Analytical Light Curves in the Realistic Model for Gamma‐Ray Burst Afterglows

Abstract

Afterglow light curves are constructed analytically for realistic gamma-ray burst remnants decelerating in either a homogeneous interstellar medium or a stellar wind environment, taking into account the radiative loss of the blast wave, which affects the temporal behaviors significantly. Inverse Compton scattering, which plays an important role when the energy equipartition factor epsilon(e) of electrons is much larger than that of the magnetic field (epsilon(B)), is considered. The inverse Compton effect prolongs the fast cooling phase markedly, during which the relativistic shock is semiradiative and the radiation efficiency is approximately constant, epsilon = epsilon(e). It is further shown that the shock is still semiradiative for quite a long time after it transits into the slow cooling phase because of a slow decreasing rate of the radiation efficiency of electrons. The temporal decaying index of the X-ray afterglow light curve in this semiradiative phase is (3p + 2 + 2epsilon)/(4 - epsilon) in the interstellar medium case and [3p - 2 - (p - 2)epsilon]/2(2 - epsilon) in the stellar wind case, where p is the distribution index of the shock-accelerated electrons. Taking p = 2.2-2.3 as implied from the common shock acceleration mechanism and assuming epsilon(e) similar to 1/3, the temporal index is more consistent with the observed (alpha(X)) similar to 1.3 than the commonly used adiabatic one. The observability of the inverse Compton component in soft X-ray afterglows is also investigated. To manifest as a bump or even dominant in the X-ray afterglows during the relativistic stage, the density must be larger than similar to1-10 cm(-3) in the interstellar medium case, or the wind parameter A(*) must be larger than similar to1 in the stellar wind case.