EDP Sciences
Free access
Issue
A&A
Volume 375, Number 3, September 2001
Page(s) 1111 - 1119
Section Physical and chemical processes
DOI http://dx.doi.org/10.1051/0004-6361:20010961


A&A 375, 1111-1119 (2001)
DOI: 10.1051/0004-6361:20010961

A stochastic approach to grain surface chemical kinetics

N. J. B. Green1, T. Toniazzo2, M. J. Pilling3, D. P. Ruffle3, N. Bell3 and T. W. Hartquist2

1  Chemistry Department, Kings College London, London WC2R 2LS, UK
2  Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
3  School of Chemistry, University of Leeds, Leeds LS2 9JT, UK

(Received 12 October 2000 / Accepted 2 July 2001 )

Abstract
A stochastic model of grain surface chemistry, based on a master equation description of the probability distributions of reactive species on grains, is developed. For an important range of conditions, rates of molecule formation are limited by low accretion rates, so that the probability that a grain contains more than one reactive atom or molecule is small. We derive simple approximate expressions for these circumstances, and explore their validity through comparison with numerical solutions of the master equation for H, O and H, N, O reaction systems. A more detailed analysis of the range of validity of several analytic approximations and numerical solutions, based on exact analytical results for a model in which H and ${\rm H}_{2}$ are the only species, is also made. Though the use of our simple approximate expressions is computationally efficient, the solution of the master equation under the assumption that no grain contains more than two particles of each species usually gives more accurate results in the parameter regimes where the deterministic rate equation approach is inappropriate. The implementation of sparse matrix inversion techniques makes the use of such a truncated master equation solution method feasible for considerably more complicated surface chemistries than the ones we have examined here.


Key words: astrochemistry -- molecular processes -- methods: analytical -- ISM: clouds -- dust, extinction -- ISM: molecules

Offprint request: T. W. Hartquist, twh@ast.leads.ac.uk




© ESO 2001