Cluster number density normalization from the observed mass-temperature relation

The number density of rich clusters in the local Universe is currently believed to provide the most robust normalization of power spectrum at a scale of 10 Mpc. This normalization depends very sensitively on the calibration between virial mass M and temperature T, which is usually taken from simulations. Uncertainties in the modelling, such as gas cooling and heating, can lead to a factor of 2 variations in the normalization and are thus not very reliable. Here we use instead an empirical M-500-T relation derived from X-ray mass determinations to calibrate the method. We use results from dark matter simulations to relate the virial mass function to the mass function at observed M-500. Using the relation of Finoguenov et al. we find that the best-fitting value in flat models is sigma(8) = (0.77 +/- 0.07) (Omega(m)/03)(-044)(Gamma/0.2)(0.08) where only the statistical error is quoted. This is significantly lower than previously obtained values from the local cluster abundance. A lower value for sigma(8) is in a better agreement with cosmic microwave background and large-scale structure constraints and helps alleviate small-scale problems of cold dark matter models. Presently the systematic uncertainties in the mass determination are still large, but ultimately this method should provide a more reliable way to normalize the M-T relation. This can be achieved by obtaining a larger sample of well-measured cluster masses out to a significant fraction of the virial radius with BeppoSAX, Chandra and XMM-Newton.