Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts

Abstract

The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is of an important role for the cosmological applications of the GRBs, which is however hindered seriously by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest to calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p relationship. Here, such a $L-E_p$ relationship is determined by reconciling the distributions of pseudo- and real redshifts of redshift-known GRBs. The values of E_p taken from Butler's GRB catalog are estimated with Bayesian statistics rather than observed. Using the GRB sample with pseudo-redshifts of a relatively large number, we fit the redshift-resolved luminosity distributions of the GRBs with a broken-power-law LF. The fitting results suggest that the LF could evolve with redshift by a redshift-dependent break luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is found that the proportional coefficient between GRB event rate and star formation rate should correspondingly decrease with increasing redshifts.

arXiv comment5 pages, 5 figures, accepted for publication in ApJL

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• The Luminosity Function and Formation Rate of A Complete Sample of Long Gamma-Ray Bursts
• Revisiting the luminosity and redshift distributions of long gamma-ray bursts
• Cosmic Evolution of Long Gamma-Ray Burst Luminosity
• Pseudo Redshifts of Gamma-Ray Bursts Derived from the L-T-E Correlation
• Determine the Lorentz factor and the viewing angle of GRB 170817A
• Search for strong gravitational lensing effect in the current GRB data of BATSE
• Constraining fast radio burst progenitors with gravitational lensing
• Gamma-ray burst cosmology: Hubble diagram and star formation history
• GRBs and fundamental physics
• Modelling the luminosity function of long Gamma Ray Bursts using SWIFT and FERMI
• Research on the redshift evolution of luminosity function and selection effect of GRBs
• The truncated lognormal distribution as a luminosity function for SWIFT-BAT gamma-ray bursts
• The star formation history inferred from long gamma-ray bursts with high pseudo-redshifts
• On the Feasibility of Deriving Pseudo-Redshifts of Gamma-ray Bursts from Two Phenomenological Correlations
• On the event rate and luminosity function of superluminous supernovae