  We test the assumption of strict hydrostatic equilibrium in galaxy cluster
MS2137.3-2353 (MS 2137) using the latest CHANDRA X-ray observations and results
from a combined strong and weak lensing analysis based on optical observations.
We deproject the two-dimensional X-ray surface brightness and mass surface
density maps assuming spherical and spheroidal dark matter distributions. We
find a significant, 40%-50%, contribution from non-thermal pressure in the core
assuming a spherical model. This non-thermal pressure support is similar to
what was found by Molnar et al. (2010) using a sample of massive relaxed
clusters drawn from high resolution cosmological simulations. We have studied
hydrostatic equilibrium in MS 2137 under the assumption of elliptical cluster
geometry adopting prolate models for the dark matter density distribution with
different axis ratios. Our results suggest that the main effect of ellipticity
(compared to spherical models) is to decrease the non-thermal pressure support
required for equilibrium at all radii without changing the distribution
qualitatively. We find that a prolate model with an axis ratio of 1.25 (axis in
the line of sight over perpendicular to it) provides a physically acceptable
model implying that MS 2137 is close to hydrostatic equilibrium at about
0.04-0.15 Rvir and have an about 25% contribution from non-thermal pressure at
the center. Our results provide further evidence that there is a significant
contribution from non-thermal pressure in the core region of even relaxed
clusters, i.e., the assumption of hydrostatic equilibrium is not valid in this
region, independently of the assumed shape of the cluster.
