Constrain the GRB jet opening angle based on the very steep decay phase

Abstract

Thanks to the rapid follow-up observations by \textit{Swift}/XRT, a good part of Gamma-Ray Bursts (GRBs) high latitude emission have been observed in X-ray band. Some of them even show a dropdown decay after this period, which strongly indicates the edge of the jet is corresponding to the breaking time. This study constrains the jet opening angles of GRBs by analyzing the very steep decay phase in the early X-ray afterglow. Using data from \textit{Swift}/XRT, we identified GRBs with significant breaks in their light curves and applied a broken power-law model to describe the decay phases. Assuming a spherical and isotropic emitting surface, we set constraints on the radiation radius ($R_{\gamma}$) to estimate jet opening angles ($\theta_{\rm jet}$) from the breaking time. Our results indicate that jet opening angles can be constrained, although they are sensitive to the assumed radiation radius. This approach provides yet another method for estimating GRB jet opening angles.