TEMPERATURE DISTRIBUTION FUNCTION OF X-RAY CLUSTERS OF GALAXIES IN A NEUTRINO DOMINATED UNIVERSE

Abstract

The temperature distribution function (TDF) of X-ray clusters is derived for different normalizations of the HDM power spectrum in an Omega_0=1 universe using the statistics of peaks of a random Gaussian field. Concerning cluster formation only, the neutrino picture appears to be marginally consistent with observations for H_0=70 km/s/Mpc provided the normalization is alpha=sigma_0/delta_s=0.42 with sigma_0 the rms variance of the fluctuations linearly evolved to the present epoch and delta_s the collapse threshold required in structure formation models. However, using the constraint that the formation epoch of QSO's puts on the HDM model, it appears that this normalization is too small to be consistent with quasars formation. Allowing higher values for the Hubble constant alleviates this problem but leads to an unacceptable short age of the universe. Moreover, the constraint put by the recent measurement of the level of fluctuations in the cosmic background radiation by COBE tends to reject models with high values of H_0. We conclude that the neutrino model fails in any case to account for the whole set of available observations in a consistent way.