The β-model problem:: The incompatibility of X-ray and Sunyaev-Zeldovich effect model fitting for galaxy clusters

We have analyzed a large sample of numerically simulated clusters to demonstrate the adverse effects resulting from the use of X-ray-fitted beta-model parameters with Sunyaev-Zeldovich effect (SZE) data. There is a fundamental incompatibility between beta-model fits to X-ray surface brightness profiles and those done with SZE profiles. Since observational SZE radial profiles are in short supply, the X-ray parameters are often used in SZE analysis. We show that this leads to biased estimates of the integrated Compton y-parameter inside r(500) calculated from clusters. We suggest a simple correction of the method, using a nonisothermal beta-model modified by a universal temperature profile, which brings these calculated quantities into closer agreement with the true values.