Many fast supernova remnant shocks show spectra dominated by Balmer lines. The H$alpha$ profiles have a narrow component explained by direct excitations and a thermally Doppler broadened component due to atoms that undergo charge exchange in the post-shock region. However, the standard model does not take into account the cosmic-ray shock precursor, which compresses and accelerates plasma ahead of the shock. In strong precursors with sufficiently high densities, the processes of charge exchange, excitation and ionization will affect the widths of both narrow and broad line components. Moreover, the difference in velocity between the neutrals and the precursor plasma gives rise to frictional heating due to charge exchange and ionization in the precursor. In extreme cases, all neutrals can be ionized by the precursor. In this paper we compute the ion and electron heating for a wide range of shock parameters, along with the velocity distribution of the neutrals that reach the shock. Our calculations predict very large narrow component widths for some shocks with efficient acceleration, along with changes in the broad- to-narrow intensity ratio used as a diagnostic for the electron-ion temperature ratio. Balmer lines may therefore provide a unique diagnostic of precursor properties. We show that heating by neutrals in the precursor can account for the observed H$alpha$ narrow component widths, and that the acceleration efficiency is modest in most Balmer line shocks observed thus far.
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