Luminosity function of GRBs

¹ Harish-chandra Research Institute, Jhusi Road, Allahabad 211 019, India e-mail: sethi@mri.ernet.in
² Indian Institute of Astrophysics, Sarjapur Road, Bangalore 560 034, India e-mail: bhargavi@iiap.ernet.in

Corresponding author: S. Sethi, sethi@mri.ernet.in

Received: 12 February 2001
Accepted: 29 June 2001

Abstract

We attempt to constrain the luminosity function of Gamma Ray Bursts (GRBs) from the observed number count-flux relation and the afterglow redshift data. We assume three classes of luminosity functions for our analysis: (a) Log-normal distribution, (b) Schechter distribution, and (c) Scale-free distribution. We assume several models of the evolution of the GRB population for each luminosity function. Our analysis shows that: (a) log-normal is the only luminosity function that is compatible with both the observations. This result is independent of the GRB evolution model, (b) for log-normal function, the average photon luminosity L₀ and the width of the luminosity function σ that are compatible with both the observations fall in the range: and , (c) the agreement of observations with other luminosity functions requires the GRB population to evolve more strongly than the evolution of the star-formation rate of the universe.