Non-relativistic Radiation Mediated Shock Breakouts. III. Spectral Properties of Supernova Shock Breakout

The spectrum of radiation emitted following shock breakout from a star's surface with a power-law density profile ρvpropxⁿ 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 ρ₀ and depend weakly on the value of n. Fitting formulae for the peak surface temperature at breakout as a function of v ₀ and ρ₀ 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 {T}_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 ≈10⁴⁵ erg s^-1 and ≈10⁴⁴ erg s^-1 in the 0.3-10 keV band are expected for blue supergiant (BSG) and red supergiant (RSG)/He-WR progenitors, respectively ( {T}_peak is well below the band for RSGs, unless their radius is ~10¹³ cm). >30 detections of SN 1987A-like (BSG) breakouts are expected over the lifetime of ROSAT and XMM-Newton. An absence of such detections would imply either that 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/SN 2008D are in tension with a non-relativistic breakout from a stellar surface interpretation.