The luminosity function and formation rate of a complete sample of long gamma-ray bursts

Author:

Lan Guang-Xuan12,Zeng Hou-Dun1,Wei Jun-Jie1ORCID,Wu Xue-Feng12

Affiliation:

1. Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210034, China

2. School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China

Abstract

ABSTRACT We study the luminosity function and formation rate of long gamma-ray bursts (GRBs) by using a maximum likelihood method. This is the first time this method is applied to a well-defined sample of GRBs that is complete in redshift. The sample is composed of 99 bursts detected by the Swift satellite, 81 of them with measured redshift and luminosity for a completeness level of $82\, {\rm per\, cent}$. We confirm that a strong redshift evolution in luminosity (with an evolution index of $\delta =2.22^{+0.32}_{-0.31}$) or in density ($\delta =1.92^{+0.20}_{-0.21}$) is needed in order to reproduce the observations well. But since the predicted redshift and luminosity distributions in the two scenarios are very similar, it is difficult to distinguish between these two kinds of evolutions only on the basis of the current sample. Furthermore, we also consider an empirical density case in which the GRB rate density is directly described as a broken power-law function and the luminosity function is taken to be non-evolving. In this case, we find that the GRB formation rate rises like $(1+z)^{3.85^{+0.48}_{-0.45}}$ for $z\lesssim 2$ and is proportional to $(1+z)^{-1.07^{+0.98}_{-1.12}}$ for $z\gtrsim 2$. The local GRB rate is $1.49^{+0.63}_{-0.64}$ Gpc−3 yr−1. The GRB rate may be consistent with the cosmic star formation rate (SFR) at $z\lesssim 2$, but shows an enhancement compared to the SFR at $z\gtrsim 2$.

Funder

National Natural Science Foundation of China

Youth Innovation Promotion Association

Key Research Program of Frontier Sciences

Chinese Academy of Sciences

Publisher

Oxford University Press (OUP)

Subject

Space and Planetary Science,Astronomy and Astrophysics

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