The rate and luminosity function of long Gamma Ray Bursts

TL;DR

This paper derives the luminosity function and formation rate of long Gamma Ray Bursts using a complete Swift sample, revealing their evolution with redshift and their relation to cosmic star formation.

Contribution

It introduces a direct method to determine GRB luminosity function and formation rate, accounting for redshift evolution and testing its reliability with simulations.

Findings

Luminosity function is a broken power law with specific slopes.

GRB formation rate peaks at z~2, mirroring star formation history.

Luminosity evolution parameter k = 2.5.

Abstract

We derive, adopting a direct method, the luminosity function and the formation rate of long Gamma Ray Bursts through a complete, flux-limited, sample of Swift bursts which has a high level of completeness in redshift z (~82%). We parametrise the redshift evolution of the GRB luminosity as L = L_0(1+ z)^k and we derive k = 2.5, consistently with recent estimates. The de-evolved luminosity function of GRBs can be represented by a broken power law with slopes a = -1.32 +- 0.21 and b = -1.84 +- 0.24 below and above, respectively, a characteristic break luminosity L_0,b = 10^51.45+-0.15 erg/s. Under the hypothesis of luminosity evolution we find that the GRB formation rate increases with redshift up to z~2, where it peaks, and then decreases in agreement with the shape of the cosmic star formation rate. We test the direct method through numerical simulations and we show that if it is applied to incomplete (both in redshift and/or flux) GRB samples it can misleadingly result in an excess of the GRB formation rate at low redshifts.