2009ApJ...690.1412W

We present a time-dependent cosmic-ray (CR) modified shock model for which the calculated Hα emissivity profile agrees well with the Hα flux increase ahead of the Balmer-dominated shock at knot g in Tycho's supernova remnant (SNR), observed by Lee et al. The backreaction of the CR component on the thermal component is treated in the two-fluid approximation, and we include thermal particle injection and energy transfer due to the acoustic instability in the precursor. The transient state of our model that describes the current state of the shock at knot g occurs during the evolution from a thermal gas dominated shock to a smooth CR-dominated shock. Assuming a distance of 2.3 kpc to Tycho's remnant, we obtain values for the CR diffusion coefficient, κ, the injection parameter, ε, and the timescale for the energy transfer, τ, of κ = 2x10²⁴ cm2/s, ε = 4.2x10^–3, and τ = 426 yr, respectively. We have also studied the parameter space for fast (300 km/s ≲ v_s≲ 3000 km/s), time-asymptotically steady shocks and have identified a branch of solutions, for which the temperature in the CR precursor typically reaches 2x10⁴ to 6x10⁴ K and the bulk acceleration of the flow through the precursor is less than 10 km/s. These solutions fall into the low CR acceleration efficiency regime and are relatively insensitive to shock parameters. This low CR acceleration efficiency branch of solutions may provide a natural explanation for the line broadening of the Hα narrow component observed in nonradiative shocks in many SNRs.