  The Balmer line profiles of nonradiative supernova remnant shocks provide the
means to measure the post-shock proton velocity distribution. While most
analyses assume a Maxwellian velocity distribution, this is unlikely to be
correct. In particular, neutral atoms that pass through the shock and become
ionized downstream form a nonthermal distribution similar to that of pickup
ions in the solar wind. We predict the H alpha line profiles from the
combination of pickup protons and the ordinary shocked protons, and we consider
the extent to which this distribution could affect the shock parameters derived
from H alpha profiles. The Maxwellian assumption could lead to an underestimate
of shock speed by up to about 15%. The isotropization of the pickup ion
population generates wave energy, and we find that for the most favorable
parameters this energy could significantly heat the thermal particles.
Sufficiently accurate profiles could constrain the strength and direction of
the magnetic field in the shocked plasma, and we discuss the distortions from a
Gaussian profile to be expected in Tycho's supernova remnant.
