Evolution of the gas mass fraction in galaxy clusters

The mass fraction of hot gas in clusters is a basic quantity whose level and dependence on the cluster mass and redshift are intimately linked to all cluster X-ray and Sunyayev-Zel'dovich measures. Modelling the evolution of the gas fraction is clearly a necessary ingredient in the description of the hierarchical growth of clusters through mergers of subclumps and mass accretion on the one hand, and the dispersal of gas from the cluster galaxies by tidal interactions, galactic winds and ram-pressure stripping on the other hand. A reasonably complete description of this evolution can only be given by very detailed hydrodynamical simulations, which are, however, resource-intensive and difficult to implement in the mapping of parameter space. A much more practical approach is the use of semi-analytic modelling that can be easily implemented to explore a wide range of parameters. We present first results from a simple model that describes the build-up of the gas mass fraction in clusters by following the overall impact of the above processes during the merger and accretion history of each cluster in the ensemble. Acceptable ranges for model parameters are deduced through comparison with results of X-ray observations. Basic implications of our work for modelling cluster statistical properties, and the use of these properties in joint cosmological data analyses, are discussed.