2011MNRAS.418.1382L

Low-luminosity gamma-ray bursts (GRBs) with the luminosity ≲ 10⁴⁹ erg/s probably constitute a distinct population from the classic high-luminosity GRBs. They are the most luminous objects detected so far within ∼100 Mpc, the horizon distance of ultra-high-energy cosmic rays (UHECRs), so they are considered to be the candidate sources of UHECRs. It was recently argued that the energy production rate in UHECRs is much larger than that in gamma-ray photons of long GRBs measured by the Fermi satellite, which, if true, would challenge the view that GRBs can be the sources of UHECRs. We here suggest that many of the low-luminosity GRBs, due to their low luminosity, cannot trigger the current GRB detectors and hence their contribution to the local gamma-ray energy production rate is missing. We find that the real local energy production rate by low-luminosity GRBs, taking into account the missing part, which constitutes a dominant fraction of the total amount, could be sufficient to account for the flux of UHECRs. Due to the low luminosity, only intermediate-mass or heavy nuclei can be accelerated to ∼10²⁰ eV. We discuss the acceleration and survival of these ultra-high-energy nuclei in low-luminosity GRBs, especially in those missing low-luminosity GRBs. At last, the accompanying diffuse neutrino flux from the whole low-luminosity GRB population is calculated.