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 Tychos supernova remnant.
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