Shock cooling emission from explosions of red supergiants – I. A numerically calibrated analytic model

Abstract

ABSTRACT Supernova light curves are dominated at early time, hours to days, by photons escaping from the expanding shock heated envelope. We provide a simple analytic description of the time-dependent luminosity, L, and colour temperature, Tcol, for explosions of red supergiants (with convective polytropic envelopes), valid up to H recombination (T ≈ 0.7 eV). The analytic description interpolates between existing expressions valid at different (planar then spherical) stages of the expansion, and is calibrated against numerical hydrodynamic diffusion calculations for a wide range of progenitor parameters (mass, radius, core/envelope mass and radius ratios, and metalicity), and explosion energies. The numerically derived L and Tcol are described by the analytic expressions with $10{{\ \rm per\ cent}}$ and $5{{\ \rm per\ cent}}$ accuracy, respectively. Tcol is inferred from the hydrodynamic profiles using frequency independent opacity, based on tables we constructed for this purpose (and will be made publicly available) including bound–bound and bound–free contributions. In an accompanying paper (Paper II) we show − using a large set of multigroup photon diffusion calculations − that the spectral energy distribution is well described by a Planck spectrum with T = Tcol, except at ultraviolet (UV) frequencies, where the flux can be significantly suppressed due to strong line absorption. We defer the full discussion of the multigroup results to paper II, but provide here for completeness an analytic description also of the UV suppression. Our analytic results are a useful tool for inferring progenitor properties, explosion velocity, and also relative extinction based on early multiband shock cooling observations of supernovae.