A Comprehensive Analysis of Textbook-version Afterglow Light Curves of Gamma-Ray Bursts and Implication for Universal Radiation Physics of Baryonic Jets

Abstract The standard external shock model in the thin-shell scenario predicts an onset bump in the early optical afterglow light curves of gamma-ray bursts (GRBs). We collect such a textbook-version light-curve sample of 30 GRBs and derive the jet properties from our joint fit to their X-ray and optical afterglow light curves. It is found that the distributions of the isotropic initial Lorentz factors (Γ 0 ), the deceleration radii ( R dec ), and the magnetic field strength ( B 0 ) are log-normal, but the distributions of the isotropic kinetic energy ( E k,iso ), medium density ( n 0 ), and magnetization parameter ( σ B ≡ ϵ B / ϵ e ) are tentatively bimodal. A tight R dec – B 0 – σ B relation is found. It infers a universal ϵ e E k,iso among bursts, plausibly supporting the previous argument of a universal GRB radiation energy among GRBs. A jet break is required for modeling the light curves of 26 GRBs. The distributions of the jet opening angles and the jet-corrected kinetic energies log-normally center at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:msub> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">j</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>rad</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.51</mml:mn> </mml:math> (standard deviation σ = 0.27) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">k</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">j</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>erg</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>51.78</mml:mn> </mml:math> ( σ = 0.54), respectively. Those GRBs (19 GRBs), whose prompt gamma-ray emission is well estimated with broad energy-band observations, satisfy the previously discovered L γ ,p,iso – E p,z –Γ 0 relation, and their gamma-ray radiation efficiencies log-normally distribute in the range from 0.04% to 10% with a central value of 0.42%. Such a low efficiency favors the baryonic fireball model, and the distribution of their baryon mass loading in the GRB ejecta log-normally centers at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>fb</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>☉</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:math> ( σ = 0.75).