Supernovae Exploding within Dense Extended Material: Early Emission Regimes and Degeneracies in Parameter Inference from Observations

TL;DR

The paper analyzes early supernova emission arising from shock interaction with optically thick extended material, presenting a analytic framework for a wind-like density profile to derive two breakout regimes: edge breakout and wind breakout. It derives key scalings for luminosity, breakout and cooling times, and cooling-temperature, showing that optical data sample the Rayleigh-Jeans tail and yield weak sensitivity to the extended-material radius $R_e$, leading to substantial degeneracies in inferred $M_e$ and $R_e$ unless early multi-band (UV/X-ray) observations are available. The work demonstrates that the same observable bolometric peak properties can correspond to different physical configurations and phases, highlighting the importance of identifying the emission phase. It argues that many SESNe could host modest extended envelopes with $R_e$ of order $10^2\,R_\odot$ rather than large CSM radii, with implications for progenitor structure and mass-loss histories, and underscores the need for UV capabilities (e.g., ULTRASAT) to break degeneracies. Overall, the study connects early light-curve morphology to progenitor environments and motivates rapid, multi-wavelength follow-up to robustly characterize extended material around SN progenitors.

Abstract

Early light curves of many core-collapse supernovae (SNe) are thought to be powered by the interaction of the shock wave with optically thick extended material, either a bound envelope or preexplosion ejected circumstellar matter (CSM). We analytically analyze the early emission produced by a shock with velocity $v$ traversing a material of mass $M_\mathrm{e}$ and opacity $κ$ extending to radius $R_\mathrm{e}$, and show the emission varies qualitatively with varying $τ_\mathrm{e}=κ\!M_\mathrm{e}/(4π\!R_\mathrm{e}^2)$: For $τ_\mathrm{e}\gg\!c/v$ a shock breakout occurs near $R_\mathrm{e}$ producing an ``edge breakout" -- a UV-dominated breakout burst followed by ``cooling emission" of the shock-heated material; for $τ_\mathrm{e}\lesssim\!c/v$ a ``wind breakout" occurs -- the breakout pulse is prolonged and followed by extended emission shifting from UV to X-ray as the shock becomes collisionless. We derive the dependence on $\{v,κ,M_\mathrm{e},R_\mathrm{e}\}$ of the duration and luminosity characterizing the different emission phases, and show that current observations typically do not allow inference of all parameters. In particular, since the optical bands lie in the Rayleigh-Jeans tail of radiation emitted during the cooling phase, the observed cooling luminosity depends weakly on radius, $\propto\!R_\mathrm{e}^{1/4}$, leading to $1-2$ orders of magnitude uncertainty in its inferred value. This suggests, e.g., that the common day-scale light curve features in Stripped-Envelope SNe do not necessarily imply material extending to $R_\mathrm{e}\sim10^3\!R_\odot$ and are often consistent with low-mass $R_\mathrm{e}\sim\!10^2\!R_\odot$ bound envelopes. Early multiband coverage (especially in UV/X-ray) can break these degeneracies; the forthcoming \emph{ULTRASAT} UV mission will allow inferring the properties of extended material around the population of SNe progenitors.

Figures (6)

• Figure 1: A schematic description of the wind density profile of the extended material, with the different characteristic radii defined in the text, shown for the "sharp truncation" case, $\Delta_\rho\ll (c/v)R_{\rm e}/\tau_{\rm e}$.
• Figure 2: Schematic demonstration of early bolometric light curves powered by shock interaction with a wind extended material that is sharply truncated at $R_{\rm e}$, at different regimes of the material optical depth $\tau_{\rm e}$ that set the location of $R_{\rm bo}$ (see text). The time and luminosity scales, as well as the breakout rise time in the different regimes, are derived in the text.
• Figure 3: The breakout rise time normalized to the extended material crossing time, $t_{\rm e}=R_{\rm e}/v$, Equation (\ref{['eq:t_e']}), as a function of $\tau_{\rm e}$, that sets the location of $R_{\rm bo}$ (see text), with $v=10^9~{\rm cm~s^{-1}}$. For $\tau_{\rm e}<(c/v)^2$, the breakout rise time is given by the intrinsic diffusion time (blue), Equation (\ref{['eq:t_bo']}), with both limits of edge and wind breakouts presented in dotted black lines. For $(c/v)^2<\tau_{\rm e}$, the observed breakout rise time is smeared to the light travel time (orange).
• Figure 4: The bolometric peak-luminosity, $L_{\rm p}$, and peak-time, $t_{\rm p}$, obtained in the different emission phases derived in Section \ref{['subsec:bol_light']} as function of $M_{\rm e}$ and $R_{\rm e}$, with fixed $v=10^9~{\rm cm~s^{-1}}$ and $\kappa=0.2\,{\rm cm^2~g^{-1}}$. Contours are shown for fixed $M_{\rm e}$ with varying $R_{\rm e}$ (dashed), and for fixed $R_{\rm e}$ with varying $M_{\rm e}$ (solid). The lower black line corresponds to the wind breakout limit, and the Emergence and Cooling contours that cross into the (shaded) Breakout region have been removed for clarity of presentation. The upper black line corresponds to the light travel time-smeared edge breakout limit, with limiting $L_{\rm p}$ and $t_{\rm p}$ obtained by holding $R_{\rm e}$ fixed and increasing $M_{\rm e}$. The peak luminosity is limited to $L_{45.5}<t_{\rm 1h}v_9^3\kappa_{0.2}^{-1}$. Over a significant fraction of the relevant $L_{\rm p}-t_{\rm p}$ plane, the values of $M_{\rm e}$ and $R_{\rm e}$ inferred from the observed $L_{\rm p}$ and $t_{\rm p}$ depend on the assumed emission phase.
• Figure 5: An example of degeneracy in the inferred values of parameters of the extended material shock cooling model: ZTF optical light curves of SN 2020bvc overlapped with STELLA radiation hydrodynamic simulations of explosions within wind density profiles (adapted from jin_effect_2021). Solid and dashed lines represent two "best-fit models" with $(E[10^{52}~{\rm erg/s}],M_{\rm e}[M_\odot],R_{\rm e}[{\rm cm}])=\{(1.2,0.1,10^{14}),(1.5,0.2,10^{13})\}$ respectively. The large uncertainty in the inferred value of $R_{\rm e}$ is apparent.