A semi-analytic afterglow with thermal electrons and synchrotron self-Compton emission

Abstract

We extend previous work on gamma-ray burst (GRB) afterglows involving hot thermal electrons at the base of a shock-accelerated tail. Using a physically-motivated electron distribution based on first-principles simulations, we compute broadband emission from radio to TeV gamma-rays. For the first time, we present the effects of a thermal distribution of electrons on synchrotron self-Compton (SSC) emission. The presence of thermal electrons causes temporal and spectral structure across the entire observable afterglow, which is substantively different from models that assume a pure power-law distribution for the electrons. We show that early-time TeV emission is enhanced by more than an order of magnitude for our fiducial parameters, with a time-varying spectral index that does not occur for a pure power law of electrons. We further show that the X-ray "closure relations" take a very different, also time-dependent, form when thermal electrons are present; the shape traced out by the X-ray afterglows is a qualitative match to observations of the traditional decay phase. INTRODUCTIONThe afterglows of gamma-ray bursts (GRBs) were initially used to localize the hosts, determine redshifts, and conclusively demonstrate the cosmological origin of these events (Costa et al. 1997; van Paradijs et al. 1997; Metzger et al. 1997;Bloom et al. 1998). Even before the first afterglows were observed, however, it was known that broadband observations would allow for the determination of the properties of GRBs and their progenitor systems (e.g., Paczyński & Rhoads 1993). A standard picture of GRB afterglows was developed, which assumed a relativistic shock accelerating electrons into a power-law distribution (Sari et al. 1998; Granot & Sari 2002, and countless others); these electrons then produced, by synchrotron radiation, the photons detected at Earth. Despite the simplicity of the model, it has been fitted with great success to numerous afterglows (