Low-luminosity gamma-ray bursts as a distinct GRB population: a firmer case from multiple criteria constraints

The intriguing observations of the Swift/Burst Alert Telescope (BAT) X-ray flash (XRF) 060218 and the BATSE-BeppoSAX gamma-ray burst GRB 980425, both with much lower luminosity and redshift compared to other observed bursts, naturally lead to the question of how these low-luminosity (LL) bursts are related to high-luminosity (HL) bursts. Incorporating the constraints from both the flux-limited samples observed with Compton Gamma-ray Observatory (CGRO)/BATSE and Swift/BAT and the redshift-known gamma-ray burst (GRB) sample, we investigate the luminosity function for both LL and HL GRBs through simulations. Our multiple criteria, including the log N− log P distributions from the flux-limited GRB sample, the redshift and luminosity distributions of the redshift-known sample and the detection ratio of HL and LL GRBs with Swift/BAT, provide a set of stringent constraints to the luminosity function. Assuming that the GRB rate follows the star formation rate (SFR), our simulations show that a simple power law (PL) or a broken power-law model of luminosity function fails to reproduce the observations and a new component is required. This component can be modelled with a broken power, which is characterized by a sharp increase in the burst number at around L < 1047 erg s−1. The lack of detection of moderate-luminosity GRBs at redshift ∼0.3 indicates that this feature is not due to the observational biases. The inferred local rate, ρ0, of LL GRBs from our model is ∼200 Gpc−3 yr−1 at ∼1047 erg s−1, much larger than that of HL GRBs. These results imply that LL GRBs could be a separate GRB population from HL GRBs. The recent discovery of a local X-ray transient 080109/SN 2008D would strengthen our conclusion if the observed non-thermal emission has a similar origin as the prompt emission of most GRBs and XRFs.