The X-ray Temperature Function.

In the absence of a mass function the next best thing would be to construct an X-ray temperature function (XTF). By measuring the number density of clusters as function of temperature at different epochs, it may be inferred how clusters of galaxies are evolving. For example, a simple consideration of hierarchical structure formation would predict that the most massive clusters of galaxies would be the most recent objects to have formed, and therefore if there should be a deficit of massive clusters at high redshift. Thus if XTFs are constructed from a sample of galaxy clusters at high redshift and at low redshift the high redshift sample would be expected to contain fewer clusters at the highest temperatures.

Unfortunately the measurement of accurate temperatures for clusters of galaxies at high redshift requires telescopes with a large collecting area and a good spectral sensitivity. Thus until the launch of Chandra and XMM accurate temperatures were difficult to determine for samples large enough to contain a reasonable number of massive, high redshift clusters.

As a result the XTF has had relatively few determinations. Recent determinations at low redshift include those of Markevitch (1998) and Ikebe et al. (2002) for low redshift clusters and Henry (2000) and Donahue & Voit (1999) for high redshift clusters. Evolution of XTF appears consistent with a low density universe, $0.2 \le \Omega_{{\rm M}} \le 0.6$ (Rosati 2002).