Simulating a faint gamma-ray burst population

There have now been three supernova-associated gamma-ray bursts (GRBs) at redshift z < 0.17, namely 980425, 030329 and 031203, but the nearby and under-luminous GRBs 980425 and 031203 are distinctly different from the `classical' or standard GRBs. It has been suggested that they could be classical GRBs observed away from their jet axes, or they might belong to a population of under-energetic GRBs. Recent radio observations of the afterglow of GRB 980425 suggest that different engines may be responsible for the observed diversity of cosmic explosions. Given this assumption, a crude constraint on a luminosity function for faint GRBs with a mean luminosity similar to that of GRB 980425 and an upper limit on the rate density of 980425-type events, we simulate the redshift distribution of under-luminous GRBs assuming BATSE and Swift sensitivities. A local rate density of about 0.6 per cent of the local supernova Type Ib/c rate yields simulated probabilities for under-luminous events to occur at rates comparable to the BATSE GRB low-redshift distribution. In this scenario the probability of BATSE/HETE detecting at least one GRB at z < 0.05 is 0.78 over 4.5 years, a result that is comparable with observation. Swift has the potential to detect 1-5 under-luminous GRBs during one year of observation.