The Event Rate and Luminosity Function of Fermi/GBM Gamma-Ray Bursts

TL;DR

This study analyzes the luminosity function and event rate of Fermi/GBM gamma-ray bursts, revealing that bright GRBs align with star formation rates, and examines how observational biases influence these measurements.

Contribution

It introduces a comprehensive analysis of GRB luminosity evolution, event rates, and biases using a large sample and advanced statistical methods, providing new insights into GRB origins.

Findings

Event rate exceeds star formation rate at low redshift.

Bright GRBs' event rate matches star formation rate, suggesting a link to massive star collapse.

Sample completeness has minimal impact on deduced event rates.

Abstract

Luminosity function and event rate of Gamma-Ray Bursts (GRBs) are easily biased by the instrument and selection effects. We select 115 Fermi/GBM GRBs with good spectra fitted by a smoothly broken power-law function. The $\tau$-statistic method is used to describe how the luminosity evolves with redshift. The non-parametric Lynden-Bell's c$^{-}$ method has been applied to get the cumulative luminosity function and event rate which is compared with the star formation history. How the selection and instrument effects bias the deduced event rate has been carefully studied. We find that the event rate always exceeds the star formation rate (SFR) at lower redshift and matches with each other at higher redshift, which is independent of energy bands and consistent with previous findings of other satellites. Furthermore, it is found that sample completeness does not affect the deduced event rate too much as mentioned for the Swift lGRBs in Dong et al.. A triple power-law function has been used to fit the cumulative flux distribution and categorize the total sample into three subsamples of bright, medium and faint GRBs. We find that the event rates of bright GRBs, unlike medium and faint ones, comply with the SFR ideally, which indicates that these bright GRBs with higher luminosity are possibly produced from the core-collapse of massive stars.