EXTRAGALACTIC HIGH-ENERGY TRANSIENTS: EVENT RATE DENSITIES AND LUMINOSITY FUNCTIONS

Several types of extragalactic 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 (GLFs; 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 GLF. Long GRBs (LGRBs) have a large enough sample to reveal features in the GLF, which is best charaterized as a triple power law (PL). All the other transients are consistent with having a single-power-law (SPL) LF. The total event rate density depends on the minimum luminosity, and we obtain the following values in units of Gpc(-3) yr(-1): 0.8(-0.1)(+0.1) for high-luminosity LGRBs above 10(50) erg s(-1); 164(-65)(+98) for low-luminosity LGRBs above 5 x 10(46) erg s(-1); 1.3(-0.3)(+0.4), 1.2(-0.3)(+0.4), and 3.3(-0.8)(+1.0) above 10(50) erg s(-1) for short GRBs with three different merger delay models (Gaussian, lognormal, and PL); 1.9(-1.2)(+2.4) x 10(4) above 10(44) erg s(-1) for SBOs, 4.8(-2.1)(+3.2) x 10(2) for normal TDEs above 10(44) erg s(-1); and 0.03(0.02)(+0.04) above 10(48) erg s(-1) for TDE jets as discovered by Swift. Intriguingly, the GLFs of different kinds of transients, which cover over 12 orders of magnitude, are consistent with an SPL with an index of - 1.6.