A morphological analysis of gamma-ray burst early optical afterglows

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.