A morphological analysis of gamma-ray burst early optical afterglows

Abstract

Within the framework of the external shock model of gamma-ray bursts (GRBs) afterglows, we perform a morphological analysis of the early optical lightcurves to directly constrain model parameters. We define four morphological types, i.e. the reverse shock dominated cases with/without the emergence of the forward shock peak (Type I/ Type II), and the forward shock dominated cases without/with \(\nu_m\) crossing the band (Type III/IV). We systematically investigate all the Swift GRBs that have optical detection earlier than 500 s and find 3/63 Type I bursts (4.8%), 12/63 Type II bursts (19.0%), 30/63 Type III bursts (47.6%), 8/63 Type IV bursts (12.7%) and 10/63 Type III/IV bursts (15.9%). We perform Monte Carlo simulations to constrain model parameters in order to reproduce the observations. We find that the favored value of the magnetic equipartition parameter in the forward shock (\(\epsilon_B^f\)) ranges from \(10^{-6}\) to \(10^{-2}\), and the reverse-to-forward ratio of \(\epsilon_B\) (\(R_B\)) is about 100. The preferred electron equipartition parameter \(\epsilon_e^{r,f}\) value is 0.01, which is smaller than the commonly assumed value, e.g., 0.1. This could mitigate the so- called "efficiency problem" for the internal shock model, if \(\epsilon_e\) during the prompt emission phase (in the internal shocks) is large (say, \(\sim 0.1\)). The preferred \(R_B\) value is in agreement with the results in previous works that indicates a moderately magnetized baryonic jet for GRBs.