T. W. Hartquist

A stochastic approach to grain surface chemical kinetics

A stochastic model of grain surface chemistry, based on a master equation description of the probability distributions of reactive species on grains, is developed. For an important range of conditions, rates of molecule formation are limited by low accretion rates, so that the probability that a grain contains more than one reactive atom or molecule is small. We derive simple approximate expressions for these circumstances, and explore their validity through comparison with numerical solutions of the master equation for H, O and H, N, O reaction systems. A more detailed analysis of the range of validity of several analytic approximations and numerical solutions, based on exact analytical results for a model in which H and H2 are the only species, is also made. Though the use of our simple approximate expressions is computationally ecient, the solution of the master equation under the assumption that no grain contains more than two particles of each species usually gives more accurate results in the parameter regimes where the deterministic rate equation approach is inappropriate. The implementation of sparse matrix inversion techniques makes the use of such a truncated master equation solution method feasible for considerably more complicated surface chemistries than the ones we have examined here.

Parametrization of C-shocks. Evolution of the sputtering of grains

Context. The detection of narrow SiO line emission toward the young shocks of the L1448-mm outflow has been interpreted as a signature of the magnetic precursor of C-shocks. In contrast with the low SiO abundances (≤10 -12 ) derived from the ambient gas, the narrow SiO emission in the precursor component at almost ambient velocities reveals enhanced SiO abundances of ∼10 -11 . It has been proposed that this enhancement of the SiO abundance is produced by the sputtering of the grain mantles at the early stages of C-shocks. However, modelling of the sputtering of grains has usually averaged the SiO abundances over the dissipation region of C-shocks, which cannot explain the recent observations. Aims. We model the evolution of the gas-phase abundances of molecules like SiO, CH 3 OH, and H 2 O, produced by the sputtering of the grain mantles and cores as the shock propagates through the ambient gas. We consider different initial gas densities and shock velocities. Methods. We propose a parametric model to describe the physical structure of C-shocks as a function of time. Using the known sputtering yields for water mantles (with other minor constituents like silicon and CH 3 OH) and olivine cores by collisions with H 2 , He, C, O, Si, Fe, and CO, we follow the evolution of the abundances of silicon, CH 3 OH, and H 2 O ejected from grains along the evolution of the shock. Results. The evolution of the abundances of the sputtered silicon, CH 3 OH, and H 2 O shows that CO seems to be the most efficient sputtering agent in low-velocity shocks. The velocity threshold for the sputtering of silicon from the grain mantles is appreciably reduced (by 5-10 kms -1 ) by CO compared to other models. The sputtering by CO can generate SiO abundances of ∼10 -11 at the early stages of low-velocity shocks, consistent with those observed in the magnetic precursor component of L1448-mm. Our model satisfactorily reproduces the progressive enhancement of SiO, CH 3 OH, and H 2 O observed in this outflow, suggesting that this enhancement may be due to the propagation of two shocks with U s = 30 km s -1 and U s = 60 km s -1 coexisting within the same region. Conclusions. Our simple model can be used to estimate the time-dependent evolution of the abundances of molecular shock tracers like SiO, CH 3 OH, H 2 O, or NH 3 in very young molecular outflows.

Dynamical and pressure structures in winds with multiple embedded evaporating clumps—I. Two-dimensional numerical simulations

Because of its key role in feedback in star formation and galaxy formation, we examine the nature of the interaction of a flow with discrete sources of mass injection. We show the results of two-dimensional numerical simulations in which we explore a range of configurations for the mass sources and study the effects of their proximity on the downstream flow. The mass sources act effectively as a single source of mass injection if they are so close together that the ratio of their combined mass injection rate is comparable to or exceeds the mass flux of the incident flow into the volume that they occupy. The simulations are relevant to many diffuse sources, such as planetary nebulae and starburst superwinds, in which a global flow interacts with material evaporating or being ablated from the surface of globules of cool, dense gas.

The turbulent destruction of clouds – I. A k–ε treatment of turbulence in 2D models of adiabatic shock–cloud interactions

The interaction of a shock with a cloud has been extensively studied in the literature, where the effects of magnetic fields, radiative cooling and thermal conduction have been considered. In many cases, the formation of fully developed turbulence has been prevented by the artificial viscosity inherent in hydrodynamical simulations. This problem is particularly severe in some recent simulations designed to investigate the interaction of a flow with multiple clouds, where the resolution of individual clouds is necessarily poor. Furthermore, the shocked flow interacting with the cloud has been assumed to be completely uniform in all previous single-cloud studies. In reality, the flow behind the shock is also likely to be turbulent, with non-uniform density, pressure and velocity structure created as the shock sweeps over inhomogeneities upstream of the cloud (as seen in recent multiple cloud simulations). To address these twin issues we use a subgrid compressible k–� turbulence model to estimate the properties of the turbulence generated in shock–cloud interactions and the resulting increase in the transport coefficients that the turbulence brings. A detailed comparison with the output from an inviscid hydrodynamical code puts these new results into context. Despite the above concerns, we find that cloud destruction in inviscid and k–� models occurs at roughly the same speed when the post-shock flow is smooth and when the density contrast between the cloud and intercloud medium, χ 100. However, there are increasing and significant differences as χ increases. The k–� models also demonstrate better convergence in resolution tests than inviscid models, a feature which is particularly useful for multiple-cloud simulations. Clouds which are over-run by a highly turbulent post-shock environment are destroyed significantly quicker as they are subject to strong ‘buffeting’ by the flow. The decreased lifetime and faster acceleration of the cloud material to the speed of the ambient flow leads to a reduction in the total amount of circulation (vorticity) generated in the interaction, so that the amount of vorticity may be self-limiting. Additional calculations with an inviscid code where the post-shock flow is given random, grid-scale, motions confirm the more rapid destruction of the cloud. Our results clearly show that turbulence plays an important role in shock–cloud interactions, and that environmental turbulence adds a new dimension to the parameter space which has hitherto been studied.

The turbulent destruction of clouds – II. Mach number dependence, mass-loss rates and tail formation

The turbulent destruction of a cloud subject to the passage of an adiabatic shock is studied. We find large discrepancies between the lifetime of the cloud and the analytical result of Hartquist et al. (1986). These differences appear to be due to the assumption in Hartquist et al. (1986) that mass-loss occurs largely as a result of lower pressure regions on the surface of the cloud away from the stagnation point, whereas in reality Kelvin-Helmholtz (KH) instabilities play a dominant role in the cloud destruction. We find that the true lifetime of the cloud (defined as when all of the material from the core of the cloud is well mixed with the intercloud material in the hydrodynamic cells) is about 6 × tKHD, where tKHD is the growth timescale for the most disruptive, long-wavelength, KH instabilities. These findings have wide implications for diffuse sources where there is transfer of material between hot and cool phases. The properties of the interaction as a function of Mach number and cloud density contrast are also studied. The interaction is milder at lower Mach numbers with the most marked differences occuring at low shock Mach numbers when the postshock gas is subsonic with respect to the cloud (i.e. M < 2:76). Material stripped off the cloud only forms a long “tail-like” feature if � � 10 3 .

Chemical signatures of shocks in hot cores

The characteristic chemistry of hot cores arises from the abrupt evaporation of icy mantles when a massive star begins to irradiate the interstellar gas in its vicinity. Such stars are also likely to generate powerful winds which may initiate shocks in the same interstellar gas. In this paper, we consider whether chemical signatures of the passage of a shock through a hot core can be identied. We nd that if hydrogenation occurs on surfaces and freeze-out of heavy gas-phase atoms and molecules is complete before the hot core is established then no such chemical signature exists. However, if some residual material is present in the gas when the hot core is established then the following molecular abundance ratios are signicantly aected by the presence of a shock: NS/CS, SO/CS, and HCO/H2CO. This result is more evident if injection of ices into the gas occurs over a nite period, rather than instantaneously. We conclude that these molecular abundance ratios may be useful tracers of the dynamical history of hot cores, and that follow-up observational studies are required.

Interstellar oxygen chemistry

We present results of chemical models for a variety of types of regions shown by SWAS observations to contain less O2 and H2O than previously expected. We identify time-dependent models for which O2 and H2O abundances meet the SWAS constraints and for which calculated abundances of other species are in harmony with measurements made primarily at millimeter wavelengths. The phases of acceptable composition are transient in these time-dependent models but are of very substantial length in many models for which CO and N2 are assumed to be returned promptly and unaltered to the gas phase though other species, except for H2 and He, freeze-out onto the dust. We also consider whether the presence of bistability in some steady-state models can account for the SWAS and other observations.

Chemistry in cosmic ray dominated regions

Molecular line observations may serve as diagnostics of the degree to which the number density of cosmic ray protons, having energies of 10s to 100s of MeVs each, is enhanced in starburst galaxies and galaxies with active nuclei. Results, obtained with the UCL\_PDR code, for the fractional abundances of molecules as functions of the cosmic-ray induced ionisation rate,

Shock-triggered formation of magnetically-dominated clouds

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Large electric fields in acoustic waves and the stimulation of lightning discharges

, are presented. The aim is not to model any particular external galaxies. Rather, it is to identify characteristics of the dependencies of molecular abundances on