  X-ray observations of galaxy cluster merger shocks can be used to constrain
nonthermal processes in the intracluster medium (ICM). The presence of
nonthermal pressure components in the ICM, as well as the shock acceleration of
particles and their escape, all affect shock jump conditions in distinct ways.
Therefore, these processes can be constrained using X-ray surface brightness
and temperature maps of merger shock fronts. Here we use these observations to
place constraints on particle acceleration efficiency in intermediate Mach
number (M ~ 2-3) shocks and explore the potential to constrain the contribution
of nonthermal components (e.g., cosmic rays, magnetic field, and turbulence) to
ICM pressure in cluster outskirts. We model the hydrodynamic jump conditions in
merger shocks discovered in the galaxy clusters A520 (M ~ 2) and 1E 0657-56 (M
~ 3) using a multifluid model comprised of a thermal plasma, a nonthermal
plasma, and a magnetic field. Based on the published X-ray spectroscopic data
alone, we find that the fractional contribution of cosmic rays accelerated in
these shocks is lower than about 10% of the shock downstream pressure. Current
observations do not constrain the fractional contribution of nonthermal
components to the pressure of the undisturbed shock upstream. Future X-ray
observations, however, have the potential to either detect particle
acceleration in these shocks through its effect on the shock dynamics, or to
place a lower limit on the nonthermal pressure contributions in the undisturbed
ICM. We briefly discuss implications for models of particle acceleration in
collisionless shocks and the estimates of galaxy cluster masses derived from
X-ray and Sunyaev-Zel'dovich effect observations.
