We study the phenomenon of diffusive radiative heat waves (Marshak waves) under general boundary conditions. In particular, we derive full analytic solutions for the subsonic case, that include both the ablation and the shock wave regions. Previous works in this regime, based on the work of [R. Pakula and R. Sigel, Phys. Fluids. 443, 28, 232 (1985)], present self-similar solutions for the ablation region alone, since in general, the shock region and the ablation region are not selfsimilar together. Analytic results for both regions were obtained only for the specific case in which the ratio between the ablation front velocity and the shock velocity is constant. In this work, we derive a full analytic solution for the whole problem in general boundary conditions. Our solution is composed of two different self-similar solutions, one for each region, that are patched at the heat front. The ablative region of the heat wave is solved in a manner similar to previous works. Then, the pressure at the front, which is derived from the ablative region solution, is taken as a boundary condition to the shock region, while the other boundary is described by Hugoniot relations. The solution is compared to full numerical simulations in several representative cases. The numerical and analytic results are found to agree within 1% in the ablation region, and within 2 − 5% in the shock region. This model allows better prediction of the physical behavior of radiation induced shock waves, and can be applied for high energy density physics experiments.

Radiative subsonic heat waves, and their radiation driven shock waves, are important hydroradiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in order to investigate the effect of the equation of state (EOS) on the propagation of radiation driven shocks. We find that using a single ideal gas EOS for both regions, as used in previous works, yields large errors in describing the shock wave. We use the fact that the solution is composed of two different self-similar solutions, one for the ablation region and one for the shock, and apply two ideal gas EOS (binary-EOS), one for each region, by fitting a detailed tabulated EOS to power laws at different regimes. By comparing the semi-analytic solution with a numerical simulation using a full EOS, we find that the semi-analytic solution describes both the heat and the shock regions well.

It was recently shown that the bolometric light curves of type II supernovae (SNe) allow an accurate and robust measurement of the product of the radiation energy in the ejecta, E r , and the time since the explosion, t, at early phases (t 10d) of the homologous expansion. This observable, denoted here ET ≡ E r t is constant during that time and depends only on the progenitor structure and explosion energy. We use a 1D hydrodynamic code to find ET of simulated explosions of 145 red supergiant progenitors obtained using the stellar evolution code MESA, and relate this observable to the properties of the progenitor and the explosion energy. We show that ET probes only the properties of the envelope (velocity, mass and initial structure), similarly to other observables that rely on the photospheric phase emission. Nevertheless, for explosions where the envelope dominates the ejected mass, M env /M ej 0.6, ET is directly related to the explosion energy E exp and ejected mass M ej through the relation ET ≈ 0.15E, where R * is the progenitor radius, to an accuracy better than 30%. We also provide relations between ET and the envelope properties that are accurate (to within 20%) for all the progenitors in our sample, including those that lost most of their envelope. We show that when the envelope velocity can be reasonably measured by line shifts in observed spectra, the envelope is directly constrained from the bolometric light curve (independent of E exp ). We use that to compare observations of 11 SNe with measured ET and envelope velocity to our sample of numerical progenitors. This comparison suggests that many SNe progenitors have radii that are 500 R ⊙ . In the framework of our simulations this indicates, most likely, a rather high value of the mixing length parameter.