In-shock Cooling in Numerical Simulations

Abstract

We model a one-dimensional shock-tube using smoothed particle hydrodynamics and investigate the consequences of having finite shock-width in numerical simulations. We investigate the cooling of gas during passage through the shock for different cooling regimes. For a shock temperature of 10^5K, the maximum temperature of the gas is much reduced and the cooling time was reduced by a factor of 2. At lower temperatures, we are especially interested in the production of molecular Hydrogen and so we follow the ionization level and H_2 abundance across the shock. This regime is particularly relevent to simulations of primordial galaxy formation for halos in which the virial temperature of the galaxy is sufficiently high to partially re-ionize the gas. The effect of in-shock cooling is substantial: the maximum temperature the gas reaches compared to the theoretical temperature was found to vary between 0.15 and 0.81 for the simulations performed. The downstream ionization level is reduced from the theoretical level by a factor of between 2.4 and 12.5, and the resulting H_2 abundance was found to be reduced to a fraction of 0.45 to 0.74 of its theoretical value. At temperatures above 10^5K, radiative shocks are unstable and will oscillate. We reproduce these oscillations and find good agreement with the previous work of Chevalier and Imamura (1982), and Imamura, Wolff and Durisen (1984). The effect of in-shock cooling in such shocks is difficult to quantify, but is undoubtedly present.