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. The luminosity and temperature of the gas are calculated assuming an appropriate distribution of halo formation times, and radiation owing to both bremsstrahlung and recombination processes. This model successfully reproduces the slope and dispersion of the luminosity-temperature relation of galaxy groups. We also present calculations of the temperature and luminosity functions for galaxy groups under the prescription of this model. This model makes two strong predictions for haloes with total masses M < 10(13) M., which are not yet testable with current data: (1) the gas mass fraction will increase in direct proportion to the halo mass; (2) the gas temperature will be higher than the virial temperature of the mass. The second effect is strong enough that group masses determined from gas temperatures will be overestimated by about an order of magnitude if it is assumed that the gas temperature is the virial temperature. The entropy required to match observations can be obtained by heating the gas at the turnaround time, for example, to about 3 x 10(6) K at z = 1, which is too high to be generated by a normal rate of supernova explosions. The isentropic 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.