Multiplicity Functions and X-ray emission of Clusters and Groups versus Galaxies and Quasars

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We use a unified analytical formulation for the multiplicity functions of clusters and galaxies which is free from the cloud-in-cloud problem encountered in earlier approaches and well adapted to the description of the non-linear clustering features. It is especially suited to simultaneously describe rich clusters, groups and galaxies, consistently with the hierarchical picture of gravitational clustering and their evolution in time. Using a simple model for the X-ray luminosity (taking into account entropy considerations), we obtain the X-ray luminosity distribution of groups and clusters. Then, using the same formalism we derive the galaxy and quasar multiplicity functions. In particular, we show that the use of the standard Press-Schechter prescription leads to erroneous conclusions at low redshifts while our approach provides a reasonable agreement with observations in a natural fashion because it is able to distinguish galactic halos from groups or clusters. Thus, we obtain a global and consistent picture of the X-ray emissions from all structures. In particular, we show that future observations (e.g., from AXAF) could provide interesting information on galaxy evolution. Indeed, they will constrain the importance of a possible hot diffuse gaseous phase in galactic halos and they could reveal massive galaxies which are just being formed, through the X-ray emission of their cooling gas.