Efficient Simulations of Interstellar Gas-Grain Chemistry Using Moment Equations

TL;DR

This paper introduces a moment equation-based method for simulating interstellar gas-grain chemistry, significantly reducing computational complexity while maintaining accuracy, especially for small grains with fluctuating reactive species.

Contribution

The paper presents a novel moment equation approach that simplifies the simulation of complex surface-reaction networks on dust grains, outperforming traditional stochastic methods in efficiency.

Findings

The method accurately reproduces results of the master equation.

It reduces the number of equations to one per species and reaction.

Demonstrated effectiveness on methanol formation network.

Abstract

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.