  Accurate mass determination of clusters of galaxies is crucial if they are to
be used as cosmological probes. However, there are some discrepancies between
cluster masses determined based on gravitational lensing, and X-ray
observations assuming strict hydrostatic equilibirium (i.e., the equilibrium
gas pressure is provided entirely by thermal pressure). Cosmological
simulations suggest that turbulent gas motions remaining from hierarchical
structure formation may provide a significant contribution to the equilibrium
pressure in clusters. We analyze a sample of massive clusters of galaxies drawn
from high resolution cosmological simulations, and find a significant
contribution (20%-45%) from non-thermal pressure near the center of relaxed
clusters, and, in accord with previous studies, a minimum contribution at about
0.1 Rvir, growing to about 30%-45% at the virial radius, Rvir. Our results
strongly suggest that relaxed clusters should have significant non-thermal
support in their core region. As an example, we test the validity of strict
hydrostatic equilibirium in the well-studied massive galaxy cluster Abell 1689
using the latest high resolution gravitational lensing and X-ray observations.
We find a contribution of about 40% from non-thermal pressure within the core
region of A1689, suggesting an alternate explanation for the mass discrepancy:
the strict hydrostatic equilibirium is not valid in this region.
