A hybrid moment equation approach to gas-grain chemical modeling

Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
e-mail: fjdu@mpifr.de

Received: 5 December 2010
Accepted: 1 April 2011

Abstract

Context. In addition to gas phase reactions, the chemical processes on the surfaces of interstellar dust grains are important for the energy and material budget of the interstellar medium. The stochasticity of these processes 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 a very powerful way to solve gas-grain chemistry. It is applicable to large gas-grain networks, and is demonstrated to have a degree of accuracy high enough to be used for astrochemistry studies. Further work should be done to investigate how to cut off the hybrid moment equation selectively to make the computation faster, more accurate, and more stable, how to make the switch to rate equation more mathematically sound, and how to make the errors controllable. 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.