2025/04/16 by Sun, Sheng-Jin, Yi, Shuang-Xi, Zou, Yuan-Chuan +4 · 1 citation
#FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE)
paper · doi:10.48550/arxiv.2504.11743
The initial Lorentz factor (Γ0) plays a crucial role in uncovering the physical characteristics of gamma-ray bursts (GRBs). Previous studies have indicated that the ambient medium density index k for GRBs falls in the range of 0 - 2, rather than exactly equal to 0 (homogeneous interstellar ambient) or 2 (typical stellar wind). In this work, we aim to constrain the Γ0 of GRBs considering their distinct circumburst medium. We select a total of 33 GRBs for our analysis, comprising 7 X-ray GRBs and 26 optical GRBs. Subsequently, by utilizing the deceleration time of fireball t\rm p, we derive the Γ0 for the 33 GRBs assuming the radiation efficiency of η= 0.2. The inferred initial Lorentz factor was found to be from 50 to 500, consistent with previous studies. We then investigate the correlation between the Γ0 and the isotropic energy E\rm γ,iso (as well as the mean isotropic luminosity L\rm γ,iso), finding very tight correlations between them, i.e., Γ0 ∝ E0.24\rm γ,iso,52 (Γ0 ∝ L0.20\rm γ,iso.49) with η=0.2. Additionally, we verify the correlation among Γ0, the isotropic energy E\rm γ,iso (or L\rm γ,iso) and the peak energy E_\rmp,z, i.e., E\rm γ,iso,52 ∝ Γ1.360E0.82_\rmp,z (L\rm γ,iso,49 ∝ Γ1.050E0.66_\rmp,z) under the same radiation efficiency (η=0.2).