Non-extensive thermostatistical approach of the peculiar velocity function of galaxy clusters

We show that the observational data recently provided by Giovanelli et al. and discussed by Bahcall and Oh concerning the velocity distribution of clusters of galaxies can be naturally fitted by a statistical distribution which generalizes the Maxwell-Boltzmann one (herein recovered for the entropie index q = 1). Indeed a recent generalization of the Boltzmann-Gibbs thermostatistics suggests for this problem that the probability function is given, within a simple phenomenological model, by P(> v)=∫vvmaxdv[1-(1-q)(v/v0)2] (q)/(1-q)/∫0vmaxdv[1-(1-q)(v/v 0)2](q)/(1-q), (Equation Presented) A remarkably good fitting with the data is obtained for q=0.23-0.05+0.07 and v0=490±5 kms-1.