Time-dependent Cooling and Grain Destruction in Hot Dusty Plasmas: A Simplified Model and Principal Results
We present a simple method of including the principal effects of interstellar dust in hot gas evolution codes, including a consistent set of elemental abundances, their distribution among gas and grains in diffuse regions, the distribution of grain sizes, the sputtering of grains by impact with nuclei, and the cooling rate from gas-grain collisions. When combined with a gas evolution code, the time-dependent evolution of gas phase abundances, ion concentrations, and gas and grain cooling can be followed.Sample calculations are presented to explore the relative timescales for grain destruction and radiative cooling, the relative importance of grain and gas cooling coefficients in evolving gas, the overall significance of grain inclusion to the thermal history of the gas, and the possibility of comparative dating of hot gas regions via their X-ray spectral characteristics. We find that the straightforward comparison between the cooling coefficient of newly heated dust with that of gas in collisional equilibrium is particularly misleading. The cooling coefficient of newly heated material is overwhelmingly dominated by the nonequilibrium gas cooling, during which the ionization is rapidly rising and dust is being sputtered. The gas cooling coefficient drops rapidly during this brief period. Dust cooling also drops, because of the reduction in grain surface area. At high temperature, gas cooling soon falls below that of the grains, but grain cooling continues to fall rapidly, raising the gas cooling via the return of elements to the gas. For material whose temperature exceeds roughly 4 x 106 K, the total radiated energy during these "ion flash" and dust destruction epochs is small compared to the total energy in the system. Conversely, for temperatures below about 4 x 105 K, both grain destruction by ion sputtering and grain cooling are small. It is a somewhat remarkable coincidence: The range of temperature for which the dust destruction and radiative cooling timescales are comparable is also the temperature range for which grain and gas cooling rates are similar. We conclude that the inclusion of dust in codes will usually have little overall effect on the thermal and dynamical history of the gas. But there can be a quite significant alteration of the X-ray spectra of recently heated gas, behind "nonradiative" shocks, for example. Dust inclusion at least at our level of complexity is required in any models purporting to examine spectral details. As an example, the inability of shockwave models to produce the surprising intensity of the [Fe X] line in the nonradiative shocks of the Cygnus Loop was once used to argue that the shock was proceeding through a medium infested with microscopic interstellar clouds, evaporating them as it went It was suggested that evaporative injection of low ion stages into the hot gas could potentially produce the [Fe X], as iron is being ionized. Dust sputtering should produce a similar effect There is probably an important spectral line whose intensity and surface brightness distribution map the pattern and rate of dust destruction in the Cygnus Loop and hot gas elsewhere, but it will not be found in gas-phase-only models. Fortunately, at the level of complexity of our modeling, dust inclusion is straightforward.