Scattering by enhanced fluctuations from the electromagnetic proton cy
clotron instability imposes an up per bound on the proton temperature
anisotropy of the form T-perpendicular to p/T-parallel to p - 1 = S-p/
beta(parallel to p)(alpha p). Here beta(parallel to p) is the proton b
eta based on T-parallel to p and the directional subscripts indicate d
irections perpendicular and parallel to the background magnetic field.
This paper describes the analysis of the proton temperature anisotrop
y in two-dimensional hybrid simulations of quasiperpendicular shocks a
nd their associated magnetosheaths. Three simulations are considered:
at low, intermediate, and high upstream Mach numbers. Considering resu
lts from well downstream of all three shocks as one data set, an upper
bound on the proton temperature anisotropy fits the above equation wi
th alpha(p) = 0.5. This compares favorably to alpha(p) values from oth
er simulations and from sheath observations.