Connecting optical and X-ray tracers of galaxy cluster relaxation

Substantial effort has been devoted in determining the ideal proxy for quantifying the morphology of the hot intracluster medium in clusters of galaxies. These proxies, based on X-ray emission, typically require expensive, high-quality X-ray observations making them difficult to apply to large surveys of groups and clusters. Here, we compare optical relaxation proxies with X-ray asymmetries and centroid shifts for a sample of Sloan Digital Sky Survey clusters with high-quality, archival X-ray data from Chandra and XMM–Newton. The three optical relaxation measures considered are the shape of the member-galaxy projected velocity distribution – measured by the Anderson–Darling (AD) statistic, the stellar mass gap between the most-massive and second-most-massive cluster galaxy, and the offset between the most-massive galaxy (MMG) position and the luminosity-weighted cluster centre. The AD statistic and stellar mass gap correlate significantly with X-ray relaxation proxies, with the AD statistic being the stronger correlator. Conversely, we find no evidence for a correlation between X-ray asymmetry or centroid shift and the MMG offset. High-mass clusters (Mhalo > 1014.5 M⊙) in this sample have X-ray asymmetries, centroid shifts, and Anderson–Darling statistics which are systematically larger than for low-mass systems. Finally, considering the dichotomy of Gaussian and non-Gaussian clusters (measured by the AD test), we show that the probability of being a non-Gaussian cluster correlates significantly with X-ray asymmetry but only shows a marginal correlation with centroid shift. These results confirm the shape of the radial velocity distribution as a useful proxy for cluster relaxation, which can then be applied to large redshift surveys lacking extensive X-ray coverage.