© The Authors 2025

1 Introduction

Interstellar methanol is considered an important building block of complex organic molecules (COMs) through surface and gas phase reactions, such as CH₂OH radical, CH₃O radical, CH₃CH₂OH (ethanol), CH₃OCH₃ (dimethyl ether), CH₃CHO (methyl formate), (CH₂OH)₂ (ethylene glycol), and other species (Charnley et al. 1992; Fuchs et al. 2009; Williams et al. 2018). Mathew et al. (2022) discussed how methanol could be the starting material for olefins, carbonyl compounds, amines, amino acids, peptides, polypeptide chains, and complex life molecules such as Ribonucleic Acid (RNA). Hence, it is crucial to investigate and understand the pathways leading to interstellar methanol formation.

The existing framework of interstellar methanol formation involves a vast network of interrelated reactions. Among these, the two formation pathways of most interest are the pure gas phase and the solid-state schemes.

In the gas phase, protonated methanol (CH₃OH₂⁺) can be produced by the radiative association reaction, which is primarily activated by cosmic rays or stellar radiation (Rxn. (1)) (Williams et al. 2018; Luca et al. 2002): $${\mathrm{CH}}_3{}^{+}+{\mathrm{H}}_2\mathrm{O}⟶{\left[{\mathrm{CH}}_3{\mathrm{OH}}_2{}^{+}\right]}^{*}⟶{\mathrm{CH}}_3{\mathrm{OH}}_2{}^{+}+hv.$$(1)

In this radiative association reaction, the protonated methanol is formed during a highly exothermic reaction, ΔH = −2.9 eV (Luca et al. 2002), where the collision complex, [CH₃OH₂⁺]^*, is formed in an energetic excited state and then stabilized by emitting a photon. Geppert et al. (2006) argued that in more complicated systems, the radiative lifetime of the excited complex can be of the same order of magnitude as the dissociative lifetime. Therefore, both processes may compete in determining the stability of the excited complex and, thereby, affecting the overall production of protonated methanol. The protonated methanol then dissociatively recombines with electrons to form methanol (Rxn. (2)) (Williams et al. 2018; Geppert et al. 2006; Yamamoto 2017): $${\mathrm{CH}}_3{\mathrm{OH}}_2{}^{+}+\mathrm{e}⟶{\left[{\mathrm{CH}}_3{\mathrm{OH}}_2\right]}^{*}⟶{\mathrm{CH}}_3\mathrm{OH}+\mathrm{H}.$$(2)

This last reaction, at ΔH = −5.7 eV, is one of the few dissociative recombination pathways possible in the gas-phase Interstellar Medium (ISM) due to the low kinetic energies prevailing there (Geppert et al. 2006). Wirström et al. (2011); Geppert et al. (2005), however, had established that the dissociative recombination step, Rxn. (2), could not be efficient enough for a pure gas phase route alone to explain the observed CH₃OH abundances.

On the other hand, solid-state methanol is an abundant constituent of ice-type mantles (McClure et al. 2023). In dense and cold regions of molecular clouds, CO molecules present in the gas phase freeze out and form an apolar coating on top of icy-dusty grains (Williams et al. 2018; Chuang et al. 2016, 2018; Linnartz et al. 2015; Santos et al. 2022). Methanol is then efficiently formed through the continuous hydrogenation of CO in the solid phase, with formaldehyde (H₂CO) as one of the intermediate products (see the CO hydrogenation mechanism in Table 1).

The CO hydrogenation, which is a Langmuir–Hinshelwood (L−H) mechanism, has been regarded as the primary route to producing methanol in dark molecular clouds. In addition, this process has been shown to effectively reproduce methanol abundances observed in translucent clouds, while pure gas phase models fail by four orders of magnitude (Turner 1998). However, recent laboratory results and Monte Carlo simulations suggest that the radical-molecule H-atom abstraction route (Rxn. (3); Santos et al. 2022; Álvarez-Barcia et al. 2018; Simons et al. 2020), which is also an L-H mechanism, is the dominant (70−90%) final step for forming CH₃OH in dark molecular clouds. This pathway replaces the hydrogenation of CH₃O in the overall CH₃OH formation mechanism (Santos et al. 2022; Álvarez-Barcia et al. 2018; Simons et al. 2020). Santos et al. (2022) suggests that the total contribution of each pathway is determined by the availability of H, CH₃O and H₂CO in the ice: $${\mathrm{CH}}_3\mathrm{O}+{\mathrm{H}}_2\mathrm{CO}⟶{\mathrm{CH}}_3\mathrm{OH}+\mathrm{HCO}\text{.}$$(3)

In addition, under H₂O-rich interstellar ice environments, Qasim et al. (2018) studied the CH₃OH formation in ice analogues and found that methanol formation is possible through the sequential surface reaction chain: CH₄+OH → CH₃+H₂O and CH₃+OH → CH₃OH. In addition, Molpeceres et al. (2021) suggest the possibility that CH₃OH could form via C+ H₂O in water-rich ices. However, Qasim et al. (2018) conclude that the CO+H reaction pathway is approximately 20 times more effective in producing CH₃OH at 10 K compared to the CH₄+ OH route. Furthermore, Jiménez-Serra et al. (2025) model the ice chemistry in the Chameleon I molecular cloud using a set of state-of-the-art astrochemical codes and found that CH₃OH ice formation occurs predominantly (>99%) via CO hydrogenation, while the contribution of reactions CH₃+OH and C+H₂O is negligible.

The present work aims to study the main interstellar methanol formation route under non-shocked and shocked scenarios, using the open source gas-grain chemical code UCLCHEM v.3.1¹ (Holdship et al. 2017). This study explores the influence of the radical-molecule H-atom abstraction route on methanol formation under shock-influenced environments, such as galactic protostellar outflows. In Section 2, we describe the chemical models performed. In Section 3, we assess the importance of gas-phase versus solid-phase methanol formation mechanisms in the framework of outflow observations. In Section 4, we analyse the impact of the radical-molecule H-atom abstraction route on HCO, H₂CO, and CH₃O. We briefly summarise our findings in Section 5.

2 Chemical modelling of methanol

We used the time-dependent open-source gas-grain chemical model UCLCHEM (Holdship et al. 2017) to model methanol formation in star-forming regions. Several physics modules are available in UCLCHEM. The so-called ‘hot core’ module allowed us to model the envelopes surrounding a forming protostar. In this model, the temperature increases following the time and radially dependent temperature profiles described by Viti et al. (2004) and adapted in Awad et al. (2010). The ‘shock’ modules (C- and J−) are instead used to model shocked regions. For this module, UCLCHEM adopts a parametrized C-shock and J-shock from Jiménez-Serra et al. (2008) and James et al. (2020) respectively, to describe the changes in gas properties over time in the presence of shocks. For this study, we only used the C-shock module.

For the C-shock models, we ran UCLCHEM for three epochs, according to the epoch of shock propagation. The preshock epoch corresponds to the time in which the initial gas kinetic temperature, T_k(t), remains low and is the same as T_k,init. The beginning of the shock is determined by the rise of T_k(t) due to shock heating, and the post-shock epoch is determined by its decrease until it once again reaches the initial cold temperature. For gas-phase chemistry, we used the UMIST12 database (McElroy et al. 2013). The surface network is provided in the UCLCHEM GitHub repository and includes the standard hydrogenation route to methanol from CO. We call this network the ‘standard’ network.

To implement the radical-molecule route (Rxn. (3)) in the UCLCHEM network, we introduced the reaction list given in Table 1. In the added network, we used the branching ratios proposed by Simons et al. (2020) and the barrier energies reported in the KIDA DATABASE (Wakelam et al. 2012) and Álvarez-Barcia et al. (2018) to implement the radical-molecule route into the UCLCHEM network. We refer to this augmented network as the ‘current’ network.

Table 2 summarises the physical conditions used to model the non-shock and shock chemistry in various physical scenarios. We ran 192 models in total, taking into account both default and current networks. The UCLCHEM modelling consists of two stages ordered in time sequence: In stage 1, diffuse gas (initial n_H2(init) = 10 cm⁻³) undergoes free-fall collapse until a density is set by the user (See Table 2). During this stage, the gas evolves from elemental atomic to the composition of a dense cloud. In the second stage, we evolved the chemistry under two scenarios: C-type shocks and ‘hot cores’, with the latter representing dense gas around protostars that has not been shocked.

During the first stage, the gas kinetic temperature of T_k,init = 10 K and the cosmic ray ionisation rate (CRIR) for molecular hydrogen is standard at ζ₀=5 × 10⁻¹⁷ s⁻¹. The cloud was allowed to evolve for ∼10⁷ years.

For the C-shock scenario, we varied the CRIR from ζ=ζ₀ to ζ=100 ζ₀, and the shock velocity (v_shock) from 10 to 50 km/s. The chosen range for v_shock allowed us to distinguish between a low-velocity shock (10 km/s as a representative value) and a high-velocity shock (50 km/s as a representative value). In high-velocity shocks, sputtering of Si from the grain-core occurs. Meanwhile, the non-shock model was simulated by heating the cloud (composed of a single gas parcel) to a final gas kinetic temperature, defined as the hot-core temperature T_H C, set to 50, 100, and 200 K, considering a 10 M ⊙ embedded protostar (Viti et al. 2004). For both shock and non-shock scenarios, the cloud was allowed to evolve for 10⁷ years for the second stage as well.

3 Interstellar C H₃ O H formation

This section presents a detailed analysis of the behaviour and formation pathways of solid-state methanol, both on the surface and in the inner layers (bulk) of the icy-dusty grain. The aim of this analysis is to verify whether the implemented radical-molecule H-atom abstraction reaction does become the dominant final step in forming solid-state CH₃OH, as stated in Simons et al. (2020) and Santos et al. (2022). The term ‘ice phase’ used below refers to the combined contribution of the grain surface and bulk.

In non-shock scenarios, the abundance of methanol in the ice remains stable throughout the model until 10⁵ yr. Any subsequent decrease, as T_k(t) reaches 200 K, is attributed to cosmic rays or thermal desorption. However, when a C-shock is present, regardless of its velocity, there is a significant decrease in the abundance of the ice phase as the shock propagates (see left panel in Fig. 1). The destruction of ice layers during the propagation of the C-shock wave results in the release of methanol from the solid to the gas phase, leading to a significant decrease in solid-state methanol abundance. As the C-shock wave dissipates, ice mantles begin to re-form, and methanol gradually re-accumulates in the solid phase as new layers grow on the grain surfaces, enhancing the abundance of solid-state methanol (see right panel in Fig. 1). The behaviour of CH₃OH in the solidstate changes when a C-shock propagates, so it is pertinent to analyse the reactions that form CH₃OH, both on the surface and in the bulk of the grain, and whether the overall CH₃OH synthesis pathway varies according to the gas kinetic temperature (T_k), the gas volume density (n_H2), the velocity of the C-shock wave (v_shock), and the CRIR (ζ). The following subsections analyse each CH₃OH state and the differences between the most important reactions at different time steps.

3.1 Grain-surface phase

In non-shock models, surface methanol (see left panel in Figure 2) is still primarily formed through the hydrogenation of CH₃O (Rxn.(4)) and CH₂OH (Rxn. (5)). The prevalence of hydrogenations may stem from the fact that these H-atom addition routes are promoted with a higher H-atom flux to the surface, allowing the accreted H-atoms to diffuse and react with both CH₃O and CH₂OH species. Methanol synthesis through CH₃O or CH₂OH hydrogenation is a process that has no barriers (Santos et al. 2022), making it ideal for enhancing methanol production at such low temperatures. Once T_k(t)=T_HC, condensation of gaseous CH₃OH and CH₃OH₂⁺ (Rxn. (6)) ascribe to the surface methanol formation: $${\mathrm{CH}}_3{\mathrm{O}}_{\text{(surf)}}+{\mathrm{H}}_{\text{(surf)}}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\text{(surf)}},$$(4) $${\mathrm{CH}}_2{\mathrm{OH}}_{\text{(surf)}}+{\mathrm{H}}_{\text{(surf)}}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\text{(surf)}},$$(5) $${\mathrm{CH}}_3{\mathrm{OH}}_2{}^{+}{}_{\left(\mathrm{g}\right)}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\left(\text{surf}\right)}+{\mathrm{H}}_{\left(\mathrm{g}\right)}.$$(6)

However, the formation of surface methanol during a shock involves an additional series of reactions. The H-atom addition reactions are replaced by the H-abstraction route (Rxn. (7); Simons et al. 2020) as T_k(t) rises in low-velocity C-shocks, while bulk-to-surface transfer dominates at the maximum T_k(t): $${\mathrm{CH}}_3{\mathrm{O}}_{\text{(surf)}}+{\mathrm{H}}_2{\mathrm{CO}}_{\text{(surf)}}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\text{(surf)}}+{\mathrm{H}}_{\text{(surf)}}.$$(7)

The main difference between the default and current networks is the prevalence of the radical-molecule H-atom abstraction route as T_k(t) increases in low-velocity shocks. In the current network, methoxy radical hydrogenation dominates as the final step in the overall CO hydrogenation mechanism on the grain surface. However, as the temperature rises due to shock heating, the abstraction route replaces radical CH₃O hydrogenation as the final step in CH₃OH formation. Hence, the methanol yield from both networks is dependent on the surface temperature. Santos et al. (2022) and Simons et al. (2020) show that there is a competition between the increase in the diffusion of H atoms and the decrease in their residence time on the ice as a function of temperature. At low temperatures, CH₃O surface radicals undergo hydrogenation. However, as the temperature exceeds 20−30 K, the residence time of H atoms on the surface decreases substantially. At the same time, radicals become mobile, allowing the abstraction reaction to compete with CH₃O radical hydrogenation.

This finding seems to contradict the results from Simons et al. (2020) and Santos et al. (2022). The former finds that the CH₃O+H pathway becomes significant only at higher temperatures (although their study only covers temperatures up to 20 K) and when the surface coverage of H₂ is low. The latter reports experimental evidence suggesting that the abstraction mechanism may already dominate at lower temperatures (10−16 K). However, their study does not distinguish between surface and bulk ice chemistry in the same way as the present model. This disagreement may stem from various reasons: (i) incomplete surface networks in our model; (ii) our different treatment of the surface of the grains where we distinguish between bulk and surface; and (iii) the different physical conditions such as density and temperature ranges. The latter in particular increases extremely fast in our shock models, and the high temperature lasts for a very short time before returning to 10 K.

Fig. 1 Chemical abundances of ice-phase methanol (left panel) and gas-phase methanol (right panel) as a function of time in non-shocked, slow C-shock (10 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ= ζ0. The dashed and solid lines correspond to the default and current schemes, respectively.

Fig. 2 Chemical abundances of surface-phase methanol (left panel) and bulk-phase methanol (right panel) as a function of time in non-shocked, slow C-shock (10 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ= ζ0. The dashed and solid lines correspond to the default and current schemes, respectively.

3.2 Grain-bulk phase

As T_k(t) increases in both non-shock and shocked models (see right panel in Fig. 2), methanol is primarily formed through the hydrogenation of CH₃O (Rxn. 8 (Simons et al. 2020), the radical-molecule route (Rxn.(9) (Simons et al. 2020), and surface-to-inner layer transfer. Transfer from surface to inner layers and the hydrogenation of CH₃O dominate until T_k(t) ∼70 K at n_{H2 (init)} = 10³ cm⁻³, after which the H-abstraction route takes over. At n_{H2 (init)} ≥ 10⁴ cm⁻³, the primary methanol formation routes are the H-abstraction reaction and surface-to-inner layer transfer: $${\mathrm{CH}}_3{\mathrm{O}}_{\text{(bulk)}}+{\mathrm{H}}_{\text{(bulk)}}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\text{(bulk)}},$$(8) $${\mathrm{CH}}_3{\mathrm{O}}_{\left(\text{bulk}\right)}+{\mathrm{H}}_2{\mathrm{CO}}_{\left(\text{bulk}\right)}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\left(\text{bulk}\right)}+{\mathrm{HCO}}_{\left(\text{bulk}\right)}.$$(9)

The radical-molecule H-atom abstraction route dominates the formation of methanol in the bulk, with the gas density being the most influential factor. High n_H2 favours the formation of H₂ and OH on the grain surface (Rxns. (10) (Cazaux & Tielens 2004), (11) (Simons et al. 2020), and (12) (Wakelam et al. 2012)), which accumulates in the bulk as new surface layers form. Due to its high reactivity, the H atom reacts with CO and O to primarily form H₂O and H₂CO in the bulk grain (Rxns. (13) (Simons et al. 2020), (14) (Simons et al. 2020), and (15) (Wakelam et al. 2012)). The H atoms must diffuse in order to react with the minor ice component, CH₃O radicals. Therefore, the dominance of the radical-molecule route is likely due to the greater availability of H₂CO in the bulk, compared to H atoms, for reacting with CH₃O, as stated in Santos et al. (2022): $${\mathrm{H}}_{\left(\text{surf}\right)}+{\mathrm{H}}_{\left(\text{surf}\right)}⟶{\mathrm{H}}_{2\left(\text{surf}\right)},$$(10) $${\mathrm{CO}}_{\left(\text{surf}\right)}\stackrel{{\mathrm{H}}_{\left(\text{surf}\right)}}{\to }{\mathrm{HCO}}_{\left(\text{surf}\right)}\stackrel{{\mathrm{H}}_{\left(\text{surf}\right)}}{\to }{\mathrm{CO}}_{\left(\text{surf}\right)}+{\mathrm{H}}_{2\left(\text{surf}\right)},$$(11) $${\mathrm{H}}_{\left(\text{surf}\right)}+{\mathrm{O}}_{\left(\text{surf}\right)}⟶{\mathrm{OH}}_{\left(\text{surf}\right)}.$$(12) $${\mathrm{CO}}_{\left(\text{bulk}\right)}\stackrel{{\mathrm{H}}_{\left(\text{bulk}\right)}}{\to }{\mathrm{HCO}}_{\left(\text{bulk}\right)}\stackrel{{\mathrm{H}}_{\left(\text{bulk}\right)}}{\to }{\mathrm{CO}}_{\left(\text{bulk}\right)}+{\mathrm{H}}_{2\left(\text{bulk}\right)},$$(13) $${\mathrm{CO}}_{\left(\text{bulk}\right)}\stackrel{{\mathrm{H}}_{\left(\text{bulk}\right)}}{\to }{\mathrm{HCO}}_{\left(\text{bulk}\right)}\stackrel{{\mathrm{H}}_{\left(\text{bulk}\right)}}{\to }{\mathrm{H}}_2{\mathrm{CO}}_{\left(\text{bulk}\right)},$$(14) $${\mathrm{O}}_{\left(\text{bulk}\right)}\stackrel{{\mathrm{H}}_{\left(\text{bulk}\right)}}{\to }{\mathrm{OH}}_{\left(\text{bulk}\right)}\stackrel{{\mathrm{H}}_{\left(\text{bulk}\right)}}{\to }{\mathrm{H}}_2{\mathrm{O}}_{\left(\text{bulk}\right)}.$$(15)

3.3 Ice phase

In our model the hydrogen abstraction reaction is more relevant in the bulk phase of the ice mantle, whereas Simons et al. (2020); Santos et al. (2022); Jiménez-Serra et al. (2025) present their results in terms of the grain-surface mantle or the ice grain without explicitly distinguishing between the surface and the interior, as we do by defining the former as the outermost layer and the latter as everything beneath the surface. Since we consider the grain to be largely composed of bulk material, we can extend our observation to the ice phase in general.

Simons et al. (2020) performed a series of simulated co-depositions of CO+H and H₂CO+H considering different H− atom binding energies (250 K, 420 K, and 670 K). In their simulations, the authors found that the radical-molecule route is the primary pathway for methanol formation. They emphasised the dependence of CH₃OH formation on the H: CO ratio. They also pointed out that the dominance of the H-abstraction reaction arises because when two H₂CO molecules are produced nearby, only one H atom is required for hydrogenation to convert CH₃O into CH₃OH and HCO. Subsequently, these species underwent rapid hydrogenation once more.

On the other hand, Santos et al. (2022) conducted experiments under ultra-high vacuum conditions and astronomically relevant temperatures. They employed H:H₂CO (or D₂CO) flux ratios of 10:1 and 30:1. Similar to Simons et al. (2020), Santos et al. (2022) observed that the radical-molecule route was the predominant pathway for methanol formation in their experiments. They specifically tested an H/H₂CO (D₂CO) ratio of 30 at 10 K and concluded that the CHD₂OH/CH₃OH ratios were negligibly different, considering the detection error. Consequently, Santos et al. (2022) suggested that a higher hydrogen flux only slightly affects the contribution of the radical-molecule H-atom abstraction route, even though a potentially higher H flux might favour the atom-addition route, which still governs the formation of CH₃OH. Our results confirm the last statement in the range of n_{H2 (init)} = 10⁴−10⁶ cm⁻³. In this range, the H-abstraction route dominates and produces similar methanol abundances. Therefore, the product yield is limited by the abundance of formaldehyde rather than the abundance of hydrogen atoms, which are in excess. These results also support the findings of Santos et al. (2022), where the contribution from each route is determined by the availability of hydrogen, formaldehyde, and methoxide radicals in the ice. In an H-abstraction reaction, the probability of the two reactants coming into contact is higher compared to a barrier-less hydrogenation reaction.

Santos et al. (2022) reports that the abstraction route accounts for approximately 80% of the contributions in the 10−16 K interval, which is consistent with the findings of Simons et al. (2020). In both studies, CH₃OH formation is independent of temperature in the 10−16 K range. Moreover, our results indicate that the H-abstraction reaction is the dominant final step in the CO hydrogenation to form CH₃OH, both at low gas kinetic temperatures, such as those found in molecular clouds, and at high gas kinetic temperatures, such as those achieved by shock heating, under n_{H2 (init)} = 10⁴−10⁶ cm⁻³. Quantum tunnelling is activated at low temperatures, but as the temperature rises, it may also become thermally activated. This last scenario is most commonly observed under low n_{H2 (init)}, where elevated temperatures could promote the radical-molecule route.

We note that in Jiménez-Serra et al. (2025), multiple models were run utilising various astrochemical codes to analyse the ice abundances recorded by JWST during the Ice Age Early Release Science programme (McClure et al. 2023), focusing on the heavily obscured background stars NIR38 and J110621 in the line of sight of the dense molecular cloud Chameleon I. In the stochastic kinetic Monte Carlo (KMC) simulations (Cuppen & Herbst 2007), which examine the H-abstraction pathway for the synthesis of CH₃OH, it was determined that methanol is primarily produced via the sequential hydrogenation of CO. The simulations indicated that approximately 60% of methanol is primarily derived from the hydrogenation of CH₂OH, which was not classified as a formation reaction since CH₂OH is exclusively generated through H-abstraction of methanol. Around 30% is produced via the hydrogenation of CH₃O, while the radical-neutral reaction CH₃O+H₂CO → CH₃OH+HCO contributes only about 10%. The discrepancies may arise from the varying grid of conditions employed in both studies (e.g. reduced extinction usage in this research).

In terms of CRIR, cosmic ray-induced photons can dissociate H₂CO and CH₃OH, producing functional group radicals such as CH₃ and CH₃O on or within the ice. Our results also suggest that high CRIR (ζ=100 ζ₀) decreases the abundance of methanol in all phases. However, this rate affects both the radical-molecule route and other possible pathways, as the energy from cosmic rays can break apart precursor molecules involved in the overall CO hydrogenation mechanism before they can react.

Figure 3 shows that in low-velocity C-shocks, ice methanol is more abundant when using the default network compared to the current one. The main difference between the two networks is that the H-abstraction reaction is the primary pathway for methanol formation in the bulk, whereas the CH₂OH hydrogenation on the grain surface has become more significant due to changes in branching ratios, especially at higher T_k(t). With the current network, we used branching ratios from Simons et al. (2020). These rates were based on quantum chemical calculations combined with a microscopic KMC simulation and yield a lower but proper amount of methanol. It should be noted that the predicted difference in bulk methanol abundance between networks is minimal ($\sim 1\times {10}^{-5},\frac{X_{\text{default}}}{X_{\text{current}}}\le 1.5$) because our network does not include other reactions (i.e. HCO+HCO reactions; Simons et al. 2020) that could also alter the molecular composition of the grain mantle. Therefore, we encourage extending the chemical reaction network to enhance completeness in future studies.

3.4 Comparison with observations

It is of interest to ascertain whether modifying the solid-state reaction network would have a direct effect on the formation of CH₃OH_(g) by introducing different abundances in the gas phase.

As mentioned in Huang et al. (2024) and Huang & Viti (2023), gas-phase methanol is a potential tool to trace C-type shocks, as shocks can substantially enhance the gas-phase abundance of CH₃OH. Therefore, we aim to analyse whether the changes in the solid-phase formation pathway alter the observable abundance of gas-phase methanol as the shock sputters the grain during its propagation.

Gas-phase methanol is mainly due to CH₃O hydrogenation and subsequent chemical desorption (Rxn. (16); Simons et al. 2020; Minissale et al. 2016), with an important contribution from CH₂OH hydrogenation (Rxn. (17); Simons et al. 2020; Minissale et al. 2016) in the models at n_{H2 (init)} = 10³ cm⁻³. As the gas kinetic temperature increases due to shock heating, the hydrogenation of CH₃O is replaced by multiple reactions such as ion-neutral Rxn. (18) (Sung Lee et al. 1992), protonated methyl alcohol (CH₃OH₂⁺) recombination in Rxn. (19) (Geppert et al. 2006), and the ion-neutral Rxn. (20) (Wakelam et al. 2012): $${\mathrm{H}}_{\left(\mathrm{s}\right)}+{\mathrm{CH}}_3{\mathrm{O}}_{\left(\mathrm{s}\right)}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\left(\mathrm{g}\right)},$$(16) $${\mathrm{H}}_{\left(\mathrm{s}\right)}+{\mathrm{CH}}_2{\mathrm{OH}}_{\left(\mathrm{s}\right)}⟶{\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{g}\right).$$(17) $${\mathrm{H}}_3{}^{+}+{\mathrm{CH}}_3\mathrm{CHO}⟶{\mathrm{CH}}_3{}^{+}+{\mathrm{CH}}_3\mathrm{OH},$$(18) $${\mathrm{CH}}_3{\mathrm{OH}}_2^{+}+{\mathrm{e}}^{-}⟶{\mathrm{CH}}_3\mathrm{OH}+\mathrm{H},$$(19) $${\mathrm{CH}}_3{\mathrm{OH}}_2^{+}+{\mathrm{NH}}_3⟶{\mathrm{CH}}_3\mathrm{OH}+{\mathrm{NH}}_4^{+}.$$(20)

However, the radical-molecule route, Rxn. (21) (Simons et al. 2020; Minissale et al. 2016; Santos et al. 2022), has an impact on gaseous methanol production only at low-velocity C-shocks with high initial gas volume densities (n_{H2 (init)} = 10⁵−10⁶ cm⁻³): $${\mathrm{H}}_2{\mathrm{CO}}_{\left(\mathrm{s}\right)}+{\mathrm{CH}}_3{\mathrm{O}}_{\left(\mathrm{s}\right)}⟶{\mathrm{CH}}_3{\mathrm{OH}}_{\left(\mathrm{g}\right)}+{\mathrm{H}}_{\left(\mathrm{g}\right)}.$$(21) Therefore, it is pertinent to contrast our UCLCHEM models with galactic protostellar outflow observations made by Holdship et al. (2019) to ascertain whether it would be possible to observationally distinguish the most favourable pathways for CH₃OH_(s) formation under shock-induced environments.

Class 0 young stellar objects, such as NGC 1333-IRAS2A and NGC 1333-IRAS4A, are associated with outflows. These outflows create shocks upon impacting the surrounding medium (van Dishoeck & Blake 1998; Holdship et al. 2019). As Holdship et al. (2019) observed, these shock regions showcase a diverse chemistry, with gas-phase methanol experiencing notable increases in abundance. In order to model the physical structure traced by CH₃OH in the protostellar outflow sources – IRAS2A-R, IRAS2A-B, IRAS4A-R, and IRAS4A-B – we used the inferred gas properties (n_{H2 (init)}) from Holdship et al. (2019). Our grid of models includes these inferred gas properties to study the influence of formation pathways (processing of interstellar ices and pure gas-phase mechanisms) on the observed interstellar methanol abundances.

To effectively compare the models with observations, we focus on those with an abundance exceeding X_CH3OH = 10⁻⁷ and a ratio between the standard and the current networks of $\frac{X_{default}}{X_{current}}\ge 2$. For gas-phase methanol, only the model with n_{H2 (init)} = 10⁵, ζ=ζ₀, and v_shock=20 km/s fulfils both characteristics at the same time. Figure 4 illustrates a comparison of gas-phase methanol column densities over time using 10−50 km/s models with the range of methanol column densities reported by Holdship et al. (2019) for IRAS2A-R, IRAS2A-B, IRAS4A-R, and IRAS4A-B. In order to compare our models directly with the observations, we derived column densities from the modelled fractional abundances by using the on-the-spot approximation: $$N\left(X\right)=X\times A_V\times B\left(H_2\right),$$(22) where A_V is the visual extinction, N(H₂) is equal to 1.6 × 10²¹ cm⁻², and the hydrogen column density corresponds to A_V= 1 mag.

As seen in Fig. 4, when comparing the models with the range of methanol column densities recorded by Holdship et al. (2019), and assuming the same A_v in both models and observations, it is not possible to establish which formation pathway is dominant, since both networks yield methanol abundances that are within the observed range.

Fig. 3 Chemical abundances of ice-phase methanol as a function of time in slow C-shock (10−20 km/s) and moderately high C-shock (30 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey lines.

Fig. 4 Column densities of gaseous CH3OH as a function of time for slow C-shock (10−20 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 105 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The hatches represent the range in the CH3OH column density reported by Holdship et al. (2019) for IRAS2A-R, IRAS2A-B, IRAS4A-R, and IRAS4A-B.

4 Impact of H-abstraction route on precursors

The addition of a new route in the chemical network has a significant impact on the immediate methanol precursors, CH₃O and H₂CO, as well as the by-product HCO, particularly in the ice phase. Since the three molecules are significantly affected by shock scenarios, we discuss below their shock behaviour and the way in which the radical-molecule reaction affects their overall chemical pathway over time.

Generally speaking, in both low- and high-velocity shocks, as well as in default and current networks, the solid abundances of HCO, H₂CO, and CH₃O drop dramatically (below 10⁻¹⁵) as the shock wave propagates. Similar to methanol, their solid-state abundances increase again once the shock wave dissipates. We discuss each precursor below.

Fig. 5 Chemical abundances of ice-phase HCO as a function of time in slow C-shock (10−20 km/s) and moderately high C-shock (30 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ=10 ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey line.

4.1 Formyl radical (HCO)

The formation of HCO_(bulk) is influenced by the insertion of the H-abstraction route into the chemical network. In scenarios with or without shock, HCO_(bulk) formation is attributed to reactions (23) (Simons et al. 2020) and (24) (Fedoseev et al. 2016), as well as the H-abstraction reaction. The latter is the preferred reaction at n_{H2 (init)} = 10⁴ cm⁻³, while in other models, especially at higher n_H2, its importance grows as T_k(t) increases: $${\mathrm{H}}_{\left(\text{bulk}\right)}+{\mathrm{CO}}_{\left(\text{bulk}\right)}⟶{\mathrm{HCO}}_{\left(\text{bulk}\right)},$$(23) $${\mathrm{NH}}_{2\text{(bulk)}}+{\mathrm{H}}_2{\mathrm{CO}}_{\text{(bulk)}}⟶{\mathrm{NH}}_{3\text{(bulk)}}+{\mathrm{HCO}}_{\text{(bulk)}}.$$(24)

With respect to HCO, in models with ζ=10 ζ₀ and $n_{{\mathrm{H}}_{2\text{(init)}}}={10}^4{\mathrm{c}\mathrm{m}}^{-3},\frac{X_{default}}{X_{current}}\ge 2$ is observed during the post-shock epoch of low-velocity C-shocks (v_shock=10−20 km/s) and moderately high-velocity C-shocks (v_shock=30 km/s). When comparing the abundance of ice formyl radicals between networks (see Fig. 5), it is generally observed that the current network predicts a higher HCO abundance: $0.76\le \frac{X_{default}}{X_{current}}\le 0.91$, when X_HCO(ice) exceeds 10⁻⁷. This is because HCO is a by-product in the radicalmolecule route. The HCO radical is an important astrochemical building block due to its ability to synthesise bio-relevant COMs, such as glycolaldehyde, ethylene glycol, and methyl formate (Woods et al. 2013; Simons et al. 2020; Li et al. 2022; Santos et al. 2022). Therefore, this new reaction must be considered in the overall ice-grain chemical network, as it influences the abundance of formyl radicals and hence the distribution of COMs in the ISM.

4.2 Formaldehyde (H₂CO)

In non-shock and shocked scenarios, the H-abstraction reaction dominates the H₂CO destruction in the grain bulk from n_{H2 (init)} = 10⁴ cm⁻³ onwards, becoming more prevalent as T_k(t) increases. The ratio $\frac{X_{default}}{X_{current}}$ increases with density, reaching values greater than 2, particularly in the post-shock epoch of the model with n_{H2 (init)} = 10⁶ cm⁻³, v_shock=10 km/s, and ζ=ζ₀ conditions, where $\frac{X_{default}}{X_{current}}\ge 3.5$ (see Fig. 6). It is generally observed that as n_{H2 (init)} increases in the default scheme, the amount of solidstate formaldehyde increases compared to the current networks: $1.03\le \frac{X_{default}}{X_{current}}\le 3.68$, when X_H2CO(ice) exceeds 10⁻⁷. This difference arises from the faster radical-molecule rate, which results in more formaldehyde being converted to ice methanol and hence consequently a lower H₂CO abundance in the current scheme.

Formaldehyde may serve as a tool for tracing C-type shocks and distinguishing between methanol formation pathways in low-velocity shocked environments. At a shock velocity of 10 km/s, gaseous H₂CO is enhanced by the shock and traces its full extent. However, in models with n_{H2 (init)} = 10³ cm⁻³ and ζ=100 ζ₀, and in all models where v_shock is 50 km/s, it is initially enhanced by the shock but subsequently destroyed as the shock raises the gas kinetic temperature. Interestingly, we can identify C-shock velocities by examining the behaviour of methanol and formaldehyde. Formaldehyde serves as a shock tracer when destroyed at high shock velocities, while methanol is enhanced by the shock and traces its full extent. Therefore, the ratio of these two species may be a good shock diagnostic.

In general, gaseous formaldehyde seems to be a great species to discern between methanol formation routes. High density (n_{H2 (init)} = 10⁵−10⁶ cm⁻³) and low-velocity C-shock (v_shock= 10 km/s) models show significant contrast between the default and current networks, with $\frac{X_{default}}{X_{current}}\ge 170$ (Fig. 7). In non-shock models, the difference becomes noticeable as the temperature increases, exceeding 2.5 as the temperature stabilizes. In addition, and of critical importance, the observed abundance ratio of H₂CO/CH₃OH may distinguish between methanol formation pathways in low-velocity shocked environments.

Similarly to our approach with gaseous methanol, we modelled the physical structure traced by H₂CO in the protostellar outflow sources IRAS4A-R and IRAS4A-B, using the initial gas densities (n_H2:(init)) inferred by Gómez-Ruiz et al. (2016). Figure 8 presents a comparison of gas-phase H₂CO column densities over time from 10−50 km/s models with the lower limits calculated assuming a gas temperature of 20 K, as reported by Gómez-Ruiz et al. (2016), for both IRAS4A-R and IRAS4A-B. As seen, it remains unclear which formation pathway is dominant, as both networks yield formaldehyde abundances that fall within the observed range.

Fig. 6 Chemical abundances of ice-phase H2CO as a function of time for slow C-shock models with a pre-shocked gas density volume of nH2 (init) = 106 cm−3 and vshock=10 km/s. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey line.

Fig. 7 Chemical abundances of gas-phase formaldehyde as a function of time for slow C-shock (left panel) and high C-shock (right panel) models with a pre-shocked gas density volume of nH2 (init) = 105 cm−3. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey line.

Fig. 8 Column densities of gaseous H2CO as a function of time for slow C-shock (10−20 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 105 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The hatches represent the range in the H2CO column density reported by Gómez-Ruiz et al. (2016) for IRAS4A-R and IRAS4A-B.

4.3 Methoxyl radical (CH₃O)

From n_{H2 (init)} = 10⁴ cm⁻³ onwards, the radical-molecule route (Rxn. (9)) and layer transfer are the primary destruction reactions for CH₃O_bulk. For most time steps, the current network in general produces more methoxyl radical, due to the change in branching ratios. We observe that as the v_shock increases, the abundance of CH₃O_(bulk) becomes greater compared to the default network, with a $\frac{X_{default}}{X_{current}}\ge 2$ (see Fig. 9).

Finally, the largest ratios are observed at grain formation following the cessation of shock influence. It can be reasonably assumed that enhancing the resolution will enable us to distinguish the preferred route of methanol formation throughout the formation and growth of the grain, particularly in its precursors, by allowing us to detect smaller fluctuations and gain deeper insights into the processes that drive molecular evolution in space. For instance, it is anticipated that by improving the resolution of the observations, the ∼10% increase in HCO_(ice) seen in the models at n_{H2 (init)} = 10⁴ cm⁻³ can be contrasted.

Fig. 9 Chemical abundances of ice-phase CH3O as a function of time for C-shock models with a pre-shocked gas density volume of nH2 (init) = 106 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey lines.

5 Conclusions

We theoretically investigated the impact of the radical-molecule H-atom abstraction route in methanol formation under shock-influenced environments. We confirm that, using the chemical model UCLCHEM, the radical-molecule pathway is the most favoured reaction for the final step in the overall CO hydrogenation mechanism leading to CH₃OH formation in the bulk-phase of interstellar ices. This finding is consistent with that of Simons et al. (2020) and Santos et al. (2022). However, its dominance is dependent on the gas kinetic temperature T_k, the gas volume density n_H2, the velocity of the C-shock wave v_shock, and the CRIR ζ.

Considering the radical-molecule route or changes in the branching ratios within the chemical network does not affect the ability of CH₃OH to trace C-shocks. This is because, in both schemes, the increase in gaseous CH₃OH abundance is achieved by releasing CH₃OH from the solid state into the gas phase through sublimation and sputtering.

Incorporating the radical-molecule H-atom abstraction route into chemical networks has a substantial impact on the abundance of the methanol precursors, CH₃O and H₂CO, as well as on the abundance of the by-product HCO. The change in the abundance of these chemical species upon introducing the reaction is more significant than the change observed for CH₃OH, particularly in the ice phase.

Gaseous formaldehyde may serve as a tool for tracing C-type shocks as well as differentiate between methanol formation pathways in low-velocity C-shocked environments, as its abundance undergoes a more significant change than that of CH₃OH when the H-atom abstraction reaction is included in UCLCHEM’s chemical network. Consequently, the abundance ratio $\frac{X_{{\mathrm{H}}_2\mathrm{CO}}}{X_{{\mathrm{CH}}_3\mathrm{OH}}}$ could serve as a useful diagnostic tool for distinguishing between methanol formation pathways in these environments.

Acknowledgements

We acknowledge the very helpful comments from an anonymous referee which led to an improvement of this manuscript. This work is financially supported by advanced ERC funding (grant ID: 833460, PI: Serena Viti) within the framework of MOlecules as Probes of the Physics of EXternal (MOPPEX) project. EMR gratefully acknowledges the Leiden/ESA Astrophysics Program for Summer Students (LEAPS) 2022, organised by Leiden University and the European Space Agency, and the support provided by the Erasmus+ ICM Grant and Observatorio Astronómico Nacional de Colombia. The project leading to this publication was initiated within the framework of this programme.

References

All Tables

All Figures

	Fig. 1 Chemical abundances of ice-phase methanol (left panel) and gas-phase methanol (right panel) as a function of time in non-shocked, slow C-shock (10 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ= ζ0. The dashed and solid lines correspond to the default and current schemes, respectively.
In the text

	Fig. 2 Chemical abundances of surface-phase methanol (left panel) and bulk-phase methanol (right panel) as a function of time in non-shocked, slow C-shock (10 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ= ζ0. The dashed and solid lines correspond to the default and current schemes, respectively.
In the text

	Fig. 3 Chemical abundances of ice-phase methanol as a function of time in slow C-shock (10−20 km/s) and moderately high C-shock (30 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey lines.
In the text

Fig. 4 Column densities of gaseous CH3OH as a function of time for slow C-shock (10−20 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 105 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The hatches represent the range in the CH3OH column density reported by Holdship et al. (2019) for IRAS2A-R, IRAS2A-B, IRAS4A-R, and IRAS4A-B.

In the text

	Fig. 5 Chemical abundances of ice-phase HCO as a function of time in slow C-shock (10−20 km/s) and moderately high C-shock (30 km/s) models with a pre-shocked gas density volume of nH2 (init) = 104 cm−3 and ζ=10 ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey line.
In the text

	Fig. 6 Chemical abundances of ice-phase H2CO as a function of time for slow C-shock models with a pre-shocked gas density volume of nH2 (init) = 106 cm−3 and vshock=10 km/s. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey line.
In the text

	Fig. 7 Chemical abundances of gas-phase formaldehyde as a function of time for slow C-shock (left panel) and high C-shock (right panel) models with a pre-shocked gas density volume of nH2 (init) = 105 cm−3. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey line.
In the text

Fig. 8 Column densities of gaseous H2CO as a function of time for slow C-shock (10−20 km/s) and high C-shock (50 km/s) models with a pre-shocked gas density volume of nH2 (init) = 105 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The hatches represent the range in the H2CO column density reported by Gómez-Ruiz et al. (2016) for IRAS4A-R and IRAS4A-B.

In the text

	Fig. 9 Chemical abundances of ice-phase CH3O as a function of time for C-shock models with a pre-shocked gas density volume of nH2 (init) = 106 cm−3 and ζ=ζ0. The dashed and solid lines correspond to the default and current schemes, respectively. The evolution of gas temperature, Tk(t), is depicted by the dotted grey lines.
In the text