Pre-heated isentropic gas in groups of galaxies

We confirm that the standard assumption of isothermal, shock-heated gas in cluster potentials is unable to reproduce the observed X-ray luminosity- temperature relation of groups of galaxies. As an alternative, we construct a physically motivated model for the adiabatic collapse of pre-heated gas into an isothermal potential that improves upon the original work of Kaiser (1991). The luminosity and temperature of the gas is calculated, assuming an appropriate distribution of halo formation times and radiation due to both bremsstrahlung and recombination processes. This model successfully reproduces the slope and dispersion of the luminosity-temperature relation of galaxy groups. The halo mass corresponding to an observed, emission weighted temperature in this model is more than an order of magnitude smaller than in the standard, isothermal model. We also present calculations of the temperature and luminosity functions for galaxy groups under the prescription of this model. The entropy required to match observations can be obtained by heating the gas at the turnaround time, for example, to about 3 X 10⁶ K at z=1, which is too high to be generated by a normal rate of supernova explosions. This model breaks down on the scale of low mass clusters, but this is an acceptable limitation, as we expect accretion shocks to contribute significantly to the entropy of the gas in such objects.