Connecting optical and X-ray tracers of galaxy cluster relaxation

Abstract

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 luminosityweighted 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 halo > 10 14.5 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.

Calibration of systematics in constraining modified gravity models with galaxy cluster mass profiles

“…refs [48,49]); furthermore, ref. [47] found that this indicator highly correlates with other relaxation proxies from X-ray analyses, suggesting that it is a suitable criterion to describe the overall dynamical state of a cluster. Deviations from Gaussianity can be quantified by the so called Anderson-Darling (AD) test [50], which determines how different are the cumulative distribution functions of the data set and of the ideal Gaussian case.…”

Dark Energy Surveyed Year 1 results: calibration of cluster mis-centring in the redMaPPer catalogues

“…On the other hand, when the redMaPPer centres are correct, the X-ray peaks may still be offset from them because of the different dynamics and relaxation time-scales of gas and galaxies (e.g. see studies about cluster state and X-ray galaxy offsets in Mantz et al 2015;Kim, Peter & Wittman 2017;Roberts, Parker & Hlavacek-Larrondo 2018), as well as observational uncertainties in identifying the X-ray peaks, 2 but these offsets tend to be small, i.e. less than tens of kpc.…”

Optical substructure and BCG offsets of Sunyaev–Zel’dovich and X-ray-selected galaxy clusters

“…The Anderson-Darling (AD) test is a normality statistical test, based on the comparison of the empirical distribution function (EDF) and the ideal case of a normal distribution (for further details see Hou et al 2009;Roberts et al 2018). The test does not require binning or graphical analysis.…”

“…For the current work we follow the simple prescription given by Roberts et al (2018) to classify Gaussian (G) and non-gaussian (NG), or relaxed or not, clusters. They chose a critical p−value of 0.10 from the AD test.…”