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.