Comprehensive Statistical Analysis of Initial Lorentz Factor and Jet Opening Angle of Gamma-Ray Bursts

Authors:
Open Access
Publisher website
Google Scholar
Abstract
The initial Lorentz factor (Γ0) and jet half-opening angle (θ jet) of gamma-ray bursts (GRBs) are critical physical parameters for understanding the dynamical evolution of relativistic jets and the true energy release of GRBs. We compile a sample of 89 GRBs that exhibit an onset bump feature in their early optical or GeV light curves, 42 of which also display a jet break feature, and derive their Γ0 and θ jet values. Using this sample, we reexamine the correlations between Γ0 and the prompt emission parameters (isotropic energy E iso, peak luminosity L iso, and peak energy E p). Our results confirm the previously reported Γ0−E iso (L iso), Γ0−E p,z, and E iso (L iso)−E p−Γ0 relations for both homogeneous interstellar medium (ISM) and Wind density profiles (Wind). Notably, we find that the short GRB 090510 complies with the Γ0−E iso relation, but significantly deviates from the Γ0−L iso and Γ0−E p,z relations. We systematically investigate the influence of θ jet on Γ0 and find a weak dependence, which reads Γ0 (ISM) ∝ θ jet − 0.18 ± 0.15 (ISM) and Γ0 (Wind) ∝ θ jet − 0.72 ± 0.14 (Wind). Additionally, we report, for the first time, three new three-parameter correlations, i.e., E iso ∝ θ jet − 0.52 ± 0.26 (ISM) Γ 0 2.21 ± 0.28 (ISM) and E iso ∝ θ jet − 0.65 ± 0.21 (Wind) Γ 0 2.08 ± 0.19 (Wind); L iso ∝ θ jet − 0.35 ± 0.27 (ISM) Γ 0 2.46 ± 0.29 (ISM) and L iso ∝ θ jet − 0.29 ± 0.28 (Wind) Γ 0 2.37 ± 0.25 (Wind); and E p , z ∝ θ jet − 0.15 ± 0.19 (ISM) Γ 0 1.11 ± 0.21 (ISM) and E p , z ∝ θ jet − 0.17 ± 0.23 (Wind) Γ 0 1.09 ± 0.21 (Wind). These tight E iso (or L iso, E p,z)−Γ0−θ jet correlations likely arise from the combined effects of radiation mechanisms, jet structure, and outflow dynamics in GRBs. In addition, we further explore the relations between the initial Lorentz factor and the jet-corrected energy, and find Γ0 (ISM) ∝ E γ , 52 0.22 ± 0.04 (ISM) and Γ0 (Wind) ∝ E γ , 52 0.40 ± 0.06 (Wind); and Γ0 (ISM) ∝ L γ , 52 0.20 ± 0.04 (ISM) and Γ0 (Wind) ∝ L γ , 52 0.30 ± 0.06 (Wind). We also find that the jet-corrected correlations remain significant, suggesting that these relations are intrinsic to the physical nature of GRBs. However, the increased dispersion after correction implies that underlying differences persist among individual GRBs.
Funding Information
  • MOST ∣ National Natural Science Foundation of China (No. 12463008)
  • 广西壮族自治区科学技术厅 ∣ Natural Science Foundation of Guangxi Zhuang Autonomous Region (No. 2022GXNSFDA035083)

This publication has 59 references indexed in Scilit: