  We present new diagnostic metrics to probe the dynamical state of galaxy
clusters. These novel metrics rely on the computation of the power spectra of
the matter and gas distributions and their cross-correlation derived from
cluster observations. This analysis permits us to cross-correlate the
fluctuations in the matter distribution, inferred from high-resolution lensing
mass maps derived from Hubble Space Telescope (HST) data, with those derived
from the emitted X-ray surface brightness distribution of the hot Intra-Cluster
medium (ICM) from the Chandra X-ray Observatory (CXO). These methodological
tools allow us to quantify with unprecedented resolution the coherence with
which the gas traces the mass and interrogate the assumption that the gas is in
hydro-static equilibrium with the underlying gravitational potential. We
characterize departures from equilibrium as a function of scale with a new
gas-mass coherence parameter. The efficacy of these metrics is demonstrated by
applying them to the analysis of two representative clusters known to be in
different dynamical states: the massive merging cluster Abell 2744, from the
HST Frontier Fields (HSTFF) sample, and the dynamically relaxed cluster Abell
383, from the Cluster Lensing And Supernova Survey with Hubble (CLASH) sample.
Using lensing mass maps in combination with archival Chandra data, and
simulated cluster analogs available from the OMEGA500 suite, we quantify the
fluctuations in the mass and X-ray surface brightness and show that new
insights into the dynamical state of the clusters can be obtained from our
gas-mass coherence analysis.
