A Comprehensive Analysis of Text-Book-Version Afterglow Light curves of Gamma-Ray Bursts and Implication for Universal Radiation Physics of Baryonic Jets

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 (Γ₀), the deceleration radii (Rdec), and the magnetic field strength (B₀) are log-normal, but the distributions of the isotropic kinetic energy (Ek, iso), medium density (n₀), and the magnetization parameter (σB≡εB/εₑ) are tentatively bimodal. A tight Rdec-B₀-σB relation is found. It infers a universal εₑ Ek,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 log θj,c/ rad=-1.51 (standard deviation σ=0.27) and log (Ek, j,c/ erg)=51.78 (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 Lγ, p, iso-Ep,z-Γ₀ 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 log (Mfb,c/Mₛᵤₙ)=-5 (σ=0.75).