A scaling relation between the SZ decrement and the Thomson depth in clusters of galaxies

In a recent study of dark matter N-body simulations, a scaling relation between the SZ decrement and the Thomson depth of a cluster of galaxies of the form DeltaT(r) proportional to tau (2)(T) has been found (Diaferio et al. 2000). In this paper, it will be shown that such a scaling relation arises if the intracluster gas is distributed similar to the dark matter density described by the NFW-profile and the finite spatial resolution of the numerical simulation is taken into account. It is furthermore investigated whether the DeltaT(r) proportional to tau (2)(T) relation holds for analytical models of an isothermal gas sphere in the gravitational potential of a dark matter halo distributed according to the NFW-profile, the available experimental data of SZE observations, and recent results from cosmological gas-dynamical simulations of clusters of galaxies. Combining such a relation with temperature estimates from X-ray observations would provide information about a dependence of T-e on tau (T). The Thomson depth might therefore emerge as another important scaling parameter in studies of clusters of galaxies. (C) 2001 MAIK "Nauka/Interperiodica".