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 protocluster gas. We investigate this from two directions: by finding the amount of 'excess energy' required in intracluster 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 and its effect on gas haloes. Excess energy is retained in the gas as gravitational, kinetic and/or thermal energy. The density profile of a gas halo is then selected according to the total energy of the gas. Our principal assumption is that in the absence of non-gravitational processes, the total energy of the gas scales as the gravitational energy of the virialized halo - a self-similar scaling law motivated by hydrodynamic simulations. This relation is normalized by matching the model to the largest observed clusters. We model the gas distributions in haloes by using a two-parameter family of gas profiles. In order to study the sensitivity of results to the model, we investigate four contrasting ways of modifying gas profiles in the presence of excess energy. In addition, we estimate the minimum excess energy required in a fiducial cluster of around 2 keV in temperature by considering all available gas profiles. We conclude that the excess energies required lie roughly in the range 1-3 keV particle(-1). The observed metallicities of cluster gas suggest that it may be possible for supernovae to provide all of the required excess energy. However, we argue that this scenario is only marginally acceptable and would lead to highly contrived models of galaxy formation. On the other hand, more than enough energy may be available from active galactic nuclei.