The cooling of shock-compressed primordial gas

We find that at redshifts z greater than or similar to 10, HD line cooling allows strongly shocked primordial gas to cool to the temperature of the cosmic microwave background (CMB). This temperature is the minimum value attainable via radiative cooling. Provided that the abundance of HD, normalized to the total number density, exceeds a critical level of similar to 10(-8), the CMB temperature floor is reached in a time which is short in comparison to the Hubble time. We estimate the characteristic masses of stars formed out of shocked primordial gas in the wake of the first supernovae, and resulting from the virialization of dark matter haloes during hierarchical structure formation to be similar to 10 M-circle dot. In addition, we show that cooling by HD enables the primordial gas in relic HII regions to cool to temperatures considerably lower than those reached via H-2 cooling alone. We confirm that HD cooling is unimportant in cases where the primordial gas does not go through an ionized phase, as in the formation process of the very first stars in z greater than or similar to 20 minihaloes of mass similar to 10(6) M-circle dot.