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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.13448 |
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| _version_ | 1866908494406352896 |
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| author | Zhang, Jian Qin, Bao-Cheng Zhang, Lu-Lu Zhang, Fu-Wen |
| author_facet | Zhang, Jian Qin, Bao-Cheng Zhang, Lu-Lu Zhang, Fu-Wen |
| contents | The initial Lorentz factor ($Γ_{0}$) and jet half-opening angle ($θ_{\rm jet}$) 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 $Γ_{0}$ and $θ_{\rm jet}$ values. Using this sample, we re-eaxmine the correlations between $Γ_{0}$ and the prompt emission parameters (isotropic energy $E_{\rm iso}$, peak luminosity $L_{\rm iso}$, and peak energy $E_{\rm p}$). Our results confirm the previously reported $Γ_{0}$$-$$E_{\rm iso}$ ($L_{\rm iso}$), $Γ_{0}$$-$$E_{\rm p,z}$, and $E_{\rm iso}$ ($L_{\rm iso}$)$-$$E_{\rm p}$$-$$Γ_{0}$ relations for both homogeneous interstellar medium (ISM) and wind density profiles (Wind). Notably, we find that the short GRB 090510 complies with the $Γ_{0}$$-$$E_{\rm iso}$ relation, but significantly deviates from the $Γ_{0}$$-$$L_{\rm iso}$ and $Γ_{0}$$-$$E_{\rm p,z}$ relations. We systematically investigate the influence of $θ_{\rm jet}$ on $Γ_{0}$ and find a weak dependence. Additionally, we report, for the first time, three new three-parameter correlations, i.e., $E_{\rm iso}$ (or $L_{\rm iso}$, $E_{\rm p,z}$)$-$$Γ_{0}$$-$$θ_{\rm jet}$ correlations. In addition, we further explore the relations between the initial Lorentz factor and the jet-corrected energy. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_13448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comprehensive Statistical Analysis of Initial Lorentz Factor and Jet Opening Angle of Gamma-Ray Bursts Zhang, Jian Qin, Bao-Cheng Zhang, Lu-Lu Zhang, Fu-Wen High Energy Astrophysical Phenomena The initial Lorentz factor ($Γ_{0}$) and jet half-opening angle ($θ_{\rm jet}$) 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 $Γ_{0}$ and $θ_{\rm jet}$ values. Using this sample, we re-eaxmine the correlations between $Γ_{0}$ and the prompt emission parameters (isotropic energy $E_{\rm iso}$, peak luminosity $L_{\rm iso}$, and peak energy $E_{\rm p}$). Our results confirm the previously reported $Γ_{0}$$-$$E_{\rm iso}$ ($L_{\rm iso}$), $Γ_{0}$$-$$E_{\rm p,z}$, and $E_{\rm iso}$ ($L_{\rm iso}$)$-$$E_{\rm p}$$-$$Γ_{0}$ relations for both homogeneous interstellar medium (ISM) and wind density profiles (Wind). Notably, we find that the short GRB 090510 complies with the $Γ_{0}$$-$$E_{\rm iso}$ relation, but significantly deviates from the $Γ_{0}$$-$$L_{\rm iso}$ and $Γ_{0}$$-$$E_{\rm p,z}$ relations. We systematically investigate the influence of $θ_{\rm jet}$ on $Γ_{0}$ and find a weak dependence. Additionally, we report, for the first time, three new three-parameter correlations, i.e., $E_{\rm iso}$ (or $L_{\rm iso}$, $E_{\rm p,z}$)$-$$Γ_{0}$$-$$θ_{\rm jet}$ correlations. In addition, we further explore the relations between the initial Lorentz factor and the jet-corrected energy. 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. |
| title | Comprehensive Statistical Analysis of Initial Lorentz Factor and Jet Opening Angle of Gamma-Ray Bursts |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2508.13448 |