Author: Xianggao Wang
Abstract: We systematic statistical study on optical afterglow data of gamma-ray bursts (GRBs). We present the brightness distributions of early optical afterglows at different epoches (t<1 hour) for the global lightcurves, the onset bump and the shallow decay segments of the afterglows with a sample of 93 gamma-ray bursts (GRBs). We further make Monte Carlo simulations to study the luminosity functions for the global lightcurves at 1000 seconds and for the afterglow onset bumps at tp as well as for the shallow decay segment at tb. Our results show that a single power-law luminosity functions is adequate to model the data, with indices -1.54± 0.10, -1.06±0.10, and -1.54± 0.22, respectively. Based on the derived luminosity function, we generate the intrinsic distribution of MR at 1000 seconds, which peaks at MR =21.8. The fraction of GRBs whose optical afterglow being dimmer than MR =22 at 103 is 47%, and this fraction is ∼18% with MR =25. The detection probabilities of the optical afterglows with ground-based robotic telescopes and UVOT onboard Swift are consistent with our results, indicating that the variation of the fractions of dark GRBs in different GRB samples may be due to the selection effect, although we cannot rule out the exist of an intrinsically dark GRB population.