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 SDSS 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 ($M_\mathrm{halo} >
10^{14.5}\,\mathrm{M_\odot}$) 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.
