Very Early Optical Afterglows for Geometric Models of X-ray Flashes and X-ray Rich GRBs

Abstract

If X-ray flashes (XRFs) and X-ray rich Gamma-ray Bursts (XRRGs) have the same origin as the Gamma-ray bursts (GRBs) but are viewed off-center from structured jets, their early afterglows may differ from those of GRBs, and when the ultra-relativistic outflow interacts with the surrounding medium, there are two shocks formed, a forward shock (FS), and a reverse shock (RS). We calculate numerically the early afterglow powered by uniform jets, Gaussian jets and power-law jets in the forward-reverse shock scenario. A set of differential equations govern the dynamical evolution. The synchrotron self-Compton effect has been taken into account in the calculation. In the uniform jets, the very early afterglows of XRRGs and XRFs are significantly lower than the GRBs and the observed peak times of RS emission are later in the interstellar medium environment. The RS components in XRRGs and XRFs are difficult to detect, but in the stellar wind environment, the reduction of the very early flux and the delay of the RS peak time are not so remarkable. In nonuniform jets (Gaussian and power-law jets), where there are emission materials on the line of sight, the very early light curve resembles equivalent isotropic ejecta in general although the RS flux decay index shows notable deviations if the RS is relativistic (in stellar wind).