Off-lattice Microscopic Monte Carlo Modeling of Molecular Hydrogen Formation on Carbonaceous Dust Grains

TL;DR

The paper presents an off-lattice microscopic Monte Carlo framework to model accretion, diffusion, and reaction of hydrogen atoms on rough carbonaceous dust grain surfaces in the diffuse ISM. It treats diffusion via thermal hopping and quantum tunnelling between local surface minima and allows H2 formation through both Eley-Rideal and Langmuir-Hinshelwood mechanisms, with no gas-phase chemistry. A key finding is that binding energies on the uneven surface are widely distributed, approximately $520$--$1800$ K, which broadens the temperature window for H2 formation to about $5$--$25$ K (and up to ~$30$ K) and affects diffusion rates. The study reports a mean binding-to-desorption energy ratio around $0.5$--$0.6$, while diffusion is largely thermally driven and tunnelling plays a secondary role; overall, the work advocates incorporating binding-energy distributions into astrochemical modeling and highlights limitations of single-value parameters in rate-equation treatments.

Abstract

In this work, we present an off-lattice Monte Carlo model of accretion and migration of hydrogen atoms on a rough surface of carbon dust grain. The migration of physisorbed atoms by means of thermal diffusion and quantum tunnelling through barriers between the surface potential minima is considered. The model is applied to simulations of molecular hydrogen formation in a cold interstellar medium for a temperature range 5-35 K. Eley-Rideal and Langmuir-Hinshelwood mechanisms for the formation of the H$_2$ molecule were taken into account. We found that the surface potential energy minima that hold the accreted hydrogen atoms (binding energy) has wide dispersion of its values. The minimum energy is three times smaller than the maximum energy for the uneven surface of the model grain. The large dispersion of the binding energies results in an extended range of temperatures where H$_2$ formation is efficient: 5-25 K. The dispersion of binding energies also reduces efficiency of diffusion due to tunnelling in comparison to that assumed in kinetic equation codes in which constant values of binding energies are employed. Thus, thermal hopping is the main source for the mobility of the hydrogen atoms in the presented off-lattice model. Finally, the model naturally provides the mean values for the ratio of binding-to-desorption energy. This ratio demonstrates weak dependence on temperature and is in the range of 0.5-0.6.

Figures (8)

• Figure 1: Grain-related processes considered in the model: accretion (a), diffusion (b) and desorption (c) of hydrogen atoms. Diffusion is possible due to thermal hopping and quantum migration. Only thermal desorption is considered.
• Figure 2: (a) "Small" grain core assembled up of 1000 carbon atoms; (b) cross-section of a "small" grain core; (c) 'large' grain core assembled up of 10000 carbon atoms; (d) cross-section of a "large" grain core.
• Figure 3: An example of a $6\times$10$^{-7}$ cm grain core with temperature of 5 K covered with hydrogen atoms. On average, $\sim$130 hydrogen atoms residing simultaneously on grain surface.
• Figure 4: Average number of atoms simultaneously residing on grain during the simulations vs. temperature.
• Figure 5: Depth distribution of visited potential wells on the "large" amorphous grain core at 5 K. Orange - number of potential wells with given depth; blue - number of visits for each potential well with given energy.