The Reliability of X-ray Constraints of Intrinsic Cluster Shapes
  Using the simulation of Katz & White 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 gradients. We restrict analysis to aggregate cluster shapes on scales of $r\sim 1-2$ Mpc to reduce our sensitivity to core subclustering. For low redshifts $(z\lesssim 0.25)$ the X-ray method accurately measures the true ellipticity of the three-dimensional cluster dark matter; assuming the gas is isothermal adds only small errors. At higher redshifts the X-ray method yields unreliable results since the gas does not trace the cluster gravitational potential. We proffer necessary conditions for the reliability of X-ray methods characterized by the amount of substructure in the X-ray surface brightness images and the isophotal shapes. We conclude that measurements of aggregate cluster shapes on scales $r\sim 1-2$ Mpc are insensitive to core substructure on scales of a few hundred kpc. Therefore our results suggest that the X-ray measurements of aggregate cluster shapes by Fabricant, Rybicki, & Gorenstein and Buote & Canizares 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. 
D. A. Buote and J. C. Tsai