High-energy neutrinos and cosmic rays from low-luminosity gamma-ray bursts?

The recently discovered gamma-ray burst GRB 060218/SN 2006aj is classified as an X-ray flash with very long duration driven possibly by a neutron star. Since GRB 060218 is very near, similar to 140 Mpc, and very dim, the 1 yr observation by Swift suggests that the rate of GRB 060218-like events might be very high so that such low-luminosity (LL) GRBs might form a different population from the cosmological high-luminosity (HL) GRBs. We found that the high-energy neutrino background from LL GRBs could be comparable with that from HL GRBs. If each neutrino event is detected by IceCube, later optical-infrared follow-up observations such as those by Subaru and HST can possibly identify a Type Ibc supernova associated with LL GRBs, even if gamma rays and X-rays are not observed by Swift. This is in a sense a new window from neutrino astronomy, which might enable us to confirm the existence of LL GRBs and to obtain information about their rate and origin. We also suggest that LL GRBs are high-energy gamma-ray and cosmic-ray sources.