An Effect Study of Structural Jets on the Long Gamma-Ray Burst Formation Rate at Low Redshift

Abstract

Gamma-ray bursts (GRBs) are considered the most violent explosions in the Universe. Numerous studies have analyzed the formation rate of long gamma-ray bursts (LGRBs), which originate from the core collapse of massive stars, in comparison with the star formation rate (SFR). It is found that the LGRB formation rate at redshift z < 1 is significantly distinct from the SFR and is higher. Moreover, due to the threshold of detectors, the structured jets of GRBs also affect detection numbers at different redshifts, which all influence the calculation of the formation rate. Thus we investigate the LGRB formation rate at low redshift and further explore the possible correlation between the LGRB formation rate under the influence of structural jets and the SFR. We use Lynden-Bell's c− method to study the luminosity function and rate of Swift LGRBs without any assumptions. After correcting for the redshift evolution, the luminosity function can be expressed as for dim LGRBs and for bright LGRBs, and the formation rate at z < 1 shows an increase. Then we use Monte Carlo simulations to create pseudo-GRBs with structured jets and calculate the formation rates assuming that the actual LGRB formation rate at low redshift is proportional to the SRF. The results demonstrate that structural jets increase the number of detections at low redshift in response to observational effects. Compared with the observed formation rate, the structured jet model with Gauss-cocoon is found to be relatively more efficient, and the parameters η of this model are limited and analyzed to [0.5, 5].