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&

HCN J=5-4 Emission in APM08279+5255 at z=3.91

We detect HCN J=5-4 emission from the ultraluminous quasar APM08279+5255 at z=3.911 using the IRAM Plateau de Bure interferometer. This object is strongly gravitationally lensed, yet still thought to be one of the most intrinsically luminous objects in the Universe. The new data imply a line luminosity L'_HCN(J=5-4) = 4.0+/-0.5 x 10^(10) K km/s pc^2. The ~440 km/s full width half maximum of the HCN J=5-4 line matches that of the previously observed high-J CO lines in this object and suggests that the emission from both species emerges from the same region: a warm, dense circumnuclear disk. Simple radiative transfer models suggest an enhanced abundance of HCN relative to CO in the nuclear region of APM08279+5255, perhaps due to increased ionization, or possibly the selective depletion of oxygen. The ratio of far-infrared luminosity to HCN luminosity is at the high end of the range found for nearby star forming galaxies, but comparable to that observed in the few high redshift objects detected in the HCN J=1-0 line. This is the first clear detection of high-J HCN emission redshifted into the 3-millimeter atmospheric window.Comment: Accepted for publication in ApJ

Polycylcic Aromatic Hydrocarbons (PAH's) in dense cloud chemistry

Virtually all detailed gas-phase models of the chemistry of dense interstellar clouds exclude polycyclic aromatic hydrocarbons (PAH's). This omission is unfortunate because from the few studies that have been done on the subject, it is known that the inclusion of PAH's can affect the gas-phase chemistry strongly. We have added PAH's to our network to determine the role they play in the chemistry of cold dense cores. In the models presented here, we include radiative attachment to form PAH-, mutual neutralization between PAH anions and small positively-charged ions, and photodetachment. We also test the sensitivity of our results to changes in the size and abundance of the PAH's. Our results confirm that the inclusion of PAH's changes many of the calculated abundances of smaller species considerably. In TMC-1, the general agreement with observations is significantly improved contrary to L134N. This may indicate a difference in PAH properties between the two regions. With the inclusion of PAH's in dense cloud chemistry, high-metal elemental abundances give a satisfactory agreement with observations. As a result, we do not need to decrease the observed elemental abundances of all metals and we do not need to vary the elemental C/O ratio in order to produce large abundances of carbon species in TMC-1 (CP).Comment: Accepted to ApJ. Astrophysical Journal (2008) accepte

A multi-transition HCN and HCO+ study of 12 nearby active galaxies: AGN versus SB environments

Recent studies have indicated that the HCN-to-CO(J=1-0) and HCO+-to-HCN(J=1-0) ratios are significantly different between galaxies with AGN (active galactic nucleus) and SB (starburst) signatures. In order to study the molecular gas properties in active galaxies and search for differences between AGN and SB environments, we observed the HCN(J=1-0), (J=2-1), (J=3-2), HCO+(J=1-0) and HCO+(J=3-2), emission with the IRAM 30m in the centre of 12 nearby active galaxies which either exhibit nuclear SB and/or AGN signatures. Consistent with previous results, we find a significant difference of the HCN(J=2-1)-to-HCN(J=1-0), HCN(J=3-2)-to-HCN(J=1-0), HCO+(J=3-2)-to-HCO+(J=3-2), and HCO+-to-HCN intensity ratios between the sources dominated by an AGN and those with an additional or pure central SB: the HCN, HCO+ and HCO+-to-HCN intensity ratios tend to be higher in the galaxies of our sample with a central SB as opposed to the pure AGN cases which show rather low intensity ratios. Based on an LVG analysis of these data, i.e., assuming purely collisional excitation, the (average) molecular gas densities in the SB dominated sources of our sample seem to be systematically higher than in the AGN sources. The LVG analysis seems to further support systematically higher HCN and/or lower HCO+ abundances as well as similar or higher gas temperatures in AGN compared to the SB sources of our sample. Also, we find that the HCN-to-CO ratios decrease with increasing rotational number J for the AGN while they stay mostly constant for the SB sources.Comment: accepted for publication in ApJ; 20 pages, 7 figures; in emulateApJ forma

Dense Molecular Gas Associated with the Circumnuclear Star Forming Ring in the Barred Spiral Galaxy NGC 6951

We present high resolution (3" - 5") observations of CO(1-0) and HCN(1-0) emission from the circumnuclear star forming ring in the barred spiral galaxy NGC 6951, a host of a type-2 Seyfert, using the Nobeyama Millimeter Array and 45 m telescope. We find that most of the HCN emission is associated with the circumnuclear ring, where vigorous star formation occurs. The HCN to CO integrated intensity ratio is also enhanced in the star forming ring; the peak value of HCN/CO ratio is 0.18, which is comparable to the ratio in the starbursts NGC 253 and M82. The formation mechanism of dense molecular gas has been investigated. We find that the shocks along the orbit crowding do not promote the formation of the dense molecular gas effectively but enhance the presence of low density GMCs. Instead, gravitational instabilities of the gas can account for the dense molecular gas formation. The HCN/CO ratio toward the Seyfert nucleus of NGC 6951 is a rather normal value (0.086), in contrast with other Seyferts NGC 1068 and M51 where extremely high HCN/CO value of ~ 0.5 have been reported.Comment: 33 pages, 17 figures, to appear in the Astrophysical Journa

Incorporation of stochastic chemistry on dust grains in the PDR code using moment equations

Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux,these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. We evaluate the formation rates of H2, HD and D2 molecules on dust grain surfaces and their abundances in the gas phase under interstellar conditions. We incorporate the moment equations into the Meudon PDR code and compare the results with those obtained from the rate equations. We find that within the experimental constraints on the energy barriers for diffusion and desorption and for the density of adsorption sites on the grain surface, H2, HD and D2 molecules can be formed efficiently on dust grains. Under a broad range of conditions, the moment equation results coincide with those obtained from the rate equations. However, in a range of relatively high grain temperatures, there are significant deviations. In this range, the rate equations fail while the moment equations provide accurate results. The incorporation of the moment equations into the PDR code can be extended to other reactions taking place on grain surfaces

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

The effect of the initial elemental abundance on gas-grain chemical models

For any chemical modeling, it is important to recognize that the adopted set of initial elemental abundances is a crucial parameter. The effect of initial abundance variation has been investigated. Using the most recent observations and theoretical grain models, we have set some constraints upon the set of the initial elemental abundances. Both gas-phase and gas-grain chemical models are used in this study. At early-time stages less than 1 Myr, there is little difference between results with different initial [C]/[O] ratios. This holds for gas-phase and gas-grain models. At a later evolutionary time or in the steady state, the result of the gas-grain model shows little or no dependence on the initial [C]/[O] ratios. By contrast, at late or steady-state times, the abundances of chemical species using gas-phase models are very sensitive to any variation of the initial [C]/[O] ratios. Sulfur depletion is needed for both gas-phase and gas-grain models to reproduce the observed sulfur-bearing molecules. Our main conclusion is that the gas-grain interaction processes such as accretion, surface reactions, and desorption minimize the vital role of the initial set of elemental abundance in gas-grain chemical models