A comprehensive study of gamma-ray burst optical emission. III. Brightness distributions and luminosity functions of optical afterglows

Abstract

We continue our systematic statistical study on optical afterglow data of gamma-ray bursts (GRBs). We present the apparent magnitude distributions of early optical afterglows at different epochs (t = 10² s, 10 ³ s, and 1 hr) for the optical light curves of a sample of 93 GRBs (the global sample) and for sub-samples with an afterglow onset bump or a shallow decay segment. For the onset sample and shallow decay sample we also present the brightness distribution at the peak time t p and break time t b, respectively. All the distributions can be fit with Gaussian functions. We further perform Monte Carlo simulations to infer the luminosity function of GRB optical emission at the rest-frame time 10³ s, t p, and t b. Our results show that a single power-law luminosity function is adequate to model the data with indices -1.40 ± 0.10, -1.06 ± 0.16, and -1.54 ± 0.22. Based on the derived rest-frame 10³ s luminosity function, we generate the intrinsic distribution of the R-band apparent magnitude M R at the observed time 10³ s post-trigger, which peaks at M R = 22.5 mag. The fraction of GRBs whose R-band magnitude is fainter than 22 mag and 25 mag and at the observer time 10³ s are ∼63% and ∼25%, respectively. The detection probabilities of the optical afterglows with ground-based robotic telescopes and the UV-Optical Telescope on board Swift are roughly consistent with that inferred from this intrinsic M R distribution, indicating that the variations of the dark GRB fraction among the samples with different telescopes may be due to the observational selection effect, although the existence of an intrinsically dark GRB population cannot be ruled out. © 2013. The American Astronomical Society. All rights reserved.