Extra-galactic high-energy transients: event rate densities and luminosity functions

Several types of extra-galactic high-energy transients have been discovered, which include high-luminosity and low-luminosity long-duration gamma-ray bursts (GRBs), short-duration GRBs, supernova shock breakouts (SBOs), and tidal disruption events (TDEs) without or with an associated relativistic jet. In this paper, we apply a unified method to systematically study the redshift-dependent event rate densities and the global luminosity functions (ignoring redshift evolution) of these transients. We introduce some empirical formulae for the redshift-dependent event rate densities for different types of transients, and derive the local specific event rate density, which also represents its global luminosity function. Long GRBs have a large enough sample to reveal features in the global luminosity function, which is best characterized as a triple power law. All the other transients are consistent with having a single power law luminosity function. The total event rate density depends on the minimum luminosity, and we obtain the following values in units of Gpc yr: 0.8 −0.1 for high-luminosity long GRBs above 10 50 erg s; 164 −65 for low-luminosity long GRBs above 5×1046 erg s−1; 1.3 −0.3, 1.2 +0.4 −0.3, and 3.3 +1.0 −0.8 above 10 50 erg s−1 for short GRBs with three different merger delay models (Gaussian, log-normal, and power law); 1.9 −1.2 × 10 4 above 1044 erg s−1 for SBOs, 4.8 −2.1 × 10 2 for normal TDEs above 1044 erg s−1; and 0.03 −0.02 above 10 48 erg s−1 for TDE jets as discovered by Swift. Intriguingly, the global luminosity functions of different kinds of transients, which cover over 12 orders of magnitude, are consistent with a single power law with an index of -1.6. Subject headings: gamma-ray burst: general-stars: luminosity function-stars: flare-supernovae: individual (SN 2006aj, SN 2008D)