Non-Gravitational Heating in the Hierarchical Formation of X-ray Clusters

The strong deviation in the properties of X-ray clusters from simple scaling laws highlights the importance of non-gravitational heating and cooling processes in the evolution of proto-cluster gas. We investigate this from two directions: by finding the amount of `excess energy' required in intra-cluster gas in order to reproduce the observed X-ray cluster properties, and by studying the excess energies obtained from supernovae in a semi-analytic model of galaxy formation. Using the insights obtained from the model, we then critically discuss possible ways of achieving the high excess specific energies required in clusters. These include heating by supernovae and active galactic nuclei, the role of entropy, and the effect of removing gas through radiative cooling. Our model self-consistently follows the production of excess energy as well as its effect on star formation in galaxies. Excess energy is retained in gas as gravitational, kinetic and/or thermal energy. The gas distribution of virialized halos are modelled with a 2-parameter family of gas density profiles; gas profiles are then chosen according to the total energy of the gas. We investigate four contrasting ways of modifying gas density profiles in the presence of excess energy, in order to study the sensitivity of results to the model. In addition, we estimate the minimum excess specific energy required when all available gas profiles are considered, using a fiducial cluster with a temperature of around 2 keV. We find that the excess specific energies required in clusters lie roughly in the range 1--3 keV/particle. (abridged)