Analytical light curves in the realistic model for GRB afterglows

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 ǫe of electrons is much larger than that of the magnetic field (ǫB), is considered. The inverse Compton effect prolongs the fast-cooling phase markedly, during which the relativistic shock is semi-radiative and the radiation efficiency is approximately constant, ǫ = ǫe. It is further shown that the shock is still semi-radiative 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 semi-radiative phase is (3p−2+2ǫ)/(4−ǫ) in the interstellar medium case, and [3p − 2 − (p − 2)ǫ]/2(2 − ǫ) 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 common shock acceleration mechanism, and assuming ǫe ∼ 1/3, the temporal index is more consistent with the observed 〈αX〉 ∼ 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, it is required that the density should be larger than ∼ 1− 10 cm in the interstellar medium case, or the wind parameter A∗ should be larger than ∼ 1 in the stellar wind case. Subject headings: gamma rays: bursts — hydrodynamics — stars: mass loss — ISM: jets and outflows — radiation mechanisms: nonthermal — relativity