Electron Heating, Magnetic Field Amplification, and Cosmic Ray Precursor Length at Supernova Remnant Shocks

We investigate the observability, by direct and indirect means, of a shock precursor arising from magnetic field amplification by cosmic rays. We estimate the depth of such a precursor under conditions of nonresonant amplification, which provides magnetic field strengths comparable to those inferred for supernova remnants. Magnetic field generation occurs as the streaming cosmic rays induce a plasma return current, and may be quenched either by nonresonant or resonant channels. In the former case, the cosmic rays become magnetized and amplification saturates at higher magnetic fields. The precursor can extend out to 10^17 - 10^18 cm and is potentially resolvable in Galactic supernova remnants. If the saturation occurs instead by resonant channels, the cosmic rays are scattered by turbulence and the precursor length will likely be too small to be resolvable with current instruments. The dependence of precursor length on shock velocity has implications for electron heating. In the case of resonant saturation, this dependence is similar to that in the more familiar resonantly generated shock precursor, which when expressed in terms of the cosmic ray diffusion coefficient κ and shock velocity v_s is κ /v_s. In the nonresonantly saturated case, the precursor length declines less quickly with increasing v_s. Where precursor length proportional to 1/v_s gives constant electron heating, as observed for instance by Ghavamian et al. and van Adelsberg et al., this increased precursor length would be expected to lead to higher electron temperatures at faster supernova remnant shocks than studied by these previous works as an indirect observation of the shock precursor. Existing results and new data analysis of SN 1006 and Cas A suggests some observational support for this idea. Work supported by NASA ADAP program and by basic research funds of the Office of Naval Research.