Non-relativistic radiation mediated shock breakouts: II. Bolometric properties of SN shock breakout

TL;DR

This paper derives exact bolometric light curves for supernova shock breakouts using non-relativistic planar solutions, providing key relations for energy, velocity, and light curve shapes based on progenitor properties.

Contribution

It introduces precise bolometric light curve calculations for supernova shock breakouts, accounting for asymmetries and providing analytic expressions for different progenitor sizes.

Findings

Total breakout energy E_BO = 8.0π R^2 / κ * c * v_0

Maximal ejecta velocity v_max = 2.0 v_0

Light curve decay L ∝ t^(-4/3) for large progenitors

Abstract

Exact bolometric light curves of supernova shock breakouts are derived based on the universal, non relativistic, planar breakout solutions (Sapir et al. 2011), assuming spherical symmetry, constant Thomson scattering opacity, \kappa, and angular intensity corresponding to the steady state planar limit. These approximations are accurate for progenitors with a scale height much smaller than the radius. The light curves are insensitive to the density profile and are determined by the progenitor radius R, and the breakout velocity and density, v_0 and \rho_0 respectively, and \kappa. The total breakout energy, E_BO, and the maximal ejecta velocity, v_max, are shown to be E_BO=8.0\pi R^2\kappa^-1cv_0 and v_max=2.0v_0 respectively, to an accuracy of about 10%. The calculated light curves are valid up to the time of transition to spherical expansion, t_sph\approx R/4v_0. Approximate analytic expressions for the light curves are provided for breakouts in which the shock crossing time at breakout, t_0=c/\kappa\rho_0v_0^2, is << R/c (valid for R<10^14 cm). Modifications of the flux angular intensity distribution and differences in shock arrival times to the surface, \Delta t_asym, due to moderately asymmetric explosions, affect the early light curve but do not affect v_max and E_BO. For 4v_0<<c, valid for large (RSG) progenitors, L\propto t^{-4/3} at max(\Delta t_asym,R/c)< t<t_sph and R may be accurately estimated from R\approx 2*10^13 (L/10^43 erg s^-1)^{2/5}(t/1 hr)^{8/15}.