2024ApJ...972..170Z

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 (R_dec), and the magnetic field strength (B₀) are log-normal, but the distributions of the isotropic kinetic energy (E_k,iso), medium density (n₀), and magnetization parameter (σ_B ≡ ϵ_B/ϵ_e) are tentatively bimodal. A tight R_dec-B₀-σ_B relation is found. It infers a universal ϵ_eE_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 $\mathrm{log}{\theta }_{{\rm{j}},{\rm{c}}}/\mathrm{rad}=-1.51$ (standard deviation σ = 0.27) and $\mathrm{log}({E}_{{\rm{k}},{\rm{j}},{\rm{c}}}/\mathrm{erg})=51.78$ (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 L_γ,p,iso-E_p,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 $\mathrm{log}({M}_{\mathrm{fb},{\rm{c}}}/{M}_{\odot })=-5$ (σ = 0.75).