Entropy evolution in galaxy groups and clusters: A comparison of external and internal heating

The entropy in hot, X-ray-emitting gas in galaxy groups and clusters is a measure of past heating events, except for the entropy lost by radiation from denser regions. Observations of galaxy groups indicate higher entropies than can be achieved in the accretion shock experienced by gas when it fell into the dark halos. These observations generally refer to the dense, most luminous inner regions where the gas that first entered the halo may still reside. It has been proposed that this nongravitational entropy excess results from some heating process in the early universe that is external to the group and cluster halos and that it occurred before most of the gas had entered the dark halos. This universal heating of cosmic gas could be due to active galactic nuclei (AGNs), Population III stars, or some as yet unidentified source. Alternatively, the heating of the hot gas in groups may be produced internally by Type II supernovae when the galactic stars in these systems formed. We investigate here the consequences of various amounts of external, high-redshift heating with a suite of gasdynamical calculations. We consider the influence of radiation losses and distributed mass dropout on the X-ray luminosity and emission-weighted temperature of the hot gas as well as its central entropy. In general, we find that externally heated flows are unsatisfactory; when the heating is high enough to bring the X-ray luminosities into agreement with observations, the gas entropy is too high. We compare these solutions with flows that are internally heated by Type II supernovae; this type of heating depends on the initial mass function (IMF) and the efficiency that the supernova energy is conveyed to the hot gas. These internally heated flows give much better agreement with X-ray observations of galaxy groups and are insensitive to the levels of supernova heating that we consider as well as to the epoch and spatial distribution of the supernova heating process. However, to fit X-ray observations, a large fraction of the energy produced by high-redshift Type II supernovae must heat the hot gas if the number of supernovae is based on a Salpeter IMF. Alternatively, only about 20% of the Type II supernova energy would be required to heat the gas if the IMF has a flatter slope than Salpeter, as suggested by stellar mass-to-light ratios.