The low-luminosity tail of the GRB distribution: the case of GRB 980425

Context. The association of GRB 980425 with the nearby supernova SN 1998bw at z = 0.0085 implies the existence of a population of gamma-ray bursts with an isotropic-equivalent luminosity that is about 10(4) times lower than in the standard cosmological case. Apart from its weak luminosity, GRB 980425 appears a "normal" burst based on all its other properties (variability, duration, spectrum), with however a rather low peak energy of E(p) similar or equal to 30-100 keV. Aims. We investigate two scenarios to explain a weak gamma-ray burst such as GRB 980425: a normal (intrinsically bright) gamma-ray burst seen off-axis or an intrinsically weak gamma-ray burst seen on-axis. Methods. For each of these two scenarios, we first derive the conditions to produce a GRB 980425-like event and then discuss the consequences for the event rate. In the second scenario, this study is done in the framework of the internal shock model. Results. If we exclude the possibility that GRB 980425 is an occurrence of an extremely rare event observed by chance during the first eight years of the "afterglow era", the first scenario implies that (i) the local rate of "standard" bright gamma-ray bursts is much higher than what is usually expected; and (ii) the typical opening angle in gamma-ray bursts ejecta is much narrower than what is derived from observations of a break in the afterglow lightcurve. In addition to this statistical problem, we show that the afterglow of GRB 980425 in this scenario should have been very bright and easily detected. For these reasons the second scenario appears more realistic. We show that the parameter space of the internal shock model indeed allows GRB 980425-like events, in cases where the outflow is only mildly relativistic and mildly energetic. The rate of such weak events in the Universe has to be much higher than the rate of "standard" bright gamma-ray bursts to allow the discovery of GRB 980425 during a short period of a few years. However, it is still compatible with the observations, as the intrinsic weakness of these GRB 980425-like bursts does not allow detection at cosmological redshift with present gamma-ray instruments. We briefly discuss the consequences of such a high local rate of GRB 980425-like events for the future prospects of detecting non-electromagnetic radiation, especially gravitational waves.