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Register a new userEfficient Simulations of Interstellar Gas-Grain Chemistry Using Moment Equations
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Networks of reactions on dust grain surfaces play a crucial role in the chemistry of interstellar clouds, leading to the formation of molecular hydrogen in diffuse clouds as well as various organic molecules in dense molecular clouds. Due to the sub-micron size of the grains and the low flux, the population of reactive species per grain may be very small and strongly fluctuating. Under these conditions rate equations fail and the simulation of surface-reaction networks requires stochastic methods such as the master equation. However, the master equation becomes infeasible for complex networks because the number of equations proliferates exponentially. Here we introduce a method based on moment equations for the simulation of reaction networks on small grains. The number of equations is reduced to just one equation per reactive specie and one equation per reaction. Nevertheless, the method provides accurate results, which are in excellent agreement with the master equation. The method is demonstrated for the methanol network which has been recently shown to be of crucial importance.
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Theoretical studies have revealed that dust grains are usually moving fast through the turbulent interstellar gas, which could have significant effects upon interstellar chemistry by modifying grain accretion. This effect is investigated in this work on the basis of numerical gas-grain chemical modeling. Major features of the grain motion effect in the typical environment of dark clouds (DC) can be summarised as follows: 1) decrease of gas-phase (both neutral and ionic) abundances and increase of surface abundances by up to 2-3 orders of magnitude; 2) shifts of the existing chemical jumps to earlier evolution ages for gas-phase species and to later ages for surface species by factors of about ten; 3) a few exceptional cases in which some species turn out to be insensitive to this effect and some other species can show opposite behaviors too. These effects usually begin to emerge from a typical DC model age of about 10^5 yr. The grain motion in a typical cold neutral medium (CNM) can help overcome the Coulomb repulsive barrier to enable effective accretion of cations onto positively charged grains. As a result, the grain motion greatly enhances the abundances of some gas-phase and surface species by factors up to 2-6 or more orders of magnitude in the CNM model. The grain motion effect in a typical molecular cloud (MC) is intermediate between that of the DC and CNM models, but with weaker strength. The grain motion is found to be important to consider in chemical simulations of typical interstellar medium.
Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux,these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. We evaluate the formation rates of H2, HD and D2 molecules on dust grain surfaces and their abundances in the gas phase under interstellar conditions. We incorporate the moment equations into the Meudon PDR code and compare the results with those obtained from the rate equations. We find that within the experimental constraints on the energy barriers for diffusion and desorption and for the density of adsorption sites on the grain surface, H2, HD and D2 molecules can be formed efficiently on dust grains. Under a broad range of conditions, the moment equation results coincide with those obtained from the rate equations. However, in a range of relatively high grain temperatures, there are significant deviations. In this range, the rate equations fail while the moment equations provide accurate results. The incorporation of the moment equations into the PDR code can be extended to other reactions taking place on grain surfaces.
We report the discovery of propylene (also called propene, CH_2CHCH_3) with the IRAM 30-m radio telescope toward the dark cloud TMC-1. Propylene is the most saturated hydrocarbon ever detected in space through radio astronomical techniques. In spite of its weak dipole moment, 6 doublets (A and E species) plus another line from the A species have been observed with main beam temperatures above 20 mK. The derived total column density of propylene is 4 10^13 cm^-2, which corresponds to an abundance relative to H_2 of 4 10^-9, i.e., comparable to that of other well known and abundant hydrocarbons in this cloud, such as c-C_3H_2. Although this isomer of C_3H_6 could play an important role in interstellar chemistry, it has been ignored by previous chemical models of dark clouds as there seems to be no obvious formation pathway in gas phase. The discovery of this species in a dark cloud indicates that a thorough analysis of the completeness of gas phase chemistry has to be done.
[Context] The stochasticity of grain chemistry requires special care in modeling. Previously methods based on the modified rate equation, the master equation, the moment equation, and Monte Carlo simulations have been used. [Aims] We attempt to develop a systematic and efficient way to model the gas-grain chemistry with a large reaction network as accurately as possible. [Methods] We present a hybrid moment equation approach which is a general and automatic method where the generating function is used to generate the moment equations. For large reaction networks, the moment equation is cut off at the second order, and a switch scheme is used when the average population of certain species reaches 1. For small networks, the third order moments can also be utilized to achieve a higher accuracy. [Results] For physical conditions in which the surface reactions are important, our method provides a major improvement over the rate equation approach, when benchmarked against the rigorous Monte Carlo results. For either very low or very high temperatures, or large grain radii, results from the rate equation are similar to those from our new approach. Our method is faster than the Monte Carlo approach, but slower than the rate equation approach. [Conclusions] The hybrid moment equation approach with a cutoff and switch scheme is applicable to large gas-grain networks, and is accurate enough to be used for astrochemistry studies. The layered structure of the grain mantle could also be incorporated into this approach, although a full implementation of the grain micro-physics appears to be difficult.
Abridged: We detail and benchmark two sophisticated chemical models developed by the Heidelberg and Bordeaux astrochemistry groups. The main goal of this study is to elaborate on a few well-described tests for state-of-the-art astrochemical codes covering a range of physical conditions and chemical processes, in particular those aimed at constraining current and future interferometric observations of protoplanetary disks. We consider three physical models: a cold molecular cloud core, a hot core, and an outer region of a T Tauri disk. Our chemical network (for both models) is based on the original gas-phase osu_03_2008 ratefile and includes gas-grain interactions and a set of surface reactions for the H-, O-, C-, S-, and N-bearing molecules. The benchmarking is performed with the increasing complexity of the considered processes: (1) the pure gas-phase chemistry, (2) the gas-phase chemistry with accretion and desorption, and (3) the full gas-grain model with surface reactions. Using atomic initial abundances with heavily depleted metals and hydrogen in its molecular form, the chemical evolution is modeled within 10^9 years. The time-dependent abundances calculated with the two chemical models are essentially the same for all considered physical cases and for all species, including the most complex polyatomic ions and organic molecules. This result however required a lot of efforts to make all necessary details consistent through the model runs, e.g. definition of the gas particle density, density of grain surface sites, the strength and shape of the UV radiation field, etc. The reference models and the benchmark setup, along with the two chemical codes and resulting time-dependent abundances are made publicly available in the Internet: http://www.mpia.de/homes/semenov/Chemistry_benchmark/home.html
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