Master Equation for Hydrogen Recombination on Grain Surfaces

Recent experimental results on the formation of molecular hydrogen on astrophysically relevant surfaces under conditions similar to those encountered in the interstellar medium provided useful quantitative information about these processes. Rate equation analysis of experiments on olivine and amorphous carbon surfaces provided the activation energy barriers for the diffusion and desorption processes relevant to hydrogen recombination on these surfaces. However, the suitability of rate equations for the simulation of hydrogen recombination on interstellar grains, where there might be very few atoms on a grain at any given time, has been questioned. To resolve this problem, we introduce a master equation that takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. The hydrogen recombination rate on microscopic grains, as a function of grain size and temperature, is then calculated using the master equation. The results are compared to those obtained from the rate equations and the conditions under which the master equation is required are identified.Comment: Latex document. 14 pages of text. Four associated figs in in PS format on separate files that are "called-in" the LaTeX documen

Formation of molecular hydrogen on analogues of interstellar dust grains: experiments and modelling

Molecular hydrogen has an important role in the early stages of star formation as well as in the production of many other molecules that have been detected in the interstellar medium. In this review we show that it is now possible to study the formation of molecular hydrogen in simulated astrophysical environments. Since the formation of molecular hydrogen is believed to take place on dust grains, we show that surface science techniques such as thermal desorption and time-of-flight can be used to measure the recombination efficiency, the kinetics of reaction and the dynamics of desorption. The analysis of the experimental results using rate equations gives useful insight on the mechanisms of reaction and yields values of parameters that are used in theoretical models of interstellar cloud chemistry.Comment: 23 pages, 7 figs. Published in the J. Phys.: Conf. Se

Molecular Hydrogen Formation on Ice Under Interstellar Conditions

The results of experiments on the formation of molecular hydrogen on low density and high density amorphous ice surfaces are analyzed using a rate equation model. The activation energy barriers for the relevant diffusion and desorption processes are obtained. The more porous morphology of the low density ice gives rise to a broader spectrum of energy barriers compared to the high density ice. Inserting these parameters into the rate equation model under steady state conditions we evaluate the production rate of molecular hydrogen on ice-coated interstellar dust grains.Comment: 20 pages, 3 tables and 10 figures. Accepted to ApJ. Minor changes made and adittional references adde

A Unified Monte Carlo Treatment of Gas-Grain Chemistry for Large Reaction Networks. I. Testing Validity of Rate Equations in Molecular Clouds

In this study we demonstrate for the first time that the unified Monte Carlo approach can be applied to model gas-grain chemistry in large reaction networks. Specifically, we build a time-dependent gas-grain chemical model of the interstellar medium, involving about 6000 gas-phase and 200 grain surface reactions. This model is used to test the validity of the standard and modified rate equation methods in models of dense and translucent molecular clouds and to specify under which conditions the use of the stochastic approach is desirable. We found that at temperatures 25--30 K gas-phase abundances of H$_2$O, NH$_3$, CO and many other gas-phase and surface species in the stochastic model differ from those in the deterministic models by more than an order of magnitude, at least, when tunneling is accounted for and/or diffusion energies are 3x lower than the binding energies. In this case, surface reactions, involving light species, proceed faster than accretion of the same species. In contrast, in the model without tunneling and with high binding energies, when the typical timescale of a surface recombination is greater than the timescale of accretion onto the grain, we obtain almost perfect agreement between results of Monte Carlo and deterministic calculations in the same temperature range. At lower temperatures ($\sim10$ K) gaseous and, in particular, surface abundances of most important molecules are not much affected by stochastic processes.Comment: 33 pages, 9 figures, 1 table. Accepted for publication in Ap

The effect of grain size distribution on H2_2 formation rate in the interstellar medium

The formation of molecular hydrogen in the interstellar medium takes place on the surfaces of dust grains. Hydrogen molecules play a role in gas-phase reactions that produce other molecules, some of which serve as coolants during gravitational collapse and star formation. Thus, the evaluation of the roduction rate of hydrogen molecules and its dependence on the physical conditions in the cloud are of great importance. Interstellar dust grains exhibit a broad size distribution in which the small grains capture most of the surface area. Recent studies have shown that the production efficiency strongly depends on the grain composition and temperature as well as on its size. In this paper we present a formula which provides the total production rate of H$_2$ per unit volume in the cloud, taking into account the grain composition and temperature as well as the grain size distribution. The formula agrees very well with the master equation results. It shows that for a physically relevant range of grain temperatures, the production rate of H$_2$ is significantly enhanced due to their broad size distribution.Comment: to appear in MNRA

H2 Formation on Interstellar Grains in Different Physical Regimes

An analysis of the kinetics of H2 formation on interstellar dust grains is presented using rate equations. It is shown that semi-empirical expressions that appeared in the literature represent two different physical regimes. In particular, it is shown that the expression given by Hollenbach, Werner and Salpeter [ApJ, 163, 165 (1971)] applies when high flux, or high mobility, of H atoms on the surface of a grain, makes it very unlikely that H atoms evaporate before they meet each other and recombine. The expression of Pirronello et al.\ [ApJ, 483, L131 (1997)] -- deduced on the basis of accurate measurements on realistic dust analogue -- applies to the opposite regime (low coverage and low mobility). The implications of this analysis for the understanding of the processes dominating in the Interstellar Medium are discussed.Comment: 4 pages, MN styl

Moment equations for chemical reactions on interstellar dust grains

While most chemical reactions in the interstellar medium take place in the gas phase, those occurring on the surfaces of dust grains play an essential role. Chemical models based on rate equations including both gas phase and grain surface reactions have been used in order to simulate the formation of chemical complexity in interstellar clouds. For reactions in the gas phase and on large grains, rate equations, which are highly efficient to simulate, are an ideal tool. However, for small grains under low flux, the typical number of atoms or molecules of certain reactive species on a grain may go down to order one or less. In this case the discrete nature of the opulations of reactive species as well as the fluctuations become dominant, thus the mean-field approximation on which the rate equations are based does not apply. Recently, a master equation approach, that provides a good description of chemical reactions on interstellar dust grains, was proposed. Here we present a related approach based on moment equations that can be obtained from the master equation. These equations describe the time evolution of the moments of the distribution of the population of the various chemical species on the grain. An advantage of this approach is the fact that the production rates of molecular species are expressed directly in terms of these moments. Here we use the moment equations to calculate the rate of molecular hydrogen formation on small grains. It is shown that the moment equation approach is efficient in this case in which only a single reactive specie is involved. The set of equations for the case of two species is presented and the difficulties in implementing this approach for complex reaction networks involving multiple species are discussed.Comment: 12 pages, submitted for publication in A&

On the master equation approach to diffusive grain-surface chemistry: the H, O, CO system

We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO2), formaldehyde (H2CO), and methanol (CH3OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.Comment: 13 pages, 5 figure

Enhanced production of HD and D_2 molecules on small dust grains in diffuse clouds

Motivated by recent observations of deuterated molecules in the interstellar medium, we examine the production of HD and D$_2$ molecules on dust grain surfaces. A mechanism for the enhanced production of these deuterated molecules is studied. This mechanism applies on grain surfaces on which D atoms stick more strongly than H atoms, under conditions of low flux and within a suitable range of temperatures. It is shown that under these conditions the production rates of HD and D$_2$ are greatly enhanced (vs. the H$_2$ production rate) compared with the expected rates based on the adsorption of gas-phase atomic abundances of D and H. The enhancement in the formation rate of HD is comparable with the enhancement due to gas-phase ion-molecule reactions in diffuse clouds.Comment: This is a preprint of an article accepted for publication in Monthly Notices of The Royal Astromnomical Societ