Reconstruction of Temperature and Density Profiles of Galaxy Cluster RX J1347.5-1145 Using the Combination of Sunyaev-Zel’dovich Effect and X-ray Observations

In this paper, we use the observations of Sunyaev-Zel’dovich effect and X-ray surface brightness to reconstruct the radial profiles of gas temperature and density under the assumption of spherically symmetric distribution of gas. The reconstruction method, firstly raised by Silk & White (1978), is directly dependent on the experimental measurements of Sunyaev-Zel’dovich effect and X-ray surface brightness. There is no need to incorporate additional assumptions such as the equation of state of gas or the hydrostatic equilibrium conditions. The method is applied on the cluster RX J1347.5-1145, which has both the SunyaevZel’dovich effect and X-ray observations with relative high precision. It is shown that it will be an effective method to get the gas distribution information in the galaxy cluster. The statistical errors of the derived temperature and density profiles of gas are estimated according to the observational uncertainties.