An X-ray Size-Temperature Relation for Galaxy Clusters: Observation and Simulation

We show that galaxy clusters conform to a tight relation between X-ray isophotal size R_I and emission weighted intracluster medium (ICM) temperature T_X. The best fit relation for 41 members of an X-ray flux limited cluster sample is: $log{R}_I=(0.93\pm 0.11)log(<T_X>\mathrm{/}6keV)-(0.08\pm 0.01)$; intrinsic scatter in size about the relation is 15%, and for 30 clusters with T_X>4 keV the scatter is reduced to 10%. The existence of the size-temperature (ST) relation indicates the ICM structure is a well behaved function of T_X. We use an ensemble of gasdynamic simulations to demonstrate that a cluster population experiencing present epoch growth nonetheless conforms to an ST relation with scatter similar to that observed; the simulations also exhibit a tight relation between M_{vir} and T_X, providing the suggestion that a similar relation holds for observed clusters. We use the scatter in R_I to estimate limits on the RMS variation in ICM mass fraction \delta f_{ICM} at constant T_X: \delta f/f_{ICM}<22% (<14% for clusters with T_X>4 keV). It appears that a mechanism like feedback from galaxy winds, which introduces systematic structural changes in the ICM, is required to reproduce the observed slope of the ST relation.