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

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

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

Exact results for hydrogen recombination on dust grain surfaces

The recombination of hydrogen in the interstellar medium, taking place on surfaces of microscopic dust grains, is an essential process in the evolution of chemical complexity in interstellar clouds. The H_2 formation process has been studied theoretically, and in recent years also by laboratory experiments. The experimental results were analyzed using a rate equation model. The parameters of the surface, that are relevant to H_2 formation, were obtained and used in order to calculate the recombination rate under interstellar conditions. However, it turned out that due to the microscopic size of the dust grains and the low density of H atoms, the rate equations may not always apply. A master equation approach that provides a good description of the H_2 formation process was proposed. It takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. In this paper we present a comprehensive analysis of the H_2 formation process, under steady state conditions, using an exact solution of the master equation. This solution provides an exact result for the hydrogen recombination rate and its dependence on the flux, the surface temperature and the grain size. The results are compared with those obtained from the rate equations. The relevant length scales in the problem are identified and the parameter space is divided into two domains. One domain, characterized by first order kinetics, exhibits high efficiency of H_2 formation. In the other domain, characterized by second order kinetics, the efficiency of H_2 formation is low. In each of these domains we identify the range of parameters in which, the rate equations do not account correctly for the recombination rate. and the master equation is needed.Comment: 23 pages + 8 figure

Use of Laboratory Data to Model Interstellar Chemistry

Our laboratory research program is about the formation of molecules on dust grains analogues in conditions mimicking interstellar medium environments. Using surface science techniques, in the last ten years we have investigated the formation of molecular hydrogen and other molecules on different types of dust grain analogues. We analyzed the results to extract quantitative information on the processes of molecule formation on and ejection from dust grain analogues. The usefulness of these data lies in the fact that these results have been employed by theoreticians in models of the chemical evolution of ISM environments

Formation of Molecular Hydrogen on Amorphous Water Ice: Influence of Morphology and Ultraviolet Exposure

In this paper, we report on the formation of molecular hydrogen on different types of amorphous water ice. We show that mass spectra of desorbing molecules upon formation are sensitive to the way in which ice is deposited on a cold substrate, to its thermal history, and to the action of UV photons. Implications that these results bear on H2 formation in dense quiescent clouds are presented and discussed

H_{2} adsorption on multiwalled carbon nanotubes at low temperatures and low pressures

We present an experimental study on H_{2} adsorption on multiwalled carbon nanotubes (MWCNTs) at low temperatures (12–30 K) and low pressures (2×10^{-5}  Torr) using the temperature programmed desorption technique. Our results show that the molecular hydrogen uptake increases nearly exponentially from 6×10^{-9}  wt. % at 24.5 K to 2×10^{-7}  wt. % at 12.5 K and that the desorption kinetics is of the first order. Comparative measurements indicate that MWCNTs have an adsorption capacity about two orders higher than that of activated carbon (charcoal) making them a possible candidate as hydrogen cryosorber for eventual applications in accelerators and synchrotrons

Laboratory Synthesis of Molecular Hydrogen on Surfaces of Astrophysical Interest

We report on the first results of experiments to measure the recombination rate of hydrogen on surfaces of astrophysical interest. Our measurements give lower values for the recombination efficiency (sticking probability S x probability of recombination upon H-H encounter $\gamma$) than model-based estimates. We propose that our results can be reconciled with average estimates of the recombination rate (1/2 n(H) n(g) v(H)A S $\gamma$) from astronomical observations, if the actual surface of an average grain is rougher, and its area bigger, than the one considered in models.Comment: 13 pages plus 5 figures (only change: this version has 5 figures included); this paper is to appear in Astrophysical Journal Letters