GAMMA-RAY BURST AFTERGLOWS - EFFECTS OF RADIATIVE-CORRECTIONS AND NONUNIFORMITY OF THE SURROUNDING MEDIUM

The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fir eball in the surrounding medium. Assuming that the expansion of the fi reball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n(ext) proportional to R-k, we study th e effects of the first-order radiative correction and the non-uniformi ty of the medium on a GRB afterglow analytically. We first derive a ne w relation among the observed time, the shock radius and the Lorentz f actor of the fireball: t(+) = R/4(4 - k)gamma(2)c, and also derive a n ew relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t(co) = 2R/(5 - k)gamma c. We next study the e volution of the fireball by using the analytic solution of Blandford & McKee. The radiation losses may not significantly influence this evol ution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We u se these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distributi on is p = 2.5, implied from the spectra of GRBs, the X-ray afterglow o f GRB 970616 is well fitted by assuming k = 2.