SZ and X-ray combined analysis of a distant galaxy cluster, RX J2228+2037

Abstract

We have performed a combined analysis of X-ray and Sunyaev-Zel'dovich data in the direction of the distant galaxy cluster, RX J2228+2037. Fitting a $\beta$-model to the high-resolution HRI data gives $r_c = 103 \pm 12 h_{70}^{-1}$ kpc and $\beta=0.54 \pm 0.03$. The dependency of the Sunyaev-Zel'dovich effect with respect to the gas temperature allows us, through the additional use of the 21 GHz data of the cluster, to determine $k_B T_e=10.4 \pm 1.8 h_{70}^{1/2}$ keV. Extrapolating the gas density profile out to the virial radius ($R_v=r_{178}=2.9$ Mpc), we derived a gas mass of $M_{g}(r<R_v)=(4.0\pm 0.2)\times 10^{14} h_{70}^{-5/2} \rm{M}_\odot$. Within the hypothesis of hydrostatic equilibrium, the corresponding extrapolated total mass for this source is: $M_{tot}(r<R_v)=(1.8 \pm 0.4)\times 10^{15} h^{-1} \rm{M}_\odot$, which corresponds to a gas fraction of $f_{gas}=0.22\pm 0.06 h_{70}^{-3/2}$. Our results on the temperature and on the cluster mass classify RX J2228+2037 among the distant, hot and very massive galaxy clusters. Our work highlights the power of the association of galaxy cluster mapping observations in X-ray and the SZ effect to derive the cluster's physical properties, even without X-ray spectroscopy.