Low-Luminosity Gamma-Ray Bursts as a Distinct GRB Population:A Monte Carlo Analysis

The intriguing observations of Swift/BAT GRB 060218 and CGRO/BATSE burst 980425, both with much lower luminosity and redshift compared to other observed bursts, lead naturally to the question whether these low-luminosity (LL) bursts constitute a separate population from high-luminosity (HL) bursts. Utilizing Monte Carlo simulations we compare various single-component luminosity function (LF) models (single power law or broken power law) with the two-component luminosity function model proposed by Liang et al. Using various criteria, we demonstrate that the singlecomponent LF models have great difficulty in simultaneously reproducing both the high local LL-GRB rate and the oberved distributions of redshift, luminosity, and log N −logP for HL-GRBs. We argue that the two-component LF model is necessary, and we use the observed BATSE and Swift log N −log P distributions to add constrains to the LL and HL-LF parameters. The LL-LF can be modeled by a smoothed, broken power law with a break at around 10 47 erg s −1, dropping steeply above this luminosity. The local rate of LL-GRBs is ∼ 100 Gpc −3 yr −1 at the break luminosity, much larger than that of HL-GRBs. The recently discovered peculiar X-ray transient XRF 080109/SN 2008D strengthens this conclusion, and requires that the LL-population LF extends further down in luminosity with a probably even higher local rate at lower luminosities.