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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  &lt; 10 47  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, ρ 0 , of LL GRBs from our model is ∼200 Gpc −3  yr −1  at  ∼10 47  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.

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