  Abundance of rich clusters in 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 two
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}. We find that
the best fitted value in flat models is sigma_8=(0.7 \pm 0.06)
(\Omega_m/0.35)^{-0.44}(\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. This 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 CDM 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 virial radius with BeppoSAX, Chandra and
XMM-Newton.
