Revisiting the luminosity and redshift distributions of long gamma-ray bursts

Abstract

In this work, we update and enlarge the long gamma-ray burst (GRB) sample detected by the Swift satellite. Given the incomplete sampling of the faint bursts and the low completeness in redshift measurement, we carefully select a subsample of bright Swift bursts to revisit the GRB luminosity function (LF) and redshift distribution by taking into account the probability of redshift measurement. Here we also explore two general expressions for the GRB LF, i.e. a broken power-law LF and a triple power-law LF. Our results suggest that a strong redshift evolution in luminosity (with an evolution index of $\delta =1.92^{+0.25}_{-0.37}$) or in density ($\delta =1.26^{+0.33}_{-0.34}$) is required in order to well account for the observations, independent of the assumed expression of the GRB LF. However, in a one-on-one comparison using the Akaike information criterion, the best-fitting evolution model involving the triple power-law LF is statistically preferred over the best-fitting one involving the broken power-law LF with a relative probability of ∼94.3 per cent versus ∼5.7 per cent. Extrapolating our fitting results to the flux limit of the whole Swift sample, and considering the trigger probability of Swift/Burst Alert Telescope in detail, we find that the expectations from our evolution models provide a good representation of the observed distributions of the whole sample without the need for any adjustment of the model free parameters. This further confirms the reliability of our analysis results.

The Stellar-mass Function of Long Gamma-Ray Burst Host Galaxies

“…Relevant studies in this field have been carried out for more than two decades, but it remains an open question whether long GRBs can be good tracers of cosmic star formation. By studying the GRB redshift distribution, there is a general agreement about the fact that the comoving GRB rate does not purely follow the cosmic SFR, but exhibits an enhancement of GRB detections at high redshifts (z  2 − 3) with respect to the expectation from the star formation history (e.g., Daigne et al 2006;Le & Dermer 2007;Guetta & Piran 2007;Kistler et al 2008;Li 2008;Wanderman & Piran 2010;Qin et al 2010;Virgili et al 2011;Robertson & Ellis 2012;Lu et al 2012;Wang 2013;Lien et al 2014;Wei et al 2014;Vergani et al 2015;Perley et al 2015Perley et al , 2016cJapelj et al 2016;Wei & Wu 2017;Palmerio et al 2019;Lan et al 2019Lan et al , 2021Ghirlanda & Salvaterra 2022). Several possible mechanisms have been proposed to reconcile the discrepancy between the GRB rate and the SFR, such as cosmic metallicity evolution Li 2008;Salvaterra et al 2012;Lloyd-Ronning et al 2019;Ghirlanda & Salvaterra 2022), an evolving initial mass function of stars (Xu & Wei 2009;Wang & Dai 2011), and an evolving luminosity function of GRBs (e.g., Lloyd-Ronning et al 2002;Firmani et al 2004;Salvaterra & Chincarini 2007;Salvaterra et al 2009a;Cao et al 2011;Salvaterra et al 2012;…”

“…In order to infer the model-free parameters, a maximum likelihood method first proposed by Marshall et al (1983) is adopted. The likelihood function  is defined as (e.g., Chiang & Mukherjee 1998;Narumoto & Totani 2006;Ajello et al 2009Ajello et al , 2012Abdo et al 2010;Zeng et al 2014Zeng et al , 2016Lan et al 2019Lan et al , 2021)…”

“…The redshifts of about 40% of all GRBs detected by the Swift satellite have been measured (Lan et al 2021). Though this is a significant improvement compared to the pre-Swift era; from the point of view of characterizing the GRB host population or redshift distribution, the sample is still far from being considered unbiased and complete.…”

Gravitationally Lensed Orphan Afterglows of Gamma-Ray Bursts

“…Using the luminosity evolution model and the corresponding parameters in Lan et al (2021), we get the redshift distribution of long GRBs detected by Swift/BAT from z s = 0 to z s = 2 with,…”

“…where Θ(P) is the detection efficiency, P is the peak flux of the burst, ψ(z) is the comoving event rate of GRBs in units of Mpc −3 yr −1 , L is the luminosity of GRBs, φ(L, z) is the normalized GRB luminosity function, and more details could be found in Lan et al (2021). For an assumed maximum viewing angle of θ v = 5 • , the final result for the lensed event rate is 5.8 × 10 −2 yr −1 sr −1 , and the lensed event rate for the whole sky is 0.7 yr −1 .…”