The characteristic stellar mass as a function of redshift

We present a model for the star formation process during the initial collapse of dark matter haloes at redshifts z = 0-30. We derive a simple formula for the characteristic stellar mass scale during this initial burst of star formation. In our picture, this characteristic scale reflects both the minimum temperature to which the gas can cool (determined by the metallicity and the temperature of the cosmic microwave background) and the pressure of overlying baryons in the collapsing halo. This prescription reproduces both the large mass scales found in simulations of Population III star formation and the near-solar values observed for star formation at low redshift.