A MEASUREMENT OF THE MASS FLUCTUATION SPECTRUM FROM THE CLUSTER X-RAY TEMPERATURE FUNCTION

We present a statistically complete sample of galaxy clusters which also has complete X-ray temperature information. Using this sample we derive the cluster bolometric luminosity and temperature functions. The temperature function constrains the shape and amplitude of the mass fluctuation power spectrum. For a power law, i.e., with the fluctuation power spectrum proportional to k(n), we find n = -(1.7(-0.35)+0.65), and an amplitude which implies that the rms value of delta-M/M is 0.59 +/- 0.02 on a scale of 8 h-1 Mpc at the present epoch.