MEASURING THE THREE-DIMENSIONAL SHAPE OF X-RAY CLUSTERS
Observations and numerical simulations of galaxy clusters strongly indicate that the hot intracluster X-ray-emitting gas is not spherically symmetric. In many earlier studies, spherical symmetry has been assumed partly because of limited data quality; however, new deep observations and instrumental designs will make it possible to go beyond that assumption. Measuring the temperature and density profiles are of interest when observing the X-ray gas; however, the spatial shape of the gas itself also carries very useful information. For example, it is believed that the X-ray gas shape in the inner parts of galaxy clusters is greatly affected by feedback mechanisms, cooling, and rotation, and measuring this shape can therefore indirectly provide information on these mechanisms. In this paper, we present a novel method to measure the three-dimensional shape of the intracluster X-ray-emitting gas. We can measure the shape from X-ray observations only, i.e., the method does not require combination with independent measurements of, e.g., the cluster mass or density profile. This is possible when one uses the full spectral information contained in the observed spectra. We demonstrate the method by measuring radially dependent shapes along the line of sight for CHANDRA mock data. We find that at least 10{sup 6} photons are required to get a 5{sigma} detection of shape for an X-ray gas having realistic features such as a cool core and a double power law for the density profile. We illustrate how Bayes' theorem is used to find the best-fitting model of the X-ray gas, an analysis that is very important in a real observational scenario where the true spatial shape is unknown. Not including a shape in the fit may propagate to a mass bias if the X-ray is used to estimate the total cluster mass. We discuss this mass bias for a class of spatial shapes.