Analytic Light Curves of Gamma‐Ray Burst Afterglows: Homogeneous versus Wind External Media

Abstract

Assuming an adiabatic evolution of a Gamma-Ray Burst (GRB) remnant\ninteracting with an external medium, we calculate the injection, cooling, and\nabsorption break frequencies, and the afterglow flux for plausible orderings of\nthe break and observing frequencies. The analytical calculations are restricted\nto a relativistic remnant and, in the case of collimated ejecta, to the phase\nwhere there is an insignificant lateral expansion. Results are given for both a\nhomogeneous external medium and for a wind ejected by the GRB progenitor.\n We compare the afterglow emission at different observing frequencies, for\neach type of external medium. It is found that observations at sub-millimeter\nfrequencies during the first day provide the best way of discriminating between\nthe two models. By taking into account the effect of inverse Compton\nscatterings on the electron cooling, a new possible time-dependence of the\ncooling break is identified. The signature of the up-scattering losses could be\nseen in the optical synchrotron emission from a GRB remnant interacting with a\npre-ejected wind, as a temporary mild flattening of the afterglow decay. The\nup-scattered radiation itself should be detected in the soft X-ray emission\nfrom GRB remnants running into denser external media, starting few hours after\nthe main event.\n