First studies for cold stars under the hyphotesis of TE : Russell (1934) Fujita (1939, 1940, 1941)

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1 First studies for cold stars under the hyphotesis of TE : Russell (1934) Fujita (1939, 1940, 1941) These models were able to predict the abundances of the most conspicous diatomic molecules detected in red giant stars (VO, TiO, CN, CH, ). These models also predicted the presence of some polyatomic molecules that were detected 50 years later. The models (Fujita) clearly indicated the role of the atomic abundances H:C:N:O in the abundances of diatomic species determined in TE. Russell was even able to apply his models to the Sun and to predict the presence of CO, CN and C 2 for temperatures below 4000 K. Tsuji 1973 : Very detailed study of the chemistry under TE in cold stars. He considered 36 elementos and hundreds of molecules

2 McCabe in 1979 introduces the concept of molecular freezing. * Molecules are formed in the innermost region of the envelope. * Refractory species condensate and form dust grains. * Radiation pression over dust grains and the star pulsation initiate the expansion of the envelope * When the density and temperature of the gas decrease due to the expansion, then chemical reactions become very slow. The time scale for dynamic evolution is faster that the formation rate of molecules. * The molecular abundances in the external layers reflect the abundances produced under TE in the innermost region. * OK for many species but of very difficult justification for radicals and large carbon-chains.

3 THREE BODY REACTIONS: A + B AB * (k 1 ) AB * + M AB + M (k 2 ) AB * A + B (k 3 ) The formation rate of the molecule AB, assuming that the activated complex reaches an equilibrium between formation and destruction is given by dn(ab)/dt = n(ab * ) n(m)k 2 dn(ab * )/dt = n(a) n(b) k 1 -n(ab * ) n(m) k 2 -n(ab * ) k 3 dn(ab * )/dt = 0 and n(a) n(b) k 1 n(ab * ) = ( k 3 +k 2 n(m) ) k 1 k 2 n(a) n(b) n(m) dn(ab)/dt= k 3 + k 2 n(m)

4 If A, B y M are neutral species then k cm 3 s -1 and k cm 3 s -1, but k s -1, and dn(ab)/dt n(a) n(b) n(m) cm -3 s -1 The best case in the ISM occurs for A=B=M= H H+H+H H 2 +H For hydrides (BH) the optimal case will correspond to A=H, M=H and B (C,N,O), i.e., n(b) 10-4 n(h) and dn(bh)/dt n 3 (H) cm -3 s -1 B (C,N,O)

5 EXAMPLE: Let us consider an atomic cloud without dust grains and without radiation field. For t=0 the density of atomic hydrogen is n and that of molecular hydrogen is 0. The formation of H 2 occurs through the reaction H + H + H = H 2 +HwitharateK=10-32 cm 6 s -1 f(t)=0.5 n(cm -3 ) t(years) (600 s) (6s) (0.0006s) The three body mechanisms is only efficient for densities larger than cm -3. Even in this case, the density is not enough taken into account the dynamical time scale of evolution of the object. For a density of cm -3, i.e., the photosphere of an AGB star, the time necessary to transform H into H 2 is yr = 5.3 hours!!!!

6 Thermodinamical equilibrium For each element we stablish a conservation law where P i, P i+, P i- are the partial pressures of i, i +, y i - and P K is the partial pressure of molecule K in which the element i appears w i K. times where w i K+w j K+...+w l K=n K, is the number of atoms in the molecule formed by the elements i,j,..,l and K p (K) (T) is the dissociation constant

7 It is easy to show that i.e., equilibrium constants can be derived from the partition functions of individual atoms and of the molecule!!!!

8 MOLECULAR ABUNDANCES AS A FUNCTION OF THE TEMPERATURE

9 Water in the Sun!!!! Thermodynamical equilibrium works nicely

10 All frequencies can be computed with a few constants! CO in the Sun

11 O-rich or C-rich, that is the question O-rich star [C]/[O] < 1 C-rich star [C]/[O] > 1 O-bearing molecules: H 2 O, SiO, OH, C-bearing molecules: C 2 H 2, HCN, CS,

12 C-rich Stars (IRC+10216) Carbon-bearing Molecules

13 Molecules with N and P Molecules with Si

14 What happens if we consider big carbon-rich molecules?

15 With PAHs Without PAHs

16 With PAHs Without PAHs

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19 Molecular abundances in O-rich stars O-rich C-rich

20 O-rich

21 METHODS Astronomical Observations at all frequencies optical, infrared and radio telescopes Radiative transfer modeling Chemical modeling

22 ASTROCHEMISTRY AS A MULTISDICIPLINAR FIELD LABORATORY SPECTROSCOPY & AB INITIO CALCULATIONS DATA PUBLIC CDMS & JPL CATALOGS OR PRIVATE SPECTRAL CATALOG (J. CERNICHARO : 2700 species of which 2400 are included in the RT codes) COLLISIONAL RATES H 2, He, H, e - CHEMICAL MODELS RADIATIVE TRANSFER LVG NON LOCAL ETL REACTION RATES GAS AND GRAIN CHEMISTY MOLECULAR ABUNDANCES New Species Source Structure Chemistry Physical Conditions

23 MODELING ASTROPHYSICAL DATA Lines arise from a region where temperature and density vary very fast The medium is not homogeneous It is necessary to use more sophisticated methods e.g. LVG multishell or non-local codes

24 METHODS: Non LTE radiative transfer (LVG and non Local Codes) u Statistical Equilibrium n j ( 4π JB ji + γ jin) + n j Aji ni (4π JBij + γ ijn) ni j i j> i j i j< i A ul 4πJB lu 4πJB ul γ ul n γ lu n n i J dn dt i = A ij radiative collisional l J = ( 1 β ) S + βi LVG codes ν bg ν n i population Ray tracing intensity n i n i n i n i frecuency

25 MODELING LVG multishell models

26 MODELING LVG multishell models

27 MODELING LVG multishell models Results T A* (K) NaCl V LSR (km s -1 )

28 METHODS: Interpreting the lines T A* (K) J=34-33 Rotational temperature Diagram 3kW log 2 8π νsμ N = log Z 3 HC 5 N en IRC J=43-42 J=53-52 rot log e E kt log (3kW/8p 3 nsm 2 ) rot up Frecuencia (GHz) E up (K) Integrated intensity of the lines Rotational temperature (T rot ) and column density (N) Very crude approach for most species! 1) rotational levels in LTE at some Trot 2) the medium has to be homogeneous 3) optically thin lines 4) no infrared pumping 5) T rot >> T CMB

29 THE SPECTROSCOPY PROBLEM Weeds How to deal with future ALMA data? What we need from laboratory groups? -isotopologues, vibrationally excited states Which direction have we to follow? => high frequency (ALMA) => Physical processes => Low frequency (GBT, VLA, SKA) => Heavy species?

30 Astrochemistry : the problem of collisional rates Getting physical and chemical conditions from data requires a detailed study of the radiative transfer through the observed source. Only a few molecules (see, e.g., BASECOL) have been studied in detail and in most cases in collisions with He. When collisional rates are not available astronomers do a lot of poor assumptions : This molecule is isoelectronic to this one, then let us use the same collisional rates!! For example HNC and HCN. A rather simple case but HNC/HCN>1 in cold dark clouds. Chemical models have problems to explain this result. However,

31 Detailed comparisons between species are only possible if collisional rates are available for both species Even for an isotopologue and its mother molecule the rates can be very different (H 2 O and HDO; CH 3 OH, CH 2 DOH and CH 3 OD, ) Source structure and isotopic shifts in the frequencies of vibrational and electronic transitions can affect the excitation of the molecule and even its chemistry (UV selfshielding). The calculation of a the collisional rates for a complex molecule can take a long time, even with the faster and cheaper computers we have nowadays We rely 100% on chemical-physics groups accepting to do the job in close collaboration with astronomers. (message for astronomers : when quoting databases, please, quote also the sources!!) SECOND TALK : THE OBSERVATIONS AND THE CHEMISTRY