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

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 color 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, metalicity), and explosion energies. The numerically derived L and Tcol are described by the analytic expressions with $10{{\%}}$ and $5{{\%}}$ 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 multi-group photon diffusion calculations, that the spectral energy distribution is well described by a Planck spectrum with T = Tcol, except at UV frequencies, where the flux can be significantly suppressed due to strong line absorption. We defer the full discussion of the multi-group 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 multi-band shock cooling observations of supernovae.

Shock Cooling and Possible Precursor Emission in the Early Light Curve of the Type II SN 2023ixf

“…In both cases, the best-fit radius is reasonable or even on the low end of the distribution of RSG radii (Levesque 2017), despite the fact that its spectra were dominated by circumstellar interaction during the time period investigated here (Bostroem et al 2023;Grefenstette et al 2023;Jacobson-Galán et al 2023;Smith et al 2023;Teja et al 2023;Yamanaka et al 2023). It remains to be seen whether future invocations of the model of Morag et al (2023) can routinely match other early SN light curves, even in the presence of CSM, or whether this result is just a coincidence.…”

“…Various physical mechanisms may be able to explain this excess early emission, in full or in combination, including precursor emission from the RSG progenitor, interaction with CSM, and emission from the core-collapse shock leading up to and including its breakout from the stellar surface. Despite this, the shock-cooling model of Morag et al (2023) provides a good fit to the data 1 day after explosion, allowing us to derive a progenitor radius of R = 410 ± 10 R e , which is consistent with an RSG progenitor although on the small end of the distribution. We show that this estimate of the radius is strongly model dependent, even between different shockcooling models.…”

“…We also compared our data with an earlier version of the shock-cooling model by Sapir & Waxman (2017), which has identical fit parameters but does not account for the very early phase in which the thickness of the emitting shell is smaller than the stellar radius. Morag et al (2023) built upon this work by interpolating between the treatment of the earlier "planar" phase by Sapir et al (2011Sapir et al ( , 2013 and Katz et al (2012) and the treatment of the later "spherical" phase by Rabinak & Waxman (2011) and Sapir & Waxman (2017). Sapir & Waxman (2017) also assume a blackbody SED at all times, whereas Morag et al (2023) account for some line blanketing in the UV.…”

“…Morag et al (2023) built upon this work by interpolating between the treatment of the earlier "planar" phase by Sapir et al (2011Sapir et al ( , 2013 and Katz et al (2012) and the treatment of the later "spherical" phase by Rabinak & Waxman (2011) and Sapir & Waxman (2017). Sapir & Waxman (2017) also assume a blackbody SED at all times, whereas Morag et al (2023) account for some line blanketing in the UV.…”

“…This emission has been modeled by Rabinak & Waxman (2011) and Sapir & Waxman (2017). Recently, Morag et al (2023) extended these models to earlier phases and proposed a modified spectral energy distribution (SED) to account for line blanketing in the UV. These models depend on, among other parameters, the radius of the progenitor star.…”