Shock cooling emission from explosions of massive stars: III. Blue Super Giants

Light emission in the first hours and days following core-collapse supernovae is dominated by the escape of photons from the expanding shock-heated envelope. In preceding papers, we provided a simple analytic description of the time-dependent luminosity, $L$, and color temperature, $T_{\rm col}$, as well as of the small ($\simeq10\%$) deviations of the spectrum from blackbody at low frequencies, $h\nu< 3T_{\rm col}$, and of `line dampening' at $h\nu> 3T_{\rm col}$, for explosions of red supergiants (RSGs) with convective polytropic envelopes (without significant circum-stellar medium). Here, we extend our work to provide similar analytic formulae for explosions of blue supergiants with radiative polytropic envelopes. The analytic formulae are calibrated against a large set of spherically symmetric multi-group (frequency-dependent) calculations for a wide range of progenitor parameters (mass, radius, core/envelope mass ratios) and explosion energies. In these calculations we use the opacity tables we constructed (and made publicly available), that include the contributions of bound-bound and bound-free transitions. They reproduce the numeric $L$ and $T_{\rm col}$ to within 10\% and 5\% accuracy, and the spectral energy distribution to within $\sim20-40\%$. The accuracy is similar to that achieved for RSG explosions.