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

Abstract

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 $\mathrm{Gp}{\mathrm{c}}^{-3}\mathrm{y}{\mathrm{r}}^{-1}$: $0.8_{-0.1}^{+0.1}$ for high-luminosity long GRBs above $10^{50}\mathrm{erg}{\mathrm{s}}^{-1}$, $164_{-65}^{+98}$ for low-luminosity long GRBs above $5\times 10^{46}\mathrm{erg}{\mathrm{s}}^{-1}$, $1.3_{-0.3}^{+0.4}$, $1.2_{-0.3}^{+0.4}$, and $3.3_{-0.8}^{+1.0}$ above $10^{50}\mathrm{erg}{\mathrm{s}}^{-1}$ for short GRBs with three different merger delay models (Gaussian, log-normal, and power law), $1.9_{-1.2}^{+2.4}\times 10^4$ above $10^{44}\mathrm{erg}{\mathrm{s}}^{-1}$ for SBOs, $4.8_{-2.1}^{+3.2}\times 10^2$ for normal TDEs above $10^{44}\mathrm{erg}{\mathrm{s}}^{-1}$, and $0.03_{-0.02}^{+0.04}$ above $10^{48}\mathrm{erg}{\mathrm{s}}^{-1}$ 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.

35 pages, 12 figures, accepted to ApJ

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