Efficient Simulations of Gas-Grain Chemistry in Interstellar Clouds

Chemical reactions on dust grains are of crucial importance in interstellar chemistry because they produce molecular hydrogen and various organic molecules. Because of the submicron size of the grains and the low flux, the surface populations of reactive species are small and strongly fluctuate. Under these conditions rate equations fail and the master equation is needed for modeling these reactions. However, the number of equations grows exponentially with the number of reactive species, severely limiting its feasibility. Here we present a method which dramatically reduces the number of equations, thus enabling the incorporation of the master equation in models of interstellar chemistry.

Figure 1

The production rates of ${\mathrm{H}}_2$ (circles), ${\mathrm{O}}_2$ (squares), ${\mathrm{H}}_2\mathrm{O}$ (triangles) and the desorption rate of OH ($\times$) per grain vs grain size, given by the number of adsorption sites $S$ and the diameter $d$. The results of the complete master equation (solid lines) and the rate equations (dashed lines) are also shown.

Figure 2

A graph describing the reaction network that results from the adsorption of H and O atoms and CO molecules. The reaction products are specified near the edges.

Figure 3

The production rates of ${\mathrm{H}}_2\mathrm{O}$, $\mathrm{C}{\mathrm{O}}_2$, and $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}$ vs grain size as obtained from the multiplane approach (circles) and the complete master equation (solid lines). The rate equation results are also shown (dashed lines).