A THREE-PHASE CHEMICAL MODEL OF HOT CORES: THE FORMATION OF GLYCINE

The three-phase model used here is described in detail by Garrod & Pauly (2011), and is based on the approach of Hasegawa & Herbst (1993). In contrast to both of those methods, MAGICKAL simulates an active ice-mantle chemistry in addition to that occurring in the surface layer of the ice or on the dust-grain surface. Previous two-phase hot-core models, such as those of G&H, GWH, and Belloche et al. (2009), have implicitly assumed a combined surface/mantle chemistry, using surface kinetics to simulate all dust-grain chemical processes, including those within the bulk ice. Although satisfactory results may be obtained through this simplification, it has become clear through experimental means (e.g., Öberg et al. 2009b) that the promotion of complex-molecule formation within organic ices by UV photolysis involves sub-surface processes, even in relatively thin ices (on the order of 10 monolayers).

In order to simulate chemical kinetics within the ice mantles, it is here assumed that the mobility of chemical reactants in the bulk ice occurs through a barrier-mediated thermal diffusion process. Other authors have assumed a swapping mechanism to be active in laboratory ice experiments (Öberg et al. 2009a; Fayolle et al. 2011), which is also implicitly assumed in this model. The swapping rate is parameterized in the same way as the surface thermal hopping, i.e.,

$$\begin{equation} k_{\mathrm{swap}}(i)=\nu _{0}(i) \ \exp [-E_{\mathrm{swap}}(i)/T_{d}], \end{equation} \tag{ 1 }$$

where ν₀ is the characteristic vibrational frequency of an harmonic oscillator, T_d is the dust temperature, and E_swap is an energy barrier associated with the swapping of species i with an adjacent water molecule, in line with the adoption of surface binding energies appropriate to amorphous water ice, following G&H and GWH.

Ratios between the surface diffusion barrier and the desorption energy of any particular species bound to an ice or any other surface are poorly constrained, and various authors have used values in the approximate range of 0.3–0.8. Garrod & Pauly (2011) found that the production of interstellar CO₂ ice could be well reproduced by the adoption of ratios E_dif:E_des ≲ 0.4; here a value of 0.35 is used. Thence, a value of E_swap:E_des = 0.7 is assumed for the swapping barrier, on the simplistic consideration that a bulk-ice molecule is bound to approximately twice the number of binding partners as a surface molecule. In analogy to the surface chemical reaction rates, the rate of reaction between mantle-species A and B is given by

$$\begin{equation} R_{\mathrm{AB}}=N_{m}(A) \ N_{m}(B) \ [k_{\mathrm{swap}}(A) + k_{\mathrm{swap}}(B)] / N_{\mathrm{M}}, \end{equation} \tag{ 2 }$$

where N_m(i) is the population of species i in the ice mantle, and N_M is the total population of the ice mantle, including all species.

As discussed by Garrod & Pauly (2011), in the three-phase model, material in the surface layer is transferred to the bulk ice according to the net rate of deposition of material onto the grain from the gas phase, with a similar, alternative transfer occurring in reverse in the case of a net desorption of mantle species into the gas phase. These transfers represent the covering or exposure of ice material as the boundary of the ice-surface layer is constantly re-defined within the model, rather than the physical transport of material. However, the inclusion of bulk diffusion within the ice should allow a true exchange of chemical species between surface and mantle, through the aforementioned swapping mechanism.

This surface–mantle swapping is a pair-wise process, and therefore requires the construction of rates for each chemical species in the mantle and in the surface layer, which must collectively produce no net transfer between the two phases. This zero net rate would be assured using an explicit pair-wise coupling of every species in the surface with every species in the grain mantle; however, such an approach is found to be computationally exhaustive, and requires estimates of the pair-wise positions of the swapped species that a rate-based model cannot provide, other than through purely statistical considerations.

Instead, the swapping rates from mantle to surface are calculated first, with rates analogous to that of Equation (2). The total rate in this direction is then matched with an identical total transfer rate from surface to mantle, apportioned to all the surface species according to their fractional contribution to the total surface-layer population. Thus,

$$\begin{equation} R_{\mathrm{swap,m}}(i)=N_{m}(i) \ \frac{N_{S}}{N_{M}} \ k_{\mathrm{swap}}(i), \end{equation} \tag{ 3 }$$

$$\begin{equation} R_{\mathrm{swap,s}}(i)= \frac{N_{s}(i)}{N_{S}} \cdot \sum _{all j} R_{\mathrm{swap,m}}(j), \end{equation} \tag{ 4 }$$

where R_{swap, m}(i) is the rate of mantle-to-surface swapping of mantle species i, R_{swap, s}(i) is the rate of surface-to-mantle swapping of surface species i, N_m(i) and N_s(i) are the mantle and surface populations, respectively, of species i, and N_M and N_S are the total mantle and surface populations. The ratio N_S/N_M in Equation (3) is taken as unity when it exceeds this value, representing the case where some surface species reside on the dust-grain surface itself and have no underlying mantle.

Because the model does not assign specific positions to each atom or molecule in the mantle, the rate of mantle-to-surface swapping, R_{swap, m}(i), is required to be representative not simply of the final diffusion step, but of the entire chain of diffusion steps by which a mantle species at arbitrary distance from the surface layer will reach the surface. The use of k_swap in Equation (3) as the rate of a typical, or average, step in this process is accurate so long as the final diffusion step from mantle to surface is relatively fast, i.e., that intramantle diffusion is the rate-limiting step in the entire journey from mantle to surface. Under the assumption that the ice is predominantly water ice (see above), the final surface-to-mantle step will be fast for species whose binding energies are less than or similar to that of water. For the small minority of species with significantly greater binding energies than this, for which there would thus be an associated endothermicity to the mantle–surface swap with a water molecule (see, e.g., Öberg et al. 2009a), the large absolute size of the swapping barrier would render the rate of mantle-to-surface diffusion negligible compared to other processes, such as the mantle-to-surface transfer associated with net surface desorption.

These rates defined in Equations (3) and (4) are also considered in the loss and gain rates used for the modified-rate calculations of Garrod (2008), which are applied in this model (using "method C"). Garrod et al. (2009) showed that this method produces a very close approximation to the results of exact Monte Carlo methods, using a large chemical network under a range of physical conditions.

The chemical network used in this model is based on that of GWH and the subsequent additions of Belloche et al. (2009), which featured a treatment for nitriles, including amino acetonitrile (NH₂CH₂CN). These networks assumed grain-surface radical–radical formation mechanisms for newly added complex organic molecules, as well as destruction mechanisms such as grain-surface and gas-phase photodissociation (by both the ambient and cosmic ray-induced UV fields), gas-phase ion–molecule reactions (including protonation) and the related electronic recombinations of the products, as well as accretion from the gas phase onto the grain surfaces, and thermal and non-thermal desorption from the grains. The initial elemental abundances used are shown in Table 1. Laas et al. (2011) constructed a network of reactions to treat the formation of trans-methyl formate, the higher energy conformer of the commonly observed cis-methyl formate; however, that study found no significant effect on the abundances of species other than trans-MF, so the omission of the related chemistry is not expected to have any effect on the models presented here.

Following the same methodology, formation and destruction processes are included for glycine and a suite of related molecules, including glycinal, propanal, and propionic acid. Radical–radical reactions for a selection of these species are shown in Table 2. Whereas in the previous models, a single complex molecule was typically assumed to be the only possible product of the addition of key grain-surface radicals, here alternative product branches are included, for the case where such a reaction could also result in a pair of stable products, and where the reaction is also exothermic. Thus, for the reaction HCO + CH₃O → HCOOCH₃, which was found by GWH to be the predominant formation route for methyl formate, alternative product branches of [CO + CH₃OH] and [H₂CO + H₂CO] are now also included. The branching ratios are in general poorly defined, and are likely to be significantly different between the gas- and solid-phase processes; statistical ratios are therefore adopted (e.g., 1:1:1 for HCO + CH₃O). In addition, the same such two-product reactions are now also included in the gas-phase chemistry, using measured rates¹ where available; otherwise, a uniform second-order rate coefficient of 10⁻¹¹ cm³ s⁻¹ is assumed. Such processes may become important in the late, high-temperature stage of hot-core evolution, during which the evaporation, protonation, and subsequent electronic recombination may lead to significant quantities of molecular radicals being present in the gas phase. However, the single-product branches are omitted from the gas-phase chemistry, because of their negligible rates, due to the absence of a grain surface to carry away excess energy and thereby stabilize the product.

Following previous models, grain-surface hydrogen-abstraction reactions are added for reactions between the new complex species and the most significant grain-surface radicals such as H, OH, CH₃, CH₂OH, CH₃O, and NH₂. Table 3 shows activation-energy barrier information used in the model, for a selection of (primarily hydrogen abstraction) reactions occurring on the grains. For atomic-hydrogen reactions relating to methanol formation, for which more complex fits to theoretical rates are employed, the simpler rectangular-barrier parameter fits are quoted, as for all other barrier-mediated reactions. The method of Hasegawa et al. (1992) is used to calculate the tunneling and thermal rates associated with these parameters, adopting the faster of the two for any given temperature. For the majority of reactions, only gas-phase data are available, in which case the activation energy derived from fits to the lowest-temperature data sets available are adopted for the surface/mantle reactions, assuming a barrier width of 1 Å. In cases where no data exist, the activation energy, E_A, is estimated using the Evans–Polanyi relationship, which states that the difference in E_A between reactions of a similar type is proportional to the difference between the enthalpy changes associated with each reaction. Parameters for the Evans–Polanyi relationship are obtained from Dean & Bozzelli (1999), or from fits using similar reactions, indicated in Table 3. Where the enthalpy change of reaction is unknown, the activation energy of a similar reaction is used directly. There is evidence that the presence of a surrounding water-ice matrix may alter activation energy barriers for specific product branches (e.g., Goumans 2011, in the case of formaldehyde-related chemistry), or lower the internal barriers to the structural re-arrangement of a product (e.g., Duvernay et al. 2005, in the case of the isomerization of cyanamide). It is therefore plausible that some of the gas-phase activation energies used in this model over-estimate the barriers in the solid phase; however, such effects are difficult to quantify without a specific computational or experimental study of each solid-phase reaction and its low-temperature tunneling characteristics.

For self-consistency, all reactions of surface radicals with complex species are now assumed to result in hydrogen abstraction, in contrast to GWH, who included a small selection of alternative substitution reactions for aldehyde group-bearing species. These reactions typically provided only minor destruction or formation routes for the species involved, and their removal has no significant influence over the glycine chemistry described below.

All processes related to grain-surface chemistry outlined above are likewise incorporated into the chemistry of the bulk ice, with identical activation energies (where present), while their reaction kinetics are instead defined by the bulk-ice diffusion parameters discussed in Section 2.1. Photodissociation of ice mantles is also included to all depths, without attenuation, in line with previous models. This is a reasonable first-order approximation; using the photon absorption cross-section of amorphous water ice for the first absorption band measured by Mason et al. (2006), Andersson & van Dishoeck (2008) calculate an absorption probability per photon of 0.007 per monolayer of water ice. The maximum quantity of water ice formed on the grains in this model corresponds to ∼114 monolayers; this would result in a UV field strength at the deepest ice layer of ∼45% of the value at the surface. This corresponds to a mean value of 69% of the assumed field strength, for the ice mantle as a whole. However, the ices formed on interstellar dust-grain surfaces constitute a mixture of various molecular species, and the absorption cross-sections for many of these are currently unknown or poorly defined.

No desorption processes are allowed from the bulk ice; thus desorption of these species must proceed via a prior transfer of material from mantle to ice surface. Reaction–diffusion competition is also included for reactions mediated by activation-energy barriers (following G&P), for both surface and bulk-ice reactions; this is perhaps the largest departure from the methods of GWH, as this change can produce reaction efficiencies many orders of magnitude different from the simple Arrhenius treatment of previous models.

Surface desorption processes included are thermal evaporation (as defined by the binding/desorption energy, E_des), reactive desorption as described by Garrod et al. (2007), and photodesorption using measured rates determined by Öberg et al. (2009c, 2009d); following G&P, all surface species are assumed to photodesorb with an efficiency of 10⁻³, in the case where values are not provided by those authors.

The indirect mechanism for CO₂ formation proposed by G&P is also included for reactions both on the surfaces and within the ice mantles.

The reproduction of the high observed abundance (∼10⁻⁸ with respect to H₂) of methyl formate (HCOOCH₃) in hot cores has proved somewhat problematic in previous astrochemical models. Garrod & Herbst (2006) showed that grain-surface formation mechanisms could produce adequate quantities of methyl formate (MF) to explain observations; however, in some cases it was found (Garrod et al. 2008; Belloche et al. 2009) that the evaporation of MF at relatively low temperatures could result (dependent on the warm-up timescale) in only a small fraction of this material surviving the transition to the gas phase. Belloche et al. (2009) adopted a higher binding energy for MF (5200 K versus 4100 K), citing the importance of hydrogen bonding in the estimation of this value; they found that this value produced results appropriate to observational abundance values for methyl formate. This value is also adopted here. Table 4 shows a selection of other binding energies used in the present model.

As found by GWH and Laas et al. (2011), the rates and branching ratios of methanol photodissociation in the ice mantles are crucial to the production rates and ratios of various complex organic molecules detected in hot cores, as the ice-mantle methanol provides a large supply of structurally complex organic material.

The present model uses the methanol branching ratios derived from the experiments of Öberg et al. (2009b) for products [CH₂OH+H]:[CH₃O+H]:[CH₃+OH] of 5:1:1. In the absence of other information, these values are applied to both the direct UV photodissociation by the interstellar radiation field, and to photodissociation by the secondary UV photons produced by cosmic rays, the latter of which is most important at the high visual extinctions of the hot-core phase. These ratios are applied throughout to the ice and gas phases, although, as found by Laas et al. (2011), the importance of gas-phase methanol photodissociation to complex molecule production is minimal.

Activation-energy treatments for CO and H₂CO use best-fit expressions to uni-molecular and bi-molecular rates recently acquired through quantum transition state theory (T. P. M. Goumans 2011, private communication; S. Andersson 2011, private communication). Hydrogen abstraction from H₂CO and CH₃OH are included, mediated by activation energy barriers, while hydrogen abstraction from HCO and CH₃O/CH₂OH are also allowed (producing H₂ + CO/H₂CO), assuming branching ratios of 1:1 with the associated hydrogen-addition channels (i.e., no activation energy).

2.4.1. Grain-surface/Mantle Chemistry

A number of potential routes have been suggested in the literature for the formation of glycine in interstellar ices, based on laboratory evidence or theoretical considerations. Experiments by Bernstein et al. (2002) and Muñoz-Caro et al. (2002) showed that UV irradiation of interstellar ice analogs containing H₂O, CH₃OH, CO, CO₂, NH₃ and/or HCN could produce significant quantities of amino acids, including glycine. Sorrell (2001) had suggested a route involving the reaction of the NH₂ radical with acetic acid (CH₃COOH), itself formed through the addition of CH₃ and HOCO, while Woon (2002) suggested that the addition reaction between radicals NH₂CH₂ and HOCO could explain the formation of glycine, with these species produced in the ices by successive hydrogenation of HCN and by the addition of CO to OH, respectively. Experimental work by Holtom et al. (2005) involving the electron bombardment of CO₂/NH₂CH₃ ices confirmed the viability of Woon's mechanism. Elsila et al. (2007) found Woon's mechanism to be consistent with the origins of the nitrogen and central carbon in the glycine molecule, while the origin of the acidic carbon was more consistent with the formation of glycine occurring via a nitrile precursor, i.e., amino acetonitrile (NH₂CH₂CN).

Here, we include a number of new radical-addition reactions relating to glycine and similar species. Each hydrogenation step suggested by Woon (2002) is included, although all but the final addition of NH₂CH₂ + HOCO was already present in the network. However, other routes are also included, such as the addition reaction NH₂CH₂ + HCO → NH₂CH₂CHO (glycinal), whose product may (for example) be photodissociated to produce the radical NH₂CH₂CO, which may further react with OH to produce glycine. There are four final processes that lead to glycine in this network,

$$\begin{eqnarray} &\mathrm{H} + \mathrm{NH}\mathrm{CH}_{2}\mathrm{COOH} \rightarrow \mathrm{NH}_{2}\mathrm{CH}_{2}\mathrm{COOH} \end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray} &\mathrm{NH}_{2} + \mathrm{CH}_{2}\mathrm{COOH} \rightarrow \mathrm{NH}_{2}\mathrm{CH}_{2}\mathrm{COOH} \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray} &\mathrm{NH}_{2}\mathrm{CH}_{2} + \mathrm{HOCO} \rightarrow \mathrm{NH}_{2}\mathrm{CH}_{2}\mathrm{COOH} \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} &\mathrm{NH}_{2}\mathrm{CH}_{2}\mathrm{CO} + \mathrm{OH} \rightarrow \mathrm{NH}_{2}\mathrm{CH}_{2}\mathrm{COOH} \end{eqnarray} \tag{ 8 }$$

although there are several ways in which each radical may come to be formed, either through chemical reaction or by photodissociation of a stable molecule. Reaction (5) is also complemented by exothermic radical-radical reactions with species (e.g., HCO) that may donate a hydrogen atom to form two stable molecules, as described in Section 2.2. Reaction (5) typically follows the photodissociation of, or H abstraction from, glycine itself; reactions (6)–(8) are thus the major potential formation routes.

Woon suggests the formation of HOCO by the reaction of CO and OH. This process is difficult to model accurately, due to the complex nature of the transition states; the reaction may also lead to the formation of CO₂ + H (see G&P, and references therein), or may dissociate back to CO + OH, dependent on the rapidity of energy loss to the surface. As such, the OH + CO reaction is modeled separately for each set of products, assuming an activation energy barrier of 2500 K for the HOCO branch, following the approach of GWH. In practice, the formation of HOCO in the model is dominated by the photodissociation of or chemical hydrogen abstraction from formic acid (HCOOH) in the ice, which is formed predominantly by HCO + OH additions (see GWH).

Also included in the model is a selection of species similar to glycine, but with alternative functional groups. For example, glycinal (NH₂CH₂CHO) and propionic acid (C₂H₅COOH) are modeled, through analogous reactions to those of glycine, while new dust-grain formation routes are added for propionaldehyde (or propanal, C₂H₅CHO), which has been detected toward Sgr B2(N) (Hollis et al. 2004). The inclusion of these other species ensures that the importance of reactions leading to glycine formation is not overestimated due to the omission of competing reaction pathways.

2.4.2. Gas-phase Chemistry

The physical model used here broadly follows that of G&H and later papers, in which a collapse phase is followed by a static warm-up phase. In the first phase, the density increases from n_H = 3 × 10³ to 10⁷ cm⁻³, under the free-fall collapse expression given by Nejad et al. (1990). However, in contrast to previous hot-core models, while the gas temperature is held at a constant 10 K, the temperature of the dust varies with visual extinction, according to Equation (17) of G&P, which describes the heating of the dust by the interstellar radiation field, assuming a dust-grain radius of 0.1 μm. At the initial visual extinction of A_V = 2, the dust temperature is ∼16 K; during collapse, this falls to a minimum temperature of 8 K.

During the subsequent warm-up phase, the core is heated from 8–400 K, with density held at 10⁷ cm⁻³. Three warm-up timescales are adopted, which are the same as previous models, in so far as they reach 200 K at the same point in time (Table 6). However, the warm-up is extended beyond this time, until 400 K is reached, so that the later evaporation and gas-phase behavior of more strongly bound species, such as glycine, may be studied over a longer period. During the warm-up phase, gas and dust temperatures are assumed to be well coupled due to the high density; the gas kinetic temperature follows that of the dust grains when T_dust >10 K. Table 6 shows the details of the three warm-up phase physical models.

Table 7 shows the composition of the dust-grain ices at the end of the collapse phase (corresponding to the starting values for each of the following warm-up models), as well as observational values for comparison.

3.1.1. Glycinal

3.1.2. Glycine

3.1.3. Amino Acetonitrile

3.1.4. Propionaldehyde and Propionic Acid

3.2.1. Methanol and Formaldehyde

3.2.2. Methyl Formate and Glycolaldehyde

The peak abundance of methyl formate (MF, HCOOCH₃), shown in Figures 1–3 panel (b), is in line with that expected from observations (around 10⁻⁸ n_H), except for the slow warm-up model. The evaporation of methyl formate prior to that of methanol and various other species leaves it vulnerable to destructive reactions with molecular ions, whose abundance would otherwise be lessened by the presence of other reaction partners. The long timescale between methyl formate and methanol evaporation in the slow model therefore leads to significant methyl formate destruction; a similar result was noted by GWH and Belloche et al. (2009), in the case of a lower assumed MF binding energy.

Methyl formate is formed entirely on the dust grains in this model, by the reaction HCO + CH₃O. Production is mainly within the ice mantles, peaking at 25 K, although significant production also occurs on the ice surface.

Glycolaldehyde (CH₂(OH)CHO), shown in Figures 1–3 panel (c), is formed similarly to its a structural isomer methyl formate, via HCO + CH₂OH. Its gas phase and ice abundance is greater than that of MF, due to the more rapid production of CH₂OH over CH₃O—by a factor of five (for photodissociation) in this model. Observations of protostellar envelopes, however, do not demonstrate this large abundance of glycolaldehyde; the recent detection by Jørgensen et al. (2012) toward the Class 0 protostellar binary IRAS 16293−2422, using the ALMA telescope, indicated a HCOOCH₃:CH₂(OH)CHO ratio of 10–15 (although the observational glycolaldehyde rotational temperature of 200–300 K is consistent with the present model results).

The discrepancy may be related to the assumed branching ratios of the reactions between HCO and either CH₃O or CH₂OH:

$$\begin{eqnarray} \mathrm{HCO} + \mathrm{CH}_{3}\mathrm{O} & \rightarrow \mathrm{HCOOCH}_{3} \ (-423 \ \mathrm{kJ \ mol^{-1}}) \end{eqnarray} \tag{ 9a }$$

$$\begin{eqnarray} & \rightarrow \mathrm{CO} + \mathrm{CH}_{3}\mathrm{OH} \ (-372 \ \mathrm{kJ \ mol^{-1}}) \end{eqnarray} \tag{ 9b }$$

$$\begin{eqnarray} & \rightarrow \mathrm{H}_{2}\mathrm{CO} + \mathrm{H}_{2}\mathrm{CO} \ (-292 \ \mathrm{kJ \ mol^{-1}}) \end{eqnarray} \tag{ 9c }$$

and

$$\begin{eqnarray} \mathrm{HCO} + \mathrm{CH}_{2}\mathrm{OH} & \rightarrow \mathrm{CH}_{2}\mathrm{(OH)CHO} \ (-290 \ \mathrm{kJ \ mol^{-1}}) \quad\quad \end{eqnarray} \tag{ 10a }$$

$$\begin{eqnarray} & \rightarrow \mathrm{CO} + \mathrm{CH}_{3}\mathrm{OH} \ (-276 \ \mathrm{kJ \ mol^{-1}}) \end{eqnarray} \tag{ 10b }$$

$$\begin{eqnarray} & \rightarrow \mathrm{H}_{2}\mathrm{CO} + \mathrm{H}_{2}\mathrm{CO} \ (-197 \ \mathrm{kJ \ mol^{-1}}). \end{eqnarray} \tag{ 10c }$$

(The enthalpy change associated with each reaction, ΔH⁰_f, is indicated in brackets.) The branching of each set of reactions is assumed to be [1:1:1] in these models. Each branch of Equations (9) and (10) is exothermic, and branches (a) and (b) would require minimal internal re-arrangement. The single-product routes in each case are the most exothermic; however, in the case of glycolaldehyde formation, the enthalpy change related to reaction branch (10b) is close to that of (10a). While the assumed efficiency of branch (c) (i.e., parity with the other two branches) may be over-estimated in both Equations (9) and (10), the production of CO and CH₃OH (10b) may be very competitive with the formation of glycolaldehyde (10a), while it may be less so in the case of methyl formate.

It thus appears plausible, by this simplistic analysis, that a difference in the efficiencies of formation of MF and glycolaldehyde via their primary grain-surface/ice-mantle formation routes could account for the order-of-magnitude discrepancy in observational abundances. However, a detailed theoretical determination of the branching behavior of these reactions in the solid phase would be necessary to confirm this theory. Alternative branching ratios in the photodissociation of methanol, to produce a significant excess of CH₃O over CH₂OH is also possible, although the current—and only—estimate of these values for solid-state methanol, based on experimental rate-fitting, suggests precisely the opposite relationship (CH₃O:CH₂OH of 1:5; Öberg et al. 2009b).

A decrease in the efficiency of glycolaldehyde production as described above would be unlikely to affect significantly the abundances of other observed species, although the production of postulated molecules related to glycolaldehyde, such as dihydroxyacetone (HOCH₂COCH₂OH) could be affected. The destruction rates of the HCO and CH₂OH radicals would remain the same, while the increased re-formation of CO and CH₃OH resulting from the alternative product branch would have only a minor effect on the already large abundances of those species.

The glycine formation routes included in this model are sufficiently independent from the glycolaldehyde chemistry that glycine production would also be unaffected by the adoption of an alternative efficiency for glycolaldehyde formation. Similarly, while acetic acid (CH₃COOH) is a structural isomer of both glycolaldehyde and methyl formate, its different structure means that its formation routes are not directly related to those of its isomers; the choice of treatment for glycolaldehyde would there have little effect on its own abundance or, through it, that of glycine. The chemical behavior of acetic acid is discussed above, in Section 3.1.1.

3.2.3. Formic Acid

3.2.4. Formamide

With the simple addition of reactions (11), the results are unchanged; the contribution of the gas-phase processes is never remotely significant compared to those on the dust grains, in spite of the availability of both reactants at similar times/temperatures.

It is noteworthy that the abundances of NH₂OH achieved in the current models are around three orders of magnitude lower than those calculated by GWH; the reason for this is that the major formation route for NH₂OH on the grains is the addition of surface/ice-mantle NH₂ and OH radicals. The availability of both these reactants is significantly curtailed in the present model by the inclusion of new hydrogen-abstraction reactions for these species (see Table 3) and by the more accurate consideration of the kinetics of grain-surface reactions that are mediated by activation energy barriers (see G&P); each reactant is more readily converted back to H₂O or NH₃ before the OH and NH₂ radicals are able to meet. A recent observational search by Pulliam et al. (2012), using the NRAO 12 m telescope, detected no NH₂OH toward a range of previously observed sources, with fractional abundance upper limits of 8 × 10⁻¹² toward Sgr B2(N). The authors noted that emission from a region more compact than 5'' would not be detectable with their instrument, while the model suggests that the NH₂OH would be at least as compact as typical hot-core molecules such as methyl formate or ethanol, based on evaporation temperatures. Nevertheless, the new model results for NH₂OH are more in line with the observational data.

However, a recent laboratory study suggests that the formation of NH₂OH by successive grain-surface hydrogenation of NO is extremely efficient (Congiu et al. 2012). While hydrogenation of NO and HNOH are already present in the network, the reaction of H with HNO has until now been assumed to lead to H-abstraction, with a barrier of 1500 K.

To increase the effect of the glycine-forming gas-phase reactions, a parallel branch is added to the surface/ice reaction set: H + HNO → HNOH. A barrier of 1500 K is also assumed; but at low temperatures, the reaction competes effectively with hydrogen diffusion, producing a reaction efficiency that is close to unity. As a result, large amounts of NH₂OH are formed, in this case during the cold collapse phase, rather than the warm-up phase. A total fractional abundance of 8 × 10⁻⁷ is present in the ice by the end of collapse, i.e., as the starting point for the warm-up phase (see Table 7). This agrees well with the cold-cloud models presented by Congiu et al. (2012).

In order to further increase the influence of the gas-phase mechanisms, the rate coefficient of reaction (11a) is increased to 10⁻⁹ cm³ s⁻¹, a plausible maximum value for this reaction.

The results of this optimized model are shown in Figure 4. The large quantities of NH₂OH present in the dust-grain ices alters the fractional abundances of various species in the model by a small degree, although with a negligible direct effect on the production of glycine within the ice. The abundance of glycine is in fact slightly reduced, as a result of the somewhat lower quantity of acetic acid present in the ice. The destruction of gas-phase acetic acid is rather faster in this model, due to reaction (11a). However, when compared to an identical model with reaction (11a) switched off (not shown), the contribution of the gas-phase reaction to the total glycine formed in this model is around 2% of the total formed on the grains. Some of the glycine that is formed in the gas phase is re-accreted onto the grains, to evaporate later with the rest, while the remainder is destroyed by ion–molecule reactions. The immediate impact on gas-phase glycine abundance by the newly included mechanisms may be seen in the small bump at around 130 K; less than 10⁻¹² n_H is produced. It may be noted that, if no glycine-production mechanisms of any kind were active in the ices, and all production thus depended on the gas-phase route, two abundance peaks would likely occur, at 130 K and 200 K, corresponding to peak production and peak evaporation, respectively.

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On the basis that this scenario represents the optimal conditions for gas-phase glycine formation to occur in a hot core (including the use of a very optimistic reaction rate), it appears that the particular gas-phase formation mechanism tested is unlikely to be significant, especially if the mechanisms for formation within the dust-grain ice mantles are in operation as suggested by the model. The plausibility of such a large hydroxylamine abundance as would be required for significant glycine production is also discussed in Section 5.3.

The warm-up phase of the chemical model produces molecular fractional abundances for pre-defined output times, each corresponding to a temperature. The resolution of these output times is chosen such that the associated temperature values are separated by less than 1%, over the 8–400 K range. Van der Tak et al. (2000) provide such physical profiles for the envelopes of 14 nearby high-mass protostellar sources. Using these temperature–radius and density–radius relations, a radius and density is assigned to each temperature value in the chemical model outputs. The fractional abundance of each species in the model at each temperature/radius value is multiplied by its local density, to produce an absolute abundance value measured in cm⁻³. The resulting molecular number-density and temperature profiles are then used to calculate the emission and absorption coefficients at each spherically symmetric radial position in the core.

Partition functions and emission-line data from the JPL line list and the Cologne Database for Molecular Spectroscopy are imported into the code as needed, using the "Splatalogue" online database.² The spectral coefficients may be calculated by this method to incorporate all molecular emission at any given frequency, allowing line blends and line confusion to be taken into account. Gaussian line profiles are assumed, using observationally determined line widths. A channel width (frequency-bin size) much smaller than the line width is chosen (in general, 0.1 MHz or ∼0.08 km s⁻¹), to ensure that the lines are well resolved.

Under conditions of local thermodynamic equilibrium, the equation of radiative transfer may be parameterized thus (Rohlfs & Wilson 2006)

$$\begin{equation} I_{\nu }(s) = I_{\nu }(0) \ e^{-\tau _{\nu }(s)} \ + \ \int _{0}^{\tau _{\nu }(s)} B_{\nu }(T(\tau)) \ e^{-\tau _{\nu }} \ {d} \tau , \end{equation} \tag{ 12 }$$

where I_ν is the specific intensity, τ_ν is the optical depth at frequency ν, T is temperature, s is the line-of-sight distance, and B_ν(T) is the Planck function (equal to _ν/κ_ν, under LTE). Using the gridded, spherically symmetric input data, this equation is integrated numerically along lines of sight (using Simpson's rule), beginning directly on-source, and moving outward through parallel lines of sight until a user-defined maximum offset is reached. Line-of-sight integrals of the absorption coefficient similarly yield the optical depths. This procedure results in an intensity map of the hot core for each frequency channel.

The final step is to convolve the emission with a Gaussian beam centered on the source, using a beam size appropriate to a chosen instrument observing at a given frequency. The intensity map is numerically integrated with the Gaussian function, over the radius of the hot-core envelope, out to a few beam widths. The technique automatically accounts for beam dilution, and makes use of the precise emission structure to calculate an intensity value at each frequency. The resulting simulated spectrum may be directly compared with main-beam temperature (T_mb) spectra obtained from the telescope for which the convolution has been produced.

The molecular mm/sub-mm line emission from a selection of the sources observed by van der Tak et al. (2000) was surveyed by Bisschop et al. (2007) using the James Clerk Maxwell Telescope (JCMT) and IRAM 30 m telescope, providing information on dozens on complex organic species. A member of this subset, the hot-core source NGC 6334 IRS1, is relatively closeby (1.7 kpc), and exhibits relatively narrow (ΔV = 5 km s⁻¹), strong emission lines (see van der Tak et al. 2000 and Bisschop et al. 2007, and references therein). It is also well situated in the sky (decl. (1950) = −35°44') for future observation with the ALMA telescope (latitude −23°). For these reasons, it may be identified as a plausible candidate for the future detection of glycine. The spectroscopic model described above is therefore used to assess the potential for the detection of glycine in this source, on the assumption that its formation and subsequent behavior are well described by the chemical model. The physical profiles provided by van der Tak et al. (2000) are used. In the case of glycine, only emission lines whose frequencies are within the observable ranges of the JCMT, IRAM 30 m, and ALMA telescopes are modeled.

Figure 5 shows—for illustrative purposes—the predicted emission from this source over the 241.350–241.425 GHz range, using a channel spacing of 0.488 MHz. These spectral calculations consider emission from all species in the model for which spectroscopic data exist, using only ground-state transitions. Glycine emission, at 241.373 GHz, is highlighted in red; glycine conformer I is simulated, but not conformer II, due to uncertainty in the partition functions. The upper panel of the figure shows the unconvolved emission for an on-source line of sight—the spectrum may be considered as that expected from a pencil beam of infinite resolution directed at the source. Individual lines are identified in the upper panel; an identification is made where more than half of the emission within a channel derives from a single molecule. The emission from glycine is seen to be slightly blended with emission from glycolaldehyde (CH₂(OH)CHO) in the line wings, but nevertheless shows a clear peak. The middle panel shows the spectrum after convolution of the emission from the entire source (same temperature scale) using a beam width of 04, which encompasses the strongest predicted emission region for glycine (see below) and which should be achievable with ALMA at these frequencies (although the simulation is for a single-dish telescope, rather than an array). The glycine peak is preserved, with a line strength on the order of 1 K. The lower panel of the figure shows the predicted spectrum (different temperature scale) using a beam width appropriate to the JCMT at these frequencies (∼104); the glycine emission line strength is on the order of 1 mK.

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A selection of the strongest emission lines from methanol, methyl formate, and glycine have been simulated using the method above. Methanol and methyl formate were both detected by Bisschop et al. (2007) toward this source; both are typically observed hot-core species. In these calculations, unlike those illustrated in Figure 5, only the emission from an individual molecule is considered at the chosen line frequency; this enables a more straightforward comparison with the unblended lines observed by Bisschop et al. (2007), and makes the calculations less computationally intensive. Furthermore, while line identifications may be made fairly easily in the unconvolved "pencil-beam" simulations, assessing the contributions made by each molecular line to the convolved emission spectra is much more time-consuming. The consideration of the detectability of each glycine line in the following analysis therefore does not consider potential line blends—simply the expected line strength. More detailed assessments of the expected line emission from various species will be made in future work.

Figure 6 shows the emission profiles predicted for the line center of a strong methyl formate line (left panel) and a strong glycine line of similar frequency (right panel; glycine emission is also shown in left panel for direct comparison). The local emission strength (i.e., assuming a pencil beam) is shown in terms of brightness temperature for lines of sight targeted on radial displacements from the source position on the sky. Figure 7 shows the same profiles mapped onto sky coordinates; these emission maps are then convolved with the beam to produce simulated detected brightness temperatures. The most significant emission from methyl formate is seen to emanate from a region of diameter ∼7000 AU, or 4''. All potentially detectable emission from glycine comes from a region ∼08 in diameter, although the most significant emission region is of diameter ∼04, corresponding to a radius of ∼1000 AU.

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5.2.1. Comparison with Observations

5.2.2. Glycine Predictions

Pulliam et al. (2012) recently looked for hydroxylamine emission toward a selection of sources including Sgr B2(N), Orion KL and W3 IRS5. They found no NH₂OH emission using data obtained with the NRAO 12 m telescope, with noise levels of a few mK. Both the GWH model and the enhanced NH₂OH model of Section 4.1 exhibit large fractional abundances for this molecule, albeit with different formation mechanisms in each case. In order to test whether the model values are consistent with the non-detections of Pulliam et al., the spectroscopic model is again applied to the chemical model results. Out of the sources observed by both Pulliam et al. (2012) and van der Tak et al. (2000), the only source present in both data sets is W3 IRS5. For this simulation, a generic line width of 9 km s⁻¹ is assumed, following Pulliam et al. (2012).

Tables 12 and 13 show the results of a selection of NH₂OH emission-line simulations for W3 IRS5, using, respectively, the standard medium warm-up timescale model results, and the results of the model of Section 4.1 that employs a gas-phase glycine formation mechanism and a large initial NH₂OH abundance on the grains, produced by the low-temperature formation of NH₂OH on dust grains during the collapse phase. The results shown in Table 12 are all consistent with the non-detection; Pulliam et al. (2012) find a 1σ noise level of 4.3 mK in their W3 IRS5 data, while the simulated intensities are of order 10 μK or less. However, the model with enhanced NH₂OH formation produces maximum convolved line intensities of around 50 mK, or around one order of magnitude greater than the noise level.