Extragalactic high-energy transients: Event rate densities and luminosity functions

Abstract

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: for high-luminosity LGRBs above 10⁵⁰ erg s^-1; for low-luminosity LGRBs above 5 � 10⁴⁶ erg s^-1; and above 10⁵⁰ erg s^-1 for short GRBs with three different merger delay models (Gaussian, lognormal, and PL); above 10⁴⁴ erg s^-1 for SBOs, for normal TDEs above 10⁴⁴ erg s^-1; and above 10⁴⁸ 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.