Apparent and actual galaxy cluster temperatures

The redshift evolution of the galaxy cluster temperature function is a powe rful probe of cosmology. However, its determination requires the measuremen t of redshifts for all clusters in a catalogue, which is likely to prove ch allenging for large catalogues expected from XMM-Newton, which may contain of the order of 2000 clusters with measurable temperatures, distributed aro und the sky. In this paper we study the apparent cluster temperature, which can be obtained without cluster redshifts. We show that the apparent tempe rature function itself is of limited use in constraining cosmology, and so concentrate our focus on studying how apparent temperatures can be combined with other X-ray information to constrain the cluster redshift. We also br iefly study the circumstances under which the non-thermal spectral features can provide redshift information.