In-shock cooling in numerical simulations

We model a one-dimensional shock-tube using smoothed particle hydrodynamics and investigate the consequences of having finite shock-width in numerical simulations caused by finite resolution of the codes. We investigate the c ooling of gas during passage through the shock for three different cooling regimes. For a theoretical shock temperature of 10(5) K, the maximum temperature of the gas is much reduced. When the ratio of the cooling time to shock-crossi ng time was 8, we found a reduction of 25 per cent in the maximum temperatu re reached by the gas. When the ratio was reduced to 1.2, the maximum tempe rature reached dropped to 50 per cent of the theoretical value. In both cas es the cooling time was reduced by a factor of 2. At lower temperatures, we are especially interested in the production of mo lecular hydrogen, and so we follow the ionization level and H-2 abundance a cross the shock. The effect of in-shock cooling is substantial: the maximum temperature the gas reaches compared with the theoretical temperature is f ound to vary between 0.15 and 0.81, depending upon the shock strength and m ass resolution. The downstream ionization level is reduced from the theoret ical level by a factor of between 2.4 and 12.5, and the resulting H-2 abund ance by a factor of 1.35 to 2.22. At temperatures above 10(5) K, radiative shocks are unstable and will oscil late. We find that the shock jump temperature varies by a factor of 20 beca use of these oscillations. We conclude that extreme caution must be exercised when interpreting the re sults of simulations of galaxy formation.