Astrochemical modelling

Isotope chemistry: Isotopically substituted molecules are valuable probes of the high-density (n_H > 10⁵ cm^-3) and low-temperature (T ~ 10 K) gas deep inside star-forming cores, where otherwise common tracer molecules such as CO freeze onto the surfaces of interstellar dust grains (and may also present optically thick emission). Furthermore, there is increasing evidence of chemical inheritance in the Solar System: isotopic abundance ratios observed in comets for example appear similar to what is expected, based on observations and theory, in clouds reminiscent of the one that the Sun was born in. Therefore, constraining the chemistry of isotopes in star-forming clouds yields important information on the initial chemical conditions for forming protostellar and planetary systems.

At CAS, we have recently investigated through theoretical means the chemical evolution of the isotopes deuterium and 13C, using a state-of-the-art chemical model that treats the chemistry in the gas phase and on grain surfaces simultaneously. Using this model, we have demonstrated that deuterated molecules, which have been thought to subsist in the gas phase even at very high volume densities, are eventually adsorbed onto grain surfaces. This has now been confirmed observationally in the case of N2D+ (Redaelli et al. 2019) and NH2D (Fig.1; Caselli et al. 2022). Our new model for the chemistry of carbon isotopic fractionation (Colzi et al. 2020) has in turn shown very clearly that the 12C/13C abundance ratio varies strongly from molecule to molecule in physical conditions corresponding to star-forming clouds. It is common practice to derive the column density of a 12C-containing molecule from the 13C-containing counterpart, if only the latter one has been observed, by means of imposing a constant 12C/13C ratio. Our model indicates that this practice may lead to significant errors, and that detailed modelling is often necessary to obtain accurate results.

Cosmic rays: Cosmic rays have a large effect on chemistry in the interstellar medium. For example, they provide the main source of gas heating in regions shielded from the interstellar radiation field, and they are able to ionize and dissociate atoms and molecules. Cosmic rays have a direct effect on the ices on grain surfaces. As a cosmic ray passes through a grain, it heats the grain transiently to a higher temperature – the grain then cools back to the equilibrium temperature via desorption of the ice on its surface, enriching the gas phase with molecules synthesized in the ice. The efficiency of this process is determined by the ratio of the heating event interval to the cooling time. Previous numerical models of cosmic ray induced desorption (CRD) have taken a constant cooling time, 10^-5 s, based on the assumption that the ice on the grains consists purely of a CO-like molecule. It is however known that the ices are in reality very heterogeneous, and a large part of the ice is made up of water which is not easily desorbed. In Sipilä et al. (2021), we presented a new numerical model for CRD in which we take the time-dependent ice composition into account, and derive a dynamically varying grain cooling time. We explored two classes of models: so-called two-phase models where gas-phase chemistry is coupled to ice chemistry occurring in a single reactive layer, and three-phase models where the ice is separated into a single reactive layer on top of a chemically inert mantle. We found that the dynamic description of CRD decreases, in two-phase chemical models, gas-phase abundances compared to the case of a constant cooling time. This is because the dynamically calculated grain cooling time is shorter than 10^-5 s and hence the desorption is less efficient. A reverse trend appears in three-phase models. Our new description of CRD is easily applicable in any gas-grain chemical model, and improves the accuracy of gas-phase abundance estimations.

Grain size distribution: Although it is often assumed in chemical models for the sake of simplicity that the dust grains are all the same size, with radius usually taken as 0.1 microns, realistically one expects instead a distribution of grain sizes. Typically the smallest grains in the distribution have the largest total surface area as they are the greatest in number, and one is tempted to think that the abundance of a given molecule in the ices would hence be the largest on the smallest grains. However, there are additional considerations to take into account: cosmic rays heat the smallest grains to much higher temperatures compared to the larger grains, meaning that the efficiency of the CRD process increases with decreasing grain radius, and this implies large differences to ice abundances depending on the grain radius. To investigate this, we built a new model where we assume a grain distribution and calculate the transient maximum temperature following a cosmic ray impact uniquely for each grain size (Sipilä et al. 2020). We also considered the effect of grain size on the equilibrium grain temperature. We found that indeed some molecules like CO are typically most abundant on the smallest grains, but others like HCN can be instead most abundant on larger grains in the distribution (but not necessarily the very largest ones). The trends may however be changed depending on the grain temperature, as shown in Fig. 2. The way the molecules are synthesized (i.e., in the gas phase or on grains) plays a role as well. Our work implies that the chemical inventory in the ice in collapsing clouds going into the protostellar stage may differ from what has been thought so far, especially if the smallest grains are removed from the distribution before the onset of gravitational collapse, for example due to grain-grain collisions.

Present and future modelling efforts. We are presently working on new chemical models for isotope chemistry, in the context of deuterated complex organic molecules as well as nitrogen isotope chemistry. We also plan to extend the new CRD model by considering a range of possible transient maximum temperatures for the grains, and taking the ice thickness into account also in the derivation of the temperature. Finally, the present and future models are coupled to representations of the physical structure of star-forming cores, so that the models can serve to explain observed phenomena.

Figure 1: Observed (black) and modelled (red) spectra for para-NH2D at six positions at and near the dust peak in L1544 (from Caselli et al. 2022). The match between the observations and the model is very good, and notably the observed line profiles cannot be reproduced without significant NH2D freeze-out toward the dust peak (position 1 in the figure). — *Figure 1*: *Observed (black) and modelled (red) spectra for para-NH*₂D at six positions at and near the dust peak in L1544 (from Caselli et al. 2022). The match between the observations and the model is very good, and notably the observed line profiles cannot be reproduced without significant NH₂D freeze-out toward the dust peak (position 1 in the figure).

*Figure 1*: *Observed (black) and modelled (red) spectra for para-NH*₂D at six positions at and near the dust peak in L1544 (from Caselli et al. 2022). The match between the observations and the model is very good, and notably the observed line profiles cannot be reproduced without significant NH₂D freeze-out toward the dust peak (position 1 in the figure).

Figure 2: Fractional abundances of N2 (left) and CO (right) ice as a function of volume density, taken from a model for L1544 at a chemical time of 104 yr. The linestyles represent grains in different size bins with the radius increasing with bin number, while the colors correspond to simulations where the equilibrium grain temperature either does (blue) or does not (red) depend on the grain radius. In the former case, there are significant variations in the ice abundances depending on the grain size at low volume densities. Adapted from Sipilä et al. (2020). — *Figure 2*: *Fractional abundances of N*₂ *(left) and CO (right) ice as a function of volume density, taken from a model for L1544 at a chemical time of 10*⁴ yr. The linestyles represent grains in different size bins with the radius increasing with bin number, while the colors correspond to simulations where the equilibrium grain temperature either does (blue) or does not (red) depend on the grain radius. In the former case, there are significant variations in the ice abundances depending on the grain size at low volume densities. Adapted from Sipilä et al. (2020).

*Figure 2*: *Fractional abundances of N*₂ *(left) and CO (right) ice as a function of volume density, taken from a model for L1544 at a chemical time of 10*⁴ yr. The linestyles represent grains in different size bins with the radius increasing with bin number, while the colors correspond to simulations where the equilibrium grain temperature either does (blue) or does not (red) depend on the grain radius. In the former case, there are significant variations in the ice abundances depending on the grain size at low volume densities. Adapted from Sipilä et al. (2020).

References

Caselli, P. et al. 2022, ApJ, 929, 13
Colzi, L. et al. 2020, A&A, 640, A51
Redaelli, E. et al. 2019, A&A 629, A15
Sipilä, O. et al. 2020, A&A 640, A94
Sipilä, O. et al. 2021, ApJ 922, 126