  The use of galaxy clusters as cosmological probes hinges on our ability to
measure their masses accurately and with high precision. Hydrostatic mass is
one of the most common methods for estimating the masses of individual galaxy
clusters, which suffer from biases due to departures from hydrostatic
equilibrium. Using a large, mass-limited sample of massive galaxy clusters from
a high-resolution hydrodynamical cosmological simulation, in this work we show
that in addition to turbulent and bulk gas velocities, acceleration of gas
introduces biases in the hydrostatic mass estimate of galaxy clusters. In
unrelaxed clusters, the acceleration bias is comparable to the bias due to
non-thermal pressure associated with merger-induced turbulent and bulk gas
motions. In relaxed clusters, the mean mass bias due to acceleration is small
(<3%), but the scatter in the mass bias can be reduced by accounting for gas
acceleration. Additionally, this acceleration bias is greater in the outskirts
of higher redshift clusters where mergers are more frequent and clusters are
accreting more rapidly. Since gas acceleration cannot be observed directly, it
introduces an irreducible bias for hydrostatic mass estimates. This
acceleration bias places limits on how well we can recover cluster masses from
future X-ray and microwave observations. We discuss implications for cluster
mass estimates based on X-ray, Sunyaev-Zeldovich effect, and gravitational
lensing observations and their impact on cluster cosmology.
