take place, as lifetimes of atoms and molecules adsorbed on grains may be extremely long, or even the grain may be a sink for the energy of stabilization (Iglesias 1977). The low kinetic temperatures of molecular clouds also have a strong effect over chemistry. Chemical reactions can be either exothermic, give off energy, or endothermic, require energy to proceed. Endothermic reactions do not occur in a significant way at the low temperatures of molecular clouds (Herbst and Klemperer 1973). However, most exothermic chemical reactions in the gas phase possess activation energy barriers (Herbst and Millar 1991). Activation energy originates from short-range barriers of maxima in the potential energy surfaces governing reactions. The barriers appear when old chemical bonds have to be broken before new ones are formed (Herbst and Millar 1991). In reactions between neutral species the potential energy during a reaction increases by an

105 3.2. Gas phase reactions 65 amount equal to the activation energy as the old bonds are broken before declining to a value below that of the reactants. Thus, the cross section for the reaction is zero unless the energy of the reactants exceeds the value of the activation energy. Under these conditions, the rate coefficient for chemical reactions that possess activation energy barriers can be derived to be k = A(T )exp[ E a /k B T ] (3.5) where E a is the activation energy, k B is the Boltzmann constant, T is the absolute temperature, and A(T ), or the so-called pre-exponential factor, is a weak function of the temperature, which depending upon the details of the collision varies widely in absolute values and temperature dependence. The activation energy term determines the temperature dependence of most rate coefficients. For instance, reactions between neutral gas phase species in singlet electronic states possess activation energies 1 ev, so that at temperatures under 100 K, typical of interstellar clouds, reactions are very slow (Herbst and Millar 1991). Although there are some exceptions to this rule (atoms and reactive species labeled as radicals in non-singlet electronic ground states often react without activation energy barriers, but they are not of much significance), exothermic ion-molecule reactions constitute a more important exception to the existence of activation energy barriers. The gas phase chemistry is thus dominated by ion-molecule reactions, which have typically negligible activation energy barriers and proceed at fast rates (k 10 9 cm 3 s 1 ) (Ziurys 1990). 3.2 Gas phase reactions It is possible to elaborate a classification of the reactions that take place in the gas phase of the interstellar medium according to the species involved, their reaction rates, and their density and temperature dependency (see Table 3.2). In this section we will discuss the more important types of reactions between atoms, molecules, ions and electrons that are thought to proceed in molecular clouds. We also discuss the effects of cosmic rays and photons, the so-called photochemistry, on the chemistry of the interstellar gas.

106 66 Chapter 3. Introduction to chemistry in molecular clouds Table 3.2: Some basic chemical processes Process A + + BC AB + + C A + B AB + hν A + BC AB + C A + + e A + hν AB + + e A + B A + + B A + B + A + e A + hν A + cosmic rays A + + e AB + hν A + B A + hν A + + e A + B:grain AB + grain Name Ion-molecule reaction Radiative association Neutral-neutral reaction Radiative recombination Dissociative recombination Charge-transfer reaction Negative ion reaction Cosmic ray ionization Photodissociation Photoionization Grain-surface formation Ion-molecule reactions The major class of reactions in which activation energy does not normally play a major role are ion-molecule reactions. An ion-molecule reaction is a reaction such as A + + BC AB + + C (3.6) or some other product channel. Ion-molecule reactions have been studied experimentally at temperatures from under 2 K to well above room temperature to determine the rate coefficient, k (see Herbst and Millar 1991, and references therein). Ion-molecule reactions are usually fast at low temperatures, being at or near the collisional limiting value. The interaction between an ion and a molecule is by its nature controlled by a long-range attractive force due to which the reactants are accelerated together and mutually orbit. It seems that ion-molecule reactions can proceed because long-range attractive forces, such as charge-dipole and chargeinduced-dipole potentials, which fall off as R 2 and R 4, respectively, correlate with short-range potential minima, known as reaction complexes, rather than maxima, and can suppress activation energy barriers in the potential surface that result from chemical interactions at intermediate separation (Graff 1989).

107 3.2. Gas phase reactions 67 Ion-molecule reactions exhibit several important characteristics (Herbst and Millar 1991): there is ordinarily no activation energy barrier and therefore there is no exponential dependence of the rate coefficient on temperature; the pre-exponential factor of equation (3.5) is either independent of temperature or inversely dependent on it; and, finally, rate coefficients are often (but not always) large and close to the same order of magnitude of 10 9 cm 3 s 1 (Watson 1978). These properties have made possible to estimate the value of unknown rate coefficients with moderate confidence, and so it is possible to model the interstellar chemistry based largely on ion-molecule reactions (Herbst et al. 1994). Rate coefficients for ion-molecule reactions are usually obtained through quantum mechanics calculations, but the theories that have been used most often are based on the capture approximation, a classical treatment of the problem in which it is assumed that if a molecule has enough energy to pass over a centrifugal barrier, then it always reacts. The maximum impact parameter for the reaction is determined by the centrifugal barrier at long range (Levine and Bernstein 1974). The strong long-range forces lead to very large coefficients at room temperature (k 10 9 cm 3 s 1 ), close to the values predicted by simple capture theories, indicated by a unit collision efficiency for the large majority of ion-molecule reactions measured (Adams and Smith 1983). The nature of the strong long-range forces (Herbst 1987) determines the reaction rate coefficients and lead to two different types of temperature dependence, depending strongly on the dipole moment of the neutral species, specially at low temperatures: i. For reactions of ions with symmetric molecules possessing no permanent dipole moment, Langevin first derived an expression for the rate coefficient. If the interaction potential is given by V (R) = e 2 /2αR 4 (3.7) where e is the electronic charge in e.s.u., α (in cm 3 ) is the polarizability of the neutral species, and R is the distance between reactants (Herbst 1987), a simple treatment of ion-molecule collisions gives a rate coefficient of k L = 2πe(α/µ) 1 2 (3.8) where µ is the reduced mass of the reactants (Watson 1978). Thus, the rate coefficient depends only slightly on the polarizability of the neutral molecule

108 68 Chapter 3. Introduction to chemistry in molecular clouds and there is little temperature dependence, as has been demonstrated by experiments down to 8 K. For stable molecules, the range of values of the polarizabilities is fairly narrow (Duley and Williams 1984), so the rate coefficients k tend to have values of the same order, typically 10 9 cm 3 s 1. However, if the reactants are in degenerate states and more than one potential surface for reaction occurs, the Langevin theory (eq. 3.8), does not apply. Then, it has to be considered what percentage of the potential surfaces are attractive in nature and whether or not there exists surface hopping (Clary et al. 1990; Herbst and Knudson 1981). In this case, the value given by the Langevin theory expression may be somewhat too large. Systems that are not in spherically symmetric states are also incorrectly treated by the simple theory (Duley and Williams 1984). ii. The Langevin treatment is inadequate for reactant molecules possessing significant permanent dipole moments. In this case, there is not a simple expression derived for the rate coefficients because the application of capture theories is not completely straightforward as the rotational motion of the molecule is strongly hindered by the presence of the ion (Clary 1985). Instead, several theoretical studies have shown that the rate coefficient increases as temperature decreases, typically as the inverse square root of temperature if the reaction is strongly exothermic (Clary 1985; Herbst and Millar 1991). Rate coefficients as large as 10 7 cm 3 s 1 can exist at temperatures of 10 K. For instance, the so-called average dipole orientation (ADO) theory, which is also a classical approximation, predicts the rate coefficients at 300 K, which are generally of the order of a few times 10 9 cm 3 s 1 (Adams et al. 1985). The ADO rate coefficient at thermal ion energies can be parameterized as [ k ADO = 2πe ( ) ] 1 α µ cµd (3.9) 2 πkt where µ D is the dipole moment of the polar molecule, T is the kinetic temperature, and c is a parameter between 0 and 1, which at constant temperature is a function of µ D /α 1 2 only. However, some ion-molecule reactions possess activation energy barriers. If the barriers are low enough, the reactions may still be important at low interstellar temperatures because of the effect of tunneling (Herbst and Millar 1991). Some reactions are slow at room temperature due to small potential energy barriers, become

109 3.2. Gas phase reactions 69 slower as temperature decreases, and then become more rapid as temperature goes significantly under 100 K. This behavior is explained if the complex formed in the reactions is so long-lived at very low temperatures that the tunneling probability to form products becomes appreciable. Two important reactions in interstellar models that have this behavior are NH H 2 NH H (3.10) which precedes the synthesis of NH 3, and C 2 H H 2 C 2 H H (3.11) There are many slow ion-molecule reactions between ions and molecular hydrogen at room temperature that may be very rapid at very low temperatures due to the tunneling phenomenon. Finally, we have to consider the existence of endothermic reactions that may also occur if the endothermicities are small and if the reactants are not quite thermal. A very well-studied example is the reaction N + + H 2 NH + + H (3.12) which is a primary reaction in the synthesis of interstellar ammonia in dense interstellar clouds (Herbst and Klemperer 1973). Under interstellar conditions, either the ion N + has an excess of translational energy and/or H 2 possess an excess of rotational energy that powers this reaction and makes it sufficiently fast under interstellar conditions to maintain an acceptable rate of production of NH 3 at temperatures down to 10 K. However, the rate coefficient of this reaction remains somewhat uncertain and values between and cm 3 s 1 have been proposed (Galloway and Herbst 1989; Millar et al. 1997). Scott et al. (1997) have proposed the reaction H N NH H (3.13) as an alternative entry route to the synthesis of NH Neutral-neutral reactions Neutral-neutral reactions can be represented as A + BC AB + C (3.14)

110 70 Chapter 3. Introduction to chemistry in molecular clouds Until recent years it had been assumed that, unlike ion-molecule reactions, most exothermic neutral-neutral reactions did not proceed at significant rates at quiescent cloud temperatures (10 K) (Bettens et al. 1995). Moreover, it was difficult to predict if neutral-neutral reactions possessed activation energy, or even the form of their temperature dependence (Herbst and Klemperer 1973). Thus, there was a great uncertainty in the determination of their reaction rates. In any case, it was usually assumed that reactions between stable neutral species were undoubtedly slow at low temperature (Graff 1989), since such reactions have short-range potential barriers which prohibit their occurrence at low temperatures. Examples of these reactions included reactions between radicals of relatively high abundance O + OH O 2 + H (3.15) O + CH CO + H (3.16) C + CH C 2 + H (3.17) C + OH CO + H (3.18) However, neutral-neutral reactions had rarely been studied below room temperature, while at room temperature, kinetic studies of neutral-neutral reactions involving important interstellar atoms and radicals (i.e., have one or more unpaired electrons) had not been undertaken (Herbst et al. 1994). Moreover, there was little evidence for the slowness of neutral reactions in which one or both of the reactants were radicals (Bettens et al. 1995). Indeed, many oxygen atom-neutral radical reactions, and reactions involving neutral carbon atoms and stable hydrocarbons were known to proceed rapidly at room temperature (Bettens et al. 1995; Liao and Herbst 1995, and references therein). Thus, neutral reactions that are rapid at room temperature may well be rapid at low temperature (Herbst et al. 1994). Fortunately, over the past years, the rate coefficients for a number of reactions between neutral species have been measured at the exceedingly low temperatures that are prevalent in dense interstellar clouds (Smith 1997). The reactions include several reaction types, not only radical-radical reactions, which might be expected to proceed without having to surmount a potential energy barrier, but also reactions of free radicals with unsaturated and saturated molecules. The result of this work has shown that a surprising number of reactions are rapid, with rate coefficients cm 3 s 1, close to the simple collisional rate at very low temperatures (Smith 1997). Therefore, it has become gradually clearer that neutral-neutral reactions may

111 3.2. Gas phase reactions 71 play a much more extensive role in the chemistry of dense interstellar clouds than had previously been thought (Herbst et al. 1994, Bettens et al. 1995, Smith 1997), and although ion-molecule chemistry works for most cases, there are particular species which have chemistries dominated by neutral-neutral reactions. However, although experiments on neutral-neutral reactions at very low temperatures have been very successful, relatively few reactions have been studied, most of which have been chosen on the criterion of being experimentally tractable rather than astrochemically important (Smith 1997). Therefore, it will be necessary to estimate many of the rate coefficients for reactions needed in astrochemical models. A variety of capture theories have been used to carry out these estimates, especially the adiabatic capture centrifugal sudden approximation of Clary and co-workers and the statistical adiabatic channel model of Troe and co-workers (Liao and Herbst 1995). Smith (1997) gives some indications about the procedure to estimate the rate coefficient of neutral-neutral reactions involving radicals depending whether the coreactant is a radical, an unsaturated molecule or a saturated molecule. Generally, if a rate constant for a neutral-neutral reaction has been found to exceed cm 3 s 1 at room temperature, then there is unlikely to be an activation energy associated with the reaction. In this case, its rate is more likely to be determined by capture and its rate coefficient will probably increase to lower temperature reaching a value close to the collisionally determined value at the temperatures of dense interstellar clouds (Smith 1997). To complicate things further, the products of some of these reactions have not been measured (Herbst et al. 1994), and an estimation of the most likely products has to be made, until future experimental and quantum chemical studies elucidate the products and reaction pathways Radiative association reactions Radiative association reactions are those in which two species A and B, which may be atoms, radicals, molecules or ions, react to form a complex structure, AB, which either dissociates into reactants or is stabilized by spontaneous emission of radiation (Herbst 1987). The process is usually written as A + B AB (3.19) AB A + B (3.20)

112 72 Chapter 3. Introduction to chemistry in molecular clouds AB AB + hν (3.21) Under laboratory conditions the excess energy is removed by a second collision during the lifetime of the complex. At densities below cm 3, stabilization of the AB complex is made through radiative processes (Herbst and Klemperer 1973). Radiative association reactions can occur for both ion-molecule reactions and neutral-neutral reactions, but the lack of activation energy in ion-molecule reactions makes this process a salient feature in those systems. Radiative association processes are thought to play an important role in the formation of complex molecules in the gas phase chemistry of dense and diffuse interstellar clouds (Herbst and Klemperer 1973; Herbst and Bates 1988; and references therein), since a number of radiative association reactions have been suggested as important chemical routes in the interstellar medium to explain the formation of complex interstellar molecules (Duley and Williams 1984; Leung et al. 1984). Although some radiative association reactions have been studied in the laboratory (Herbst 1985 and references therein), these reactions are very inefficient processes at very low laboratory densities, and it has been very difficult to determine experimentally its rate coefficients. Thus, for many years, the rate coefficients were calculated theoretically only (Bates and Herbst 1988). A significant part of the theoretical treatment of radiative association reactions is the determination of the radiative stabilization rate of the intermediate complex formed by the reactants (Herbst and Bates 1988). For most of the calculated values of radiative association rate coefficients tabulated in the literature, it has been considered that the complex is formed in its ground electronic state and radiative stabilization happens when spontaneous emission occurs from excited vibrational states lying above the dissociation limit of AB into stable vibrational states lying below this energy limit. On the other hand, far larger stabilization rates can be achieved (Herbst and Bates 1988) if the complex is formed in a excited electronic state possessing dipole-allowed transitions to stable vibrational levels of the ground electronic state, or if the complex is formed in a ground electronic state that possesses transitions to lower-lying vibrational levels of excited electronic states. A crude estimate of the size of the radiative association rate can be found (Herbst and Klemperer 1973). The process can be represented as A + B k 1 k 1 AB (3.22)

113 3.2. Gas phase reactions 73 AB k 2 AB + hν (3.23) Then, the overall rate of formation of the AB molecule is, if no other processes are involved, k RA = k 1k 2 k 2 + k 1 n(a)n(b) cm 3 s 1 (3.24) For diatomics, Duley and Williams (1984) estimate the value of the rate coefficients of each reaction in the following way. The time range available to the system for the emission of radiation to stabilize the complex is about the duration of the collision. Then, we can assume k s 1. The Einstein transition probability for a strong transition is k s 1. Finally, the collision rate coefficient for neutrals can be estimated as k cm 3 s 1. Thus, the resulting expected rate coefficient for neutrals would be about k RA cm 3 s 1. A variety of calculations have shown that radiative association reactions between reactants with small numbers of atoms have rate coefficients significantly smaller than the collisional limit (Herbst and McEwan 1990), but the efficiency improves as the size of the reactants increases, as the temperature is lowered, and as the potential energy surface becomes more attractive (Herbst and Millar 1991). When radicals or molecules are involved in this reactions, the situation is different because there are a number of bonds which may share the energy and an appreciable time may pass before the necessary energy for dissociation appears in a single bond and disrupts the molecule. The rate coefficient k 1 decreases very rapidly as the number of bonds in the system increases (Duley and Williams 1984). Equation (3.24) shows that if the coefficient rate k 2 exceeds or is of the order of k 1, the overall radiative association rate is comparable to the collision rate. The strong variation of k 1 with the number of bonds, implies that, even for relatively simple molecules, radiative association reactions can be rapid. Ion-molecule radiative association reactions involving smaller reactants are normally only critical in interstellar chemistry if the reactants cannot react more rapidly to produce exothermic products. But, as reactants get larger, it may be that radiative association reactions become so efficient as to dominate the chemistry. Calculations by Herbst and McEwan (1990) showed that at low temperatures, radiative association reactions for systems with roughly ten or more atoms begin to approach unit efficiency, even in the presence of competitive exothermic channels. Thus, the gas phase production schemes in dense interstellar clouds for these molecules will be enhanced.

114 74 Chapter 3. Introduction to chemistry in molecular clouds Radiative recombination Radiative recombination is the process in which an atomic ion recombines with an electron, releasing the surplus energy as radiation A + + e A + hν (3.25) This process may also occur for molecular ions, but the recombination of molecular ions usually follows a different mechanism, dissociative recombination, as we shall see below in section The main ions in diffuse interstellar clouds are C +, arising in the photoionization of C atoms, and H + formed from cosmic ray ionized hydrogen. The radiative recombination of electron on to these ions is the process controlling the level of ionization. In dense clouds, where ionization from photons is excluded, the ionization is still affected by radiative recombination on atomic ions, Si +, S +, and atomic metal ions principally, and also processes involving molecular ions. The determination of the radiative recombination rates has usually been made from theoretical calculations (Verner and Ferland 1996, and references therein), because laboratory studies are dominated by the faster processes of dissociative recombination. A simplified approach to the calculation of the radiative recombination coefficient is to consider that it is the inverse of photoionization, A + hν A + + e (3.26) Assuming the principle that the transition probabilities for a process and its inverse are equal, the radiative recombination coefficient is related to the photoionization rate, which can be calculated using quantum mechanics. These calculations show rate coefficients on the order of cm 3 s 1 and a decrease of the reaction rate with increasing temperature (Duley and Williams 1984). Further quantum mechanical calculations and fits show rate coefficients of this order (see Péquignot et al. 1991; Verner and Ferland 1996) Dissociative recombination Dissociative recombination is the process in which molecular positive ions recombine with electrons and dissociate in neutral products AB + + e A + B (3.27)

115 3.2. Gas phase reactions 75 Figure 3.1: Diagram showing the arrangement of potential energy curves for AB + and AB necessary for dissociative recombination to occur. Taken from Duley and Williams (1984). Dissociative recombination of molecular ions plays a key role in the chemistry of the interstellar medium, since it controls the level of ionization of the gas and hence the rate of chemical reactions in interstellar clouds, and determines the abundance of some ions, as H + 3, which play a critical role in the chemical evolution of the gas. Moreover, it produces many new, and often very reactive, radical neutral species (Adams et al. 1991). Figure 3.1 shows a diagram of the conditions required for dissociation of the molecular ion to occur. A repulsive potential surface of the parent neutral species has to cross the bound ionic surface near its equilibrium point. Then, if the incident electron excites the ion-electron system into excited rovibrational states of a highlying Rydberg electronic state of the neutral species, a second crossing may occur to a repulsive state of the parent neutral, which fragments the molecule (Herbst and Millar 1991). However, until a few years ago few laboratories had performed measurements of dissociative recombination rate coefficients (see Mitchell 1990), and even fewer have examined reacting branching ratios, which still remain an area of uncertainty in most cases (Canosa et al. 1991; Millar et al. 1997). The laboratory measurements

116 76 Chapter 3. Introduction to chemistry in molecular clouds of dissociative recombination reactions find that they typically occur with large rate coefficients at room temperature, in the range k = cm 3 s 1, and with a weak inverse temperature dependence (Herbst and Millar 1991). However, very few of those dissociative recombinations used in interstellar chemistry have been studied in the laboratory (Herd et al. 1990) Charge transfer reactions Charge transfer reactions are of the type A + + B A + B + (3.28) Charge transfer reactions are of some importance in interstellar chemistry, although some of them are of crucial importance in initiating reactions. For instance, an important part of the chemistry rests on the initiating reaction H + + O H + O + (3.29) to form the reactive species O +. Charge transfer reactions should occur if two conditions are met (Figure 3.2). Firstly, there must be near energy resonance between some state of A with a state of B. Secondly, the Franck-Condon principle has to be satisfied, i.e. the overlap integral of the wave functions describing nuclear motions should be large (Duley and Williams 1984). In cases where these criteria are met, expected values for the rate coefficients, also borne out by experimental studies, are on the order of 10 9 cm 3 s 1 (Watson 1978). Because the range of temperatures is limited in the interstellar case, no temperature dependence is included. In cases where any of the criteria is not satisfied, the rate coefficient may be much smaller. For polyatomic molecules the requirements are not so rigid. In these cases, the density of states per unit energy is large and the energy resonance condition will usually be met. Molecular distortion in the interaction can break the Franck-Condon principle Negative ion reactions Although the major processes considered in the study of the gas phase chemistry of dense interstellar clouds are ion-molecule reactions, or even neutral-neutral reactions, several processes involving negative ions can be found in interstellar clouds.

117 3.2. Gas phase reactions 77 Figure 3.2: Diagram showing the arrangement of potential energy curves for charge transfer to take place in a diatomic system. Wave functions are indicated schematically. Taken from Duley and Williams (1984). However, it has been concluded that negative ions are scarce and their role in the chemistry has usually been regarded as minimal (Dalgarno and McCray 1973; Herbst 1981), mainly caused by the generally slow rate of radiative attachment. In any case, several processes forming negative ions have been investigated. Herbst (1981) proposed radiative attachment A + e A + hν (3.30) to be relatively efficient for small radical neutral species with large electron affinities, although the rate coefficient should be much smaller than that for radiative recombination, because the electron-neutral interaction is very much weaker. Quantum mechanical calculations suggest rate coefficients on the order of cm 3 s 1 (Duley and Williams 1984). Exothermic dissociative attachment e + AB A + B (3.31) has been shown to produce negative ions, such as CN (Petrie 1996) within dense interstellar clouds. In principle, dissociative attachment reactions would appear to be a more efficient manner of producing negative ions than radiative attachment, but for most species dissociative attachment is endothermic because the energy of the bond broken exceeds the electron affinity (Petrie and Herbst 1997).

118 78 Chapter 3. Introduction to chemistry in molecular clouds There are also several pathways involved in the destruction of negative ions: photodetachment A + hν A + e (3.32) which is fairly efficient in interstellar clouds, because there is a wide range of photons able to detach the electron due to the low interaction energy between the electron and the neutral. A rate of about 10 7 s 1 for H has been calculated (de Jong 1972). Similar values are expected for other systems, since the nature of the neutral is not so important in this process. It can generally be neglected in dense clouds for negative ions of several electronvolts stability (Duley and Williams 1984). associative detachment, A + B AB + e (3.33) which occurs if a repulsive potential surface of A and B crosses some bound state surface of the neutral AB. Then, reaction is expected to occur in nearly all collisions, and the rate coefficient would be approximately equal to the collisional rate coefficient, 10 9 cm 3 s 1 (Schmeltekopf et al. 1967), and approximately constant with temperature (Dalgarno and Browne 1967). However, if there is no crossing of a bound state surface, there will be no reaction. Experiments show that, if A and B are atoms, all exothermic associative reactions are fast (Duley and Williams 1984). The same cannot be said if A and B are molecules, in which case reactions may be slow. mutual neutralization A + B + A + B (3.34) which is a fast process, where the interaction is dominated by long range Coulomb forces, with very large cross sections. The reaction may occur if there is a possible transition between the potential curve of A and B + to a near one of AB. The rate coefficients calculated from theory and from laboratory experiments are large and with a weak temperature dependence, with typical values of 10 6 T 0.5 cm 3 s 1 (Dalgarno and McCray 1973). Negative ion reaction rates may usually be lower than the rates of positive ion chemistry, but in some situations negative ion routes can make important contributions. For example, they supply the fastest gas phase routes forming H 2 (de Jong

119 3.2. Gas phase reactions ), although they cannot compete with faster grain surface reactions (Duley and Williams 1984) Cosmic ray ionization Galactic cosmic rays, composed principally by protons, represent a potentially large source of energy input into the interstellar medium. Cosmic rays traversing a dense interstellar cloud produce ionization, dissociation, and heating. Because of the ionization, the cloud is coupled to the interstellar medium by the galactic magnetic field, and the fractional ionization must play a role in the collapse of interstellar clouds and the formation of stars (Spitzer 1978). The ionization also sets an important initiating route into interstellar chemistry, e.g., the primary ionization step in the ion-molecule chemistry of dense interstellar clouds begins with the ionization caused by the collisions of the flux of cosmic rays with molecular hydrogen to produce H + 2 (Herbst and Klemperer 1973; Cravens and Dalgarno 1978; Herbst 1987). Another important ionization is caused by collisions of cosmic rays with atomic helium to produce He +. Moreover, the heating caused by cosmic rays controls the thermal balance during the evolution of clouds, and the H atoms produced in the dissociation of molecular hydrogen may be an important further source of heating as they recombine. The cross section for ionization of H atoms by energetic protons is well known, and varies inversely with energy. Cosmic ray proton of relatively low energy, about 2-10 MeV, are most effective in causing interstellar ionization (Black 1987). In dense molecular clouds, cosmic rays with energies between 10 and 100 MeV ionize H 2 (Gredel et al. 1989) and generate secondary electrons with a mean energy of about 30 ev. The rate of ionization, per atom or molecule, caused by the cosmic rays becomes then a very important parameter in the study of interstellar chemistry. However, the cosmic ray ionization rate, ζ, cannot be calculated directly from observations because the shielding of the solar wind impedes the arrival of the flux of low energy cosmic rays ( < 10 9 ev) at the Earth. These difficulties notwithstanding, several independent estimates as to the range of possible values of ζ have been made (Duley and Williams 1984). The spectrum of the high energy cosmic rays allows a calculatation of a lower limit of ζ > s 1 per H atom (Spitzer and Tomasko 1968). An estimate of an upper limit to ζ can be made from the thermal balance of the gas,

120 80 Chapter 3. Introduction to chemistry in molecular clouds taking into account that cosmic rays are a heat source for the gas, and the required electron densities. For diffuse clouds, where starlight is a more effective agent, assuming thermal equilibrium and that cosmic rays are responsible for the heating gives ζ < s 1 per H atom (Dalgarno and McCray, 1972; O Donnell and Watson 1974). If thermal balance is applied to dark clouds, where visible and ultraviolet photons from starlight are excluded, the value obtained is ζ < s 1 per H 2 molecule. Analysis of ionization and molecular abundances in diffuse clouds suggests a typical hydrogen ionization rate of s 1 (van Dishoeck and Black 1986). Given this wide range of estimates, the cosmic ray ionization rate is then usually treated as a parameter to be determined by modeling the interstellar chemistry. The results of the chemical modeling of the chemistry in diffuse and dense clouds tend to support a value of ζ on the order of s 1 (Herbst and Klemperer 1973; Herbst and Millar 1991), which is a value sufficiently small that dense cloud remain overwhelmingly neutral, although the small abundance of ions produced are critical for the gas phase formation of polyatomic neutral molecules. As we will see in more detail in section 3.4, the ionization by cosmic rays of hydrogen atoms, hydrogen molecules, and helium atoms is of major importance in interstellar chemistry. For two reasons: first, H +, H 2 + and He + are significant reactants in many interstellar situations, and second, they provide the main entry routes into the chemistry of oxygen-, carbon-, and nitrogen-bearing molecules, so to some extent, ion-molecule chemistry in dense clouds begins with the ionization of neutral species by cosmic-rays (Herbst and Millar 1991) Photochemistry When the effects of the interaction between the interstellar radiation field and the molecules of the gas phase of the interstellar medium are taken into account, it turns out that the interstellar radiation field is the primary means of destruction of molecules under low gas density conditions (Henning 1981). Indeed, Stief et al. (1972) showed that the lifetimes against photodestruction for a representative sample of small interstellar molecules increase dramatically as a function of visual extinction. Thus, interstellar clouds can then be divided into diffuse regions of low visual extinction where photons penetrate appreciably and photodestructive events affect the chemistry, or dense clouds where the visual extinction is sufficiently large that photodestructive effects need not be considered or they are not rapid compared

121 3.2. Gas phase reactions 81 with competing gas phase processes (Herbst 1987). The main processes that take place as a result of the interaction between molecules and the photons of the interstellar radiation field are photodissociation and photoionization. The photodissociation and photoionization cross-sections of some simple interstellar species have been studied in the laboratory (Watson 1978; van Dishoeck and Black 1986). However, there is neither a detailed knowledge of the intensity of the interstellar UV radiation field nor of the absorption and scattering properties of dust grains. This leads to a high degree of uncertainty in the calculation of photorates, which gives large uncertainties in the calculated molecular abundances. Photodissociation In unshielded regions of the interstellar medium, photodestruction of atomic and molecular species occurs on a time-scale of years (Herbst and Millar 1991). In diffuse clouds, where gas density is 100 cm 3, the photodestruction timescale is about 10 4 years. The photodissociation rate for a molecule exposed to the full interstellar radiation field is obtained by evaluating the expression (Duley and Williams 1984) β 0 = 4π E=0 F (E)σ pd (E)dE (3.35) where σ pd is the photodissociation cross section, F (E) is the interstellar radiation flux, E is the photon energy in ev, and the integration covers all absorption bands of the molecule between 0 and ev. Typical values for β 0 lie between 10 9 and s 1. In the presence of dust, the photodissociation rate is significantly reduced. An approximation for the variation in the photodissociation rate can be made assuming plane parallel geometry and neglecting the effect of scattering by dust β = β 0 exp( αa V ) (3.36) where β 0 is the photodissociation rate in the unshielded radiation field, β is the rate at a point within a cloud where the visual extinction is A V, and α is a numerical factor that measures the relative importance of ultraviolet and visual wavelengths in photodissociation (Black and Dalgarno 1977).

122 82 Chapter 3. Introduction to chemistry in molecular clouds However, H 2 and CO, the two most important molecular species, are not destroyed by continuum photons but by line photons, which enables these species to self-shield against the UV radiation field (Wagenblast 1992; van Dishoeck and Black 1988), thus reducing considerably the photodissociation effects. Some mutual shielding of CO by H 2 also occurs (Herbst and Millar 1991). Photodissociation can also be a source for small molecules in diffuse clouds if the destruction of a large molecule leads to smaller molecules. An example of this is CH 4, which in the range of 150 to 100 nm yields CH, CH 2 and CH 3 (Duley and Williams 1984). In dust clouds or in regions far from star-formation in giant molecular clouds, it has long been thought that photodestruction by the interstellar radiation field is unimportant. However, this may no longer be a valid approach if molecular clouds are highly clumped. Boissé (1990) showed that the presence of clumpiness induces an enhancement of the energy density inside molecular clouds by several orders of magnitude as compared to that in a uniform cloud containing the same amount of material. The effect will be most noticeable in the UV where the dust opacity is the largest. Additionally, the cosmic-ray ionization of H 2 in dense clouds leads to an internally generated flux of ultraviolet photons caused by fluorescent emission from H 2 which is excited by electron collisions (Prasad and Tarafdar 1983). This flux of cosmic-ray-induced photons can lead to more photodissociaton or photoionization reactions, as we will see below. Photoionization The only species to be ionized to any degree in diffuse clouds are those with ionization potentials less than 13.6 ev, because H is the most abundant element. Thus, while N and O atoms remain neutral, C is converted to C +. With respect to molecules, the abundant molecules H 2 and CO are also neutral, while the H 2 O and H 2 CO molecules can be photoionized to H 2 O + and H 2 CO + respectively (Duley and Williams 1984). The primary effect of photoionization in diffuse clouds occurs then through the formation of C + : C + hν C + + e (3.37) The ion C + then participates in ion-molecule reactions. The photoionization of C is important only at short wavelengths, where the extinction due to dust is greatest. So, it has been found that the balance C + /C total is quite sensitive to the presence of

123 3.2. Gas phase reactions 83 dust. This ratio is 1 in the intercloud region and in many diffuse clouds. However it is 1 in denser clouds, where the optical depth τ ν > 1. Cosmic-ray induced photodissociation and photoionization Since the interstellar ultraviolet radiation field cannot penetrate into the interior of dense clouds, these regions were assumed dark, and cosmic ray ionization was thought to be the sole driver of the gas phase chemistry. However, the ionization of H 2 by cosmic rays with energies between 10 and 100 MeV releases secondary electrons with a mean energy of 30 ev (Cravens and Dalgarno 1978). Since the fractional ionization of dense molecular clouds is generally low, the secondary electrons lose their energy mainly by exciting and ionizing H 2 (Prasad and Tarafdar, 1983). The calculated number of excitations produced by cosmic rays is 0.15 ζ n(h 2 ) cm 3 s 1, where n(h 2 ) is the number density of molecular hydrogen (Sternberg et al. 1987) and ζ s 1 is the cosmic ray ionization rate. The excited states radiate photons in the ultraviolet region. The UV photons are produced throughout the molecular cloud, and they are predominantly absorbed by dust grains. However, a small fraction of the produced photons is absorbed by molecules in photodissociation and photoionization events, since the UV photons have enough energy to cause photodissociation of CO and photoionization of C (Gredel et al. 1987). The calculated photorates due to these photons (Sternberg et al. 1987; Gredel et al. 1989) show that, although somewhat dependent on the physical conditions, the rates vary from times the cosmic-ray ionization rate. This results in most species having photorates s 1 for a standard cosmic-ray ionization rate. However, the effects occurring as a result of these ultraviolet photons are not expected to be very profound, except for certain species (Herbst and Millar 1991). On the other hand, the loss rates of unreactive molecules and the formation rates of their dissociation products may be considerably modified. Particularly affected are saturated species which undergo reactions with positive ions whose products reenter the chemical formation cycle, and complex species which are the products of a lengthy chain of reactions that can be interrupted at several intermediate stages. Such may be the case of hydrocarbons (Sternberg et al. 1987). Photoionization produces ions which feed back into the chemical cycles so that its effects are less dramatic. However, it does modify the chemical pathways and may influence substantially the abundances of specific molecules (Sternberg et al. 1987).

124 84 Chapter 3. Introduction to chemistry in molecular clouds 3.3 Grain chemistry Dust grains contribute a minor amount of the mass of the galaxy, about 1% of the mass of the interstellar medium (Spitzer 1978), but because they have a strong interaction with the stellar and gas components, the study of cosmic dust grains becomes essential in understanding the dynamical, thermal and chemical properties of the dense phases of the interstellar medium. As an example of its importance, dust obscures all but the relatively nearby regions at visual and ultraviolet wavelenghts and reradiates the absorbed energy in the far-infrared part of the spectrum, thereby providing a major part ( 30%) of the total luminosity of the Galaxy (Mathis 1990) General properties of grains The cosmic dust consists of several well-distinguished populations typical of the environments in which they are formed and/or modified. Each population is a multi-component system containing grains or grain ingredients of different chemical composition and physical structure. Henning (1997) differentiates at least four different populations: 1. Stellar outflow dust (stardust). It is primarily formed in circumstellar shells of cool high-luminosity stars (AGB and post AGB stars), and then injected into the interstellar medium through stellar winds. The process of dust formation in supernovae is poorly understood and might not be sufficiently efficient (Jones and Tielens 1994). 2. Dust in the diffuse interstellar medium (interstellar dust). It proceeds from various sources and should develop into a homogeneous sample, because of the frequent reprocessing of grains due to the passage of shocks, adsorption of gaseous species, irradiation by the interstellar UV field and cosmic rays, and being in the molecular cloud phase for several periods (Tielens et al. 1994; Tielens 1998). 3. Dust in dense cool clouds (molecular cloud dust). The adsorption of gas phase species and surface chemistry leads to the formation of ice mantles, which are expected to be composed (which is partly proved by observations) of H 2 O

125 3.3. Grain chemistry 85 CH 3 CO, CO and CO 2 and some other molecules with admixtures of impurities such as carbonaceous particles (Whittet 1993). The size distribution should be modified by grain coagulation to form larger composite and fluffy grains (Ossenkopf and Henning 1994). In very dense protostellar cores, these processes are expected to happen at a much higher rate. 4. Circumstellar dust around young stellar objects (YSO dust). Grains are at least partially reprocessed by chemical reactions. Additionally, grain properties are expected to suffer dramatic changes due to coagulation, collisional and chemical destruction, sublimation, and condensation (Schmitt et al. 1997). The understanding of the evolution of the dust component in a protoplanetary nebula is crucial for explaining the formation of planetary systems. Cosmic dust grains have been studied from X-ray to radio wavelengths. Evidence for the presence of interstellar dust has been found in ultraviolet, visual and near-infrared extinction and polarization curves; extended red emissions observed in reflection nebulae, H II regions, and planetary nebulae and peaking between 650 and 700 nm; infrared emission and absorption features; and infrared and (sub)millimeter thermal continuum emission (see Henning 1997 and references therein). The infrared 10 and 18 µm features, in emission and absorption, which are generally attributed to silicates, detected in the spectra of a wide variety of sources (compact H II regions, Herbig Ae/Be stars, T Tauri stars, etc.) and along lines of sight going through the diffuse interstellar medium show that silicates are a significant component of dust in molecular and diffuse clouds (Williams 1991, Henning 1997 and references therein). The presence of graphite seems to be less certain, although infrared spectra and the depletion of carbon indicate that a carbonaceous solid is a major component of interstellar dust. It is usually assumed that this carbonaceous solid takes the form of amorphous carbon (Williams 1991). The presence of other refractory components such as sulfides and oxides is still doubtful (Henning 1997). Infrared spectroscopy also revealed numerous bands of cosmic ices between 2 and 15 µm in the spectra of deeply embedded molecular cloud sources (see Whittet 1993). The most abundant mantle molecule is H 2 O, which is observed in a wide variety of sources. Solid CO was also detected in the infrared spectra of deeply embedded and luminous young stellar objects (Lacy et al. 1984; Whittet and Duley 1991). Solid CO 2 was first detected in the IRAS LRS spectra of a few embedded

126 86 Chapter 3. Introduction to chemistry in molecular clouds infrared sources (d Hendecourt and Jourdain de Muizon 1989), and later confirmed by ISO observations in several YSO (de Graauw et al. 1996; Gürtler 1996; Whittet et al. 1996). Another ice component which seems to be much less important is CH 3 OH (Skinner et al. 1992). In order to emphasize the importance of cosmic dust, we briefly list some of the major roles that dust grains may play in both diffuse and molecular clouds: Dust dominates the heating and cooling of clouds through energetic photoelectrons and gas-grain collisions (Mathis 1990, Tielens et al. 1994). Dust grains are also the dominant source of opacity longward of the Lyman limit, and they therefore dominate the radiative balance of the interstellar medium (Tielens et al.1994). The optical properties of starlight are affected by the presence of dust grains, mainly by absorption, scattering and polarization, which may be significant in molecular clouds especially in regions with a high radiation field such as star-forming regions.the far-infrared radiation from dust removes the gravitational energy of collapsing clouds, allowing star formation to occur (Mathis 1990). Dust grains also determine the spectrum of dust-enshrouded objects (Ossenkopf and Henning 1994). Thermal continuum emission from dust grains at infrared and (sub)millimeter wavelengths is used as an important indicator for the presence of cold protostars, and of circumstellar disks and envelopes around young stellar objects (André 1994). Other optical effects caused by dust grains, in diffuse clouds and in the edges of molecular clouds, are luminescence and heating of gas by photoelectric effect (Williams 1991). Dust opacity effects may also drive or influence instabilities in protostellar flows and accretion disks (Noh et al. 1991). Dust grains are also carriers of electric charge, positive and negative in diffuse clouds, weakly negative in molecular clouds (Williams 1991). Dust may carry then a substantial fraction of the charge in dense, weakly ionized cosmic plasmas and, therefore, influence the electrodynamics of these regions (Ciolek and Mouschovias 1993). Dust has a crucial effect on interstellar chemistry. Firstly, dust grains regulate the penetration of far-uv photons, which can dissociate and ionize molecules (Mathis 1990). The reduction of the UV radiation allows a more complex chemistry to take

127 3.3. Grain chemistry 87 place. Therefore, dust is an important influence on the composition of molecular clouds. Secondly, dust grains provide surfaces for the reaction of gas-phase species. Molecular hydrogen, the most abundant gas species, is formed in grain surfaces in diffuse clouds, although it is not known whether this process is equally efficient in molecular clouds (Williams 1991). Surface reactions on dust grains may also contribute to diffuse cloud chemistry, and other gas phase molecules might result from reactions on grain surfaces as well, such as H 2 O, NH 3, H 2 CO (Tielens et al. 1994). However, the significance of this contribution cannot yet be determined from observations. Thirdly, dust grains are both a sink and a source for gas phase molecules, which affects the chemical composition of clouds, especially molecular clouds, through the depletion of elements and molecules from the gas phase, solid state reactions, and ejection of material through mantle or grain destruction. In molecular clouds, dust grains are likely to have a direct contribution to the chemistry by the immediate ejection of the products of surface reactions to the gas. A more indirect contribution of dust grains to the chemistry in molecular clouds is the retention of the products as part of the molecular mantles, to be ejected at some later time, by photodesorption or by cosmic rays, or by the effect of star formation. Dust grains are also responsible of the depletion from the gas phase of refractory elements such as C, Mg, Si, and other metals observed in both diffuse and molecular clouds (Jones et al. 1994). Additionally, molecular ices indicate that there must also be a significant further depletion of C and O (Mathis 1990). The importance of the mantles of molecular ices is evident if we realise that mantles may contain significant fractions of the interstellar elemental abundances. Observations show that typically 10% of the elemental oxygen is locked up in solid H 2 O, comparable to the gas phase abundance of CO (Tielens and Whittet 1997). Therefore the destruction of mantles, either if they are destroyed continuously or abruptly in a single event, may significantly modify the gas phase chemistry. On the other hand, if the molecular mantles of the grains would grow unrestrictedly, it would lead to the depletion in a relatively short time of all the heavy elements from the gas phase, with consequences for the gas temperature and ionization. Thus, some mechanism that prevents this from happening, and mantains an equilibrium between molecules in the gaseous and solid phases will have to be considered (d Hendecourt et al. 1985, Williams 1991).

128 88 Chapter 3. Introduction to chemistry in molecular clouds Interaction between gas and dust grains At the low temperatures generally found in molecular clouds, collisions between the neutral component of the gas and the dust are likely to lead to retention of the gas phase particles on the surface because their thermal energy is much less than typical adsorption energies and because excess kinetic energy can be transferred rapidly to the surface (Herbst and Millar 1991). Leitch-Devlin and Williams (1985) made detailed calculations showing that the fraction of collisions which lead to retention is , depending on the species and the nature of the surface. Depending on the grain charge, this fraction may be zero for ions. The widespread detection of molecular mantles in molecular clouds points to the fact that the sticking of heavy atoms and molecules at the surfaces of cold dust grains is efficient. Moreover, the observed mantles show a significant thickness, which seems to rule out the possibility that the sticking efficiency declines as successive monolayers are accreted (Williams 1991). For a typical gas-to-dust ratio in interstellar clouds, the time-scale for the collision of any gas phase particle with a grain is τ coll n years (3.38) where n is the total particle density in cm 3 (Leitch-Devlin and Williams 1985). This indicates that the interaction between the gas and dust is potentially important in almost all environments in which interstellar molecules are detected, because for densities n > 100 cm 3, gas phase particles collide at least once with a dust grain within a typical lifetime of an interstellar cloud, while in dense clouds, n 10 4 cm 3, collisions are frequent unless some process, such as grain coagulation, acts to reduce the effective surface area of the dust (Herbst and Millar 1991). Moreover, if the sticking efficiency is high, the depletion timescale for gas densities typical of molecular dense cores, 10 5 cm 3 to several 10 6 cm 3, may be years (Mundy and McMullin 1997), significantly shorter than dense cores and molecular clouds lifetimes, so molecular depletions must be widespread. The time required for substantial mantles to form, if we make the assumption that no material returns from solid to gas is t m ( 10 4 cm 3 n ) ( 1 S ) ( cm 2 πa 2 0n g /n ) ( ) T (3.39)

129 3.3. Grain chemistry 89 where n is the total hydrogen number density, S is the effective sticking probability for the main component of the mantle (e.g. H 2 O, CO, etc.) on grains which have effective radius a 0 and number density n g, and T is the gas temperature (Williams 1991). The normalization is to the grain surface area per hydrogen atom for dust causing the visible and UV extinction (Duley and Williams 1984). If only the larger grains accrete mantles, t m will be larger. If small grains can accrete mantles, and if there is a larger population of very small grains, then t m would be smaller; but this seems unlikely (Williams 1991). For typical molecular clouds, t m could be short compared to both the expected age of such clouds, 10 7 years, and the time needed to achieve chemical steady-state, and could be comparable to the free-fall time (Brown and Charnley 1990). Thus, chemical steady-state is not possible if there exist no mechanisms to return mantle material efficiently to the gas. As a result, mantle growth will affect significantly the chemistry and the physical development of the cloud. Iglesias (1977) showed that accretion on to the dust eventually dominates the evolution, and that total freeze-out of gas molecules is inevitable for non-zero sticking efficiency when no continuous desorption processes act to remove mantle material. For gas densities of more than 10 4 cm 3, all the gas phase molecules, except H 2 H + 3, CO, N 2, and a few other weakly polar molecules, should accrete onto grain surfaces in about 10 5 years. The depletion rate will be even faster for greater densities, as those of disk material, > 10 6 cm 3, since it scales inversely with density (Langer et al. 2000). The desorption of grain mantles, and the reinjection of the frozen-out molecules into the gas phase, complicates even more the chemical history (Willacy and Williams 1993). Grain-surface chemistry An extensive solid state chemistry it is believed to occur in the icy mantles on dust in molecular clouds (Tielens and Allamandola 1987). Under typical conditions, the rate accretion of gas phase species onto a grain is of about 1 species a day (Tielens and Whittet 1997). Laboratory measurements show that the migration timescales of the atoms H, D, C, N, and O, at low temperatures, 10 K, are short compared to the accretion timescale, while heavier atoms, radicals and molecules are immobile. A migrating species, then, can scan the whole surface for a coreactant and react before another species is accreted (Tielens and Allamandola 1987). Moreover, although many of these reactions have activation barriers, the long timescale for reaction may

130 90 Chapter 3. Introduction to chemistry in molecular clouds still allow them to proceed on grain surfaces (Langer et al. 2000). Grain surface chemistry at conditions of low temperature and density is dominated by hydrogenation and oxidation reactions of simple species accreted from the gas phase (Langer et al. 2000). Hydrogenated species such as H 2 O, NH 3, and CH 4 are produced owing to the high mobility of atomic hydrogen on the cold surfaces, and are expected to be the dominant constituents of the grain mantle (Brown, Charnley and Millar 1988). Since CO is the gas-phase dominant C-bearing species, the chemistry of CO is particularly relevant for the organic reservoir of interstellar ices (Langer et al. 2000). Hydrogenation of solid CO can lead to H 2 CO and CH 3 OH, although there is still some discussion on the efficiencies of these reactions (Tielens and Whittet 1997). The long timescale between accretion of reactive radicals may also allow oxidation reactions to occur, especially of CO. The reaction of O with CO may be the predominant grain surface chemistry route towards CO 2 in dark clouds (Langer et al. 2000). At higher temperatures, the diffusion of heavier species, such as radicals, over the surface becomes significant and a more complex but poorly understood surface chemistry proceeds (e.g. Caselli et al. 1993). Above 60 K, polymerization reactions involving H 2 CO, NH 3 and CH 3 OH-ice can produce compounds of high molecular weight (Schutte et al. 1993). Photochemical reactions within the ices can be triggered by UV radiation originating from internal sources, such as embedded protostars or cosmic-ray-induced photons, or from the penetration of the diffuse galactic radiation field (Prasad and Tarafdar 1983). Ultraviolet photolysis of ices containing H 2 O, CO, NH 3, and CH 4 produces small radicals such as H, O, OH, N, NH, NH 2, C, CH, CH 2, CH 3, which react with each other and the parent species resulting in, for example, H 2 O 2, N 2 H 2, CO 2, radicals such as HCO, HO 2, and even large organic species, which are available for further reactions (Bernstein et al. 1995; Gerakines et al. 1996). Additionally, ultraviolet photons provide energy which enables new reaction pathways to proceed, which differ from those resulting from simple warming because of the presence of radicals. Photolysis of ice mixtures containing H 2 O, NH 3, and CO or CH 3 OH often leaves a non-volatile organic residue containing a variety of complex oxygen- and nitrogen-rich organic molecules (d Hendecourt et al. 1982; Bernstein et al. 1995; van Dishoeck and Hogerheijde 1999).

131 3.3. Grain chemistry 91 Mantle-growth limiting processes Under the conditions found in cold molecular clouds, gas phase molecules (other than H 2 ) are expected to accrete onto grain surfaces on a time scale /n H α years, where α is the sticking coefficient which is thought to lie between 0.1 and 1.0 (Williams 1991; Willacy and Williams 1993; Mundy and McMullin 1997). Thus, if this process continues unchecked, with no return of the adsorbed species to the gas phase, for a typical dark cloud density of 10 4 cm 3 virtually all accreting molecules should disappear from the gas phase in less than 10 6 years (van Dishoeck and Blake 1998). However, since molecules are commonly detected in these regions, in both solid and gas phases, then either the clouds are fairly young or there must exist efficient desorption mechanisms even in the coldest, most quiescent clouds, which return the accreted species to the gas phase and maintain significant gas-phase populations of molecules during the expected lifetime of the clouds. Therefore, several mechanisms limiting mantle growth have been proposed, and developed in detail, to account for the detected abundances observed in molecular clouds. There are two, not mutually exclusive, main groups of solution to this problem: intermittent, or sporadic, and continuous desorption of mantle ices. Star formation is expected to disrupt the dense cores of gas from which stars are formed, redistributing the gas in molecular clouds (as originally proposed by Norman and Silk 1980), and in the process removing the icy mantles by sublimation from warm grains or by sputtering in shocks in non-quiescent chemical evolution (Brown and Charnley 1990). The result is the creation of populations of molecules very different from those typical of cold clouds, and characteristic of hot molecular cores: large abundances of saturated molecules, including small species such as H 2 O, NH 3, H 2 S and CH 4, and large species, such as CH 3 OH, C 2 H 5 OH, C 2 H 5 CN, with abundances larger by a factor of at least 10 3 over those in cold clouds (Millar 1997). The modeling of situations where dust grains are heated by the radiation of a newly born near bright star and the mantles are abruptly evaporated, returning both processed and unprocessed material to the gas phase, shows that the detected (Hot Core) abundances reflect a transient situation, but not the local cloud conditions (Brown et al. 1988; Nejad et al. 1990, Willacy and Williams 1993). In this situation, some species formed in low temperature chemistry, such as HCN, HC 3 N, H 2 CO, are frozen-out in the mantle, to be released in the Hot Core phase, while other species, such as saturated molecules (H 2 O, NH 3, CH 3 OH, CH 3 CH 2 ON, and so on)

132 92 Chapter 3. Introduction to chemistry in molecular clouds that are difficult to form in pure gas-phase chemical reaction schemes, could be formed in high abundance in the cold collapsing cloud via surface reactions, to be later evaporated (Ohishi 1997). The mantle molecules are then liberated into a hot, dense and essentially neutral gas, because cosmic-ray ionisation is less efficient at high density. The hot gas is stable for time-scales of at least years (Millar 1997), until eventually these species are destroyed to form new species, some of which may also be very complex. In fact, the evaporation may not be abrupt. Viti and Williams (1999) have shown that the turn-on time for a star may be comparable to the age of a hot core, so that weakly bound molecules will be evaporated from ices before more strongly bound species. However, in order to explain the existence of heavy molecules in the gas phase in dense cores which show no evidence of star formation, and which may be relatively long-lived compared to the freeze-out time for heavy molecules, models have been made in which mantles are released efficiently and continuously into the gas (d Hendecourt et al. 1985). Several mechanisms have been proposed: The direct passage of heavy cosmic rays (e.g. Fe nuclei) through dust grains causes local heating, leading to the evaporation of weakly bound molecules such as CO (see Willacy and Williams 1993, and references therein). However, Léger et al. (1985) showed that only volatile mantle molecules would be ejected, while H 2 O, NH 3 and other polar molecules would not be removed from the mantles, and they should be almost totally frozen-out in dense, long-lived quiescent regions. The heating effect may be localized at a hotspot on the larger grains or may be distributed throughout small grains. The desorption efficiency is dependent on whether the heating is localized or affects the whole grain (Léger et al. 1985; Willacy, Rawlings and Williams, 1994). The rate of desorption by cosmic ray heating is R crh = πa 2 n g φm s (CO) cm 3 s 1, (3.40) where a is the grain radius, n g is the number density of dust grains, φ is the evaporation rate (φ = 70 molecules cm 2 s 1 (Léger et al. 1985), and M s (i) is the fraction of the mantle consisting of species i (Willacy, Rawlings and Williams, 1994).

133 3.3. Grain chemistry 93 As we have seen in Section 3.2.9, cosmic-ray-induced photodesorption results from the process in which H 2 is excited by energetic electrons released in the cosmic ray ionization of H 2 (Prasad and Tarafdar 1983). The resulting UV radiation field can dissociate molecules in the mantle ice, particularly H 2 O (Hartquist and Williams 1990). The dissociation products (especially the energetic H atoms) can heat their vicinity leading to desorption from a hotspot (Hartquist and Williams 1990). This mechanism is not selective, and all mantle species may be desorbed (Willacy, Rawlings and Williams 1994), although the photodissociation products (especially OH) can only be lost from the mantle if the dissociation takes place in the outermost layers of the mantle, giving a yield per UV photon of 0.1 (Hartquist and Williams 1990). The rate of photoinduced desorption, of a species i is given by R crpd = πa 2 n g Y F p M s (i) cm 3 s 1, (3.41) where F p is the photon flux, and Y the yield per photon. Hartquist and Williams (1990) give the ratio of the desorption rate to the rate at which heavy molecules stick to grains as ( ) 1 X ( n ) ( ) ζ cm s 1 (3.42) where X is the fractional abundance of heavy species in the gas phase. Thus, the freeze-out of of molecules may be expected to dominate photodesorption in cloud interiors, for densities greater than 10 3 cm 3. Exothermic mantle reactions, such as the formation of H 2, can result in a local hotspot heating of the grain mantle (Willacy, Williams and Duley 1994, Duley and Williams 1993), which may be sufficient to desorb thermally any molecules in the area which have a very low binding energy, such as CO or N 2. This mechanism may be highly efficient while the H atom abundance is sufficiently high, because each formation event could be capable of desorbing several molecules. The desorption rate of a species i is given by R hf = ɛr H2 M s (i) cm 3 s 1, (3.43) where ɛ is the desorption factor, which is a measure of how many molecules are returned to the gas phase by the process, and R H2 is the rate of formation of H 2 on grains (Willacy, Rawlings and Williams 1994). Although the value of ɛ is uncertain, even at low efficiencies, ɛ 0.01, the desorption rate is significantly

134 94 Chapter 3. Introduction to chemistry in molecular clouds larger than the freeze-out rate in molecular clouds for the molecules affected by this mechanism, and the effects of freeze-out in the gas-phase species can be postponed until many times the nominal freeze-out time. If ɛ > 3 ices may not accumulate because desorption can dominate freeze-out. Willacy, Williams, and Duley (1994), in a detailed study of this mechanism in quiescent dark clouds, found that for values of ɛ greater than about 0.01, this process is at least as important as the two cosmic-ray-induced mechanisms discussed above, even if the desorption is limited to those molecules with binding energies less than or equal to that of CO, such as N 2, C 2, O 2 and NO. Table 3.3: Interstellar ice composition and evaporation temperatures. From van Dishoeck and Hogerheijde (1999) Species Abundance a T ev b (K) H 2 O CO CO CH CH 3 OH 4 80 XCN 2? OCS NH N O 2 < a Abundances are relative to H 2 O = 100, and refer to NGC 7538 IRS9 (Whittet et al., 1996). Abundances are variable from source to source dut to differential outgassing and thermal processing. The H 2 O abundance is typically 10 4 with respect to H 2. b Evaporation temperatures for pure ices under interstellar conditions. There are other mechanisms of desorption which may come into operation in special circumstances: Thermal effects near bright stars. Although thermal evaporation is effective only at higher temperatures once the star has formed, T d > 20 K (van Dishoeck and Blake 1998), the ice mantles formed in cold pre-stellar and collapse phases can be heated by the young star. This leads to the restructuring of the ice

135 3.4. Initial gas phase reactions 95 matrix and outgassing when the temperature is near its sublimation point (van Dishoeck and Hogerheijde 1999). In Table 3.3 there is a summary of the sublimation temperatures of various species under interstellar conditions (van Dishoeck and Hogerheijde 1999; Sandford and Allamandola 1993). Since interstellar ices are not pure, but composed of mixed ices, the evaporation of each component is largely determined by its own sublimation behavior, unless the abundance of one of the species is less than 5%. Grain-grain collisions may play a role if stored radicals, which may be produced by UV photolysis, are present in the ice. This process is also only effective for volatile molecules, but not for H 2 O- and CH 3 OH-rich ices which contain strong hydrogen bonds (Langer et al. 2000). Grain-grain collisions or sputtering in interstellar shocks may erode or destroy the mantles, and even possibly the refractory cores (Tielens et al. 1994). Thus, these processes modify the abundance and size distribution of the dust and make an important contribution to gas phase processes in the shock. For instance, the presence of charged grains in MHD C-type shocks can form an additional fluid which contributes to the ion-neutral drag and may modify the shock structure. These effects may become pronounced in dense clouds, where the ionization is low and dust grains are the dominant charge carriers (Pilipp et al. 1990). 3.4 Initial gas phase reactions To complete the review of chemistry in interstellar clouds, we will briefly describe some of the reactions that initiate the synthesis of molecular species. Additionally, we will gain some insight into the complexity of the chemistry that takes place in dense interstellar clouds. The primary ionization step in the ion-molecule chemistry of dense interstellar clouds is caused by the collisions of cosmic rays with the abundant ambient molecular hydrogen to produce H + 2. H 2 + cosmic rays H e (3.44)

136 96 Chapter 3. Introduction to chemistry in molecular clouds The H + 2 ion reacts immediately with ubiquitous H 2 H H 2 H H (3.45) to yield the H + 3 molecule, which is a reactive, yet stable, species of great importance in the chemistry of dense clouds since it can react with many of the atomic species assumed to be present in the initial chemical stages of the dense cloud gas via proton transfer processes. Another important ionization is caused by the collisions of cosmic rays with atomic helium to produce He +. Helium ions are particularly important in dissociative ionization of stable molecules such as CO and H 2. Oxygen chemistry The reaction of H + 3 with O provides an entry route into the oxygen chemistry. H O OH + + H 2 (3.46) followed by OH + + H 2 OH H (3.47) OH H 2 H 3 O + + H (3.48) Another entry route into the oxygen chemistry is made from H + ions, also produced by collisions with cosmic rays. Since the ionization potentials of H and O are almost exactly equal, the charge transfer between protons and oxygen H + + O H + O + (3.49) provides an efficient entry into the chemistry of oxygen-bearing molecules. This reaction is the source of O + ions and the most important loss route for protons (Duley and Williams 1984). Dissociative recombination of H 3 O + results in OH and H 2 O H 3 O + + e OH + H 2 (3.50) H 3 O + + e H 2 O + H (3.51) H 2 O is a stable neutral species, and can only be destroyed by ion-molecule reactions. On the other hand, OH, a reactive radical, can be destroyed by neutral-neutral reactions such as OH + O O 2 + H (3.52)

137 3.4. Initial gas phase reactions 97 ζ 0 H + 2 H 2 H + 3 O H, H 2 H 2 OH + H 2 O + H 2 H 3 O + ζ 0 + H H O O + H 2 + H e e ν e + HCO OH HCO + 2 H 2 + H H + 3 e,c H + 3 e OH + CO CO CO 2 H C + C + C ν ν, H + C O OH O 2 O + 2 C ν ν H + 3 H 2 H 2 O, e O O 2 H + + C + HCO Figure 3.3: A simplified version of oxygen chemistry and its coupling with carbon chemistry (after Prasad et al. 1987) which gives a formation route for O 2. The OH radical also leads to the formation of CO via reactions with C + OH + C + CO + + H (3.53) CO + + H CO + H + (3.54) or to the formation of CO 2 via reaction with CO OH + CO CO 2 + H (3.55) The important ion HCO + can be formed via the reactions CO + + H 2 HCO + + H (3.56) H 2 O + C + HCO + + H (3.57) In dense clouds, CO is then mainly produced from HCO + ions HCO + + e CO + H (3.58) HCO + + C CO + CH + (3.59) Figure 3.3 shows a simplified scheme of the more important reactions in the oxygen chemistry family.

138 98 Chapter 3. Introduction to chemistry in molecular clouds Carbon chemistry The initial reactions in the carbon chemistry, and hydrocarbon production, can be made via the reactions C + H + 3 CH + + H 2 (3.60) which quantum chemical calculations show that it has no barrier (Herbst and Millar 1991), or through the radiative association reaction (Black and Dalgarno 1977) C + + H 2 CH hν (3.61) Once CH + or CH + 2 are formed, a sequence of H-atom transfer reactions with molecular hydrogen followed by dissociative recombination reactions lead to the formation of CH 4 and less saturated single carbon atom hydrocarbons CH + H 2 CH + H 2 2 CH + H 2 3 CH + 5 (3.62) CH e CH 4 + H (3.63) or CH CO CH 4 + HCO + (3.64) which provides another formation route for HCO +. Figure 3.4 shows a scheme of the most relevant reactions in carbon chemistry and its coupling to the oxygen chemistry. Nitrogen chemistry Helium ions provide an entry route to the chemistry of nitrogen-bearing molecules. As the ionization potential of nitrogen, 14.5 ev, is quite different from that of hydrogen, the charge transfer between H and N does not occur. dissociative ionization of N 2 with He + ions However, the N 2 + He + N + N + + He (3.65) can be an important source of N + ions, which, when thermalized, follow the sequence N + H 2 NH + H 2 NH + 2 H 2 NH + 3 H 2 NH + 4 (3.66) These ions can produce NH 3, NH 2, NH, via dissociative recombination reactions (Herbst and Klemperer 1973).

139 3.4. Initial gas phase reactions 99 C H + 3 e, ν ν + C e ν He + CO e H H ν 2 O ν ν C + CH CH + e H 2 CH C O H + ν, ν C + H ν, 2 H e ν C 2 C + HCO + O, O 2 CH + e 3 CH + e C 2 C 2 H 2 O CO CO H 2 M ν H 2 ν H 2 e CH + 5 H H 2 CH + 4 e e H + 3 CH 3 CH 4 + C ν + C 2 H 2 O + HCO e e C 2 H CO + C C 3 + O + C H 2 CO e H + 3 H 3 CO + Figure 3.4: A simplified version of carbon chemistry and its coupling with oxygen chemistry (after Prasad et al. 1987) N 2 H + N + H 2 NH + H 2 NH + 2 H 2 NH + 3 H 2 NH + 4 e + ζ H He + e,h e 0 3 e e e e C + e He + H + + ν ν ν 3, HCO N 2 N NH NH 2 NO,NH NH 3 e C + CH ν CN + + C + C N H 2 C 2 C 2 + N N CN e C 2 N + N + C N ν e e HCN N H + 3 e H + 3 N HCN + N C H + 2 H 2 CN + N C H + 3 C 2 + H C 2 + H 2 Figure 3.5: A simplified version of nitrogen chemistry and its coupling with carbon chemistry (after Prasad et al. 1987)

140 100 Chapter 3. Introduction to chemistry in molecular clouds An alternative entry into the nitrogen chemistry is also possible based on H + 3 and N atoms N + H + 3 NH H (3.67) followed by the previous sequence. However, the viability of this reaction has been largely discounted in favor of the previous mechanism (Huntress 1977) on the basis that reactions of H + 3 invariably proceed by proton transfer and not H + 2 transfer. Therefore, and because no laboratory measurement were available, this reactions has usually not been considered by modelers. However, Scott et al. (1997) have measured this reaction recently in the laboratory at room temperature. They have found it is sufficiently fast (k = cm 3 s 1 ) to provide a larger source of NH 3 in dense interstellar clouds at 10 K than the previous established mechanism. Finally, although the effects of cosmic rays over the major molecular constituents occur indirectly via reaction with H + 3 or He +, rather than direct ionization, a third entry route to nitrogen chemistry comes from the ionization of N atoms or N 2 molecules by cosmic rays. The reactions of nitrogen atoms with NH + and NH + 2 reaction ions, as well as the neutral NH + N H + N 2 (3.68) initiates the synthesis of N N bonds in molecules and ions (Prasad and Huntress 1980). In this way, the reaction N 2 + H + 3 N 2 H + + H 2 (3.69) yields the N 2 H + ion, widely used in the studies of dense molecular cores. At higher densities, the reaction N 2 H + + CO N 2 + HCO + (3.70) becomes competitive, and is the main depletion route for N 2 H + (Herbst et al. 1975). Similarly, the neutral reactions OH + N NO + H (3.71) NH + O NO + H (3.72) and the reactions NH O HNO + + H (3.73) NH O HNO + + H 2 (3.74)

141 3.4. Initial gas phase reactions 101 N, N + e He + N 2 H + H 2 He + e, CO H + 3 H He + N + N + 2 NH N H 2 NH N N 2 + NH 2 OH O N e NO N ν C + H + S + H + 3 e, CO HNO + O O N + NH 3 H 2 NO + H 2 O + CO Figure 3.6: A simplified version of nitrogen chemistry and its coupling with oxygen chemistry (after Prasad and Huntress 1980) initiate the formation of species containing N O bonds (Prasad and Huntress 1980). C N bond molecules can be formed with the inclusion of atomic nitrogen at each step of the rapid C + CH + 3 CH 2, CH 3 chain: CH + + N CN + + H (3.75) CH N HCN + + H (3.76) or via the reaction of the NH and NH 2 radicals with C + (Prasad and Huntress 1980) NH + C + CN + + H (3.77) NH 2 + C + HCN + + H (3.78) Figures 3.5 and 3.6 show the main chemical reactions involved in nitrogen chemistry coupled to carbon and oxygen chemistry. Synthesis of complex species The detection of large and complex molecules in dense interstellar clouds indicate that the synthesis of complex hydrocarbon neutrals and ions is basic to our understanding of the chemistry of organic molecules, because hydrocarbons are the

142 102 Chapter 3. Introduction to chemistry in molecular clouds simplest organic species and because the synthesis of other families of molecules, such as cyanopolyynes require hydrocarbons as precursors. The gas phase synthesis of hydrocarbons can generally proceed via three major pathways: carbon insertion reactions, condensation reactions, and radiative association between small hydrocarbon ions and neutrals (Herbst 1987). Carbon insertion reactions (Herbst 1983) involve C + ions and C atoms with smaller hydrocarbon neutrals and ions respectively. The ionic products of these reactions will subsequently react with H 2 if possible, or via dissociative recombination reactions with electrons or by reaction with heavy neutral species (Herbst and Millar 1991). Some examples are: C + + CH 4 C 2 H H 2 (3.79) C 2 H H 2 C 2 H H (3.80) C 2 H e C 2 H 2 + H (3.81) C + + C 2 H 2 C 3 H + + H (3.82) This mechanism is the most efficient for the production of some very unsaturated hydrocarbons, but does not lead to the production of more saturated species, because hydrocarbon ions with more than one carbon atom tend not to react rapidly with H 2, unless they are very unsaturated (Herbst and Leung 1989). To illustrate this point, these authors show that while the initial hydrogenation step C + n + H 2 C n H + + H (3.83) is efficient for n=5 through n=8, the second hydrogenation reaction C n H + + H 2 C n H H (3.84) does not appear to occur for n =5, 7, and 9. Those hydrocarbons not produced via carbon insertion can be synthesized by condensation reactions involving smaller hydrocarbons and neutrals, followed by dissociative recombination reactions (Mitchell and Huntress 1979). This route can lead to more saturated hydrocarbons. Some well studied condensation reactions are (Herbst and Millar 1991): CH CH 4 C 2 H H 2 (3.85) C 2 H C 2 H 2 C 4 H H (3.86)

143 3.4. Initial gas phase reactions C H 2 CH 2 + C 2 H 2 H 2 CH 3 + CH 3 + H 2 C 2 H 3 + e C 2 H 2 + C C 3 H + H 2, CH 4 C 3 H 3 + C C 4 H 2 + CH 5 + H 2 e CH 4 + C e H C 2 H 3 C H 2 H 2 e e CH 4 + e CH 3 + C C 2 H 2 + H 2 C 2 H 4 + C C 3 H 2 + C C 4 H CH 3 e e C 3 H 2 N C 2 H 4 C 2 H C 3 H C C 3 H 3 CN, HCN N C 3 N N e + HCO N e HC 3 NH + H 2 HC 3 N + N HC 3 N HCN CN Figure 3.7: A basic hydrocarbon-hc 3 N chemistry scheme (after Turner et al. 2000) As the reacting species get larger, radiative association reactions become more important (Field, Adams and Smith 1980; Herbst 1980; Herbst and Leung 1989; Herbst and Millar 1991), such as C 4 H C 2 H 2 C 6 H hν (3.87) However, the reaction rates of these reactions have to be large, if they have to compete with condensation reactions. Cyanopolyynes, which are linear organo-nitrogen species with structure following HCC n CN, are probably the most important non-hydrocarbon family of complex interstellar molecules. Herbst and Leung (1990) found a fast route of synthesis if neutral-neutral reactions between the CN radical and neutral hydrocarbons occur rapidly at low temperature. Then the reaction CN + H 2 C 2 HC 3 N + H (3.88) dominates at higher densities. There is also another route via reaction of N atoms with hydrocarbons which dominates at lower densities N + C 3 H 2 HC 3 N + H (3.89)

144 104 Chapter 3. Introduction to chemistry in molecular clouds In general, the cyanopolyynes are formed by N + C n H + m HC 3 N + H (3.90) or C n H 2 + CN HC n CN + H (3.91) Turner et al. (2000). A basic scheme of the hydrocarbon-hc 3 N chemistry is shown in figure 3.7.

145 Bibliography Adams N. G., Herd C. R., Geoghegan M., et al., 1991, Journal of Chemical Physics, 94, 4852 Adams N. G., Smith D., 1983, in Fontijn A., Clyne M. A. A., eds., Reactions of Small Transient Species. Academic Press, London, p. 311 Adams N. G., Smith D., Clary D. C., 1985, The Astrophysical Journal, 296, L31 André P., 1994, in Montmerle Th., Lada Ch. J., Mirabel I. F., Trân Thanh Vân J., eds., The Cold Universe. Editions Frontières, Gif-sur-Yvette, p. 179 Bates D. R., Herbst E., 1988, in Millar T. J. and Williams D. A., eds., Rate Coefficients in Astrochemistry. Kluwer, Dordrecht, p. 17 Bernstein M. P., Sandford S. A., Allamandola L. J., Chang S., Scharberg M. A., 1995, The Astrophysical Journal, 454, 327 Bettens R. P. A., Lee H.-H., Herbst E., 1995, The Astrophysical Journal, 443, 664 Black J. H., 1987, in Hollenbach J. and Thronson H. A., eds., Interstellar Processes. Reidel, Dordrecht, p. 731 Black J. H., Dalgarno A., 1977, The Astrophysical Journal Supplement Series, 34, 405 Boissé P., 1990, Astronomy and Astrophysics, 228, 483 Brown P. D., Charnley S. B., 1990, Monthly Notices of the Royal Astronomical Society, 244, 432 Brown P. D., Charnley S. B., Millar T. J., 1988, Monthly Notices of the Royal Astronomical Society, 231,

146 106 BIBLIOGRAPHY Canosa A., Rowe B. R., Mitchell J. B. A., Gomet J. C., Rebrion C., 1991, Astronomy and Astrophysics, 248, L19 Caselli P., Hasegawa T. I., Herbst E., 1993, The Astrophysical Journal, 408, 548 Ciolek G. E., Mouschovias T. Ch., 1993, The Astrophysical Journal, 418, 774 Clary D. C., 1985, Molecular Physics, 54, 605 Clary D. C., Dateo C. E., Smith D., 1990, Chemical Physical Letters, 167,1 Cravens T. E., Dalgarno A., 1978, The Astrophysical Journal, 219, 750 Dalgarno A., Browne J. C., 1967, The Astrophysical Journal, 149, 231 Dalgarno A., McCray R. A., 1972, Annual Review of Astronomy and Astrophysics, 10, 375 Dalgarno A., McCray R. A., 1973, The Astrophysical Journal, 181, 95 de Graauw Th., Whittet D. C. B., Gerakines P. A., et al., 1996, Astronomy and Astrophysics, 315, L345 de Jong T., 1972, Astronomy and Astrophysics, 20, 263 d Hendecourt L. B., Allamandola L. J., Baas F., Greenberg J. M., 1982, Astronomy and Astrophysics, 109, L12 d Hendecourt L. B., Allamandola L. J., Greenberg J. M., 1985, Astronomy and Astrophysics, 152, 130 d Hendecourt L. B., Jourdain de Muizon M., 1989, Astronomy and Astrophysics, 223, L5 Duley W. W., Williams D. A., 1984, Interstellar Chemistry, Academic Press, London Duley W. W., Williams D. A., 1993, Monthly Notices of the Royal Astronomical Society, 260, 37 Field D., Adams N. G., Smith D., 1980, in Andrew B. H., ed., Interstellar Molecules. Reidel, Dordrecht, p. 289 Galloway E. T., Herbst E., 1989, Astronomy and Astrophysics, 211, 413

147 BIBLIOGRAPHY 107 Gerakines P. A., Schutte W. A., Ehrenfreund P., 1996, Astronomy and Astrophysics, 312, 289 Graff M. M., 1989, The Astrophysical Journal, 339, 239 Gredel R., Lepp S., Dalgarno A., 1987, The Astrophysical Journal, 323, L137 Gredel R., Lepp S., Dalgarno A., Herbst E., 1989, The Astrophysical Journal, 347,289 Gürtler J., Henning Th., Kömpe C., Pfau W., Krätschmer W., Lemke D., 1996, Astronomy and Astrophysics, 315, L189 Hartquist T. W., Williams D. A., 1990, Monthly Notices of the Royal Astronomical Society, 247, 343 Henning K., 1981, Astronomy and Astrophysics Supplement Series, 44, 405 Henning Th., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 343 Herbst E., 1980, in Andrew B. H., ed., Interstellar Molecules. Reidel, Dordrecht, p. 317 Herbst E., 1981, Nature, 289, 656 Herbst E., 1983, The Astrophysical Journal Supplement Series, 53, 41 Herbst E., 1985, The Astrophysical Journal, 291, 226 Herbst E., 1987, in Hollenbach D. J. and Thronson H. A., eds., Interstellar Processes. Reidel, Dordrecht, p. 611 Herbst E., Bates D. R., 1988, The Astrophysical Journal, 329, 410 Herbst E., Bohme D. K., Payzant J, D., Schiff H, I., 1975, The Astrophysical Journal, 201, 603 Herbst E., Klemperer W., 1973, The Astrophysical Journal, 185, 505 Herbst E., Knudson S., 1981, The Astrophysical Journal, 245, 529 Herbst E., Lee H.-H., Howe D, A., Millar T, J., 1994, Monthly Notices of the Royal Astronomical Society, 268, 335

148 108 BIBLIOGRAPHY Herbst E., Leung C. M., 1989, The Astrophysical Journal Supplement Series, 69, 271 Herbst E., Leung C. M., 1990, Astronomy and Astrophysics, 233, 177 Herbst E., McEwan M. J., 1990, Astronomy and Astrophysics, 229, 201 Herbst E., Millar T. J., 1991, in James R. A. and Millar T. J., eds., Molecular Clouds. Cambridge University Press, Cambridge, p. 209 Herd C. R., Adams N. G., Smith D., 1990, The Astrophysical Journal, 349, 388 Huntress W. T., 1977, The Astrophysical Journal Supplement Series, 33, 495 Iglesias E., 1977, The Astrophysical Journal, 218,697 Jones A. P., Tielens A. G. G. M., 1994, in Montmerle Th., Lada Ch. J., Mirabel I. F., Trân Thanh Vân J, eds., The Cold Universe. Editions Frontières, Gif-sur-Yvette, p. 35 Jones A. P., Tielens A. G. G. M., Hollenbach D. J., McKee C. F., 1994, The Astrophysical Journal, 433, 797 Lacy J. H., Baas F., Allamandola J. L., et al., 1984, The Astrophysical Journal, 276, 533 Langer W. D., van Dishoeck E. F., Bergin E. A., Blake G. A., Tielens A. G. G. M., et al., 2000, in Mannings V., Boss A. P., and Russell S. S., eds., Protostars and Planets IV. University of Arizona Press, Tucson, p. 29 Léger A., Jura M., Omont A., 1985, Astronomy and Astrophysics, 144, 147 Leitch-Devlin M. A., Williams D. A., 1985, Monthly Notices of the Royal Astronomical Society, 213, 295 Levine R. D., Bernstein R. B., 1974, Molecular Reaction Dynamics, Oxford University Press Liao Q., Herbst E., 1995, The Astrophysical Journal, 444, 694 Leung C. M., Herbst E., Huebner W. F., 1984, The Astrophysical Journal Supplement Series, 56, 231 Mathis J. S., 1990, Annual Review of Astronomy and Astrophysics, 28, 37

149 BIBLIOGRAPHY 109 Millar T. J., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 75 Millar T. J., Farquhar P. R. A., Willacy K., 1997, Astronomy and Astrophysics Supplement Series, 121, 139 Mitchel J. B. A., 1990, Physics Reports, 186, 215 Mitchell G. F., Huntress W. T., 1979, Nature, 278, 722 Mundy L. G., McMullin J. P., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 183 Nejad L. A. M., Williams D. A., Charnley S. B., 1990, Monthly Notices of the Royal Astronomical Society, 246, 183 Noh H., Vishniac E. T., Cochran W. D., 1991, The Astrophysical Journal, 383, 372 Norman C., Silk J., 1980, The Astrophysical Journal, 238, 158 O Donnell E. J., Watson W. D., 1974, The Astrophysical Journal, 191, 89 Ohishi M., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 61 Ossenkopf V., Henning Th., 1994, Astronomy and Astrophysics, 291, 943 Péquignot D., Petitjean P., Boisson C., 1991, Astronomy and Astrophysics, 251, 680 Petrie S., 1996, Monthly Notices of the Royal Astronomical Society, 282, 807 Petrie S., Herbst E., 1997, The Astrophysical Journal, 491, 210 Pilipp W., Hartquist T. W., Havnes O., 1990, Monthly Notices of the Royal Astronomical Society, 243, 685 Prasad S. S., Huntress W. T., 1980, The Astrophysical Journal Supplement Series, 43, 1 Prasad S. S., Tarafdar S. P., 1983, The Astrophysical Journal, 267, 603 Prasad S. S., Tarafdar S. P., Villere K. R., Huntress W. T., 1987, in Hollenbach J. and Thronson H. A., eds., Interstellar Processes. Reidel, Dordrecht, p. 631 Sandford S. A., Allamandola L. J., 1993, The Astrophysical Journal, 417, 815

150 110 BIBLIOGRAPHY Schmeltekopf A. L., Fehsenfeld F. C. Ferguson E. E., 1967, The Astrophysical Journal, 148, L155 Schmitt W., Henning T., Mucha R., 1997, Astronomy and Astrophysics, 325, 569 Schutte W. A., Allamandola L. J., Sandford S. A., 1993, Science, 104, 118 Scott G. B. I., Freeman C. G., McEwan M. J., 1997, Monthly Notices of the Royal Astronomical Society, 290, 636 Skinner C. J., Tielens A. G. G. M., Barlow M. J., Justtanont K., 1992, The Astrophysical Journal, 399,L79 Smith I. W. M., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer, Dordrecht, p. 259 Spitzer L., 1978, Physical Processes in the Interstellar Medium. New York, Wiley- Interscience Spitzer L., Tomasko M. G., 1968, The Astrophysical Journal, 152, 971 Sternberg A., Dalgarno A., Lepp S., 1987, The Astrophysical Journal, 320, 676 Stief L. J., Donn B., Glicker S., Gentieu E. P., Mentall J. E., 1972, The Astrophysical Journal, 171, 21 Tielens A. G. G. M., 1998, The Astrophysical Journal, 499, 267 Tielens A. G. G. M., Allamandola L. J., 1987, in Hollenbach D. and Thronson H., eds., Interstellar Processes. Reidel, Dordrecht, p. 397 Tielens A. G. G. M., McKee C. F., Seab C. G., Hollenbach D. J., 1994, The Astrophysical Journal, 431, 321 Tielens A. G. G. M., Whittet D. C. B., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 45 Turner B. E., Herbst E., Terzieva R., 2000, The Astrophysical Journal Supplement Series, 126, 427 van Dishoeck E. F., Black J. H., 1986, The Astrophysical Journal Supplement Series, 62, 109

151 BIBLIOGRAPHY 111 van Dishoeck E. F., Black J. H., 1988, The Astrophysical Journal, 334, 771 van Dishoeck E. F., Blake G. A., 1998, Annual Review of Astronomy and Astrophysics, 36, 317 van Dishoeck E. F., Hogerheijde M. R., 1999, in Lada C. J. and Kylafis N. D., eds., The Origin of Stars and Planetary Systems. Kluwer Academic Publishers, p. 97 Verner D. A., Ferland G. J, 1996, The Astrophysical Journal Supplement Series, 103, 467 Viti S., Williams D. A., 1999, Monthly Notices of the Royal Astronomical Society, 305, 755 Wagenblast R., 1992, Monthly Notices of the Royal Astronomical Society, 259, 155 Watson W. D., 1978, Annual Review of Astronomy and Astrophysics, 16,585 Whittet D. C. B., 1993, in Millar T. J. and Williams D. A., eds., Dust and Chemistry in Astronomy. IoP, Bristol, p. 9 Whittet D. C. B., Duley W. W., 1991, Astronomy and Astrophysics Review, 2, 167 Whittet D. C. B., Schutte W. A., Tielens A. G. G. M., et al., 1996, Astronomy and Astrophysics, 315, L357 Willacy K., Rawlings J. M. C., Williams D. A., 1994, Monthly Notices of the Royal Astronomical Society, 269, 921 Willacy K., Williams D. A., 1993, Monthly Notices of the Royal Astronomical Society, 260, 635 Willacy K., Williams D. A., Duley W. W., 1994, Monthly Notices of the Royal Astronomical Society, 267, 949 Williams D. A., 1991, in James R. A. and Millar T. J., eds., Molecular Clouds. Cambridge University Press, Cambridge, p. 295 Ziurys L. M., 1990, in Blitz L., ed., The Evolution of the Intestellar Medium. ASP Conf. Ser., 12, San Francisco, p. 229

152 112 BIBLIOGRAPHY

153 Chapter 4 Modeling the chemistry in interstellar clouds In chapter 3, we have shown several types of chemical reactions that can take place in the interstellar medium, some chemical rate equations and the reaction rates associated with them. After making some assumptions and simplifications, some conclusions can be drawn from these equations and some predictions on the resulting chemistry can be made (see e.g. Duley and Williams 1984; Herbst 1987; Herbst and Millar 1991). Some examples could be that nearly all hydrogen in dark clouds will be in the form of hydrogen molecules, or that CO should be an abundant molecule. However, it is difficult to go any further and, for instance, explain in detail what the individual molecular abundances will be. Thus, in order to make a substantial progress in the understanding of the chemistry of molecular clouds, we have to step away from simplifying assumptions. The chemistry has to be made as full as possible, so that the destruction and formation rates for all relevant species are established, and it must be studied under conditions appropriate to interstellar clouds. The immediate consequence is that the modeling grows fast in complexity, as even the simpler schemes involve many different species and an even greater number of reactions in which these species participate. The modeling of the chemistry of interstellar clouds, and in particular dense molecular clouds, seeks to identify the species that might be present in the interstellar medium, the chemical routes that are involved in the formation and destruction of these species, and the processes that are significant in the regimes that are being 113

154 114 Chapter 4. Modeling the chemistry in interstellar clouds Table 4.1: Processes, and mechanisms involved, found in astrochemistry process mechanism timescale (yr) ion mol chemistry cosmic ray ionization (10 17 /ζ) cooling molecular radiation (at 10 K) collapse gravity 10 8 /n 1/2 ambipolar diffusion ion neutral drift X(i)/10 8 freeze-out on dust gas grain collision /n desorption surface chemistry /n(h) ζ is the cosmic ray ionization rate of hydrogen, s 1 ; n = n(h) + 2n(H 2 ) cm 3 is the total density of hydrogen nuclei; n(x) is the number density of species X; and X(i) = n(ions)/n. described, in order to gain meaningful information about the physical conditions of the regions where these species exist. From the point of view of astrophysics, some regions where molecules are formed are interesting particularly because they are the sites of star formation. However, we are immediately faced with several important difficulties, which we should bear in mind when we try to model the chemistry of interstellar clouds. The first one is to choose among the several processes that take place in the interstellar medium related to astrochemistry, and to identify which of them is significant in the regime we intend to describe. As it is often the case, this regime may be timedependent and dynamically evolving, which adds to the complexity of the problem. Table 4.1 sumarizes some of the main processes, and the mechanisms that produce them (Williams 1998). It is important to note the different timescales in which these processes take place, and their strong dependence on such physical parameters as the total density of hydrogen nuclei, n, the cosmic ray ionization rate of hydrogen, ζ, and the electron number density, n e. Then, we have to choose which chemical reactions are to be included in our model. Although the initiating chemistry might be clear, we have to remember that there are uncertainties associated to many reaction rate coefficients. Adding more species to the model, only exacerbates this problem. In spite of considerable efforts, both experimentally and theoretically, the number of rate coefficients that are merely

155 4.1. Gas-phase models 115 estimated is high (Herbst 1997). For instance, many of the rate coefficients for neutral neutral reactions will have to be estimated for the foreseeable future (Smith 1997) because of both experimental and theoretical difficulties. Therefore, these rates and especially their temperature dependence are subject to large uncertainties. Other sources of uncertainty lie in the determination of not only reaction rates, but also the primary reaction products, their internal energy and the dynamics of their formation (Alagia et al. 1997). In addition to the uncertainties concerning gas-phase reactions, the gas dust interaction has proven to be a poorly understood subject, which might play a key role in our interpretation of observational data and of our understanding of the physical situation (Williams 1998). Part of the uncertainty is in the composition of dust, but it is mainly due to the limited knowledge we have of surface processes themselves. These reasons explain the importance which has taken the study of surface reactions and solid state processes in later years (see Tielens and Whittet 1997; van Dishoeck and Hogerheijde 1999). 4.1 Gas-phase models The calculation of the abundances in star-forming regions requires a physical model in which the temperature, density, radiation field, and other physical variables are specified as functions of position and/or time. In their simplest form, two different classes of gas-phase models are usually considered: 1. Steady-state models, or depth-dependent, in which the abundances of molecules do not change with time, but are function of depth into the region. They are used, for instance, for models of the translucent outer envelopes, but they are generally not applied to the bulk of star-forming regions. 2. Time-dependent models, or depth-independent, in which the abundances are calculated as functions of time at a single position deep inside the cloud. Models of this category are models of dark pre-star-forming clouds or collapsing envelopes. The time scale for reaching chemical equilibrium ranges from 10 5 to 10 7 years, depending on the degree of ionization, temperature, density, and the species involved (van Dishoeck and Blake 1998).

156 116 Chapter 4. Modeling the chemistry in interstellar clouds The variety of physical parameters needed to define conditions in interstellar clouds is another source of difficulties for the modeling of the chemistry and the calculation of chemical abundances in dense clouds and YSOs. Some of these parameters are included in every model, such as the elemental abundances of C, O, N, metals...; and the primary cosmic ray ionization rate, ζ. Others depend on the class of model that is being considered. Thus, for steady state models, additional parameters are the geometry (e.g. spherical, plane-parallel); the interstellar radiation field incident on the cloud; the density, n = n(h)+2 n(h 2 ), as a function of position; the grain parameters, i.e. extinction curve, albedo and scattering function. Density and temperature may be obtained from the modeling or, alternatively, they may be constrained from observations and provided as additional input parameters (Duley and Williams 1984; van Dishoeck and Blake 1998). For time-dependent models, additional parameters are: the density as a function of time, and the visual extinction, A V, at the position in the cloud. The temperature can again be obtained from the thermal balance, but it is usually set at 10 K for both the gas and the dust, which is typical of a dark cloud shielded from ultraviolet radiation and heated by cosmic rays only. In these models, the ratios of the local concentrations are taken to be equal to the ratios of the column densities integrated over depth. It has to be noted that this procedure may lead to incorrect results for molecules such as radicals whose abundances do not peak in the center of the cloud, but in the outer part of the envelope. It should be noted that in some circumstances, e.g. the collapse of dense cores in star-formation, models must incorporate both space and time dependence. 4.2 Modeling the gas dust interaction The modeling of the interaction between the gas and grain chemistries has met with several difficulties which have afflicted attempts to model the chemistry occurring on interstellar grains: a poor understanding of the exact nature of the grain surfaces, limitations in our knowledge of surface chemistry at low temperatures, and problems in the actual modeling of time-dependent grain chemistry. The first two difficulties are being remedied by ISO observations and laboratory studies, but the third one still remains (Henning 1997; Schutte 1997).

157 4.2. Modeling the gas dust interaction 117 There are two main different approaches in the modeling of grain chemistry (Tielens and Whittet 1997): the accretion limited regime, which under most circumstances is theoretically more precise, where interstellar grain surface chemistry is usually limited by the rate at which reactive gases are transported to the surface, and the reaction limited regime where it is limited by surface reaction rates once the species are adsorbed. In the accretion limit (Tielens and Hagen 1982), successive reactive species sticking to a particular grain are likely to react with one another if at least one of them migrates on the grain rapidly enough to find its co-reactant before yet another reactive species is adsorbed. In this situation, rate coefficients describing the actual diffusive rate of adsorbed reactive species play a limited role, and the chemistry can be approximated by following the sticking of successive species to a grain using a Monte-Carlo method (see Shalabiea et al. 1998, and references therein). This approach has been established mainly for time-independent chemical models, but unfortunately it still has not been formulated for a time-dependent model of interstellar clouds. In the reaction limit (Hasegawa and Herbst 1993), the opposite holds true so that many reactive species are present on a grain surface and reaction is controlled by surface concentrations, as well as kinetic parameters. This approach to grain chemistry is more tractable, and makes use of rate equations analogous to those used for gas phase models. Time derivatives of concentrations of species on grains are set equal to the sums of rates of formation and destruction reactions plus adsorptions and desorption terms. The calculated abundances of species are averages, which are exact only in the limit in which large numbers of reactive species are present on each grain. However, this condition is usually not met under dark cloud conditions, since the accretion times are long, grains are small, and reactions are fast, so that at most one reactive species is present on a grain at a time. Most of the chemical models incorporating gas grain interactions have been formulated in the reaction limited regime because, unlike the Monte Carlo approach, this technique is easily implemented in time-dependent chemical models. More recently, Caselli et al. (1998) have attempted to modify the rate equations to take into account the shortcomings of the reaction limited approach. Shalabiea et al. (1998) discuss its consequences for the models.

158 118 Chapter 4. Modeling the chemistry in interstellar clouds 4.3 Setting up the equations Once we have chosen the physical model that better describes the conditions of the region we intend to study, we have to select the set of species, i.e. molecules, atoms and ions, that need to be included in order to explain the chemistry of the region. The criteria used in this selection has to take into account that each species is created and destroyed in several type of reactions: be it reacting with another species or by interaction with photons, cosmic rays or grains. Thus, we have to select the species we wish to study, the ones we have positive proof that are present in that region, plus other species that, although not detected yet, are probably present because they are closely related to the species already included, or the known reactions between them. Therefore, the selection of the species of our model implies establishing an usually large and complex chemical reaction network which rules the abundances of the species of our model Writing down the rate equations In general, all reactions other than cosmic ray ionization, photodissociation, and photoionization are regarded as two-body reactions. Grain surface reactions, in which the grain is the third body, are also described in terms of two-body reactions, since one incident atom striking a grain finds its reaction partner already on or in the grain surface. Then, if we have a molecule X formed by various reacting pairs A and B destroyed by reaction with various partners C A + B k AB X + Y, (4.1) X + C k XC D + E, (4.2) or destroyed by photodestruction X + hν β X products, (4.3) or if X is an ion formed from ionization by cosmic rays of species X X + c.r. ζ X X, (4.4)

159 4.3. Setting up the equations 119 the general rate equation for molecule X can be written as d dt n X = ζ X n X + A ( ) k AB n A n B k XC n C + β X n X (4.5) B C where all densities, n X, and all photodestruction rates, β X, are functions of position within the cloud. There is one equation of the type (4.5) for each of the N s species in the problem, atoms ions or molecules. In addition, there are several conservation equations for the important elements in the problem which have to be included. For instance, in the model used in chapters 5 and 6, we state mathematically that the number of atoms of a particular element, per unit volume, remain constant. For the element M, with number density in all forms n 0 M, there is an equation of the form n 0 M = i n i c M i (4.6) where c M i is the number of atoms of element M in the species i. Similarly, charge conservation gives n e = j n j c e j (4.7) where n e is the number density of electrons, and c e j is the charge (positive or negative) associated with species j. As it is, the problem is one of solving N s non-linear algebraic equations of the type (4.5) together with the element and charge conservation equations (4.6) and (4.7), and the density changes for all our species, n X. The time dependent solution of this equations by numerical means is a demanding exercise, because the equations are mathematically stiff, i.e. the solutions to these equations show major changes occurring in a short time scale. Solutions to stiff equations require sophisticated techniques, which are usually employed using computer programs. In our case, the calculations on time dependent chemistry have been made using the Gear method (Gear, 1971). The Gear method is an implicit, linear multistep method that utilizes variable time step and error control techniques to preserve the required accuracy during the integration.

160 120 Chapter 4. Modeling the chemistry in interstellar clouds Table 4.2: Example of reaction set reactants products α β γ 1 H H 2 H H H 4.67E H C CH ν 1.00E H CH C H E H CH C H H 6.00E H CH 2 CH H E H 2 e H e H 3.22E H 2 H 2 H H H E H 2 C CH 2 ν 1.00E H 2 cr H + 2 e 1.20E H 2 cr H H 1.30E NO crp NO + e 1.30E where ν represents photons, e electrons, cr cosmic rays, and crp cosmic-ray-induced photons Choosing the reaction set Having seen the general form of the equations that relate the several parameters of the chemical model, the next step is to select a reaction set, i.e. all the reactions between the species we have chosen and the processes that we consider take place in the region we are studying, specifying the reactants, products, and rate coefficent of each reaction. The reaction set that it is used in order to write down the system of differential equations (4.5) for each species is usually chosen from one of the published reaction databases for astrochemistry, such as the one we used in chapters 5 and 6: the UMIST database (Millar et al. 1997); or the New Standard Model for pure gas phase chemistry (Bettens et al. 1995; Herbst et al. 2000) later extended to cover surface chemistry (Ruffle and Herbst 2000, 2001). Table 4.2 shows a few rows from a typical reaction set: the reactant species, columns (2) and (3); the reaction products, columns (4) to (6); and three coeficients,

161 4.3. Setting up the equations 121 α, β and γ, columns (7) to (9). For each reaction, α, β and γ are used to calculate the rate coefficient, k, by different means: For two-body reactions, by k = α(t/300) β exp( γ/t ) cm 3 s 1 (4.8) where T is the gas temperature For direct cosmic-ray ionisation, by k = α s 1 (4.9) For interstellar photoreactions, by k = αexp( γa V ) s 1 (4.10) where α represents the rate in the unshielded interstellar ultraviolet radiation field, A V is the extinction at visible wavelengths caused by interstellar dust, and γ is the parameter used to take into account the increased extinction of dust at ultraviolet wavelengths For cosmic-ray-induced photoreactions, by k = αγ/(1 ω) s 1 (4.11) where ω is the grain albedo in the far ultraviolet (Gredel et al. 1989), α the cosmic-ray ionisation rate, and γ is the probability per cosmic-ray ionisation that the appropriate photoreaction takes place. Depending on the type of problem to be considered, some or all of these reactions can be included. As can be easily seen from reaction (4.8), the β coefficient indicates, for two body reactions, a temperature dependency of the reaction rate, either it goes faster or slower at different temperatures. On the other hand, the γ coefficient shows the existence of an activation barrier for the reaction, meaning that below this temperature the reaction will not take place. Thus, following these dependencies, if our physical model requires it, we can edit out from the reaction set those reactions which will surely not take place or which will be highly inefficient. For instance, reaction 42 of Table 4.2 has a high temperature activation barrier and will not

162 122 Chapter 4. Modeling the chemistry in interstellar clouds Table 4.3: Fractional elemental abundances relative to n H, referred to a dark or a diffuse cloud model (Ruffle et al., 1998). A dark B diffuse He C N O S Si M (a) (a) Low ionization potential metals, such as sodium and magnesium probably take place when modeling dense cores of the interstellar medium, where we usually assume temperatures 10 K. However, with the speed of modern computers it is not much more costly to compute a chemical model with all the reactions of the rate file, and having experienced that reactions previously thought to possess activation energies do not and vice versa, it is usual to include the whole reaction set. In any case, the reaction network should be chemically closed, i.e. each molecule formed should also be destroyed Running the model Once we have build our reaction set, the model can be run. The code starts with an initial set of conditions in the model cloud, as density, visual extinction, elemental abundance, and ionization rates. Given these initial conditions and the library of reactions, the program determines the appropriate chemical production and loss mechanisms, and starts the time-dependent solution. As the solution proceeds, the production and loss mechanisms are updated at pre-established times, at which we can obtain a full chemical status report, and the most important production and loss mechanisms, and their relative contribution, for each species included.

163 4.3. Setting up the equations 123 The elements usually chosen to initiate the chemistry when modeling the gas phase of the interstellar medium are those with higher relative cosmic abundances: H, He, C, O, N and S. Depending on the complexity of the model or of the chemical network selected, other elements may be included, such as a P or Si, or reference metals as Mg or Na. We also have to impose the form in which these elements are initially found. For instance, H might be partly in atomic form and partly in molecular form. Depending on the model, some elements such as C and S might be completely ionized, while the rest might be in neutral form. Alternatively, we can start with some molecules apart from H 2 already formed. As an example, Table 4.3 shows different initial fractional abundances depending if we start with a typical dark or a diffuse cloud model. In any case, we could first let our system evolve until it achieves chemical equilibrium before applying other physical actions, such as collapse of the cloud, the arrival of high velocity shocks, or the ignition of external/internal sources of radiation. Some elements might be given an initial abundance clearly apart from the relative cosmic abundance value. One such element, as we shall see in chapter 5, is sulphur, which is often presented in a depleted form, in order to be able to explain the observed abundances of some of the molecules which contain it, such as the CS, SO or SO 2 molecules, the abundances of which are linearly dependent with the initial elemental sulphur abundance, or to reproduce observed abundances of other species (Caselli et al. 1994). Of course, elements such as carbon and silicon that compose the refractory (i.e. non-ice) grains must also be significatnly depleted from the gas. It is then assumed that, for some reason, elemental sulphur is heavily depleted by two or more orders of magnitude in relation to elemental carbon, oxygen and nitrogen in some regions of the interstellar medium (Ruffle et al. 1999). The depleted sulphur is generally assumed to be locked up in icy grain mantles. Metal abundances also differ depending the cloud conditions that are being considered. It is generally accepted that high elemental metal abundances are more appropriate for diffuse cloud gasphase chemistry, whereas low elemental metal abundances are more suited for dense cloud chemistry (Nejad and Wagenblast 1999). The differences between the sulphur and metal abundances are important, as both significantly affect the ionization structure of the cloud. As we have mentioned in section 3.2.8, the value of the cosmic-ray ionization rate, ζ, is not well determined, and it is usually taken as a free parameter of the model. The effects this has on the final abundances of molecules might give some indication

164 124 Chapter 4. Modeling the chemistry in interstellar clouds 10 7 (a) 10 7 (b) log[n(cs)/n(h)] log[n(nh 3 )/n(h)] x10 6 4x10 6 6x10 6 8x10 6 time (yrs) x10 6 4x10 6 6x10 6 8x10 6 time (yrs) Figure 4.1: Chemical fractional abundances of a) CS and b) NH 3 as a function of time for several values of the cosmic-ray ionization rate, ζ, in units of s 1, using a free-fall collapse model with initial density n H = cm 3 and A V = 0.5, halted at density n H = cm 3, with collapse factor B = 1, and freeze-out parameter F R = 0.01 (see chapter 5). that help to constrain the true value of ζ. As an example, figure 4.1 shows some tests that we ran, with the model we explain in chapter 5, to investigate the effect that changing the assumed value of ζ might have on the relative abundances of CS and NH 3, which could represent two different families of molecules. Higher values of ζ make the chemistry evolve faster for both molecules, e.g. the maximum abundances are reached at earlier times. The effects over the abundances are clearly different. Peak abundance of CS does not change effectively, although its abundance has a steeper decline the higher the value of ζ is. The final abundance is approximately the same, although it is larger with higher ζ. NH 3 on the contrary, has a clearly higher peak and overall relative abundance as ζ grows, probably because the higher cosmic-ray ionization rate produces a lot more N + in the inital stages which initiates the reaction chain to nitrogen bearing molecules. Additionally, some studies have shown (Nejad and Wagenblast 1999) that the introduction of the cosmic-ray-induced photoreactions makes an order-of-magnitude difference in the predicted abundances of some species notably those whose maximum abundances are reached at early times of a few times 10 5 years, mainly because of a substantial increase in the abundance of C +. Moreover, the degree of fractional

165 4.3. Setting up the equations 125 ionization in these models is higher. The effects of additional photons generated by cosmic-rays are most significant at early times, up to a few 10 5 yrs, and with increasing visual extinction. Thus, it is essential to include the effects of cosmic-ray-induced photoionisation and photodissociation in models of dense cores. As written, equation (4.5) applies to a cloud in which the total density remains constant. In the model presented in the following chapters, the total density is changing. Then, an additional needs to be included which takes into account the changes in density. It usually is included as if it was another species. We calculated the increase of the number density of hydrogen nuclei, n H, from an initial value, n Ho, to a final value, n Hf, following the expression of Rawlings et al. (1992): ( ) { [ dn H n 4 1/3 ( ) ]} 1/3 1/2 = B H nh 24πGm H n H 1 (4.12) dt n Ho n Ho where t is the time, G, the gravitational constant, m H, the mass of a hydrogen atom, n H, the number density of hydrogen nuclei. B is a numerical constant that controls the velocity of the increase of density, i.e, the velocity of collapse. It may be thought of as a retardation factor. If B = 1 then it corresponds to a free-fall collapse, whereas if it has a value less than 1, it may be considered that it manifests the effects of magnetic and rotational support. As can be expected, the variation of density has some immediate effects over chemistry. First, the rate of evolution of the chemistry tends to go faster with higher densities. This might not be the case in some situations if the increase in density implies the shutting down of fast reactions, such as photoreactions when certain levels of visual extinction are reached, and slower reactions take then control of the chemistry (Duley and Williams 1984). Second, the variation in density affects the reaction rates of a lot of reactions, and apart from modifying the resulting distribution of abundances it also enhances the abundances of some molecules particularly sensitive to density, such as is the case of NH 3. Naturally, if we include a variation of density, we have to take into account the change in visual extinction along the dense cloud it implies. The visual extinction, A V, can be calculated from the expression A V = a + b ( nh n Ho ) 2/3 (4.13) where a represents the extinction of the ambient medium, if any, and b that of the collapsing cloud, and consequently density dependent.

166 126 Chapter 4. Modeling the chemistry in interstellar clouds The model in chapters 5 and 6 also takes into account the depletion of molecules from the gas onto the grains. Following Rawlings et al. (1992), the rate per unit volume at which a species, i, freezes out onto a grain may be governed by dn(i) dn = d g a 2 T 1/2 CnS i m 1/2 i n(i) cm 3 s 1 (4.14) where d g is the ratio of the number densities of grains to hydrogen nuclei, a is the grain radius in cm, S i is the sticking coefficient (in the range 0 to 1), and m i is the molecular mass of species i in amu. electrostatic effects. C is a factor which takes into account Considering that the average grain charge in dark clouds is about 1 (Umebayashi and Nakano 1980), then { 1 for neutral species C = 1 + ( /at ) for singly charged positive ions (4.15) Therefore, the ionic species will freeze out faster than the neutrals by a factor of order 10 (for a = 10 5 cm) (Rawlings et al. 1992). The grain surface area per hydrogen atom can be represented by the quantity πd g a 2. However, since there is more than one grain population, and the grain size distribution is unknown, this value is usually estimated and left as a free parameter of the model (Mathis et al. 1977; Nejad et al. 1990; Rawlings et al. 1992). Finally, as we indicated in chapter 3, laboratory measurements and quantum-mechanical calculations suggest that the sticking coefficient, S i (Leitch-Devlin and Williams 1985) for all species interacting with realistic grain materials.

167 Bibliography Alagia M., Balucani N., Cartechini L., Casavecchia P., Volpi G. G., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer, Dordrecht, p. 271 Bettens R. P. A., Lee H.-H., Herbst E., 1995, The Astrophysical Journal, 443, 664 Caselli P., Hasegawa T. I., Herbst E., 1994, The Astrophysical Journal, 421, 206 Caselli P., Hasegawa T. I., Herbst E., 1998, The Astrophysical Journal, 495, 309 Duley W. W., Williams D. A., 1984, Interstellar Chemistry, Academic Press, London Gear, C. W., 1971, Numerical Initial Value Problems in Ordinary Differential Equations. Englewood Cliffs, NJ. Prentice Hall Gredel R., Lepp S., Dalgarno A., 1989, The Astrophysical Journal, 347, 289 Hasegawa T. I., Herbst E., 1993, Monthly Notices of the Royal Astronomical Society, 263, 589 Henning Th., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 343 Herbst E., 1987, in Hollenbach D. J. and Thronson H. A., eds., Interstellar Processes. Reidel, Dordrecht, p. 611 Herbst E., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer, Dordrecht, p. 1 Herbst E., Millar T. J., 1991, in James R. A. and Millar T. J., eds., Molecular Clouds. Cambridge University Press, Cambridge, p

168 128 BIBLIOGRAPHY Herbst E., Terzieva R., Talbi D., 2000, Monthly Notices of the Royal Astronomical Society, 311, 869 Leitch-Devlin M. A., Williams D. A., 1985, Monthly Notices of the Royal Astronomical Society, 213, 295 Mathis J. S., Rumpl W., Nordsieck K. H., 1977, The Astrophysical Journal, 217, 425 Millar T. J., Farquhar P. R. A., Willacy K., 1997, Astronomy and Astrophysics Supplement Series, 121, 139 Nejad L. A. M., Wagenblast R., 1999, Astronomy and Astrophysics, 350, 204 Nejad L. A. M., Williams D. A., Charnley S. B., 1990, Monthly Notices of the Royal Astronomical Society, 246, 183 Rawlings J. M. C., Hartquist T. W., Menten K. M., Williams D. A., 1992, Monthly Notices of the Royal Astronomical Society, 255, 471 Ruffle D. P., Hartquist T. W., Rawlings J. M. C., Williams D. A., 1998, Astronomy and Astrophysics, 334, 678 Ruffle D. P., Hartquist T. W., Caselli P., Williams D. A., 1999, Monthly Notices of the Royal Astronomical Society, 306, 691 Ruffle D. P., Herbst E., 2000, Monthly Notices of the Royal Astronomical Society, 319, 837 Ruffle D. P., Herbst E., 2001, Monthly Notices of the Royal Astronomical Society, 322, 770 Schutte W. A., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer, Dordrecht, p. 331 Shalabiea O. M., Caselli P., Herbst E., 1998, The Astrophysical Journal, 502, 652 Smith I. W. M., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer, Dordrecht, p. 259 Tielens A. G. G. M., Hagen W., 1982, Astronomy and Astrophysics, 114, 245

169 BIBLIOGRAPHY 129 Tielens A. G. G. M., Whittet D. C. B., 1997, in van Dishoeck E. F., ed., Molecules in Astrophysics: Probes and Processes. Kluwer Academic Publishers, Dordrecht, p. 45 Umebayashi T., Nakano T., 1980, Publications of the Astronomical Society of Japan, 32, 405 van Dishoeck E. F., Blake G. A., 1998, Annual Review of Astronomy and Astrophysics, 36, 317 van Dishoeck E. F., Hogerheijde M. R., 1999, in Lada C. J. and Kylafis N. D., eds., The Origin of Stars and Planetary Systems. Kluwer Academic Publishers, p. 97 Williams D. A., 1998, Faraday Discussions, 109, 1

170 130 BIBLIOGRAPHY

171 Chapter 5 The distribution of CS and NH 3 in star-forming regions Introduction Since molecular cores were found to be associated with sites of low mass starformation much effort has been concentrated on detecting such cores, particularly those in the process of collapse. These cores are dense, cold objects and hence tracers have been molecular species that are only excited at higher density, chiefly ammonia (e.g. Benson and Myers 1989), but also molecules such as HC 3 N (Benson and Myers 1983), H 2 CO (Evans et al. 1994) and CS (e.g. Snell et al. 1984). Even before the link with star-formation was established it was clear that there existed a discrepancy between the maps of ammonia and those of CS (Ungerechts et al. 1980, Snell et al. 1982). Zhou et al. (1989) looked for the CS (J=2 1) and (J=3 2) transitions in a number of cores previously mapped in ammonia by Myers and Benson (1983). They found the CS to be more widespread despite theoretically being excited at higher density n, and also that the CS linewidths were rather larger. They concluded that optical depth effects probably could not explain the enhanced linewidths and speculated that chemical differentiation might be the cause. Relatively extended CS emission in L1455 led Juan et al. (1993) to suggest that NH 3 is not present in the outer regions of the cloud and that this lack was due to chemical effects. In Published in Taylor S. D., Morata O., Williams D. A., 1996, Astronomy and Astrophysics, 313, 131

172 132 Chapter 5. The distribution of CS and NH 3 in star-forming regions a systematic study of 16 cores Myers et al. (1991) found CS to be about twice as large in extent than NH 3 on average. Pastor et al. (1991) observed a number of star-forming regions previously mapped in the NH 3 (1,1) inversion transition using the CS (J=1 0) line, later extending the sample to 11 (López et al. 1994). These transitions have critical densities of cm 3 and cm 3 respectively, but are expected to show emission at similar n (Evans 1989); again they found the same lack of correlation. The effect seems to occur regardless of source distance (cf also Zinchenko et al for more distant objects), but of particular interest are the observations by Pastor et al. of the nearby (d 150 pc) objects L1524 and L43, the maps of which clearly show that the CS emission is far more extended than NH 3 and that the intensity peaks of the two molecules are displaced from each other. In L1524 they were also able to observe the J=1 0 transition in C 34 S and hence determine the optical depth, and for this reason the analysis in this chapter concentrates on this source. Separations in the emission peaks of molecules have been noted in the exceptionally chemically rich source TMC 1, which appears to be a sequence of cores when mapped in CCS (Hirahara et al. 1992). Howe et al. (1996) presented chemical models of the collapse of such cores that confirmed how CS was likely to be associated with cores in earlier stages of collapse than those showing strong ammonia emission. That study has suggested the motivation for this work: can the different time-dependencies of the CS and NH 3 chemistries account for the different spatial distributions observed for these two molecules? 5.2 Gas-phase chemistry of CS and NH 3 Since both molecules are used extensively to trace regions of possible protostar formation, it is important to realise that they are formed and destroyed in very different ways. Traditional chemical models of dark clouds (i.e opaque to visual and UV radiation) have started from the premise that all elements are in atomic form except for hydrogen which is fully molecular, a situation that could have a physical basis if most dark clouds have collapsed from more translucent origins (Howe et al. 1996). It has been suggested that dynamical mixing occurs between the cloud and its surroundings, maintaining a high atomic content (Chièze et al. 1991), although this would be difficult if the cloud had an ordered magnetic field (Nejad and Hartquist 1994). The chemical consequences of turbulent mixing layers driven by star formation has been explored (see Nejad et al. 1994, and references

173 5.2. Gas-phase chemistry of CS and NH therein). In all such cases an appreciable fraction of the gas may be ionised, in the form of C +, S + and metal ions. In most circumstances CS is formed from its ion, CS + + H 2 HCS + + H (5.1) HCS + + e CS + H (5.2) where CS + can be formed from atomic and ionised sulphur, H S HS + + H 2 (5.3) HS + + C CS + + H (5.4) S + + CH CS + + H (5.5) S + + C 2 CS + + C (5.6) Large abundances of CS can be formed because it has no neutral reaction destruction pathways through O and C (Millar and Herbst 1990), unlike other sulphur molecules. Many reactions with molecular ions simply recycle CS, and the primary destruction occurs through dissociative charge exchange with helium ions: He + + CS S + + C + He (5.7) C + + S + He. (5.8) Ammonia is formed from ions undergoing successive hydrogen abstraction reactions followed by recombination, N + + H 2 NH + NH + 2 NH + 3 NH + 4 (5.9) and NH e NH 3 + H (5.10) where the atomic nitrogen ion is created by cosmic-ray ionisation. This sequence (5.9) has been the subject of some debate, since the first reaction is slightly endothermic (85 K in our calculations) and the reaction of NH + 3 with H 2 possesses an activation barrier. In practice, the consequent low rate coefficients for these reactions do not seriously affect the abundance of NH 3 since neither the destruction of N + by CO nor the recombination of NH + 3 with electrons dominates. The alternative

174 134 Chapter 5. The distribution of CS and NH 3 in star-forming regions Table 5.1: Total initial gas-phase elemental abundances used in all cloud models Element Initial abundance [n(x)/n(h)] H 1.0 He 0.14 O N C S Mg initiating state is the reaction of nitrogen atoms with H + 3, but this possesses either a high endothermicity or a large activation barrier depending on the products (Herbst, DeFrees and McLean 1987), so that ammonia is comparatively slow to form. It is prevented from containing a large fraction of the total nitrogen by charge exchange with ions such as H +, C +, He +,O + 2, and by cosmic ray induced photodissociation. Another proposed route of formation for NH 3 is by hydrogenation of N atoms on the surface of dust grains (see e. g. Wagenblast and Williams, 1993), but we have not included this process in our calculations. The reaction set we use is taken from the UMIST RATE92 data set, and includes 103 gas species and 1578 reactions. The elemental abundances adopted are given in Table 5.1. Cosmic ray induced photodissociation of molecules is accounted for according to the results of Gredel et al. (1989) and we have assumed an efficiency for this process of 200 for molecules not included by those authors. 5.3 Models of CS emission The ratio of the (J=1 0) peak antenna temperatures, T A, of C 32 S (the main isotope, here denoted CS) and C 34 S in L1524 is 6.5, much less than the terrestrial isotope ratio of 22, implying that the CS is optically thick in this source. Since T A (CS) is only 0.51 K, the detected emission is either subthermal or suffering beam dilution.

175 5.3. Models of CS emission 135 Figure 5.1: The C 32 S (J=1 0) and C 34 S0 (J=1 0). (a) The C 32 S (J=1 0) antenna temperature as a function of C 32 S column density for molecular media with n H = 300, 900, 2700, 8100, cm 3, respectively. (b) The ratio of the C 34 S (J=1 0) antenna temperature to that of C 32 S (J=1 0) as a function of C 32 S column density for molecular media with n H = 300, 900, 2700, 8100, cm 3, respectively (curves are virtually identical) The likelihood of subthermality can be investigated to first order by constructing a homogenous slab model in order to examine the excitation and radiative transfer. We have calculated the emergent intensity from such a cloud for various values of the H 2 number density and CS column density using a microturbulent escape probability approximation (cf Taylor et al. 1995), taking the full width at half maximum linewidth to be 1 km s 1, an isotope ratio of 22 and a kinetic temperature of 10 K. The CS-H 2 collision cross-sections are from Green and Chapman (1978). Figure 5.1 shows both the absolute value of T A (CS) and the ratio T A (C 34 S)/T A (CS) as a function of CS column density. Each curve represents a different density (cm 3 ). It is clear that the two quantities, which have observed values of 0.51 K and 0.15 K respec-

176 136 Chapter 5. The distribution of CS and NH 3 in star-forming regions tively, constrain the physical parameters to n(h 2 ) cm 3 and N(CS) cm 2. The NH 3 emission from L1524 traces a much higher density (Anglada et al. 1989) but clearly this emission occupies a much smaller volume than the CS, and so in the absence of observations of other CS transitions this density is not a contradiction. The diameter of the CS emitting region is 0.5 pc (Pastor et al. 1991) and adopting this as the size along the line of sight, the total column of hydrogen nuclei is cm 2. Hence the implied CS fraction is 10 8 per hydrogen nuclei which is consistent with values obtained from dark cloud models (Millar and Herbst 1990). This total column density implies a visual extinction to the cloud centre of 2, given a normal gas to dust ratio, and it might be expected that photodissociation would be a major destruction channel, but in fact CS can still be formed at fractions of 10 8 given the quite modest total sulphur gas phase fraction of However, the optical depth in the line is 6 and would be expected to show noticeable self-reversal; such a profile is not seen. We conclude that subthermality in CS is inconsistent with the observations. Two other possibilities exist; either that contained within the beam are a number of unresolved clumps, or that a low density envelope surrounds a dense core. Fuller (1988) has discussed the latter extensively, and using a Monte Carlo radiative transfer method showed that if the transition is optically thick the envelope can scatter the core emission giving the impression of a wider emitting area, and also pointed out that line self-reversal is reduced if the core has a smaller linewidth than the envelope according to the empirical scaling law that is a general feature of molecular cloud observations. Fuller suggested that the effect of the distribution of the NH 3 in the envelope over the hyperfine components of the (J, K)=(1,1) level might account for the scattering having an observable effect on the CS lines only. In fact, there is also a chemical basis for the appearance of CS alone in the envelope, since NH 3 is less robust to photodissociation than CS and has a destruction route through C +. Figure 5.2 shows chemical abundances (fraction relative to H nuclei) as a function of radius for a core-envelope model at two different times ( early and late ). Freeze-out onto dust grains is not included. The relative extents of the core and the envelope are chosen to be comparable with the models of Fuller (1988) and hence the envelope has n = cm 3 whilst the core has n = cm 3. The temperature in kept constant at T =10 K. In both instances NH 3 has a much lower abundance in the envelope whereas CS is still quite abundant. Whether the combination of the low antenna temperature and five times bigger CS emitting area can be accounted for by this model is unclear.

177 5.4. Chemical Model 137 Figure 5.2: Chemical fractional abundances (relative to H nuclei) as a function of depth for a core-envelope static cloud model. The envelope density is n(h 2 )= cm 3, the core density is n(h 2 )= cm 3 and the transition occurs at a visual extinction of 2.5 magnitudes. a) Chemical evolution timescale t = y. b) t = y The third possibility is that there are a number of unresolved clumps in the beam that preferentially manifest CS emission. We discuss this in the next section. 5.4 Chemical Model A model in which the cloud is a conglomeration of clumps is favourable for a number of reasons. It can explain the lack of coincidence of the molecular emission peaks and also the larger CS linewidth. It can continue to explain the observations even when the CS lines are optically thin, as appears to be very nearly the case in L43

178 138 Chapter 5. The distribution of CS and NH 3 in star-forming regions (Pastor et al. 1991). Although the core-envelope model of Fig. 5.2 shows CS to be much more abundant than NH 3 in the envelope ( 10 9 fraction), much higher abundances could be attained in a clumpy medium. Analyses of cores associated with H II regions have suggested that unresolved clumps best fit the details of the excitation (Wang et al. 1993) and that a scattering envelope is incompatible with HCN observations (Zinchenko et al. 1994). We consider that the difference in emission between CS and NH 3 is due to the relative evolution of these clumps. This evolution is both chemical and physical due to differences in density or in collapse stage. The collapse may occur from relatively diffuse conditions that would imply that only hydrogen is fully molecular. The chemistry is then similar to that described in Sect. 5.2, but additionally we also include the effects of changing density due to collapse and the freeze-out of molecules onto dust grains. The model is illustrative in that it is a one-point calculation, i.e. it only reflects conditions at the center of a collapsed fragment. Since the collapse is from a diffuse state we need to account for the self-shielding of CO. We do this by considering two extreme cases. Firstly, we neglect it entirely in which case the dissociation rate of CO is reduced purely as a result of grain attenuation of UV radiation. Secondly, we assume that the fractional abundance we calculate at the clump center at a given time holds throughout the cloud for the next timestep for the purposes of calculating a CO column density that is used to derive the self-shielding factor, by applying the results of van Dishoeck and Black (1988; cf Wagenblast 1992). This factor is effectively an upper limit since the fraction of CO will decrease towards the cloud edge and hence the CO column density will also be lower. We find only minor differences for the purposes of our model between these two approaches and so our results are not sensitive to this approximation. Current models of collapse of uniform clouds suggest a relaxation to an equilibrium state that may occur essentially along magnetic field lines (Ciolek and Mouschovias 1994). This equilibrium state consists of a core envelope, and the relaxation is followed by a subsequent slow evolution of the core as the magnetic flux responsible for support is lost via ambipolar diffusion (Lizano and Shu 1989; Fiedler and Mouschovias 1993). When this process is completed, dynamical collapse of the core to a protostellar object may begin. Unless the observed cores are undergoing this rapid final collapse, it is likely that they are in the quasi-static phase during which they are supported by the field. Here, we follow on much of the work of Rawlings et al. (1992) and in the case of collapse to this stage use their modified

179 5.4. Chemical Model 139 free-fall formulae (which includes a factor B that linearly scales the collapse rates), but halting at an arbitrary density that in practice depends on the balance of forces. We also note that this picture is dependent on the formed cores being magnetically subcritical. In modelling the chemistry we have been most concerned with the relative abundances of NH 3 and CS and not with the absolute column densities of these molecules. Howe et al. (1996) have shown that it is difficult to fit the observed columns in TMC-1 for more complex species, and additionally found that all species appeared underabundant if enhanced rate coefficients for certain reactions (not studied in the laboratory) between ions and highly polar neutrals were invoked (Clary 1985). Such enhanced rate coefficients can depress abundances both via chemical reaction and also by making certain species peak before the clump has had time to collapse to its equilibrium state, i.e. the chemical timescale becomes shorter than the dynamical timescale. This latter effect means that by the time a core has collapsed to its densest state, and hence the column density of gas observed is at its maximum, the fractional abundance in that gas of many species has already passed its peak so that the column densities of such species observed in this dense phase will be lower than might be inferred from a constant density model. In the absence of these rates we show below that the relative abundances implied by the observations of NH 3 and CS can be reproduced by the chemistry. We use a sulphur fraction relative to H nuclei of For grain accretion we assume that all neutral species can accrete onto grains with the same efficiency and that ionic species stick as a neutral counterpart (the grains being negatively charged); also if the ion contains at least one H atom then one H atom is lost to the gas phase. We use the formula of Rawlings et al. to calculate the rate per unit volume at which a species i freezes out, dn(i) dt = n C S i D T 1/2 n(i) m 1/2 i (5.11) where m i is the mass of species i, T is the kinetic temperature of the gas, C accounts for electrostatic effects, and n is the gas density. There are two free parameters; S i the sticking efficiency and D a factor that accounts for differences in the surface area of grains due to changes in the grain population (higher D means a greater number of smaller grains and hence an increased accretion rate). We combine these two factors into a single freeze-out parameter F R. The value of F R is hard to estimate, but evidence for freeze-out occurs directly from infrared absorption measurements

180 140 Chapter 5. The distribution of CS and NH 3 in star-forming regions (Whittet 1993) and from the discrepancy between estimates of the mass of cores from infrared and C 18 O measurements (Krugel and Chini 1994). No mantle desorption processes have been included, but may significantly affect the rate of accretion. This would be accounted for by a lower effective value of F R. Figures 5.3 and 5.4 show results for a collapse with initial density 1000 cm 3 and visual extinction 0.5 (edge to center), and final density cm 3. C, Mg and S are taken to be ionised initially. Collapse factor B = 1 is chosen; this minimises the effect of the collapse on the peak abundances, since slower collapse timescales tend to prevent transient species from attaining high fractions (Howe et al. 1996). Each graph shows chemical profiles (abundance per hydrogen nuclei) as a function of time for different values of F R. For F R = 0.01, both NH 3 and CS are able to achieve high abundances, NH 3 doing so at rather later times than CS. At F R = 0.1 however, freezeout affects CS preferentially whereas NH 3 is still able to achieve its peak abundance before falling off as all species eventually do. This selectivity in the degree to which species are affected by grain accretion was noted by Brown and Charnley (1990) and in some cases can lead to transient enhancements in the fractional abundance of a molecule. In this instance, CS is affected to a greater degree because its formation rate is low at the time when freezeout becomes important. In the absence of grain accretion, the CS retains a high abundance because of the lack of an efficient gas phase destruction route, but NH 3 has a high enough formation rate at later times that it can counteract the destructive loss even if freezeout occurs. At high F R neither species achieves high abundance. From this picture it can be seen that for a maximum (and hence probably observable) fraction of CS to exist in the gas phase it is necessary for the effective rate of freeze-out onto grains to be not too rapid, and this being the case NH 3 only achieves its maximum abundance for times later than > 2 Myr. To avoid this conclusion it is necessary that the gas phase sulphur fraction be significantly higher than the value we have taken. Since the peak abundances are affected detrimentally by values of F R as low as 0.1, it seems very likely that rather than the sticking coefficient being very low there are in fact desorption processes occurring that limit the mantle growth. If the abundance of NH 3 at the peak of the CS fractional abundance is such that its emission is not observable, it is reasonable to associate the relatively large extent of the CS emission with unresolved cores that have existed on timescales of 2 Myr or less, and which therefore have not had time to form large quantities of ammonia. Furthermore, rather than remain static it is likely that the density of the

181 5.4. Chemical Model 141 n(x)/n(h) C S+ C+ NH3 FR = 1.0 n(x)/n(h) CH CO NO NH FR = S CS C NH N+ CO CN N+ HCN 10-4 C+ C FR = CO FR = 0.1 n(x)/n(h) S S+ CS NH3 CS S NH3 C CS S+ C+ S n(x)/n(h) CH HCN CN NO N+ NO NH HCN NO CN NH CN CH N+ CN HCN n(x)/n(h) C+ C S+ S NH3 CS S FR = 0.01 NH3 C+ n(x)/n(h) CS S+ C NH CN HCN N CH NO CN NH CO FR = 0.01 HCN NO N+ NH CH time (yrs) time (yrs) Figure 5.3: Chemical fractional abundances (relative to H nuclei) as a function of time for a free-fall collapse model halted at density n H = cm 3. Initially n H = cm 3 and A V = 0.5. (a) freeze-out parameter F R = 1.0, corresponding to an average value of the product of the dust to gas number density ratio and square of the grain radius < n d a 2 >= cm 2. (b) F R = 0.1. (c) F R = 0.01

182 142 Chapter 5. The distribution of CS and NH 3 in star-forming regions AV D 6.0 ) -3 Density (cm AV time (yrs) Figure 5.4: Density and visual extinction as a function of time for the chemical models of Fig. 5.3 collapsed core will continue to slowly increase over time hence increasing the column of ammonia further and rendering it observable. This increase in density will only offset the decrease in the CS column due to chemistry over this time, hence the peak in CS emission need not coincide with that of ammonia. It is interesting to note that for F R = 0.1 not only does ammonia continue to achieve its peak abundance, but it now does this at an earlier time, almost coincident with the timescale for collapse. It may be that, as an alternative to a greater degree of evolution, cores exhibiting high ammonia emission indicate a match of macroscopic (collapse) and microscopic (freeze-out/desorption) timescales. Our results are dependent on the final density and the sulphur depletion. Densities a lot higher than cm 3 decrease the peak abundance of ammonia so that it does not get any higher than its value at the CS peak. CS tends to scale with the sulphur fraction and we have chosen a value of 10 7 simply because it produces the correct scaling with NH Discussion It is possible that the cores that have formed CS only are transient because a lack of external pressure causes their dispersion on a timescale short compared with that required for them to become magnetically supercritical. Alternatively, since the

183 5.5. Discussion 143 difference in timescale between the two types of core is only a factor of a few it might be simply that the ammonia core has undergone an accelerated evolution, perhaps because it is denser or more massive. This seems very likely; in the collapse of a lower density cloud to form a number of clumps, some must inevitably be denser (and therefore more rapidly evolving) than others. Perhaps these are the clumps involved in star formation. The production of numerous clumps could be the consequence of the gravitational instability of a molecular cloud of a few hundred solar masses (Chièze and Pineau des Forêts 1987). Another interesting feature of the observations is that the ammonia is displaced from the IR source in both L1524 and L43. One might expect that ammonia accreted onto grains in the vicinity of the star would be released by IR radiation and would make a substantial contribution to the emission. Such a scenario is postulated in the Orion hot core where a dense region is irradiated by the light of a newly formed massive star (cf Millar 1993). We believe there is observational evidence that this is not a factor here however; if thermal evaporation due to dust absorption of IR radiation occurs then it seems likely that at such densities the gas itself will exhibit enhanced temperatures, but the observations indicate cold (T 10 K) gas (Anglada et al. 1989). It may be the case that in low mass star forming regions the IR flux that impinges on gas that has been unaffected by outflows is too weak to cause desorption. Another observational result lends itself to this model. It has been noted that the CS lines have systematically larger widths than those of ammonia (Pastor et al. 1991; Zhou et al. 1989). A conglomeration of randomly moving clumps would naturally tend to have a larger linewidth than the intrinsic emission from a single clump, although the nature of the correlation between the linewidths is a matter for conjecture. HC 5 N has also been observed in such cores. The models of Howe et al. show HC 3 N to have a similar collapse abundance profile to CS, with a peak at around 2 Myr but a much steeper fall off with time. We would expect HC 5 N to have a similar profile and therefore full maps might be expected to show a similar distribution to CS, i.e. not necessarily coincident with the ammonia, however it is more transient and less abundant and therefore more difficult to detect away from its peak position. Figure 5.3 shows the chemical profiles of a number of species of interest that may provide diagnostics of the validity of this model. It appears that there

184 144 Chapter 5. The distribution of CS and NH 3 in star-forming regions would be support for the model if HCN were observed to correlate with CS rather than ammonia. The model suggests that the parameter F R is fairly small, < 0.1, possibly somewhat smaller than other investigations have indicated. The parameter F R takes into account the effective freeze-out rate, including any desorption mechanisms. A rather low value of F R would, therefore, support the view that desorption processes are occurring and may offset to some extent the freeze-out. In summary, therefore, we propose that the mismatch between CS and NH 3 maps arises from the clumpy nature of molecular clouds. The clumps are probably magnetically supported. Most clumps dissipate before NH 3 abundances build up to significant levels but contain substantial CS. A few clumps, possibly slightly denser or more massive, are sufficiently longer lived to allow NH 3 to increase in abundance; these may be the cores that continue to collapse to form stars. In recent years, observations made by Langer et al. (1995), Wolkovitch et al. (1997), and Peng et al. (1998) have resolved microstructure on a scale of pc in core D of TMC-1, which seems to provide supporting evidence for the existence of very small, and presumably transient, clumps in molecular clouds.

185 Bibliography Anglada G., Rodríguez L. F., Torrelles J. M., et al., 1989, The Astrophysical Journal, 341, 208 Benson P., Myers P. C., 1983, The Astrophysical Journal, 270, 589 Benson P., Myers P. C., 1989, The Astrophysical Journal Supplement Series, 71, 89 Brown P. D., Charnley S. D., 1990, Monthly Notices of the Royal Astronomical Society, 244, 432 Chièze J. P., Pineau des Forêts G., 1987, Astronomy and Astrophysics, 183, 98 Chièze J. P., Pineau des Forêts G., Herbst E., 1991, The Astrophysical Journal, 373, 110 Ciolek G. E., Mouschovias T. Ch., 1994, The Astrophysical Journal, 425, 142 Clary D. C., 1985, Molecular Physics, 54, 605 Duley W. W., 1989, in Winnewisser G. and Armstrong J. T., eds., The Physics and Chemistry of Interstellar Molecular Clouds. Springer Verlag, Berlin Heidelberg, p. 353 Evans N. J., 1989, Revista Mexicana de Astronomia y Astrofisica, 18, 21 Evans N. J., Zhou S., Kömpe C., Walmsley C. M., 1994, Astrophysics and Space Science, 212, 139 Fiedler R. A., Mouschovias T. Ch., 1993, The Astrophysical Journal,415, 680 Fuller G. A., 1989, PhD Thesis, University of California, Berkeley 145

186 146 BIBLIOGRAPHY Gredel R., Lepp S., Dalgarno A., Herbst E., 1989, The Astrophysical Journal, 347, 289 Green S., Chapman S., 1978, The Astrophysical Journal Supplement Series, 37, 169 Herbst E., DeFrees D. J., McLean A. D., 1987, The Astrophysical Journal, 321, 898 Hirahara Y., Suzuki H., Yamamoto S., et al., 1992, The Astrophysical Journal, 394, 539 Howe D. A., Taylor S. D., Williams D. A., 1996, Monthly Notices of the Royal Astronomical Society, 279, 143 Juan J., Bachiller R., Kömpe C., Martin-Pintado J., 1993, Astronomy and Astrophysics, 270, 432 Krügel E., Chini R., 1994, Astronomy and Astrophysics, 287, 947 Langer W. D., Velusamy T., Kuiper T. B. H., et al., 1995, The Astrophysical Journal, 453, 293 Lizano S., Shu F. H., 1989, The Astrophysical Journal, 342, 834 López R., Morata O., Sepúlveda, et al., 1994, Astrophysics and Space Science, 216, 151 Millar T. J., 1993, in Millar T. J. and Williams D. A., eds., Dust and Chemistry in Astronomy. IOP Publishing, Bristol, p.249 Millar T. J., Herbst E., 1990, Astronomy and Astrophysics, 231, 466 Myers P. C., Fuller G. A., Goodman A. A., Benson P. J., 1991, The Astrophysical Journal, 376, 561 Myers P. C., Benson P., 1983, The Astrophysical Journal, 266, 309 Nejad L. A. M., Hanquist T. W., 1994, Astrophysics and Space Science, 220, 253 Nejad L. A. M., Hartquist T. W., Williams D. A., 1994, Astrophysics and Space Science, 220, 261 Pastor J., Estalella R., López R., Anglada G., Planesas P., Buj J., 1991, Astronomy and Astrophysics, 252, 320

187 BIBLIOGRAPHY 147 Peng R., Langer W. D., Velusamy T., Kuiper T. B. H., Levin S., 1998, The Astrophysical Journal, 497, 842 Rawlings J. C. M., Hartquist T. W., Menten K. M., Williams D. A., 1992, Monthly Notices of the Royal Astronomical Society, 255, 471 Snell R. L., Langer W. D., Frerking M. A., 1982, The Astrophysical Journal, 255, 149 Snell R. L., Mundy L. G., Goldsmith P. F., Evans N. J., Erickson N. R., 1984, The Astrophysical Journal, 276, 625 Taylor S. D., Hartquist T. W., Dyson J. E., Blitz L., Williams D. A., 1995, submitted to The Astrophysical Journal Ungerechts H., Walmsley C. M., Winnewisser G., 1980, Astronomy and Astrophysics, 88, 259 van Dishoeck E. F., Black J. H., 1988, The Astrophysical Journal, 334, 771 Wagenblast R., 1992, Monthly Notices of the Royal Astronomical Society, 259, 155 Wagenblast R., Williams D. A., 1993, in Millar T. J. and Williams D. A., eds., Dust and Chemistry in Astronomy. IoP Publishing, Bristol, p. 171 Wang Y., Jaffe D. T., Evans N. J., et al., 1993, The Astrophysical Journal, 419, 707 Whittet D. C. B., 1993, in Millar T. J. and Williams D. A., eds., Dust and Chemistry in Astronomy. IOP Publishing, Bristol, p. 9 Wolkovitch D., Langer W. D., Goldsmith P. F., Heyer M., 1997, The Astrophysical Journal, 477, 241 Zhou S., Wu Y., Evans N. J., Fuller G. A., Myers P. C., 1989, The Astrophysical Journal, 346, 168 Zinchenko I., Forsström V., Lapinov A., Mattila K., 1994, Astronomy and Astrophysics, 288, 601

188 148 BIBLIOGRAPHY

189 Chapter 6 The distribution of molecules in star-forming regions Introduction Radio intensity maps of molecules in transitions with critical densities n cr > 10 4 cm 3 show emission mostly localised to 0.1 pc cores that are known to be sites of starformation. It is therefore reasonable to assume that this dense material is the consequence of the partial collapse of the more diffuse gas that surrounds it, traced, for example, in CO (J=1 0) emission. The molecules most commonly used to detect these cores are ammonia and carbon monosulphide (e.g. Benson and Myers 1989; Snell et al. 1984), and a puzzling discrepancy became apparent very early in these studies. Although CS should trace higher densities than NH 3 the surveys of Zhou et al. (1989), Myers et al. (1991), and Pastor et al. (1991) showed the CS (J=3 2), (J=2 1) and (J=1 0) emission to cover systematically wider areas than the NH 3 (1,1) inversion transition. The same conclusions for further sources were drawn by Juan et al. (1993), López et al. (1994) and Zinchenko et al. (1994). In addition, the CS linewidths were larger, and it was noted that there was a significant difference in the positions of the peaks of emission of CS and NH 3. However, the denser gas (traced in CS) should be more confined than the less dense gas (traced in NH 3 ) Published in Taylor S. D., Morata O., Williams D. A., 1998, Astronomy and Astrophysics, 336, 149

190 150 Chapter 6. The distribution of molecules in star-forming regions The differences are not caused by the use of different instruments, and continue to appear whenever studies are made at similar angular resolution. Possible explanations for the anomaly may lie either in the effects of optical depth or of chemical differentiation. In the former case, Fuller (1989) proposed that a low density envelope would scatter photons from the core within, giving the impression of a wider emitting area, the effect occurring preferentially in CS since the NH 3 (1,1) population is distributed over all the hyperfine components. In the latter case, in chapter 5 (Taylor et al. 1996), we proposed a solution based on the differences in the chemistry of the two molecules, and furthermore using chemical models and an analysis of the excitation of CS in a particular source (L1524) came to the conclusion that the extended CS emission was due to unresolved clumps rather than homogeneous gas. In this model, the difference is due to the speed at which the molecules form, NH 3 only being present in observable amounts in longer-lasting clumps, perhaps only those that become star-forming cores. This model has the further advantages that it can continue to explain the observations when the CS lines are optically thin, and also the lack of coincidence of the molecular emission peaks and the larger CS linewidth. In this chapter we extend the work of chapter 5 to examine whether there are other potentially observable molecules that should show extended emission like CS, or more compact emission like NH 3, if this unresolved clump model is correct. Although sulphur-containing molecules are some of the most useful in observing these regions, quantitative chemical modelling is hampered by the lack of information on the elemental depletion of sulphur; hence, we are especially interested in other signature molecules. The reliability of the chemistry that leads to these predictions is also discussed. 6.2 Model If the telescope beam includes a number of unresolved clumps then the difference in emission may be due to the differences in the physical, and hence chemical, evolution between them. We proposed in chapter 5 that all clumps had collapsed from a relatively diffuse state, in which only hydrogen is predominantly molecular. As the gas collapses, a large amount of free carbon is available to form molecules such as CS, before the carbon is swallowed up in CO. These early-time carbon-based molecules (like CS) exhibit a peak in fractional abundance (= n(x)/n H, where n(x) is the

191 6.2. Model 151 number density per unit volume of the molecule X and n H is the number density of hydrogen nuclei) before falling off at later times. Other molecules may simply achieve their maximum abundance at the same time as the peak of the early-time molecules and then remain at constant abundance (being in chemical equilibrium), but some termed late-time only peak in abundance at significantly later times due to bottlenecks in the their formation routes caused by low reaction rates. Ammonia is an example of this latter type since the reactions involved in its formation N + + H 2 NH + + H (6.1) NH H 2 NH H (6.2) appear to be considerably slower at 10 K than other comparable reactions. Only cores that are stable upon the initial collapse will be detectable in these molecules. Other cores, perhaps dispersed quickly because they are too small or are not in pressure equilibrium with the external medium, will not be detectable in late-time species. Our chemical model is described in detail in chapter 5; the important points are reiterated here. In a single point calculation chemical abundances are followed from initial conditions typical of a diffuse cloud (n H = 10 3 cm 3, visual extinction A V = 0.5) through a free-fall collapse (increasing n H and A V ) until n H = cm 3 and A V 7, after which both of these parameters are kept constant. The formula used for this collapse is given in Rawlings et al. (1992), and includes a scaling parameter, B, that we have normally taken to be unity. This description is intended to represent the relaxation to an equilibrium state in magnetohydrodynamic numerical collapse models, which in those simulations is followed by a longer phase in which magnetic support for the core is slowly removed by ambipolar diffusion so that the core can then collapse further to form a star. The formation of a number of such clumps may be the result of the fragmentary collapse of a larger scale ( 1 pc) cloud. Observational evidence for such clumps comes from the small scale structure of core D in TMC1 (Langer et al. 1996), and from the clumpy emission seen ahead of bow shocks in a number of sources (Taylor and Williams 1996). The observations pertinent to chapter 5 could only be explained if the effective freeze-out parameter, F R, was low. This parameter accounts for the efficiency of adsorption of gas molecules onto dust grain surfaces and for the grain size distribution (which affects the surface area available for gas species to stick to), and its low value may be an indication of effective desorption rather than inefficient stick-

192 152 Chapter 6. The distribution of molecules in star-forming regions ing. There are a number of methods of desorption, described e.g. in Williams and Taylor (1996), and amongst the more recent to be considered are desorption due to the heat emitted from the exothermic formation of molecular hydrogen on the grain surface (Willacy et al. 1994), and the desorption of CO by transfer of energy form the O-H vibration at 3.1 µm (Dzegilenko and Herbst 1995). As in chapter 5, we normally take F R = 0.01, and we also use the same elemental abundances. However, the chemical data has been updated, and also extended, by increasing the carbon chain chemistry to include species as complex as HC 3 N (there are now 138 gas phase species and 1996 reactions), and the revised UMIST ratefile has also been used (Millar, Farquhar, and Willacy 1997). 6.3 Results and Chemistry The present chapter aims to establish whether there are potentially observable molecules that belong to the CS and NH 3 families of early and late time formation. Figure 6.1 shows the fractional abundances of a number of relevant species as a function of time, the associated changes in the n H and A V values are shown in Fig. 5.4 of chapter 5. Figure 6.1a details the C + /C/CO conversion that takes place as free carbon is converted into CO; this transition takes place as the gas reaches its final density and as it occurs a number of carbon based molecules achieve peaks in their abundance (most of these peaks being rather more pronounced than CS) these are the early-time molecules. These peaks occur at t yr. A number of the other molecules achieve their maximum abundance (usually their equilibrium chemical abundance) at least yr later these are the late-time molecules. The actual time of the peak of the early-time molecules is not particularly relevant since this is just the free-fall time, these molecules form immediately the gas is dense and opaque in this sense they are dynamically led, whereas the late-time species occur at a subsequent time dictated by a chemical timescale Early-time molecules Initially, most of the carbon is in the form of C +, and this can react with H 2 by hydrogen abstraction to form ions such as CH + 5 which may recombine to produce molecules such as CH 3 and CH 4. Since oxygen is predominantly atomic, formalde-

193 6.3. Results and Chemistry 153 (c) (d) -6-6 H ] -4-4 CH4 log [n(x)/n C H 2 C H x10 time (yrs) HC N 3 6 3x10 SO2 + HCO C N 3 CCN 6 4x10 H ] log [n(x)/n CS x10 SO time (yrs) CN 6 3x10 HNC HCN H CS 2 6 4x10 (a) (b) -4-6 C+ C CO H O N2 NO O2 H ] log [n(x)/n -8 CH OH C H 2 2 H ] log [n(x)/n -8 NH3 H CO 2 OCN N2 H x10 time (yrs) 6 3x10 6 4x x10 time (yrs) 6 3x10 6 4x10 Figure 6.1: Chemical fractional abundances (relative to H nuclei) as a function of time for a free-fall collapse model halted at density n H = cm 3. Initially n H = cm 3 and A V =0.5. Freeze-out parameter F R = Note that each panel shows different molecules

194 154 Chapter 6. The distribution of molecules in star-forming regions hyde can be formed via O + CH 3 H 2 CO + H (6.3) These hydrocarbons can also react with nitrogen atoms, N + CH CN + H (6.4) N + CH 2 HCN + H (6.5) Sulphur is in the form S +, so that H 2 CS can also be formed S CH + 4 H 3 CS + e H 2 CS (6.6) Further reaction of C + with CH 4 leads to the C 2 H + 3 and C 2 H + 4 ions which recombine to give the important acetylene molecule, which is the precursor to a number of carbon-chain molecules, C + C 2 H 2 C 3 H + H (6.7) N + C 3 H C 3 N + H (6.8) O + C 3 N CCN + CO (6.9) CN + C 2 H 2 HC 3 N + H (6.10) Late-time molecules Ammonia does not achieve its maximum fraction until t > yr, mostly because the slight endothermicity (equivalent to 85 K) of reaction 6.1 slows the NH 3 formation. Oxygen atoms cannot be ionised by UV photons in these regions, and oxygen atom reaction with H 2 is endothermic. Thus, when the clump has collapsed to the extent that molecules are not photodissociated, it is still necessary for sufficient time to elapse for oxygen to be ionised by cosmic rays before hydrogenating reactions can take place. H + 3 can react with O, but the formation of this molecule also requires cosmic-ray ionisation (of H 2 ). Thus, OH is a late-time molecule; O c.r. O + H 2 OH + H 2 H2 O + e OH (6.11) A number of other molecules then follow from OH, O + OH O 2 + H (6.12) CN + O 2 OCN + O (6.13)

195 6.4. Discussion 155 N + OH NO + H (6.14) N + NO N 2 + O (6.15) S + OH SO + H (6.16) NO can also be formed from via reaction of O with NH 2, but NH 2 (which forms during the NH 3 production) is itself a late-time molecule. SO is also formed by reaction of the molecules HS and O 2, and again both of these molecules are late time (HS being late time because the reaction of S + with H 2 is endothermic and theretofore slow at low temperature). HCO + is an important ion that forms late, mostly through the reaction of H + 3 with CO. Table 6.1 gives the enhancements in abundance of these late-time molecules over their values at the time of the CS peak. Note that ammonia has one of the smallest enhancements. The larger this factor the greater the chance that the molecule will be seen in long-lived cores. 6.4 Discussion Observability A complication of this analysis is that it is not enough to argue that NH 3 family molecules will cover smaller areas of the sky than CS family molecules. We have postulated in chapter 5 that this is the case for NH 3 only by assuming that it is at such an abundance that it is undetectable in the CS clumps, and this may not be the case for other molecules of the NH 3 family. What can be said, however, is that at similar angular resolution molecules of the NH 3 family should show a much steeper decrease in intensity from peak, i.e. a smaller half-contour. In order to sample fully the area a resolution of 1 is preferable for mapping purposes, though higher resolution would be required to resolve most of the individual clumps. On the other hand, the excitation conditions for particular transitions are important, so for example a member of the CS family will not appear widespread compared with NH 3 if the transition n cr is so high that it is only significantly excited in the densest

196 156 Chapter 6. The distribution of molecules in star-forming regions Table 6.1: List of late-time molecules, along with the factor increase in their fractional abundance at their own peak compared with their abundance at the CS family peak time of t = yr. For some of these molecules the late time peak occurs at times even later than those shown in Figure 6.1. Molecule Factor Increase OH 7 O SO 333 NH 3 3 NO 32 N 2 2 HCO + 7 OCN 52 C 2 H 2 36 of cores (e.g. CS (J=5 4)). Mappings of molecules in low-mass star-forming regions on the 10 scale are rare in the literature, so this discussion is concerned more with potential observability. In Table 6.2 we show line information concerning transitions, frequencies and estimated line strenghts for the most relevant molecules discussed. Early-time molecules HCN (J=1 0) was mapped in two cores in high-mass star-forming regions by Zinchenko et al. (1994), and those authors remark that the spatial extent follows CS rather than ammonia, as predicted here. The molecule is easily observable in low-mass sources as well (e.g. van Dishoeck et al. 1995). We anticipate that CN will follow the same distribution. H 2 CO is now widely observed since it appears to be a good indicator of infall due to collapse (e.g. Myers et al. 1995). Its emission appears widespread in diffuse clouds (Turner 1994), which may not be star-forming, but mappings of star-forming

197 6.4. Discussion 157 Table 6.2: Transitions of relevant early- and late-time molecules with the estimated line strength relative to the CS (J=1 0) line intensity. Calculations have been made assuming LTE, T ex =10 K and a line width V=1 km s 1. Molecule Transition ν T mb (GHz) T mb (CS) HCN J= /4.9 J= /22.7 H 2 CS J K 1,K+1 = /0.2 J K 1,K+1 = /0.2 H 2 CO J K 1,K+1 = /1.3 J K 1,K+1 = /0.5 J K 1,K+1 = /0.8 J K 1,K+1 = /1.1 J K 1,K+1 = /0.5 HC 3 N J= /0.5 J= /0.4 J= /0.7 HCO + J= /3 J= /3.4 SO J K = /0.5 NO J=3/2 1/ /0.1 cores would probably be better in transitions like (rather than at cm wavelengths) which is at a high enough frequency ( 141 GHz) that the required resolution can be achieved. H 2 CS is clearly observable (e.g. Minh et al. 1991) and mapping would be possible. Like H 2 CO, however, there has been speculation that this molecule is formed on grains rather than in the gas, which could affect our conclusions. We predict a number of carbon chains to be members of the CS family, most prominantly C 3 N, HC 3 N, and C 3 H. Although their abundances are probably inflated in our models since the chemical network for species with four or more carbon atoms is incomplete, their early-time behaviour should not be affected. The original

198 158 Chapter 6. The distribution of molecules in star-forming regions impetus to this work came from our analysis (Howe et al. 1996) of observations of HC 3 N and NH 3 (together with CCS and C 4 H) in TMC-1 by Hirahara et al. (1992). This exceptionally rich source shows at least five distinct cores, the carbon chains and ammonia showing intensity peaks in different cores. We interpreted this spatial difference as being due to sequential time evolution. By associating C 3 H with C 4 H there does not seem to be any doubt that all three of these molecules could be mapped in other star-forming regions. CCS appears well suited to core observation and, although not included in these models, is also early-time. HC 5 N ought to follow the distribution of HC 3 N, and was mapped in four sources by Benson and Myers (1983), however the maps were not extensive and the comparison with NH 3 is indeterminate. Our models predict CCN to belong to the CS family, but the molecule is yet to be observed. Late-time molecules HCO + is another commonly used tracer of infall, though again maps are rare. However, Butner et al. (1995) do show the coverage of DCO + in a number of sources previously mapped in CS/NH 3, and it is apparent that for the most part this molecule is closer to ammonia than CS. Assuming that HCO + follows DCO + then these observations are consistent with our prediction that HCO + is a late-time molecule. Since we presume the late-time molecules to emit from far fewer clumps than the early time molecules (perhaps only one clump), it follows that their peaks of emission ought to coincide. In this respect it is encouraging that HCO + has been observed in L1251 by Sato et al. (1994) and the emission is smaller than, but coincident with, the NH 3 mapped by Anglada et al. (1997), and shown in Figure 2.8. The molecule SO has been mapped by Chernin et al. (1994) in a number of low to intermediate-mass sources. The emission is quiescent (rather than being associated with molecular outflows) and seems to be compact, although none of the sources appear to coincide with those of the CS/NH 3 surveys. An understanding of the behaviour of SO is impeded by lack of information on the elemental depletion of sulphur. However, a comparison with CS would be very interesting. Emission from NO at 150 GHz is clearly detectable (e.g. Gerin, Viala, and Casoli 1993) and maps ought to be possible at the required resolution, though none appear to exist at present. OCN peaks at yr in our model and so can be

199 6.4. Discussion 159 classed as late-time, but has not been observed. A number of archetypal late-time molecules (O 2, N 2, C 2 H 2 ) are unfortunately not observed in emission because of their lack of dipole moment. The chemistry of C 2 H 2 is unusual in that it exhibits an early-time peak due to formation through C + and CH 4, but experiences a larger late-time peak because its main destruction paths through C and C + are reduced as these species are removed from the gas-phase Chemistry A glance at the chemical equations in section 6.3 confirms that neutral-neutral reactions are surprisingly important, although much of interstellar chemistry is based on ion-molecule chemistry. It is important to confirm that these neutral-neutral reactions proceed at 10 K; in fact, most of these reactions have only been studied at room temperature, if they have been studied at all. The CS family chemistry, in particular, depends on efficient neutral-neutral reactions. For the NH 3 family, the removal of these predominant pathways will probably lead to even slower formation. Certain neutral-neutral reactions have indeed been studied at low temperatures. The reaction of CN with C 2 H 2 (reaction 6.10) has been examined by Sims et al. (1993), and of CN with O 2 (reaction 6.13) by Rowe et al. (1993). Gerin et al. (1992) show that N with OH (reaction 6.14) proceeds with a negligible barrier. The reaction C + C 2 H 2 (reaction 6.7) was studied recently by Kaiser et al. (1997) and found to proceed, and also in the correct ratio of cylic to linear C 3 H product. The reaction of O with OH is thought to have a barrier of 30K, low enough to be a significant barrier in cold clouds. For the schemes used here, OH reactions are based on the assumption that atom-radical reactions can in fact proceed without barrier, given the evidence above (cf. Herbst et al. 1994). The initial condition of the gas that is adopted in these studies has been typical of fairly diffuse interstellar material, and we have further assumed that most of the carbon is in the form of C +. We have, however, also explored the consequences of starting with significant quantities of carbon in CO. The results are not greatly different from those illustrated in Fig This is because the photodissociation of CO before the collapse dominates (at yr) always ensures enough free carbon to drive the carbon chemistry, as described in Section 6.3.

200 160 Chapter 6. The distribution of molecules in star-forming regions The initial condition also sets the sulphur abundance at about 1% of its cosmic value. This is clearly incorrect under the near-diffuse conditions at the start of the collapse; in diffuse clouds sulphur is observed to have a relative abundance close to the cosmic value. However, in calculations that we have made using higher values of the sulphur relative abundance, sulphur-bearing molecules are found to have abundances that are much too high when compared to the observed values. Evidently, these calculations are telling us that sulphur is being heavily depleted during the collapse process. The physical mechanism by which this depletion occurs is unknown, and is currently a topic of study by us. Until this mechanism is understood, we have chosen to adopt a (low) fractional abundance of sulphur that is necessary to give approximately the abundances of the S-bearing family of molecules. As mentioned earlier (Section 6.3), the dynamical and chemical timescales control the appearance of early and late families of molecules. In this simple model, the dynamical timescale is controlled by the scaling parameter, B (Section 6.2). The value of B has been set equal to unity in the calculations reported here. We have, however, also explored the consequences of a slow collapse (B = 0.1). In this case, the early time abundance peaks are suppressed. These peaks are a consequence of the cloud having attained a high density before the gas can respond chemically. With the slower collapse, represented by B = 0.1, the chemical timescale is shorter than the dynamical timescale, so these peaks are smoothed out. The arguments of chapter 5 and of Howe et al. (1996) therefore suggest that collapses as slow as those modelled by B = 0.1 are excluded. 6.5 Summary A plausible explanation for the anomalously widespread emission of CS compared with NH 3 in low-mass star-forming regions is the formation (in the collapse process) of many clumps of dense gas, only some of which go on to form stars or at any rate persist for a long enough time to be visible in late-time molecules such as NH 3, but all of which may be observable in early-time molecules such as CS. Here, models of this collapse process are used to predict which other molecules will fall into each of the CS and NH 3 families, and which will be suitable for study at the appropriate resolution, if they have not already been mapped. HCN, H 2 CO, H 2 CS, C 3 N, HC 3 N, and C 3 H are found to fall into the CS family, whilst HCO +, SO, NO, OH, N 2 H + and

201 6.5. Summary 161 OCN are in the ammonia family. The reliability of the neutral-neutral chemistry that is predominantly responsible for their formation is also considered.

202 162 Chapter 6. The distribution of molecules in star-forming regions

203 Bibliography Anglada G., Sepúlveda I, Gómez J. F., 1997, Astronomy and Astrophysics, 121, 255 Benson P., Myers P. C., 1983, The Astrophysical Journal, 270, 589 Benson P., Myers P. C., 1989, The Astrophysical Journal Supplement Series, 71, 89 Butner H. M., Lada E. A., Loren R. B., 1995, The Astrophysical Journal, 448, 207 Chernin L. M., Masson C. R., Fuller G. A., 1994, The Astrophysical Journal, 436, 741 Dzegilenko F., Herbst E., 1995, The Astrophysical Journal, 443, L81 Fuller G. A., 1989, PhD Thesis, University of California, Berkeley. Gerin M., Viala Y., Pauzat F., Ellinger Y., 1992, Astronomy and Astrophysics, 266, 463 Gerin M., Viala Y., Casoli F., 1993, Astronomy and Astrophysics, 268, 212 Herbst E., Lee H.-H., Howe D. A., Millar T. J., 1994, Monthly Notices of the Royal Astronomical Society, 268, 335 Hirahara Y., Suzuki H., Yamamoto S., et al., 1992, The Astrophysical Journal, 394, 539 Howe D. A., Taylor S. D., Williams D. A., 1996, Monthly Notices of the Royal Astronomical Society, 279, 143 Juan J., Bachiller R., Kömpe C., Martin-Pintado J., 1993, Astronomy and Astrophysics, 270,

204 164 BIBLIOGRAPHY Kaiser R. I., Stranges D., Lee Y. T., Suits A. G., 1997, The Astrophysical Journal, 477, 982 Langer W. D., Velusamy T., Kuiper T. B. H., et al., 1996, The Astrophysical Journal, 453, 293 López R., Morata O., Sepúlveda I., et al., 1994, Astrophysics and Space Science, 216, 151 Minh Y. C., Irvine W. M., Brewer M. K., 1991, Astronomy and Astrophysics, 244, 181 Millar T. J., Farquhar P. R. A., Willacy, K. 1996, Astronomy and Astrophysics, 121, 139 Myers P. C., Fuller G. A., Goodman A. A., Benson P. J., 1991, The Astrophysical Journal, 376, 561 Myers P. C., Bachiller R., Caselli P., et al., 1995, The Astrophysical Journal, 449, 65 Pastor J., Estalella R., Anglada G., Planesas P., Buj J., 1991, Astronomy and Astrophysics, 252, 320 Rawlings J. M. C., Hartquist T. W., Menten K. M., Williams D. A., 1992, Monthly Notices of the Royal Astronomical Society, 255, 471 Rowe B. R., Canosa A., Sims I., 1993, J. Chem. Soc. Faraday Trans., 89, 2193 Sato F., Mizuno A., Nagahama T., et al., 1994, The Astrophysical Journal, 435, 279 Sims I. R., Queffelec J.-L., DeFrance A., et al., 1993, Chemical Physics Letters, 211, 461 Snell R. L., Mundy L. G., Goldsmith P. F., Evans N. J., Erickson N. R., 1984, The Astrophysical Journal, 276, 625 Taylor S. D., Morata O., Williams D. A., 1996, Astronomy and Astrophysics, 313, 269 Taylor S. D., Williams D. A., 1996, Monthly Notices of the Royal Astronomical Society, 282, 1343

205 BIBLIOGRAPHY 165 Turner B. E., 1994, The Astrophysical Journal, 437, 658 van Dishoeck E. F., Blake G. A., Jansen D. J., Groesbeck T. D., 1995, The Astrophysical Journal, 447, 760 Willacy K., Williams D. A., Duley W. W., 1994, Monthly Notices of the Royal Astronomical Society, 267, 949 Williams D. A., Taylor S. D., 1996, Quarterly Journal of the Royal Astronomical Society, 37, 565 Zhou S., Wu Y., Evans N. J., Fuller G. A., Myers P. C., 1989, The Astrophysical Journal, 346, 168 Zinchenko I., Forström V., Lapinov A., Mattila K., 1994, Astronomy and Astrophysics, 288, 601

206 166 BIBLIOGRAPHY

207 Chapter 7 Multitransitional observations of the CS core of L Introduction Low-mass star formation takes place in dense cores of molecular clouds (Beichman et al. 1986; Benson and Myers 1989). The emission of several molecules, such as CS, NH 3, and HCO +, known to be good tracers of high density molecular gas, was used for studying these dense cores. However, very soon large discrepancies between the emission of these molecules were found in some sources (Zhou et al. 1989; Myers et al. 1991). To clarify the intrinsic differences between the emission of these molecules and how this emission is related to the actual distribution of the high density gas, we began a systematic comparison between the emission of the CS (J=1 0) and NH 3 (J, K)=(1,1) transitions under similar conditions of angular resolution (Pastor et al. 1991; Morata et al. 1997; see chapter 2). The comparison of the distribution of the CS and NH 3 emission in 14 condensations of 11 star-forming regions confirmed the discrepancies. In particular, we found that there is a separation 0.2 pc between the emission peaks of both molecules; regions traced by CS are larger than those traced by NH 3 ; and CS lines are 0.5 km s 1 wider than those of NH 3. To explain these results, we developed a chemical model in chapter 5 (Taylor et al. 1996) in which high density condensations, or dense cores, are formed by clumps < 0.1 pc in size, which would be unresolved at moderate angular resolution observations such as the ones made in our study, of different mass, age, size and density. 167

208 168 Chapter 7. Multitransitional observations of the CS core of L673 Most of the clumps disperse before NH 3 abundances build up to significant levels, though these clumps contain substantial CS, so its emission should be observable. A few clumps, those sufficiently long lived, or being in a more advanced stage of physical and chemical evolution because of being denser or more massive, form a significant content of NH 3, while CS abundance decreases with time. These clumps would possibly continue their evolution to eventually form stars. This model would account for the difference in size and separation between emission peaks of the CS and NH 3 molecules. Our chemical model explains the differences as a result of the speed at which the molecules form. Therefore, a classification could be made between early-time molecules and late-time molecules, according to the time at which these molecules reached their peak fractional abundance. In chapter 6, we examined whether there were other potentially observable molecules that should show extended emission like CS, or more compact emission as NH 3 (Taylor et al. 1998). Several candidates were found for both groups: e.g. HCN, H 2 CO or HC 3 N are found in the CS family, whilst HCO +, SO, NO or N 2 H + are in the NH 3 family. In order to test the predictions of the model, we carried out high angular resolution observations towards L673 of several transitions corresponding to molecules of both families of species. The L673 high density condensation was previously detected in the CS (J=1 0) transition at moderate angular resolution by Morata et al. (1997; see chapter 2).The L673 CS condensation is located at R.A. (J2000)=19 h 20 m 52 ṣ 1, Decl. (J2000)= , at 9. 5 to the southeast of IRAS This condensation is well suited to our purposes for several reasons. A high density condensation has been detected nearby in the NH 3 (J, K)=(1,1) transition by Sepúlveda et al. (2001), which shows the same general behaviour found in the other sources of our survey: a separation from the CS emission peak 2, and a NH 3 condensation size clearly smaller than the CS condensation size. It is located nearby, the estimated distance to the L673 cloud is 300 pc (Herbig and Jones, 1983), which helps in the study of the smaller size structure of the cloud. Finally, the condensations detected in CS and NH 3 show no signs of tracers of star formation, such as infrared or radio continuum sources, Herbig-Haro objects or molecular outflows, which indicates that it is probably a quiescent core, maybe in the first stages of collapse, before forming a stellar core or a Class 0 star, as were the conditions of the chemical model we developed.

209 7.2. Observations 169 Table 7.1: Transitions observed RMS Spectral Molecule Transition ν per channel resolution Detected? (GHz) (Jy/beam) ( km s 1 ) HCO Yes C 3 S No N 2 H Yes C 2 S No OCS No CS Yes HNCS 9 1,8 8 1, No C 2 S No HC 3 N No SO marginally OCS No 7.2 Observations The observations of the L673 region were carried out in 1998 May with the 10- antenna BIMA array 1 at the Hat Creek Radio Observatory in the C configuration. The phase calibrators were and 3C395. In order to include the positions of the CS (J=1 0) and NH 3 (J, K)=(1,1) transitions single-dish emission peaks of the maps by Morata et al. (1997) and Sepúlveda et al. (2001), we made a two-point mosaic with one of the fields centered approximately at the position of these two peaks. Thus, one of the fields was centered at the position α(2000) = 19 h 20 m 52 ṣ 2, and δ(2000) = , and the other located 90 to the North. Three frequency setups were used, centered at 91, 96 and 107 GHz. The digital correlator was configured to observe simultaneously several molecular line transitions at moderately high spectral resolution, 0.3 km s 1. The target molecular lines were HCO + (J=1 0), N 2 H + (J=1 0), CS (J=2 1), SO (J K = ) and C 18 O (J=1 0). 1 The BIMA array is operated by the Berkeley-Illinois-Maryland Association with support from the National Science Foundation.

210 170 Chapter 7. Multitransitional observations of the CS core of L673 System temperatures for the 91, 96 and 107 GHz setups were in the K, K and K range, respectively. The calibration and data reduction were performed using the MIRIAD software package (Sault, Teuben and Wright 1995). Maps were done with the visibility data weighted by the associated system temperatures and using natural weighting. The resulting synthesized beam for the 91, 96 and 107 GHz setups were , P A = 14 ; , P A = 17 ; and , P A = 8, respectively. The transitions of all the observed lines, their velocity resolution and the achieved rms noise with this velocity resolution are listed in Table 7.1. For the continuum emission we used the data from the 96 GHz correlator setup, which provided a bandwdith of 800 MHz centered at the frequency of 95.9 GHz. No emission was detected at above 8 mjy beam 1 (at a 3-σ level). 7.3 Results Morphology of the BIMA emission We detected emission in three of the transitions: CS (J=2 1), N 2 H + (J=1 0) and HCO + (J=1 0). We detected marginally, at 2σ level, the SO ( ) transition. The remaining transitions of Table 7.1, which where observed mainly because they were found inside the frequency range of the observations, were not detected. It must be noted that all these undetected transitions have an upper level energy with temperatures higher than 15 K, and most of them, OCS is the exception, have also a high dipole moment. Thus, the temperature and density conditions of the L673 core, and the low abundances expected for these molecules make them very difficult to detect. Figures 7.1 to 7.3 show the maps of the zero-order moment (integrated intensity) of the emission of the detected molecules. These maps were obtained after convolving the original maps with a Gaussian function, with a resulting beam of 20 15, in order to make a more meaningful comparison between the emission of each molecule. A clumpy distribution of the emission is shown in the integrated intensity map of the CS (J=2 1) transition (Fig. 7.1). The more intense emission is found in two clumps near the position of the single-dish NH 3 (J, K)=(1,1) emission peak: one almost coinciding with its nominal position, and the other peaking 30 to the

211 7.3. Results CS 16 DECLINATION (J2000) N E W S RIGHT ASCENSION (J2000) Figure 7.1: Integrated emission of the CS (J=2 1) line for the V LSR range km s 1. Contours are 0.96, 1.20, 1.44, 1.68, 1.92, 2.16, 2.40, 2.64 Jy beam 1 km s 1. The beam ( ) is shown in the bottom left-hand corner. The upright crosses indicate the nominal position of the single-dish emission peak of the CS (J=1 0) line (north) and NH 3 (J, K)=(1,1) line (south). The tilted crosses indicate the position of the four points selected for further study (see Table 7.2). The bordering contour indicates the two fields observed west. Weaker emission is found in a clump near the position of the single-dish CS (J=1 0) emission maximum, 1. 5 to the north. Figure 7.2 shows the integrated intensity map of N 2 H + (J=1 0). Two clumps of emission are found, one almost coincident with the nominal position of the NH 3 (J, K)=(1,1) emission peak, and the other, more intense, 35 to the south. No emission is detected around the position of the CS (J=1 0) single dish emission peak. The integrated intensity map of the HCO + (J=1 0) emission (Fig. 7.3) shows several isolated emission enhancements distributed around the positions of the CS

212 172 Chapter 7. Multitransitional observations of the CS core of L N 2 H + 16 DECLINATION (J2000) N E W S RIGHT ASCENSION (J2000) Figure 7.2: Same as in Figure 7.1 for the N 2 H + (J=1 0) line for the V LSR range km s 1. Contours are 2.55, 3.06, 3.57, 4.08, 4.59, 5.10, 5.61, 6.12, 6.63, 7.14 Jy beam 1 km s 1. The beam ( ) is shown in the bottom left-hand corner. and NH 3 single-dish emission peaks. The most intense emission tends to be around the position of the CS (J=1 0) emission peak or in-between the two peaks, with a N S elongation. Another intense enhancement is found 1. 1 south-east of the NH 3 emission peak nominal position. Comparing the integrated intensity maps of the three molecules, we found that N 2 H + emission was more concentrated than CS and HCO + emission, which were found more spread all over the region. CS (J=2 1) emission in the southern region coincided with the northern clump of N 2 H + emission. Moreover, the northern N 2 H + emission peak was found between the two CS (J=2 1) local emission enhancements. CS (J=2 1) and HCO + emission were found to coincide closely at the northern part of the region, especially around the CS (J=1 0) emission peak. On the contrary, N 2 H + and HCO + emission coincided only marginally in general. Finally, we were

213 7.3. Results HCO + 16 DECLINATION (J2000) N E W S RIGHT ASCENSION (J2000) Figure 7.3: Same as in Figure 7.1 for the HCO + (J=1 0) line for the V LSR range km s 1. Contours are 0.96, 1.08, 1.20, 1.32, 1.44, 1.56, 1.68 Jy beam 1 km s 1. The beam ( ) is shown in the bottom left-hand corner. also able to find an emission enhancement in the marginally detected SO emission very near the position of the N 2 H + northern clump. Table 7.2 lists the four positions we selected in the mapped region in order to compare the physical parameters of the gas traced by each molecule. The selected positions were related to the most prominent higher resolution clumps found in our observations, and corresponded to local intensity peaks in the emission of the detected molecules. The four positions were labelled as S, E, W and N, and roughly correspond to the South peak position of the N 2 H + integrated intensity map, the East CS local maximum, the West CS maximum, and the North enhancement in the HCO + emission near the CS (J=1 0) emission peak, respectively.

214 174 Chapter 7. Multitransitional observations of the CS core of L673 Table 7.2: Selected positions Position α (J2000) δ (J2000) map counterpart South (S) 19 h 20 m s N 2 H + (J=1 0) south peak East (E) 19 h 20 m s CS (J=2 1) eastern peak West (W) 19 h 20 m s CS (J=2 1) western peak North (N) 19 h 20 m s HCO + (J=1 0) NE enhancement Kinematic structure Figure 7.4 shows the spectra obtained for the three transitions detected in the region in the four selected points, after convolving the data with a gaussian function to obtain a resulting beam of 32, which is the distance between the two CS enhancements. Table 7.3 lists the fitted line parameters for each detected transition. CS emission is detected, with varying intensity, in all four positions, whereas HCO + emission is only detected at the N and W positions, and N 2 H + emission at the S and E positions. Line center velocities for CS and HCO + at the positions where a well determined fit could be obtained are compatible with being originated in the same bulk of gas. The difference in the line center velocity is km s 1, which is the velocity resolution of our observations. However, line center velocities for the N 2 H + spectra were shifted > 0.7 km s 1 from the CS line velocities. Using the much better determined frequency for the main N 2 H + (J=1 0) component (F 1, F = 2, 3 1, 2) given by Caselli et al. (1995): GHz, we found a very good agreement with CS spectra line velocities, < 0.1 km s 1. We have corrected the N 2 H + line velocities accordingly, as table 7.3 shows. Line-widths are < 0.9 km s 1, very similar to the observed values in the single-dish observations. Figure 7.5 shows the position velocity diagram obtained for the CS (J=2 1) line around the position of the western emission peak along the NE SW direction (P.A. 73 ). The position velocity diagram marginally shows an elliptical structure, roughly symmetrical about V LSR 6.9 km s 1, with a stronger blue wing and weaker red wing. This structure may suggest inward motions in the condensation,

215 7.3. Results 175 Figure 7.4: Spectra of the CS (J=2 1), HCO + (J=1 0), and N 2 H + (J=1 0) transitions at the four selected positions in our mapped region. as in the case of the starless core L1544 (Ohashi et al. 1999). In order to check for this possibility, we considered a model of a spatially thin ring with both infall and rotation seen edge-on by the observer. The parameteres of the model were the inner and outer radii of the ring, R inn and R out, the infall and rotation velocities, V infall and V rot, and the line width V core. We computed the position velocity diagram along the projected maxor axis of the ring, assuming that the intensity was constant for R inn < R < R out, to compare with the observed diagram. The best fit was obtained for radii of the ring, R inn = 4200 AU, R out = 6000 AU, velocities V infall = 0.45 km s 1, V rot = 0 km s 1, and intrinsic line width V core = 0.65 km s 1. Figure 7.5 also shows the synthetic position velocity diagram Physical parameters We were able to estimate the excitation temperature for the N 2 H + data at the two positions, S and E, where we had good signal-to-noise spectra. The values obtained

216 176 Chapter 7. Multitransitional observations of the CS core of L673 Figure 7.5: Bottom panel: Position Velocity diagram of CS J=2 1 emission along the NE SW direction, P.A. 73, around the position of the western emission peak. Top panel: Synthetic emission of an infalling thin disk with: an infall velocity of 0.45 km s 1, no rotation, a inner and outer radius of 4200 and 6000 AU, respectively, and intrinsic line width of 0.65 km s 1 at both positions are 4 K, assuming a beam filling factor f = 1, compatible with the value obtained from the CS (J=1 0) observations, 4.2 K (Morata et al. 1997), and slightly lower than the value obtained from the NH 3 (J, K)=(1,1) observations, 5.7 K (Sepúlveda et al. 2001). The total line opacity of the N 2 H + (J=1 0) transition at both positions is 0.9. We estimated an upper limit for the beam averaged column density using the value for the excitation temperature obtained from the CS (J=1 0) and N 2 H + (J=1 0) observations, T ex = 4 K, and assuming a filling-factor f = 1. However, the filling-factor could be f < 1. In this case, the excitation temperature would be greater than 4 K, but likely less than 10 K, because the kinetic temperature in low-mass dense cores is typically about