ON THE FORMATION OF GLYCOLALDEHYDE IN DENSE MOLECULAR CORES

Sorrell (2001) discusses the theory of processing icy grain mantles in the interstellar medium with ultraviolet (UV) radiation, producing high concentrations of free radicals (particularly OH and CH₃). These radicals then react in the grain mantles in order to produce large organic molecules such as amino acids and sugars, with the energy for thermal hopping coming from grain–grain collisions. The resulting large organics (including glycolaldehyde) would then be desorbed into the gas phase following mantle explosions, and despite some fraction of these large molecules being destroyed in the process, some would remain intact.

Bennett & Kaiser (2007b) simulated the bombardment of grain mantles with cosmic-ray particles by irradiating laboratory methanol/carbon monoxide ices with energetic electrons at 11 K. Cosmic rays can penetrate entire grains, producing up to 100 suprathermal particles each, which then ionize (methane) ice molecules (Kaiser et al. 1997; Kaiser 2002). The resulting high-energy electrons (∼5 keV) may then affect the mantle chemistry by forming radicals, which subsequently react to form large organic molecules. In a methanol/carbon monoxide ice these large organics include C₂H₄O₂ isomers. The experiment showed that both glycolaldehyde and methyl formate were formed, in addition to many smaller molecules and radicals. Acetic acid was not detected, but can be formed in methane/carbon dioxide ices (Bennett & Kaiser 2007a).

Halfen et al. (2006) postulate that glycolaldehyde may be formed in the gas phase through acid-catalyzed reactions of formaldehyde, based on research on formose reactions (Butlerow 1861; Breslow 1959). Formaldehyde would react with its protonated form to create an intermediate species, which would then undergo reorganization into protonated glycolaldehyde. There is some experimental evidence for this method, although it is unclear whether the resulting C₂H₄O₂ isomer is in fact glycolaldehyde (Jalbout et al. 2007).

Beltrán et al. (2009) highlighted the potential importance of the HCO radical in glycolaldehyde formation. They suggested that reactions between HCO and methanol (or methanol derivatives) or formaldehyde could occur rapidly on grain surfaces in hot cores. Gas-phase routes would be too inefficient. The simplicity of the reaction pathway, which is driven by rapid hydrogenation and the reaction of small surface radicals, means that glycolaldehyde formation could be efficient when densities are high. Only small amounts of CO would need to be processed on grains.

Charnley & Rodgers (2005) suggested that complex molecules build up on grain surfaces through the aggregation of common atoms, since at low temperatures only atoms are likely to be mobile. At early times, atoms such as C, N, or O may accrete significantly, whereas at late times, when most heavy atoms will have frozen out, hydrogenation of molecules will dominate. Such a scheme could not only lead to the formation of glycolaldehyde, but also to other large molecules such as acetic acid and aminomethanol. Methyl formate, however, cannot be formed through this kind of pathway, but only through the combination of relatively large surface radicals.

The model is a two-phase time-dependent model which follows the collapse of a prestellar core (phase I), followed by the subsequent warming and evaporation of grain mantles (phase II). We only consider phase I, since in this work we wish to investigate the potential formation of glycolaldehyde at low temperatures, as suggested by experiment (Öberg et al. 2009; Bennett & Kaiser 2007b). In phase I, a diffuse cloud of density 10² molecules cm⁻³ undergoes free-fall collapse until it has reached a density of ∼10⁷ cm⁻³. This occurs on a timescale of half a million years and at a temperature of 10 K. During the collapse, atoms and molecules collide with, and freeze on to, grain surfaces. We assume that hydrogenation occurs rapidly on these surfaces, so that, for example, some percentage of carbon atoms accreting will rapidly become frozen out methane, CH₄. Initial atomic abundances are taken from Sofia & Meyer (2001), as in Viti et al. (2004). We employ the reaction rate data from the UDfA06³ astrochemical database, augmenting it with grain-surface (hydrogenation) reactions and those reactions included in Table 1. In the formation of glycolaldehyde we only consider the most propitious of circumstances. We discount the destruction of glycolaldehyde on the grains through cosmic ray strikes, photodissociation or further reaction, so that the quantity of glycolaldehyde formed can be regarded as an upper limit. We also assume that, due to the cold temperature, no species will desorb from the grains except H and He. This assumption is reasonable when considering thermal desorption, but neglects the effect of non-thermal desorption mechanisms on both glycolaldehyde and the reactants which go into its formation. Any proposed reaction pathways that do not produce reasonable amounts of glycolaldehyde under these conditions can surely be dismissed from consideration.

First, we investigate the five schemes individually, varying key model parameters, such as the rate coefficients, the final collapse density, the incident UV field, the cosmic-ray ionization rate, and the hydrogenation efficiency of accreted molecules. Finally, we look at all the mechanisms together, to find which is the most efficient in competition.

Many of the rate coefficients of the reactions in Table 1 are completely unknown. In light of this, we consider a wide parameter space, covering up to 14 orders of magnitude in reaction rate. Our aim is to understand the behavior of the reactions in each mechanism, and what effect they have on the abundance of glycolaldehyde, not to determine reaction rates. However, through our investigation we may be able to better constrain possible reaction rates. Where practical, we adopt identical or similar gas-phase reaction rates from UDfA06 or KIDA⁴ for unknown grain-surface rates as a conservative initial estimate (Table 3), given that the grain surface is thought to act as a catalyst. Glycolaldehyde is not included in the standard UDfA06 database, so we utilize rates from analogous reactions which produce methyl formate, or we make very conservative estimates. In varying the rates, we vary only the α-parameter in the rate coefficients: k = α(T/300 K)^βexp (− γ/T) for two-body reactions, k = α for reactions with cosmic rays, and k = αexp (− γA_V) for photoreactions.

We test two final collapse densities, n_f = 10⁶ and 10⁷ cm⁻³, which also have implications for the freezeout percentage of molecules. Viti et al. (2001) argued that in hot cores freezeout is never total and in fact some gaseous CO is always observed, even in regions where no millimeter continuum is detected (e.g., Molinari et al. 2000). Hence, we impose the constraint that a maximum of 90% of the circumstellar material is frozen out at a final density of n_f = 10⁷ cm⁻³, and 75% at 10⁶ cm⁻³.

The strength of the impinging UV field within the core was adjusted solely for mechanism A, since it involves the UV processing of molecules on grains. We investigated the effects of scaling the standard interstellar UV field strength, G₀, by up to 30 times. When investigating reaction B1, we increase the cosmic-ray ionization rate in the model globally by up to 1000 times.

Finally, we tested two different grain-surface hydrogenation regimes, one where the products were more saturated ("f2") and one less saturated ("f1"). These regimes are represented in Table 2. Hydrogenation rates on grain surfaces are unknown, but the calculation of hydrogen-atom hopping and tunneling rates shows that they are rapid in comparison to other grain-surface reactions (Goumans et al. 2007; Tielens 1989). At low temperatures, the recombination of physisorbed atomic hydrogen with chemisorbed atoms dominates. At temperatures <20 K, molecular hydrogen formation efficiency on grain surfaces is near unity (Cazaux & Tielens 2004; Williams et al. 2007). We assume that hydrogenation of species on grain surfaces is instantaneous.

We combine these free parameters into a grid of model results.

In order to explore the effects of enhanced UV irradiation of surface ices in mechanism A (Table 1), we have used the standard reaction rates as shown in Table 3, and the more conservative hydrogenation regime (Table 2). We varied the strength of the UV field by up to a factor of 30 over the standard interstellar field, and the results are plotted in Figure 1. Intuitively, one would expect that increased grain processing of surface-bound H₂O and CH₄ would lead to a greater production of glycolaldehyde. However, higher UV fluxes mean that the gas-phase species which go on to form CH₄ in particular on the grains are destroyed by reaction with abundant photodissociation products like H⁺₃ and H⁺. Thus, the limited abundance of grain-surface CH₄ limits the formation of glycolaldehyde. Water ice increases very marginally in abundance when the core is under higher levels of irradiation.

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Results of the model can be found in Figure 2, where we plot the fractional abundance of glycolaldehyde obtained at the final density of the collapse, n_f, against the scale factor of the "standard" rates, as found in Table 3. We compare models with differing n_f and in the two different hydrogenation regimes, f1 and f2. The fractional abundance of glycolaldehyde in the model is highly dependent on the rate of the final reaction of mechanism A, A5—it scales linearly with the rate until 1–10 times the standard rate, after which the curve turns over to a maximum abundance of x(CH₂OHCHO) ∼ 10⁻⁵. The effect of the differing hydrogenation regimes is minimal. The fractional abundance of glycolaldehyde is fairly insensitive to the rates of reactions A1–A3, increasing by only a factor of 10 or so while the rate coefficients span a range of 10¹⁴. Reactions A1 and A2 compete with grain-surface hydrogenation of O and C in the provision of OH and CH₃ radicals, respectively. As core density increases, photons become increasingly absorbed, meaning that reaction A3 proceeds with reactants that are products of grain-surface hydrogenation rather than grain-surface photolysis (see, Peeters et al. 2006). Reaction A3 itself is competing with the hydrogenation of adsorbed CO, which dominates at high densities, meaning that the abundance of glycolaldehyde is relatively independent of reactions A1–A3 in general.

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Reaction A3 has been studied in the literature, as part of investigations into methanol formation. Experiments on H₂O–CO ice at T < 20 K by Hidaka et al. (2004) do not show any evidence of methane production, which implies that abundances of CH₃ are low. It seems likely that methanol production results mainly from the successive hydrogenation of CO (i.e., CO ⟶ HCO ⟶ H₂CO ⟶ CH₃O ⟶ CH₃OH) rather than via reaction A3 (Hidaka et al. 2004).

Reaction A4 has also been well studied in the literature (e.g., Hudson & Moore 1999; Watanabe et al. 2003), and is a crucial reaction in many of the mechanisms studied here (it is identical to B2, D2, and E1). HCO ice has not been detected in the interstellar medium, implying that its formation is slower than subsequent reactions, e.g., $\mathrm{H} + \mathrm{HCO} \longrightarrow \ \mathrm{H_2CO}$, which have lower activation energies (Watanabe & Kouchi 2002). Indeed, the formation of H₂CO in this way has been shown to be barrierless (Goumans et al. 2007). CO + H has a barrier of several thousand Kelvin in the gas phase (see summary by Hidaka et al. 2007), but barriers on a surface depend on the composition and structure of that surface (Watanabe et al. 2004; Goumans et al. 2008), with, in some cases, the reaction being completely barrierless (Goumans et al. 2008). Hidaka et al. (2007) calculate a rate for A4 from an experiment involving various combinations of CO and H₂O ice. They find that the product k_Hn_H is ∼5 × 10⁻³ s⁻¹, which for 10⁻³ H atoms per square centimeter of surface (n_H; typical for a large grain) gives a reaction timescale on the order of seconds. For small grains, the timescale could be on the order of a year (i.e., fast by astrophysical standards).

Reaction A5 requires the diffusion of molecules and radicals across a grain surface, which is a slow process at 10 K. However, experimental results show that there is some evidence of complex surface reactions, even at 10 K (e.g., Watanabe & Kouchi 2002). Figure 2 suggests that even at rates slower than our conservative standard rate, significant amounts of glycolaldehyde form via this mechanism.

Increasing n_f by an order of magnitude from 10⁶ to 10⁷ cm⁻³ has the effect of increasing glycolaldehyde production for a given reaction rate by a corresponding order of magnitude, approximately. This reflects the greater collisional rate between molecules and grains, and thus a greater freezeout rate. The peak fractional abundance of glycolaldehyde produced via mechanism A, x(CH₂OHCHO) ∼ 10⁻⁵, is unaffected by the change in n_f, showing that a significant proportion of the available carbon ends up in glycolaldehyde at the most extreme rates investigated, something which is unlikely to occur naturally.

The reaction mechanism suggested by Bennett & Kaiser (2007b), which was identified experimentally in the laboratory, is very inefficient at producing glycolaldehyde at 10 K. Even under conditions where the cosmic-ray ionization rate is increased by seven orders of magnitude, less than x(CH₂OHCHO) ∼ 10⁻⁹ results (Figure 2). The rates adopted for reactions B1 and B3 are critical to the amount of glycolaldehyde produced, with the yield scaling linearly with the adopted rate. Using our standard rates for B1 and B3, x(CH₂OHCHO) ∼ 10⁻¹³–10⁻¹⁴, significantly lower than that observed in G31.41+0.31 (Beltrán et al. 2009). Moreover, we do not include the hydrogenation of the hydroxymethyl (CH₂OH) radical to methanol in our reaction scheme, which surely must be rapid and compete with reaction B3.

Mechanism C, the only gas-phase reaction mechanism we investigate, is also not particularly efficient in the production of glycolaldehyde, producing x(CH₂OHCHO) ≲ 10⁻¹⁰ at the most enhanced values of the reaction rate coefficients. We do not increase the rate coefficient of reaction C1 beyond 6.3 × 10⁻⁷ cm³ s⁻¹, since this would be incredibly fast for a gas-phase reaction. In fact, we only vary the rate of C1 for completeness, since the standard reaction rate (from Tanner et al. 1979) is accurate to 25% according to the UDfA database. Both reactions C1 and C2 produce linearly increasing amounts of CH₂OHCHO with increasing reaction rate coefficient, producing x(CH₂OHCHO) = 10⁻¹³ at the standard rates. The limiting factor in this mechanism is the availability of gas-phase formaldehyde, which at 10 K is only 1% of the total formaldehyde, the rest being frozen onto grain surfaces. However, we do not include non-thermal desorption mechanisms in our simple model, which could increase the amount of formaldehyde in the gas phase. Roberts et al. (2007) show that non-thermal desorption can return a large proportion of H₂CO to the gas phase in extreme cases. It is not clear how their results would apply to our situation, where the density is larger, and thus freezeout more rapid.

This grain-surface reaction based on the work of Beltrán et al. (2009) involves the products of rapid hydrogenation of CO and HCO⁽⁺⁾, meaning that the only instructive reaction rate to investigate is that of reaction D3. We simplify the three-body reaction proposed by Beltrán et al. (2009) with a two-body reaction by assuming that the H-atom addition is rapid. A maximum fractional abundance of glycolaldehyde of ∼10⁻⁶ is produced when the standard rate for the reaction is increased by 1000–10,000, depending on n_f. At the standard rate, x(CH₂OHCHO) ≈ 10^{−9... − 10}, somewhat smaller than derived from their observations, but within their error constraints (see Section 5).

The atom-addition mechanism suggested by Charnley & Rodgers (2005) is the most complex that we have considered, involving six two-body reactions. Three of these reactions are reactions with H, which are assumed rapid, but the surface migration of heavier atoms is significantly slower due to the large diffusion barriers involved (e.g., Leitch-Devlin & Williams 1984). The rates of reactions E2–E4 have little effect on the abundance of glycolaldehyde, showing largely flat profiles in Figure 2. The gradient of reaction E5, where an oxygen atom is added to the molecule, is somewhat steeper, but reaction E6 is the crucial reaction in this mechanism. We have assumed a fairly conservative value of 3 × 10⁻¹⁷ s⁻¹ for this reaction, due to a potential barrier in the H-addition process, but if the reaction were 10^3...5 times faster than expected, then it could produce x(CH₂OHCHO) ∼ 10⁻⁶.

The analysis performed thus far has been somewhat artificial, since if the reactions contained in the suggested mechanisms occur, then they likely occur in competition with each other (and other reactions), i.e., reactions in other mechanisms are not "switched off." To investigate this, we performed two further experiments where we set the rates of all the reactions considered to their standard rates, and where we set them to "optimal" rates. By optimal here we mean adopting α values for where the rate profiles in Figure 2 turn over to become flat. Rates for mechanism C were kept as standard, since the rate profiles do not turn over.

We find that, when using standard rates for all reactions, x(CH₂OHCHO) = 1.5 × 10⁻⁷. In this competitive environment, reactions A5 and E6 are the dominant routes to the formation of glycolaldehyde, with A5 being the most efficient by a considerable margin as the core collapses (see Figure 3, left). When using "optimal" rates, an extremely large amount of glycolaldehyde can form, x(CH₂OHCHO) = 1.1 × 10⁻⁵, which is approximately 6% of the elemental carbon abundance of the core. In this case, the most dominant reaction for its formation at later times is B3 (the rate of which has been enhanced 10⁵ times); E6 dominates at early times, with a rate enhancement of 10⁷. Given these extreme rate enhancements, this scenario is unlikely.

Building on the astrophysical models, we now consider reactions A, D, and E from a physicochemical perspective, taking account of the intrinsic thermodynamic stability of reagents and products. A full treatment of this is underway, but due to the computationally expensive nature of such an investigation, here we only consider general principles. First, in mechanism A, reaction A5 is found to be particularly efficient at producing glycolaldehyde:

$$\begin{eqnarray*} &&\nonumber \rm {CH_3OH} + \rm {HCO} \longrightarrow \ \rm {CH_2OHCHO} + \rm {H}. \end{eqnarray*}$$

However, A5 is the reaction of a stable molecule (methanol) with a reactive radical (formyl) to give stable glycolaldehyde and an H monoatom. The H monoatom is extremely reactive and even at low temperatures is very mobile, hence the rate of the backward reaction (addition of H to glycolaldehyde) could be expected to be competitive with that of the forward reaction. Preliminary ab initio calculations conducted at the coupled-cluster level with single, double, and triple excitations (CCSD(T)) and a triple-zeta quality basis set shows that, in fact, reaction A5 is endothermic, and consequently the rate of the reaction yielding glycolaldehyde would be very unfavorable.

Reaction D3,

$$\begin{eqnarray*} &&\nonumber \rm {H_2CO} + \rm {HCO} + \rm {H} \longrightarrow \ \rm {CH_2OHCHO}, \end{eqnarray*}$$

is a three-body reaction which has a vanishingly small probability of occurring, further hindered by the low temperatures considered here. However, the products could be obtained by two sequential two-step reactions: first, reaction of H with HCO yields H₂CO, a barrierless process in the gas phase, according to published theoretical work (Goumans et al. 2007), which could combine with another H₂CO molecule to yield the glycolaldehyde product. However, H₂CO is rather stable and hence the reaction rate for the condensation of two H₂CO molecules could be expected to be rather slow and hence improbable. A second possibility is the reaction of H with H₂CO which according to past work (Woon 2002; Saebo et al. 1983) yields H₃CO as the kinetic product. H₃CO could react with HCO to give glycolaldehyde, and this reaction ought to have a low barrier since both H₃CO and HCO are reactive radical species.

In mechanism E, the final promising path identified from the astrophysical models, glycolaldehyde is assembled from a building block of CO via six stepwise monatomic addition reactions. Although the constituent reactions of mechanism E are chemically viable, consideration of the physical conditions and the reaction probabilities suggest that this pathway may be an unlikely source of glycolaldehyde. Under the conditions of a temperature of 10 K, only monatomic H is mobile; C and O are static and only become mobile during warm-up, which implies that reactions E2 and E5 are highly unlikely to occur. Hence, these reactions are likely to be rate-limiting. Construction of glycolaldehyde via monatomic addition also depends on a well-defined consecutive set of reactions. In this scheme, HCO reacts with monatomic C (reaction E2), yet monatomic H is present at higher abundance and is known to react without a barrier (Goumans et al. 2007) with HCO, the product of E1, to give H₂CO rather the product of E2, HC₂O. Since mechanism E is composed of six reactions which are expected to be limited by at least two of those reactions (E2 and E5), we consider this pathway to not be very probable or efficient.

Of the reactions identified by the astrophysical models, it is suggested that mechanism D is the most probable according to chemical considerations. Detailed ab initio calculations are underway to assess the influence of substrates on the reaction barriers and hence quantify the efficiency of mechanisms A, D, and E. It should be noted that mechanisms B and C are viable from a chemical standpoint and these will also be considered in comparison to A, D, and E to assess the most viable scheme.