Nakar 2011 非相对论性的shock breakout

主要内容:
主要用于超新星的早期辐射。
（那如果是稳态的呢？）
认为主要的辐射不是来自于tau=1的地方，而是tau=c/v的地方。
还有就是辐射谱可以是幂律的。

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Title:		Early Supernovae Light Curves Following the Shock Breakout
Authors:		Nakar, Ehud; Sari, Re'em
Affiliation:		AA(Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel), AB(Racah Institute for Physics, The Hebrew University, Jerusalem 91904, Israel)
Publication:		The Astrophysical Journal, Volume 725, Issue 1, pp. 904-921 (2010). (ApJ Homepage)
Publication Date:		12/2010
Origin:		IOP
ApJ Keywords:		radiative transfer, shock waves, supernovae: general
DOI:		10.1088/0004-637X/725/1/904
Bibliographic Code:		2010ApJ...725..904N

Abstract

The first light from a supernova (SN) emerges once the SN shock breaks out of the stellar surface. The first light, typically a UV or X-ray flash, is followed by a broken power-law decay of the luminosity generated by radiation that leaks out of the expanding gas sphere. Motivated by recent detection of emission from very early stages of several SNe, we revisit the theory of shock breakout and the following emission, paying special attention to the photon-gas coupling and deviations from thermal equilibrium. We derive simple analytic light curves of SNe from various progenitors at early times. We find that for more compact progenitors, white dwarfs, Wolf-Rayet stars (WRs), and possibly more energetic blue-supergiant explosions, the observed radiation is out of thermal equilibrium at the breakout, during the planar phase (i.e., before the expanding gas doubles its radius), and during the early spherical phase. Therefore, during these phases we predict significantly higher temperatures than previous analysis that assumed equilibrium. When thermal equilibrium prevails, we find the location of the thermalization depth and its temporal evolution. Our results are useful for interpretation of early SN light curves. Some examples are (1) red supergiant SNe have an early bright peak in optical and UV flux, less than an hour after breakout. It is followed by a minimum at the end of the planar phase (about 10 hr), before it peaks again once the temperature drops to the observed frequency range. In contrast, WRs show only the latter peak in optical and UV. (2) Bright X-ray flares are expected from all core-collapse SNe types. (3) The light curve and spectrum of the initial breakout pulse hold information on the explosion geometry and progenitor wind opacity. Its spectrum in more compact progenitors shows a (nonthermal) power law and its light curve may reveal both the breakout diffusion time and the progenitor radius.

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