An unexplored regime of shock breakout with a distinct spectral signature

TL;DR

This work identifies and characterizes an unexplored INERT shock-breakout regime in which gas–radiation non-equilibrium is followed by rapid thermalization on a timescale shorter than the light-crossing time, producing a distinctive, smeared spectrum that combines a blackbody component with a Comptonized free-free component. The authors develop a parameter-space framework using dimensionless quantities such as $oldsymbol{ m chi}$ and $oldsymbol{ m zeta}$ and extend the model to breakout in extended envelopes with density profiles $ ho(r) \npropto (R_{ m env}-r)^n$, including the $oldsymbol{n ightarrow 0}$ limit that connects to wind-edge breakout and cooling-envelope scenarios. A spectral model is constructed that evolves from self-absorbed free-free emission to a blackbody, with light-travel-time smearing producing a multi-temperature spectrum and modest Comptonization (characterized by $oldsymbol{oldsymbol{\xi_{ m bo}}}$ and $oldsymbol{y_{ m bo}}$). The INERT regime is most plausible for breakout velocities around $oldsymbol{v_{ m bo} obreak\sim 0.1c}$ and sufficiently high breakout densities, notably for blue supergiant progenitors or shocks breaking out from extended envelopes; this framework offers testable predictions for early multi-wavelength signals and motivates joint timing/energy measurements with current and upcoming missions. Overall, the paper provides a unified treatment linking classic breakout theory to new spectral phenomenology, with concrete closure relations and observable signatures that can distinguish INERT breakouts from standard blackbody or fully Comptonized scenarios.

Abstract

The first light that escapes from a supernova explosion is the shock breakout emission, which produces a bright flash of UV or X-ray radiation. Standard theory predicts that the shock breakout spectrum will be a blackbody if the gas and radiation are in thermal equilibrium, or a Comptonized free-free spectrum if not. Using recent results for the post-breakout evolution which suggest that lower-temperature ejecta are probed earlier than previously thought, we show that another scenario is possible in which the gas and radiation are initially out of equilibrium, but the time when thermalized ejecta are revealed is short compared to the light-crossing time of the system. In this case, the observed spectrum differs significantly from the standard expectation, as the non-negligible light travel time acts to smear the spectrum into a complex multi-temperature blend of blackbody and free-free components. For typical parameters, a bright multi-wavelength transient is produced, with the free-free emission being spread over a wide frequency range from optical to hard X-rays, and the blackbody component peaking in soft X-rays. We explore the necessary conditions to obtain this type of unusual spectrum, finding that it may be relevant for bare blue supergiant progenitors, or for shocks with a velocity of $v_{\rm bo} \sim 0.1c$ breaking out from an extended medium of radius $R_{\rm env}$ with a sufficiently high density $ρ_{\rm bo} \gtrsim 4\times 10^{-12}\text{ g cm}^{-3} (R_{\rm env}/10^{14} \text{cm})^{-15/16}$. An application to low-luminosity gamma-ray bursts is considered in a companion paper.

Figures (9)

• Figure 1: An illustration of the system's geometry when $t_{\rm bo} < t_{\rm eq,ls} < t_{\rm lc}$. A source of size $R$ produces a flash of free-free emission lasting for a time $t_{\rm eq,ls}$ (shown in blue), and subsequently radiates as a blackbody (shown in red). Each panel shows where the radiation has reached at a different time. The black dashed line indicates the slice probed by the observer at time $t$. The inset shows the emission regions that an observer who could resolve the source would see. Panel a): For times $t < t_{\rm eq,ls}$, the source produces free-free emission. The leading edge of the radiation has travelled a distance $ct$, as indicated by the dark green bar. Only a small part of the surface, which is within a distance of $ct$ from the dashed line (corresponding to angles within $\theta \la (2t/t_{\rm lc})^{1/2}$ of the line of sight), can be observed. Panel b): For times $t>t_{\rm eq,ls}$, the surface is radiating as a blackbody. The blackbody emission has travelled a distance of $c(t-t_{\rm eq,ls})$, as shown by the purple bar. Only the blackbody radiation emitted within a distance of $c(t-t_{\rm eq,ls})$ from the dashed line (or within an angle of $\theta \la [2(t-t_{\rm eq,ls})/t_{\rm lc}]^{1/2}$) has had time to reach the observer. For $t<t_{\rm lc}$, free-free emission is observed from a ring, with $[2(t-t_{\rm eq,ls})/t_{\rm lc}]^{1/2} \la \theta \la (2t/t_{\rm lc})^{1/2}$, while emission from near the equator, which has travelled a distance of $ct < R$, still has not arrived. The free-free emission produced at the equator finally arrives at $t=t_{\rm lc}$ and it lasts for a time $t_{\rm eq,ls}$ after that. Panel c): At $t=t_{\rm lc}+t_{\rm eq,ls}$, the blackbody emission from the equator finally arrives. From this point on, the entire source is visible and only blackbody radiation is observed.
• Figure 2: $\zeta$ versus $\eta_{\rm{bo}}$ for $\chi = (1,2,5,10)$. When $\chi \le 1$, $\zeta$ is independent of $\chi$. The region where the conditions $\eta_{\rm{bo}} > 1$ and $\zeta < 1$ are satisfied is shown by a heavy line.
• Figure 3: The $v_{\rm{bo}}$ versus $\rho_{\rm{bo}}$ parameter space for $n = (0,1.5,3)$ (columns, left to right) and $R_{\rm bo} = (5,50,500,5000)\,\mathrm{R}_\odot$ (rows, top to bottom). All panels have the same limits for both axes. Colour indicates the value of $\zeta$ (red for $\zeta \ll 1$, yellow for $\zeta \sim 1$, and blue for $\zeta \gg 1$; values greater than $10^5$ or less than $10^{-5}$ are solid blue or red, respectively). Lines indicate the conditions $\chi = 1$ (solid), which separates diffusion-dominated and light-travel dominated breakouts; $\eta_{\rm{bo}} = 1$ (dashed), which separates thermal and non-thermal breakouts; and $\zeta = 1$ (dot-dashed), which determines whether or not thermalization occurs within a light-crossing time. The pair creation threshold $kT_{\rm{obs,bo}} \ga 50\,$keV, as well as the relativistic shock breakout condition $v_{\rm{bo}} \ga 0.6 c$ suggested by katz and fs2, are also shown as heavy solid and dotted lines, respectively (as labelled in the bottom left panel). The diagonal hatching indicates where our model breaks down due to pair creation. In the grey region, the breakout takes place far from the edge of the system and our assumption of $R_{\rm bo} \approx R$ is invalid. The line $v_{\rm bo} t_{\rm bo} = R_{\rm bo}$, which marks the boundary of the gray region, is labelled in the $n=1.5$ and $R = 50\,\mathrm{R}_\odot$ panel. In that same panel, we have also labelled the regions I--V corresponding to the five types of breakout discussed in the text. The magenta stars show estimated values for several progenitors: a red supergiant (RSG), a blue supergiant (BSG), a Wolf-Rayet star (WR), and a breakout in an extended convective envelope (EE). All results assume a value of $q=1$.
• Figure 4: The $M_{\rm{env}}$ versus $R_{\rm{env}}$ parameter space for $n = (0,1.5,3)$ (columns, left to right) and $E_0 = (10^{49},10^{50},10^{51})\,$erg (rows, top to bottom). All panels have the same limits for both axes. As in Fig. \ref{['fig:rhovplot']}, colour indicates the value of $\zeta$ (using the same scale), and we show the curves $\chi = 1$ (solid), $\eta_{\rm{bo}} = 1$ (dashed), and $\zeta = 1$ (dot-dashed); refer to the labels in the middle left panel. The breakout regimes I--V are denoted in the central panel. In the gray region, $\tau_{\rm{env}}<c/v_0$ and shock breakout occurs far from the edge of the envelope, contrary to our assumptions. Hatched regions show where our model assumptions break down, either because pair creation is relevant (diagonal hatching), or because $\tau_{\rm{env}} \sim c/v_0$ (dotted hatching). The boundaries of these regions are also labelled in the middle left panel. All results assume a value of $q=1$.
• Figure 5: The $E_0$ versus $M_{\rm{env}}$ parameter space for $n = (0,1.5,3)$ (columns, left to right) and $R_{\rm{env}} = (50,500,1000)\,\mathrm{R}_\odot$ (rows, top to bottom). All panels have the same limits for both axes. The colouring, hatching, and linestyles are as in Fig. \ref{['fig:MRplot']}. The lines $\chi = 1$ (solid), $\eta_{\rm{bo}} = 1$ (dashed), and $\zeta = 1$ (dot-dashed) are labelled in the middle left panel, along with the boundary where pair creation becomes relevant. The breakout regimes I--V are denoted in the central panel. In cases where region II is present, we have plotted a magenta line indicating the approximate velocity for which INERT breakout can occur. The locations where $\tau_{\rm{env}} = c/v_0$ or $\tau_{\rm{env}} = 3c/v_0$ are marked in the lower right panel. All results assume a value of $q=1$.