Non-relativistic radiation mediated shock breakouts: III. Spectral properties of SN shock breakout

Abstract

The spectrum of radiation emitted following shock breakout from a star's surface with a power-law density profile $\rho \propto x^n$ is investigated. Assuming planar geometry, local Compton equilibrium and bremsstrahlung emission as the dominant photon production mechanism, numerical solutions are obtained for the photon number density and temperature profiles as a function of time, for hydrogen-helium envelopes. The temperature solutions are determined by the breakout shock velocity $v_0$ and the pre-shock breakout density $\rho_0$, and depend weakly on the value of n. Fitting formulas for the peak surface temperature at breakout as a function of $v_0$ and $\rho_0$ are provided, with $T_{peak}\approx 9.44\exp{[12.63(v_0/c)^{1/2}]}$ eV, and the time dependence of the surface temperature is tabulated. The time integrated emitted spectrum is a robust prediction of the model, determined by $\mathcal{T}_{\rm peak}$ and $v_0$ alone and insensitive to details of light travel time or slight deviations from spherical symmetry. Adopting commonly assumed progenitor parameters, breakout luminosities of ~10^45 erg/s and ~10^44 erg/s in the 0.3-10 keV band are expected for BSG and RSG/He-WR progenitors respectively (T_{peak} is well below the band for RSGs, unless their radius is ~10^13 cm). >30 detections of SN1987A-like (BSG) breakouts are expected over the lifetime of ROSAT and XMM-Newton. An absence of such detections would imply that either the typical parameters assumed for BSG progenitors are grossly incorrect or that their envelopes are not hydrostatic. The observed spectrum and duration of XRF 080109/SN2008D are in tension with a non-relativistic breakout from a stellar surface interpretation.