Effects of Leakage Neutral Particles on Shocks
  In this paper we investigate effects of neutral particles on shocks propagating into the partially ionized medium. We find that for 120 km/s < u_{sh} < 3000 km/s (u_{sh} is the shock velocity), about ten percent of upstream neutral particles leak into the upstream region from the downstream region. Moreover, we investigate how the leakage neutral particles affect the upstream structure of the shock and particle accelerations. Using four fluid approximations (upstream ions, upstream neutral particles, leakage neutral particles and pickup ions), we provide analytical solutions of the precursor structure due to leakage neutral particles. It is shown that the upstream flow is decelerated in the precursor region and the shock compression ratio becomes smaller than without leakage neutral particles, but the total compression ratio does not change. Even if leakage of neutral particles is small (a few percents of total upstream particles), this smaller compression ratio of the shock can explain steep gamma-ray spectra from young supernova remnants. Furthermore, leakage neutral particles could amplify the magnetic field and heat the upstream region. 
Yutaka Ohira
astro-ph.HE