Fast Radiation Mediated Shocks and Supernova Shock Breakouts

We present a simple analytic model for the structure of non-relativistic and relativistic radiation mediated shocks. At shock velocities β s ≡ v s / c ≳ 0.1, the shock transition region is far from thermal equilibrium since the transition crossing time is too short for the production of a blackbody photon density (by bremsstrahlung emission). In this region, electrons and photons (and positrons) are in Compton (pair) equilibrium at temperatures T s significantly exceeding the far downstream temperature, T s ≫ T d ≈ 2(ε n u ℏ 3 c 3 ) 1/4 . T s ≳ 10keV is reached at shock velocities β s ≈ 0.2. At higher velocities, β s ≳ 0.6, the plasma is dominated in the transition region by e ± pairs and 60keV ≲ T s ≲ 200keV. We argue that the spectrum emitted during the breaking out of supernova (SN) shocks from the stellar envelopes (or the surrounding winds) of blue supergiants and Wolf–Rayet stars, which reach β s >0.1 for reasonable stellar parameters, may include a hard component with photon energies reaching tens or even hundreds of keV. Our breakout analysis is restricted to temperatures T s ≲ 50keV corresponding to photon energies h ν ≲ 150keV, where pair creation can be neglected. This may account for the X-ray outburst associated with SN2008D, and possibly for other SN-associated outbursts with spectra not extending beyond few 100keV (e.g., XRF060218/SN2006aj).