The spectra of a radiative reprocessing outflow model for fast blue optical transients

TL;DR

This work investigates a radiative reprocessing outflow as the origin of the UV–optical–NIR emission from fast blue optical transients, focusing on AT2018cow. By incorporating frequency-dependent absorptive opacities (free-free and bound-free) and a two-region outflow split by the photon trapping radius $r_{\rm tr}$, the authors derive the emergent spectrum and identify a characteristic NIR excess with $\lambda L_{\lambda} \propto \lambda^{-3/2}$. They fit multi-epoch SEDs with an MCMC approach to constrain the mass-loss rate $\dot{M}$, outflow velocity $v_{\rm out}$, and color temperature $T(r_{\rm tr})$, obtaining a total outflow mass $M_{\rm out} \approx 5.7^{+0.4}_{-0.4}\,M_{\odot}$ and a central object mass $M_{\rm obj} \gtrsim 14\,M_{\odot}$, consistent with a stellar-mass black hole. The results imply a BH-dominated central engine and support a fallback/accretion-driven outflow scenario for AT2018cow, with potential applicability to other FBOTs exhibiting persistent central engines and NIR reprocessing signatures.

Abstract

The radiation reprocessing model, in which an optically-thick outflow absorbs the high-energy emission from a central source and re-emits in longer wavelengths, has been frequently invoked to explain some optically bright transients, such as fast blue optical transients (FBOTs) whose progenitor and explosion mechanism are still unknown. Previous studies on this model did not take into account the frequency dependence of the opacity. We study the radiative reprocessing and calculate the UV-optical-NIR band spectra from a spherical outflow composed of pure hydrogen gas, for a time-dependent outflowing mass rate. Electron scattering and frequency-dependent bound-free, free-free opacities are considered. The spectrum deviates from the blackbody at NIR and UV frequencies; in particular, it has $νL_ν \propto ν^{1.5}$ at NIR frequencies, because at these frequencies the absorption optical depth from the outflow's outer edge to the so-called photon trapping radius is large and is frequency dependent. We apply our model to the proto-type FBOT AT2018cow by {the spectra} to the observed SED. The best-fit mass loss rate suggests that the total outflow mass in AT2018cow is $M_{\rm out} \approx 5.7^{+0.4}_{-0.4} \, M_{\odot}$. If that equals the total mass lost during an explosion, and if the progenitor is a blue supergiant (with a pre-explosion mass of $\sim 20 \, M_{\odot}$), then it will suggest that the central compact remnant mass is at least $\approx \, \rm{14 \, M_{\odot}}$. This would imply that the central remnant is a black hole.

Figures (5)

• Figure 1: Schematic of the reprocessing model. The photon trapping radius $r_{\rm tr}$ (Eq. \ref{['trap_cal']}) separates the outflow into two radial regions: the inner adiabatic-cooling dominated region ($r < r_{\rm tr}$), and the outer radiative-transport dominated region ($r > r_{\rm tr}$). The frequency-dependent thermalization radius $r_{\rm th, \nu}$ defines the last absorption radius for photons of frequency $\nu$ (Eq. \ref{['eff_dep']}). Only those photons emitted at $r > r_{\rm th, \nu}$ are not absorbed on its way out.
• Figure 2: The opacities for the bound-free photoionization, and the free-free transitions at the different wavelengths for pure hydrogen gas at $\rho = 7.6 \times 10^{-14} \, \rm{cm \, g^{-1}}$, $T = 2.2 \times 10^4 \, \rm{K}$ (note these conditions correspond to the density and temperature at $r_{\rm tr}$ for the numerical example in Figure \ref{['fig:specpng']}). In the NIR band and even longer wavelengths, the absorptive opacity is dominated by $\kappa_{\rm ff, \nu}$. We neglect the bound-bound opacity here since we aim to fit the model results to the observed SED, so the line features are ignored.
• Figure 3: An example of the emergent spectrum from a reprocessing outflow, numerically calculated from Eq. \ref{['spec_def']}. The parameters are set as $\dot{M} = 10^{-6} \, \rm{M_{\odot} \, s^{-1}}$, $v_{\rm out} = 2 \times 10^{9} \, \rm{cm \, s^{-1}}$, $T(r_{\rm tr})= 2 \times 10^{4} \, \rm{K}$. The black dash-dotted line is the black-body spectrum whose temperature is $T(r_{\rm tr})$. The dashed line is the asymptotic shape (Eq. \ref{['spec_num']}) for the NIR excess. The UV sharp dropoff at $\lambda \lesssim 913 \AA$ is due to the absorptive opacity being dominated by hydrogen $\kappa_{\rm bf, \nu}$ there (see Figure \ref{['kappa_1127']}), which leads to an increase of $r_{\rm th, \nu}$, hence a lower temperature. Although the radiating area increases, the lower $T$ results in a decrease in the radiative intensity $B_{\nu} [T(r_{\rm th, \nu})]$ at these wavelengths, ultimately causing a significant drop in $L_{\nu}$ (Eq. \ref{['spec_def']}).
• Figure 4: The results of fitting the reprocessing outflow model to the SED data of AT2018cow at eight observing epochs ($t =$ 1.6 to 14.6 days) Perley2019. The black solid lines are the best-fit results, and the green solid lines correspond to the 1$\sigma$ uncertainty. We set the time $t = 0$ as the first detection of AT2018cow, $MJD58285$ in the ATLAS $o$-band Perley2019. Note that there were no UV band observations for $t < 3.0$ days. The UV band data at $t = 2.9$ days were obtained through a temporal extrapolation from the $t = 3.0$ day data, which might introduce a systematic error. Thus for the $t = 2.9$ day SED UV-band data, we introduce a systematic error equivalent to $10 \%$ of the observed value.
• Figure 5: The best-fit parameters obtained from fitting the outflow reprocessing model to the SED data of AT2018cow. The top panel shows the evolution of the mass loss rate $\dot{M}$. The middle panel shows the evolution of the outflow velocity $v_{\rm out}$. The bottom panel shows the evolution of $T(r_{\rm tr})$. The data points are best-fit parameters. The dash-dotted lines are the power-law function fit to the data points. The grey region marks the temperature obtained by fitting the SED to blackbody (BB) $+$ power law model with 1 $\sigma$ confidence. The first data point has exceptionally large error bars due to the lack of observations in the UV band at $t = 1.6$ days.