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

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 $\nu L_{\nu} \propto \nu^{1.5}$ 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.