The Optical Luminosity Function of Gamma-ray Bursts deduced from ROTSE-III Observations

TL;DR

This study derives the optical luminosity function of gamma-ray bursts using ROTSE-III data, revealing that certain models fit the data well while others are statistically rejected, enhancing understanding of GRB optical emissions.

Contribution

It provides the first comprehensive optical luminosity function of GRBs based on a uniform ROTSE-III sample, considering detection biases and different functional forms.

Findings

Optical luminosity at 100s follows an ERPLD, BPL, and Schechter function.

Single power-law luminosity function is statistically rejected.

Detection function and star-formation rate assumptions are crucial for fitting the data.

Abstract

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). The $R$ band fluxes 100s after the onset of the burst for these two sub-samples are derived. The optical LFs at 100s are fitted by assuming that the co-moving GRB rate traces the star-formation rate. The detection function of ROTSE-III is taken into account during the fitting of the optical LFs by using Monte Carlo simulations. We find that the cumulative distribution of optical emission at 100s is well-described with an exponential rise and power-law decay (ERPLD), broken power-law (BPL), and Schechter LFs. A single power-law (SPL) LF, on the other hand, is ruled out with high confidence.