The Reliability of X-Ray Constraints of Intrinsic Cluster Shapes

Using the simulation of Katz & White (1993) we have tested the viability of X-ray analysis for constraining the intrinsic shapes of clusters of galaxies considering the effects of both substructure and steep temperature radients. We restrict our analysis to the aggregate shapes of clusters on scales of r ~ 1-2 Mpc in order to educe our sensitivity to subclustering in the core. For low redshifts (z <~ 0.25) the X-ray method accurately measures the true ellipticity of the three-dimensional cluster dark matter provided the inclination of the cluster is known to within ~30^deg^; assuming the gas is isothermal adds only small errors to the derived shapes. At higher redshifts the X-ray method yields unreliable results since the gas does not trace the cluster gravitational potential. We offer some necessary conditions for the reliability of X-ray methods characterized by both the amount of substructure in the X-ray surface brightness images and the shapes of the isophotes. We conclude that measurements of the aggregate shapes of clusters on scales r ~ 1-2 Mpc are insensitive to core substructure representing scales of a few hundred kpc. Therefore our results suggest that the X-ray measurements of aggregate cluster shapes by Fabricant Rybicki, & Gorenstein (1984) and Buote & Canizares (1992) are valid provided that they do not suffer from serious projection effects. A substantial number of Abell clusters observed with the ROSAT PSPC will be amenable to X-ray shape analysis.