Synchrotron Self-Compton Model of TeV Afterglows in Gamma-Ray Bursts

Abstract: The detection of a very-high-energy TeV spectral component in the afterglow emission of gamma-ray bursts (GRBs) has opened a new probe into the energetics of ultra-relativistic blast waves and the nature of the circumburst environment in which they propagate. The afterglow emission is well understood as the synchrotron radiation from the shock-accelerated electrons in the medium swept up by the blast wave. The same distribution of electrons also inverse-Compton upscatters the softer synchrotron photons to produce the synchrotron self-Compton (SSC) TeV emission. Accurate modeling of this component generally requires a computationally expensive numerical treatment, which makes it impractical when fitting to observations using Markov Chain Monte Carlo (MCMC) methods. Simpler analytical formalisms are often limited to broken power-law solutions and some predict an artificially high Compton-Y parameter. Here we present a semi-analytic framework for a spherical blast wave that accounts for adiabatic cooling and expansion, photon escape, and equal-arrival-time-surface integration, in addition to Klein-Nishina effects. Our treatment produces the broadband afterglow spectrum and its temporal evolution at par with results obtained from more sophisticated kinetic calculations. We fit our model to the afterglow observations of the TeV bright GRB\,190114C using MCMC, and find an energetic blast wave with kinetic energy $E_{k, \rm iso} = 9.1^{+7.41}_{-3.13} \times 10^{54} \, \rm erg$ propagating inside a radially stratified external medium with number density $n(r)\propto r^{-k}$ and $k=1.67^{+0.09}_{-0.10}$. A shallower external medium density profile ($k<2$) departs from the canonical approximation of a steady wind ($k=2$) from the progenitor star and may indicate a non-steady wind or a transition to an interstellar medium.