Effective grain surface area in the formation of molecular hydrogen in interstellar clouds

TL;DR

This study investigates how the effective grain surface area influences molecular hydrogen formation in interstellar clouds, revealing a dependency on hydrogen influx rate and grain size through numerical simulations.

Contribution

It introduces a model where the effective grain surface area scales with actual area as a power law, depending on hydrogen flux, supported by numerical simulations.

Findings

Effective surface area scales as S^α, with α depending on hydrogen flux.

High accretion rates lead to grain saturation and inhibited H2 formation.

At low accretion rates, the number of sites needed exceeds actual sites, increasing α.

Abstract

In the interstellar clouds, molecular hydrogens are formed from atomic hydrogen on grain surfaces. An atomic hydrogen hops around till it finds another one with which it combines. This necessarily implies that the average recombination time, or equivalently, the effective grain surface area depends on the relative numbers of atomic hydrogen influx rate and the number of sites on the grain. Our aim is to discover this dependency. We perform a numerical simulation to study the recombination of hydrogen on grain surfaces in a variety of cloud conditions. We use a square lattice (with a periodic boundary condition) of various sizes on two types of grains, namely, amorphous carbon and olivine. We find that the steady state results of our simulation match very well with those obtained from a simpler analytical consideration provided the `effective' grain surface area is written as $\sim S^{\alpha}$, where, $S$ is the actual physical grain area and $\alpha$ is a function of the flux of atomic hydrogen which is determined from our simulation. We carry out the simulation for various astrophysically relevant accretion rates. For high accretion rates, small grains tend to become partly saturated with $H$ and $H_2$ and the subsequent accretion will be partly inhibited. For very low accretion rates, the number of sites to be swept before a molecular hydrogen can form is too large compared to the actual number of sites on the grain, implying that $\alpha$ is greater than unity.