New models of interstellar gas±grain chemistry ± I. Surface diffusion rates

Transcription

1 Mon. Not. R. Astron. Soc. 319, 837±850 (2000) New models of interstellar gas±grain chemistry ± I. Surface diffusion rates Deborah P. Ruffle 1 and Eric Herbst 2w 1 Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA 2 Departments of Physics and Astronomy, The Ohio State University, Columbus, Ohio 43210, USA Accepted 2000 July 21. Received July 17; in original form 2000 April 3 1 INTRODUCTION Much evidence has been amassed that the chemistry in dense interstellar clouds occurs in both the gas phase and on grain surfaces (e.g. van Dishoeck & Blake 1998). Two approaches to modelling the surface chemistry have been implemented. The more widely used method was first developed by Pickles & Williams (1977) and has since been employed by a number of different authors (d'hendecourt, Allamandola & Greenberg 1985; Brown 1990; Brown & Charnley 1990; Hasegawa, Herbst & Leung 1992, hereafter HHL; Hasegawa & Herbst 1993a,b, hereafter HH93a, HH93b; Caselli, Hasegawa & Herbst 1993; Caselli, Hasegawa & Herbst 1994, hereafter CHH94; Willacy & Williams 1993; Shalabiea & Greenberg 1994; Willacy & Millar 1998). In this approach, the grain-surface chemistry is treated through the use of rate equations in an analogous manner to the gas-phase chemistry. The rate equations describe the temporal evolution of molecular concentrations on grains as a function of accretion, formation, destruction and desorption terms. An intrinsic problem of this method, though, is that the abundances calculated for species are averages. It is only in the limit of a large number of reactive species on a grain that these averages are exact; this case is known as the `reaction' limit. Unfortunately, this limit does not typically pertain to small interstellar dust particles. In the second method, the chemistry is `accretion' limited by w herbst@mps.ohio-state.edu ABSTRACT In recent years it has become evident that large differences can exist between model results of grain-surface chemistry obtained from a rate equation approach and from a Monte Carlo technique. This dichotomy has led to the development of a modified rate equation method, in which a key element is the artificial slowing down of the diffusion rate of surface hydrogen atoms. Recent laboratory research into the surface diffusion rate of atomic hydrogen suggests that atomic hydrogen moves more slowly on grains than heretofore assumed. This research appears to lessen the need for modifications to the rate equation method. Based on the new laboratory work, we have developed appropriate models of gas-phase and grainsurface chemistry in quiescent dense cloud cores to examine the chemical effects of slowing down the rate at which atomic H can scan over dust surfaces. Furthermore, we have investigated the effect of slowing down the rate at which all species can move over grain surfaces. Key words: molecular processes ± stars: formation ± ISM: abundances ± ISM: clouds ± ISM: molecules. the rate at which gas-phase species adsorb on to the grain surface rather than by the surface reaction rates (Allen & Robinson 1977). Consider the adsorption of two reactive species on to a grain. As long as one of them can migrate over the surface easily and not evaporate too soon, the pair will react before another species is adsorbed. The chemistry can be described in a Monte Carlo manner, by following the sticking of successive species on to an individual grain. Several authors have used this approach for timeindependent chemical models (Tielens & Hagen 1982; Tielens & Allamandola 1987; Charnley, Tielens & Rogers 1997; Tielens & Charnley 1997). It has so far proved impossible to couple the Monte Carlo approach with a fully time-dependent chemistry, nor is it obvious that the accretion limit always pertains. Until recently, most modelling studies with coupled gas-phase and granular chemistry contained the rate equation approach of Pickles & Williams (1977) despite its shortcomings. In our laboratory, a variety of such studies were published, mainly appropriate for quiescent dense cores, rather than for regions of active star formation, which have higher gas and dust temperatures. In the first study, HHL explored models of coupled gasphase and grain-surface chemistry, and studied the production of surface species via reactions on the grain-surface or resulting due to accretion from the gas phase. The only desorption mechanism considered was thermal evaporation. In HH93a, the chemical network used was expanded to include organo-sulphur reactions, both in the gas phase and on grain surfaces. In addition, surface reactions of the type q 2000 RAS

2 838 D. P. Ruffle and E. Herbst X 1 H 2! XH 1 H (where X is a radical) were included, albeit with uncertain activation energies. It was found that if the barriers for these reactions are low enough such that efficient tunnelling through them can occur, then the formation of complex molecules on dust grain surfaces is greatly reduced. Moreover, a non-thermal desorption mechanism, cosmic ray-induced impulsive heating of the entire grain, was added to the model, following the work of LeÂger, Jura & Omont (1985). In HH93b, a new three-phase approach to the modelling of surface chemistry was developed, in which a chemical distinction is made between species in the grain mantle and those that are on the grain surface. Species in the mantle were taken to be inert; they can neither react nor desorb. The differences to the earlier two-phase (gas±surface) models were found to be minor for inert species, yet for reactive species substantial alterations were found, particularly at late times. This approach has not been used by us subsequently, due both to its complexity and to the increasing awareness that the rate equation method has severe shortcomings. The shortcomings were dramatically illustrated in a talk at a conference given by Tielens (1995, unpublished), who showed for a simple model of grain chemistry, involving a limited number of reactants, that the rate equation approach could not reproduce the results of a Monte Carlo technique in the accretion limit, particularly for atomic hydrogen-poor conditions (see also Charnley et al. 1997; Tielens & Charnley 1997). In response, Caselli, Hasegawa & Herbst (1998, hereafter CHH98) developed a series of semiempirical modifications to the rate equation approach, appropriate for a grain temperature of 10 K, such that the results are in good agreement with those of the Monte Carlo method for simple systems akin to that of Tielens. The modifications focus on atomic hydrogen, the most mobile surface species, and involve replacing the atomic hydrogen diffusion rate in the expression for reaction rate coefficients when the accretion limit pertains. Briefly, these modifications are: (i) the efficiency of H atom reactions with heavier, less mobile species is reduced by slowing the diffusion rate of H atoms to the shorter of the evaporation and accretion time-scales; (ii) the surface recombination of H atoms is altered to allow explicitly for the fact that one H atom may evaporate from the surface before another lands on the same grain; (iii) an empirical adjustment to the first modification is made when the evaporation rate (the inverse of the time-scale for evaporation) of H is larger than its accretion rate. Following this work, Shalabiea, Caselli & Herbst (1998, hereafter SCH) examined the effects of the modifications for models of dense cloud cores at 10 K with a complex gas-phase and grain-surface reaction network, utilizing a variety of different initial conditions. Discrepancies between the results of unmodified and modified models were found, yet these were seen to be particularly dependent on the initial form of hydrogen chosen. When molecular hydrogen is taken to be dominant initially, some significant differences exist for the early evolutionary stages, yet, at late times the unmodified and modified results appear to converge, especially for the main grain mantle components. On the other hand, when atomic H is dominant initially, the differences between unmodified and modified model results are minimal. Unfortunately, SCH reduced reaction rates for reactions between H and stable species such as CO that possess activation energy in the same manner as they reduced the rates for barrierless reactions. This approach is now recognized via comparison with Monte Carlo studies (Caselli & Herbst, in progress) to underestimate the rates of reactions with barriers. After the paper by SCH appeared, new laboratory work by Katz et al. (1999) concerning the recombination of H atoms on cold olivine and amorphous carbon surfaces was published. This work indicates that hydrogen atoms diffuse much more slowly on grain surfaces than anticipated by astrochemists. Previous studies of grain surface chemistry adopted values for the barriers against atomic hydrogen diffusion and desorption following Tielens & Hagen (1982). Tielens & Hagen estimated the barrier values from their own experiments on the mobility of hydrogen atoms within cold ice matrices and from the experimental results of Govers, Mattera & Scoles (1980) on the binding of H 2 on water ice. Katz et al. (1999) also determined that the atoms appear to thermally hop from well to well as they scan over the grains rather than tunnelling from site to site, as had heretofore been assumed. The effect of these results is to lessen the need for the first and third modifications in the modified rate method, without affecting the need for the second. But the results of Katz et al. (1999) raise another important question: do other species on grain surfaces diffuse much more slowly than has been assumed in the past, or was the diffusion rate of H atoms uniquely poorly estimated? In this work we present new model results of coupled gas-phase and grain-surface chemistry appropriate to quiescent dense cloud cores at 10 K, utilizing a reduced version of the modified rate equation approach that incorporates only the second of the modifications of CHH98. An updated chemical network is utilized. We explore separately the effects of slowing the diffusion of atomic hydrogen according to the results of Katz et al. (1999) and of slowing the diffusion rates of all species across the grain surface. In a separate paper, (Ruffle & Herbst, in progress), we investigate how the inclusion of photochemistry affects grainsurface populations. Parallel work by Caselli & Herbst (in progress) is being undertaken on simple networks of grain reactions to supply appropriate modifications to surface reaction rates at temperatures above 10 K. In the following section we describe in more detail the diffusion rates used, the new modified rate equation approach for 10-K grains, and the model network employed. In Section 3 we present our results. Finally in Section 4 we discuss the effects of slowing down the rate at which hydrogen and other species diffuse across the surface. 2 GRAIN-SURFACE RATES AND MODELS For the unmodified rate equation approach, expressions for the concentration of a species i in the gas-phase, n(i), and on the grain-surface, n s (i), are given by the differential equations dn i =dt ˆ X X K lj n l n j 2 n i X K ij n j 2 k acc i n i j j l 1 k evap i 1 k crd i Šn s i ; 1 dn s i =dt ˆ X X k lj n s l n s j 2 n s i X k ij n s j 1 k acc i n i j j l 2 k evap i 1 k crd i Šn s i 2 (HHL; HH93a; SCH), where K lj and k lj represent the gas-phase and grain-surface rate coefficients, respectively. The gas-phase and grain-surface chemistries are linked through accretion and desorption terms. With the assumption of unit sticking efficiency,

3 New models of interstellar gas±grain chemistry 839 the rate coefficient for accretion of species i on to grains, k acc (i), is given by k acc i ˆsy i n d where s is the grain cross-section, y(i) is the thermal speed of the species and n d is the grain number density n d ˆ n H 1: cm 23 ; HHL). The rate coefficients k evap (i) and k crd (i) account for the two desorption processes incorporated in the model ± thermal evaporation (HHL) and non-thermal cosmic rayinduced desorption (HH93a), respectively. The grain-surface rate coefficients k ij represent the sum of diffusion rates for the reactive species over the entire grain times the probability of reaction converted into units the same as those for second-order gas-phase rate coefficients (HHL); diffusion can occur via thermal hopping or quantum mechanical tunnelling between adjacent potential wells. Diffusion rates depend on the activation energy barrier against diffusion, E b, while desorption rates depend on the desorption energy, E D. In the modified rate equation approach, the modified rate coefficients, k 0 ij, are similar to their unmodified counterparts, k ij, except that the hydrogen atom diffusion rate is replaced with the slower of the accretion or evaporation rates. Additional modifications (CHH98) are not used here (see below) and there are no changes to the form of the rate law. The recent laboratory work of Katz et al. (1999) has yielded hydrogen atom activation energy barriers for diffusion, E b (H), and desorption energies for atomic and molecular hydrogen, E D (H) and E D (H 2 ), for both olivine and amorphous carbon surfaces. The values obtained are given in Table 1. The new energy barriers for H-atom diffusion derived by Katz et al. (1999) are both significantly larger than the previous value used in our models (Tielens & Hagen 1982; HHL; HH93a,b; CHH94; SCH), which is also listed in Table 1. They are appropriate for `bare' grain surfaces. In dense interstellar clouds, ice mantles rapidly form on grains. The diffusion barrier for ice surfaces has not been measured directly and may be quite different. The older work of Tielens & Hagen (1982), used previously by us, indicates a smaller value but the work of Bergin & Langer (1997) may indicate the opposite. Experiments are clearly needed on ice surfaces. Katz et al. (1999) determined, in addition, that the reaction of two H atoms to form H 2 does not proceed via quantum mechanical tunnelling of H atoms through the barriers separating adsorption sites. Rather, it occurs via thermal hopping of H atoms over the barriers. The increase in the height of the barrier and the need for thermal hopping act to slow down the diffusion rate of atomic H on grain surfaces; this decrease may have important effects on the grain-surface chemistry. To determine these effects, we have chosen to investigate the chemistry occurring on olivine, because the diffusion barrier of H on this surface, though higher than the energy used in the past, is still low enough that a diffusive chemistry at 10 K can occur. The chemistry on amorphous carbon at 10 K, on the other hand, may well require the Eley±Rideal mechanism, in which reaction occurs only when a gas-phase species lands directly atop an adsorbed atom. Perhaps in the future, gas±grain models will be able to incorporate a timedependent barrier against diffusion as the nature of the surface changes. We have chosen to investigate two models, designated Model 1 (M1) and 2 (M2). Tables 1 and 2 contain barriers against diffusion and desorption energies for H and assorted other reactive species used in these models. Other than for H and H 2, the desorption energies remain unchanged from previous models. The new 3 Table 1. Diffusion barriers and desorption energies (K) for H and H 2. desorption energy for H is only slightly greater (373 versus 350 K) than the previously used value, whilst the new desorption energy for H 2 is considerably lower than that used previously (315 versus 450 K). Even the small increase in E D (H) raises the thermal evaporation time at 10 K for H atoms from 530 to 5200 s. Conversely, H 2 is now much more efficiently desorbed in M1 and M2; the thermal evaporation time is 24 s, a huge decrease from the previous value of 1: s: This large decrease lowers the importance of molecular hydrogen as a reactant on grains. The major changes in our new models involve diffusion rates. In M1, the barrier against diffusion for H is raised from 100 K, the value used in previous models, to 200 K. No other barriers against diffusion are changed. With this increased barrier and the lack of tunnelling, the surface migration of atomic H occurs at approximately the same rate as does that of other atoms such as C, N, and O. Were the barrier raised to the Katz et al. (1999) value of 287 K, H atoms would travel more slowly than their heavier counterparts, a result we find unreasonable. In M2, we increase the H diffusion barrier to the value measured by Katz et al. (1999) for olivine, but we also raise the analogous barriers for other reactive species by a significant amount. The criterion selected is that each species i should have the same relative values as atomic H between the diffusion barrier, E b (i), and the desorption energy, E D (i). From inspection of Table 1, this can be expressed as E b i ˆ0:77 E D i ; E b (H) E D (H) E D (H 2 ) Olivine Amorphous carbon Old Models Model M Model M Table 2. Assorted desorption energies and diffusion barriers (K). Species M1±2 M1 M2 E D (i) E b (i) E b (i) H He C N O S CH NH OH which is in stark contrast with our previous proportionality constant of 0.3, obtained from Tielens & Allamandola (1987). The need for rate modifications of the type advocated by CHH98 is greatly reduced when the efficiency of atomic hydrogen diffusion across the surface is lowered. Essentially, in our models, atomic H is rarely in the accretion limit, which is defined by N H! 1 (where N(H) refers to the average number of hydrogen atoms on the grain surface), as can be seen later in Section 3. In the work of CHH98, the unmodified H atom diffusion rate is times greater than the evaporation rate, whereas in M1 it is 4

4 840 D. P. Ruffle and E. Herbst only 32 times the evaporation rate. Hence, for the 10-K grains utilized in our model calculations, the first modification is marginally needed for model M1. In M2, the modification does not apply at all because the unmodified diffusion rate for H is actually less than 0.01 of the evaporation rate. Performing the first modification for M1 results in changes in abundances of at most a factor of a few for dominant surface and gaseous species, so this modification has been ignored. The second modification concerns H 2 formation in the situation where the rate of evaporation of H from grains exceeds the accretion rate onto grains. The original exponential form of this modification has recently been shown to be in error since it does not incorporate the random nature of the time-interval between successive H landings on a particular grain (Hollenbach, private communication; Biham, private communication). Correct incorporation of this randomness leads to the simpler expression k 0 H;H ˆ 2 k for x $ 1 5 where k is the H atom evaporation rate (s 21 ) and x is the evaporation rate divided by the accretion rate (k acc (H)n(H). The expression, which applies only if the evaporation rate is less than the diffusion rate, is essentially identical with the first modification. It is marginally necessary only for M1, where it has been included. We note that our model results do not appear to be sensitive to the change in modification 2. The third modification was found to be unimportant in complex models by SCH, and we ignore it here. A new modification concerning reactions with barriers is being implemented by Caselli & Herbst (in progress); use of their preliminary results had little effect. 2.1 Gas±grain network The model network used derives from that employed in SCH and HH93a, yet many modifications to the rate-file have been made. For the gas-phase chemistry, we use the latest `new standard model' network described by Herbst, Terzieva & Talbi (2000), which includes 8 new species and 358 new gas-phase reactions. For the neutral species, grain-surface counterparts have been added (we do not consider charged grain-surface species) and reaction and desorption terms for these species have been included where appropriate. For the interaction of neutral species with grains, we adopt a sticking coefficient of 0.5. Atomic positive ions recombine with negatively charged grains to be neutralized and desorbed. Molecular positive ions in dense clouds typically recombine with electrons in the gas phase long before they strike dust grains; nevertheless we allow the ions HCO 1 and H 1 3 to recombine dissociatively on negatively charged grains, following the work of Aikawa, Herbst & Dzegilenko (1999). We have added photodissociation reactions so that all gas-phase molecules in the network can undergo this process. Molecules for which photodissociation pathways were included tend to be large in size (e.g. C n H 4, n ˆ 4±9; H 2 C m N, m ˆ 3; 5; 7; 9 : We have included photodissociation due to both the background interstellar and the cosmic ray-induced radiation fields (Prasad & Tarafdar 1983; Gredel, Lepp & Dalgarno 1987; Sternberg, Dalgarno & Lepp 1987; Gredel et al. 1989). The rate coefficient for cosmic ray-induced photodissociation, k CR, is given by k CR s 21 ˆAz: Values of A have been determined for many species (Gredel et al. 1989). When including this process for species for which 6 calculated rate coefficients are not available, we utilize values of the efficiency, A, for similarly sized and similar element-bearing molecules. For dissociation by the background photons, the rate coefficient, k UV, can be expressed as k UV s 21 ˆB exp 2CA V Š: where A V is the visual extinction. Where available, we have used the rate coefficients and products for large species from Bettens & Herbst (1995). The grain-surface chemistry that we use is similar to those of SCH and HH93a, except that some new reactions have been added, and we have significantly altered the method by which methanol is produced. In SCH, model results were presented for two differing values of the reaction barrier for molecular hydrogen with carbon chains and hydrocarbons: H 2 1 C n! C n H 1 H and H 2 1 C n H! C n H 2 1 H; where n ˆ 2±9: The barriers, 2100 and 4200 K, were first introduced in HH93a. In this paper, we have taken the higher value for the barriers, such that the formation of complex molecules is not drastically reduced, as is found when the barrier is taken to be 2100 K (HH93a; SCH). For the surface production of methanol, we now use the simple hydrogenation of CO via successive addition reactions with atomic hydrogen (e.g. Charnley et al. 1997). Based on calculations of Woon (private communication), we have adopted a value for the activation energy barrier of 2500 K for the association reactions of H atoms with both CO and with H 2 CO. Previous work (Charnley et al. 1997) has used much lower values for these activation barriers of 1834 and 1000 K, respectively, based on some experimental observations of Hiraoka et al. (1994). 2.2 Initial conditions All the models for which we present results in the next section contain a value for the total hydrogen number density, n H, where n H ˆ n H 1 2n H 2 ; of cm 23 ; which is appropriate for dense cores. We adopt a gas and dust temperature of 10 K and assume a value for the visual extinction, A V, of 10 mag. We use the standard value for the cosmic ray ionization rate, z, of 1: s 21 : Desorption from the grains occurs thermally and via impulsive heating induced by cosmic rays. Model results for gas± grain chemistry are dependent on the initial form of hydrogen adopted, atomic or molecular, as atomic H is critical for hydrogenation of grain-surface species. Following the nomenclature in our earlier papers (HHL; HH93a,b; SCH), case A denotes that gaseous hydrogen is in molecular form initially, whereas case B indicates that gaseous atomic hydrogen predominates initially. In case A models, the gaseous atomic H abundance remains low whilst, in case B models, the initially high abundance of atomic H slowly decreases to the case A value. In case B there will therefore be more atomic H available to undergo surface hydrogenation for a considerable amount of time. We shall refer to the case A and B versions of the models as M1/A, M1/B, M2/A, and M2/B. For the initial elemental gaseous abundances, we assume `low metal' abundances following Lee, Bettens & Herbst (1996); these are listed in Table 3. In Table 4 we summarize and contrast the model conditions used in SCH and our models M1 and M

5 New models of interstellar gas±grain chemistry RESULTS Three general features of our results should be mentioned before they are discussed in detail. First, diffusive surface chemistry occurs for both models M1 and M2. In others words, despite the slowing of the diffusion rate for H in one case, and for all reactive species in the other case, surface chemistry still plays an important role in the gas±grain models. Surface reactions between two heavy species are no longer competitive, however, in M2. Secondly, although the case B models contain atomic hydrogen initially, a boon to surface hydrogenation reactions, the amount of gas-phase hydrogen in atomic form is eventually reduced to the value of the case A models. Consequently, given a continually active chemistry, the results of the two cases tend in many cases to converge at times afterward. Thirdly, the gas-phase abundances of many polyatomic molecules show in addition to a peak at early time, as is customary in purely gas-phase models, a secondary peak at rather late times (cf. Section 3.3). This second peak, which is especially strong for M2, occurs despite the eventual depletion of all heavy molecules on to the dust grains. This non-intuitive result was first discussed by Ruffle et al. (1997) for the molecule HC 3 N. Smaller gas-phase species in M2 tend to maintain large abundances through 10 7 yr without showing a strong doublepeaked evolution. In Tables 5±8 we list the results of models M1/A, M2/A, M1/B, and M2/B for four times: 10 2,10 5,10 6 and 10 7 yr. The grainsurface results for M1/A and M2/A are in Table 5, while the gas-phase results for these models are in Table 6. Similarly, the grain-surface results for M1/B and M2/B are in Table 7 while the gas-phase results are in Table 8. The tables include surface species which are dominant in our calculation and gas-phase species of interest. The results, given as absolute abundances, can be converted into fractional abundances by division by the total hydrogen number density, n H. The surface abundances can be Table 3. Initial elemental fractional abundances. Element Fractional (initial form) abundance H 1.00 He 1.4(21) N 2.14(25) O 1.76(24) C 1 7.3(25) S 1 8.0(28) Si 1 8.0(29) Fe 1 3.0(29) Na 1 2.0(29) Mg 1 7.0(29) P 1 3.0(29) Cl 1 4.0(29) Table 4. Summary of different model conditions. converted into number of species per grain by division by < cm 23 ; the grain concentration. In describing the behaviour of the abundances of particular species below, we refer to the grain-surface species unless otherwise stated. The temporal evolution of individual species on grains and in the gas reflects competing formation and depletion routes which can lead to complex patterns. For surface species, we can divide the molecules into four categories depending on these formation and depletion processes. The categories, shown in Table 9, determine, especially at early times, in which model and case the surface molecules tend to be most abundant. At later times, when adsorption from the gas becomes a competitive formation route for surface molecules, surface chemistry can become less important and the categories can become obscured. Consider one category: molecules formed by surface reactions involving heavy species. These surface molecules tend to be produced more efficiently in M1 models, since the species diffuse more rapidly, and in case A, because there is less surface H available to process the reactants. Molecules can fall into more than one category or can switch categories as a function of time, in which cases their relative abundances in the differing models are especially difficult to predict. Individual species, discussed below, illustrate this complexity. One should note that a suitably modified rate method simulates the Monte Carlo approach, which in the accretion limit yields results insensitive to diffusion rates as long as they are sufficiently rapid to cause reaction before evaporation or another accretion event occurs. So, why should the M1 and M2 results differ? Of course, Monte Carlo approaches do not include competition from gas-phase chemistry. But, in addition, the scanning times for H over an entire grain are very different in the two models ± <160 s in M1 and <10 6 s in M2 ± with the former actually less than the hydrogen evaporation time (5200 s). The result is that whereas in M1 H-heavy species reactions compete favorably with evaporation, the opposite can be true in M H 2 O, CO, CH 3 OH and CO 2 In Fig. 1 the evolution of the fractional abundance of water ice for models M1 (circles) and M2 (squares) is plotted. The case A results are given by filled symbols and solid lines, whereas the case B results use hollow symbols and dashed lines. Water is mainly produced by the hydrogenation of atomic oxygen by H atoms: H 1 O! OH followed by the hydrogenation of OH: H 1 OH! H 2 O; although there is another, less important, sequence of reactions Model E b (H) E D (H) E D (H 2 ) E b i =E D i a H reactions b CHH98 modifications c (K) (K) (K) (K) SCH QT Yes Yes Yes M TH No Yes No M TH No No No a i stands for all species other than H and H 2. b QT, via quantum mechanical tunnelling; TH, via thermal hopping. c See Introduction.

6 842 D. P. Ruffle and E. Herbst Table 5. Case A abundances for surface species (cm 23 ). Species 10 2 yr 10 5 yr 10 6 yr 10 7 yr M1 M2 M1 M2 M1 M2 M1 M2 H 2 O 2.6E E E E E E E E100 CO 1.7E E E E E E E E201 CO 2 1.4E E E E E E E E203 H 2 CO 9.0E E E E E E E E201 CH 3 OH 8.6E E E E E E E E201 H 2 O 2 6.2E E E E E E E E205 CH 4 2.4E E E E E E E E201 NH 3 8.0E E E E E E E E202 H 2 3.2E E E E E E E E208 H 3.0E E E E E E E E208 N 2 3.2E E E E E E E E202 O 2 2.8E E E E E E E E206 HCN 1.9E E E E E E E E202 HNC 3.6E E E E E E E E202 HNO 1.3E E E E E E E E202 HNCO 1.9E E E E E E E E202 C 2 H 2 3.6E E E E E E E E205 C 2 H 4 8.0E E E E E E E E207 C 2 H 6 1.1E E E E E E E E202 C 3 H 2 4.8E E E E E E E E206 C 3 H 4 5.6E E E E E E E E202 C 4 H 4 1.7E E E E E E E E203 C 5 H 2 3.4E E E E E E E E206 C 5 H 4 1.8E E E E E E E E203 C 6 H 2 2.6E E E E E E E E206 C 6 H 4 1.2E E E E E E E E203 C 7 H 2 1.3E E E E E E E E206 C 7 H 4 5.0E E E E E E E E203 CH 5 N 2.4E E E E E E E E203 HC 3 N 2.2E E E E E E E E207 NH 2 CHO 1.8E E E E E E E E205 CH 3 CN 1.1E E E E E E E E204 C 3 H 3 N 1.2E E E E E E E E208 H 3 C 5 N 7.2E E E E E E E E203 H 5 C 3 N 1.1E E E E E E E E204 H 3 C 9 N 1.7E E E E E E E E206 NH 2 CN 5.2E E E E E E E E203 that produces water from O 2. Water is depleted slowly by desorption. Although there is a partial distinction among models and cases for very early times, by, yr the model results have very nearly converged. Water ice reaches a fractional abundance of by 10 6 yr in all models, at which time it consumes a considerable proportion of the elemental abundance of O in our models. One would naively expect based on the categories elucidated above that at very early times water would be most abundant in model M1/B but in reality only model M2/A, which contains a small abundance of slowly moving surface H atoms, shows significantly reduced water abundances. Even in this model, surface reactions are important in the production of water ice. Fig. 1 shows the temporal evolution of water ice if no surface reactions are allowed to occur except for the formation of H 2. Here H 2 O builds up only gradually on grain surfaces; still if one waits long enough, a considerable amount of surface water is produced. In Fig. 2 the evolution of the fractional abundance of surface CO for models M1/A, M2/A, M1/B and M2/B is plotted, using the same symbols as in Fig. 1. At early times, CO is most abundant in M1/A and least abundant in M1/B and M2/B. The relatively high abundance in M1/A is caused by surface reactions of C with O, O 2 and OH; accretion becomes important at later times. These surface reactions are very slow for M2 models, where accretion of gaseous CO dominates as a formation mechanism at all times. The CO molecule is not bound very tightly to grains, hence desorption via cosmic rays is an important loss mechanism. It is also processed into HCO by reaction with H and (for M1/A) into CO 2 by reactions with OH and O. The reaction with H, which occurs with an activation energy of 2500 K, is more effective under atomic H-rich conditions, hence the depletion of CO is greater for case B at early times, helping to drive down the CO abundance. Eventually, the results for the M1 models converge (<10 6 yr). For the M2 models, CO is always more abundant under case A conditions. Carbon monoxide reaches a peak fractional abundance of < in M2/A at a time slightly greater than 10 6 yr, at which time its abundance is comparable with the gas-phase value. The inexorable decrease in CO at times.10 6 yr occurs as it is slowly processed by reaction with H into HCO and its source, gasphase CO, itself declines, especially for M1. In Fig. 3 we display the evolution of CH 3 OH for all 4 models used. Methanol is formed by successive hydrogenation of CO: H 1 CO! HCO; H 1 HCO! H 2 CO; H 1 H 2 CO! CH 3 O; H 1 CH 3 O! CH 3 OH: The first and third reactions of the sequence are relatively slow,

7 Table 6. Case A abundances for gas-phase species (cm 23 ). New models of interstellar gas±grain chemistry 843 Species 10 2 yr 10 5 yr 10 6 yr 10 7 yr M1 M2 M1 M2 M1 M2 M1 M2 since they have activation energy barriers of 2500 K. Since reactions (13) and (15) are barrierless there is little accumulation of surface HCO and CH 3 O. The radical CH 3 O can also be produced by the reaction O 1 CH 3! CH 3 O; H 1.2E E E E E E E E101 CH 2.2E E E E E E E E204 CN 8.2E E E E E E E E203 CO 1.8E E E E E E E E202 CS 4.4E E E E E E E E208 H 2 1.0E E E E E E E E104 N 2 1.7E E E E E E E E202 O 2 3.2E E E E E E E E204 C 2 H 1.1E E E E E E E E204 C 2 S 1.2E E E E E E E E209 CH 2 6.2E E E E E E E E204 CO 2 4.8E E E E E E E E204 H 2 O 3.6E E E E E E E E204 HCN 1.6E E E E E E E E203 HNC 2.0E E E E E E E E203 HNO 6.4E E E E E E E E205 C 3 H 3.2E E E E E E E E204 C 2 H 2 6.4E E E E E E E E204 H 2 CO 2.0E E E E E E E E204 H 2 O 2 9.2E E E E E E E E214 NH 3 5.4E E E E E E E E203 HNCO 7.0E E E E E E E E211 C 4 H 9.0E E E E E E E E204 C 3 H 2 6.4E E E E E E E E204 CH 4 3.0E E E E E E E E203 HC 3 N 1.8E E E E E E E E205 HC 2 NC 1.4E E E E E E E E206 HCNC 2 4.2E E E E E E E E208 HNC 3 1.3E E E E E E E E207 NH 2 CN 1.6E E E E E E E E204 C 5 H 6.6E E E E E E E E206 C 2 H 4 8.0E E E E E E E E207 CH 3 CN 3.6E E E E E E E E206 CH 3 OH 1.1E E E E E E E E207 NH 2 CHO 1.3E E E E E E E E206 C 5 H 2 1.3E E E E E E E E206 C 3 H 4 2.0E E E E E E E E206 C 3 H 3 N 4.6E E E E E E E E208 CH 5 N 1.6E E E E E E E E206 HC 5 N 2.8E E E E E E E E205 C 6 H 2 3.2E E E E E E E E205 C 2 H 6 6.6E E E E E E E E211 C 7 H 2 2.4E E E E E E E E206 H 5 C 3 N 5.0E E E E E E E E222 H 3 C 5 N 5.0E E E E E E E E224 HC 7 N 4.6E E E E E E E E206 HC 9 N 5.6E E E E E E E E207 H 3 C 9 N 5.0E E E E E E E E which is competitive at very early times, before the build-up of CO. Methanol is depleted slowly by desorption. For times earlier than,10 5 yr, methanol is most abundant in models M1/B and M1/A. By 10 5 yr, model M2/B converges on the M1 results. Methanol has a much lower abundance until very late times (*10 7 yr) in model M2/A. The reduction in CH 3 OH at early times in M2/A and M2/B is due to the relative slowness of reaction (16). At intermediate times, the large activation barriers in reactions (12) and (14) coupled with the small H diffusion rate tend to slow the conversion of CO into methanol. However, for M2/B the increased abundance of surface hydrogen compensates, resulting in the steep rise in CH 3 OH production. For M2/A, it is not until late times that the surface abundance of H is sufficient to overcome the reduced reaction rates. Even for significant cloud ages (,10 6 yr), model M2/A produces far less methanol than the other three cases. In Fig. 4 we plot the evolution of CO 2. Carbon dioxide is produced by the reaction of O and HCO: O 1 HCO! CO 2 1 H; by the association of CO and O: CO 1 O! CO 2 ; and, especially for M2 models, by accretion from the gas phase,

8 844 D. P. Ruffle and E. Herbst Table 7. Case B abundances for surface species (cm 23 ). Species 10 2 yr 10 5 yr 10 6 yr 10 7 yr M1 M2 M1 M2 M1 M2 M1 M2 H 2 O 5.4E E E E E E E E100 CO 2.4E E E E E E E E202 CO 2 1.2E E E E E E E E203 H 2 CO 2.0E E E E E E E E202 CH 3 OH 9.6E E E E E E E E100 H 2 O 2 2.4E E E E E E E E206 CH 4 1.9E E E E E E E E201 NH 3 6.8E E E E E E E E202 H 2 4.6E E E E E E E E208 H 9.0E E E E E E E E208 N 2 7.2E E E E E E E E202 O 2 3.0E E E E E E E E207 HCN 1.2E E E E E E E E202 HNC 1.9E E E E E E E E202 HNO 4.2E E E E E E E E202 HNCO 5.4E E E E E E E E202 C 2 H 2 2.0E E E E E E E E206 C 2 H 4 2.2E E E E E E E E208 C 2 H 6 9.6E E E E E E E E203 C 3 H 2 6.0E E E E E E E E207 C 3 H 4 2.0E E E E E E E E204 C 4 H 4 2.6E E E E E E E E204 C 5 H 2 8.2E E E E E E E E208 C 5 H 4 2.4E E E E E E E E204 C 6 H 2 5.0E E E E E E E E208 C 6 H 4 2.4E E E E E E E E205 C 7 H 2 4.4E E E E E E E E209 C 7 H 4 2.4E E E E E E E E205 CH 5 N 4.0E E E E E E E E204 HC 3 N 5.0E E E E E E E E208 NH 2 CHO 3.8E E E E E E E E206 CH 3 CN 7.2E E E E E E E E204 C 3 H 3 N 2.6E E E E E E E E209 H 3 C 5 N 2.0E E E E E E E E205 H 5 C 3 N 3.0E E E E E E E E205 H 3 C 9 N 2.0E E E E E E E E208 NH 2 CN 5.0E E E E E E E E203 where it is produced mainly by the reaction between CO and OH. This reaction can also occur on dust particles, especially for M1 models. Desorption is the only loss mechanism for CO 2. Reaction (17) must compete with reaction (13), which it does more successfully under H-poor conditions. Carbon dioxide fits neatly into the category of molecule formed by surface reactions with heavy species, and so is most abundant in the M1/A model until late times. 3.2 Other surface species Methane and ammonia are important surface molecules, reaching abundances that are,0.01±0.2 of the water ice abundance. The formation mechanisms for CH 4 and NH 3 are similar to that of water so that one would expect a similar temporal evolutionary pattern, in which case B models show enhanced abundances at early time, but eventually all models/cases converge. The distinction at early time is indeed present. For the M2 cases, convergence occurs by 10 5 yr, whilst for M1, reality is more complex than expectation. Convergence between cases A and B occurs for NH 3 only at very late times, whereas for CH 4, the abundance is always lower in the A case. In addition, both ammonia and methane are enhanced in M2/A with respect to M1/A at all times, because the radical precursors can only react efficiently with H. The diatomics N 2 and O 2 show very different behaviour for models M1 and M2. Molecular nitrogen is reduced at all times in M2 with respect to M1, presumably because the surface reactions that form it involve two heavy species and its destruction is only by desorption. Molecular oxgyen, however, is enhanced in M2 at all times past 10 2 yr, despite the obvious fact that the surface chemistry of formation will doubtless be more rapid for M1. The M2 abundances can be large ± at 10 6 yr O 2 is,0.3 per cent of the water ice abundance in M2/A. Presumably, a rapid surface destruction of O 2 in M1 more than compensates for the relatively rapid formation. In M1 O 2 is produced mainly from the surface reactions of two oxygen atoms and of atomic hydrogen with ozone. Accretion becomes dominant at late times. Oxygen is processed on the surface by several reactions in M1; the important ones are reaction with H to form O 2 H, oxidation to form O 3 and reaction with CH to form HCO and O. For M2 the majority of the O 2 comes from accretion, while desorption now becomes an important loss mechanism. Interestingly then, the surface abundance of O 2 in M2 is not much affected by any surface reactions. For the remaining species in Tables 5 and 7 we find that the majority are at first decreased in M2/A relative to the M1/A

9 Table 8. Case B abundances for gas-phase species (cm 23 ). New models of interstellar gas±grain chemistry 845 Species 10 2 yr 10 5 yr 10 6 yr 10 7 yr M1 M2 M1 M2 M1 M2 M1 M2 H 2.0E E E E E E E E101 CH 1.1E E E E E E E E205 CN 2.8E E E E E E E E204 CO 4.6E E E E E E E E203 CS 1.1E E E E E E E E209 H 2 6.0E E E E E E E E104 N 2 7.4E E E E E E E E202 O 2 3.0E E E E E E E E205 C 2 H 6.8E E E E E E E E205 C 2 S 3.6E E E E E E E E210 CH 2 2.0E E E E E E E E204 CO 2 1.3E E E E E E E E206 H 2 O 1.5E E E E E E E E204 HCN 1.4E E E E E E E E203 HNC 1.5E E E E E E E E203 HNO 4.6E E E E E E E E206 C 3 H 1.8E E E E E E E E206 C 2 H 2 1.2E E E E E E E E205 H 2 CO 5.4E E E E E E E E206 H 2 O 2 5.0E E E E E E E E215 NH 3 2.2E E E E E E E E203 HNCO 4.6E E E E E E E E211 C 4 H 3.2E E E E E E E E206 C 3 H 2 6.0E E E E E E E E206 CH 4 1.1E E E E E E E E203 HC 3 N 3.6E E E E E E E E206 HC 2 NC 8.8E E E E E E E E207 HCNC 2 1.4E E E E E E E E209 HNC 3 6.2E E E E E E E E208 NH 2 CN 3.2E E E E E E E E204 C 5 H 1.6E E E E E E E E208 C 2 H 4 2.8E E E E E E E E207 CH 3 CN 1.9E E E E E E E E206 CH 3 OH 3.8E E E E E E E E208 NH 2 CHO 2.0E E E E E E E E207 C 5 H 2 4.0E E E E E E E E208 C 3 H 4 4.6E E E E E E E E207 C 3 H 3 N 4.0E E E E E E E E208 CH 5 N 4.6E E E E E E E E205 HC 5 N 6.8E E E E E E E E206 C 6 H 2 1.4E E E E E E E E207 C 2 H 6 8.8E E E E E E E E212 C 7 H 2 3.8E E E E E E E E209 H 5 C 3 N 4.4E E E E E E E E222 H 3 C 5 N 5.0E E E E E E E E226 HC 7 N 1.8E E E E E E E E209 HC 9 N 9.2E E E E E E E E210 H 3 C 9 N 5.0E E E E E E E E227 Table 9. Categories of surface molecules. Category Formed by reactions involving H atoms Destroyed by reactions involving H atoms Formed by surface reactions of heavy species Destroyed by surface reactions of heavy species Model/ case for high abundance M1/B M2/A M1/A M2 values, indicating an important role for surface chemistry in forming the species, but by times around 10 7 yr the results either agree well or the species generally become more abundant in M2/A. Similar behaviour is seen for the comparison of M1/B and M2/B, yet the early-time differences between the case B results are less severe since most species are formed via reactions with atomic H and since large early-time abundances of H can often overcome smaller reaction rate coefficients. 3.3 Gas-phase species When we compare the gas-phase results presented in Tables 6 and 8 we find that at early times many species are reduced in the case B models relative to the case A values. Ion±molecule chemistry is not initiated until there is an appreciable abundance of H 2 ; this does not occur until,10 5 yr for the case B models. At times only slightly later than this, adsorption on to grains can become important. The case A results show the standard early-time peaks (,10 5 yr) for organic molecules seen in pure gas-phase models. Comparing M1/A with M2/A and, analogously, M1/B with M2/B, we find that most gas-phase species have very similar abundances until 10 6 yr. By 10 7 yr large differences exist between M1 and M2, especially for case A results. The majority of the species are enhanced in the gas-phase for M2 models; for M2/A there is a sizeable second, `late-time' peak for organic species roughly equal