The optical luminosity function of gamma-ray bursts deduced from ROTSE-III observations

We present the optical luminosity function (LF) of gamma-ray bursts (GRBs) estimated from a uniform sample of 58 GRBs from observations with the Robotic Optical Transient Search Experiment III (ROTSE-III). Our GRB sample is divided into two sub-samples: detected afterglows (18 GRBs) and those with upper limits (40 GRBs). We derive R-band fluxes for these two sub-samples 100 s after the onset of the burst. The optical LFs at 100 s are fitted by assuming that the co-moving GRB rate traces the star formation rate. While fitting the optical LFs using Monte Carlo simulations, we take into account the detection function of ROTSE-III. We find that the cumulative distribution of optical emission at 100 s is well described by an exponential rise and power-law decay, a broken power law, and Schechter LFs. A single power-law (SPL) LF, on the other hand, is ruled out with high confidence.