Model-independent limits on the line-of-sight depth of clusters of galaxies using X-ray and Sunyaev-Zel'dovich data

Abstract

We derive a model-independent expression for the minimum line-of-sight extent of the hot plasma in a cluster of galaxies. The only inputs are the 1-5keV X-ray surface brightness and the Comptonization from Sunyaev-Zel'dovich (SZ) data. No a priori assumptions regarding equilibrium or geometry are required. The method applies when the X-ray emitting material has temperatures anywhere between 0.3keV and 20keV and metallicities between 0 and twice solar-conditions fulfilled by nearly all intracluster plasma. Using this method, joint APEX-SZ and Chandra X-ray Observatory data on the Bullet Cluster yield a lower limit of 400 ± 56kpc on the half-pressure depth of the main component, limiting it to being at least spherical, if not cigar-shaped primarily along the line of sight. © 2011. The American Astronomical Society. All rights reserved.