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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 log θ j , c / rad = − 1.51 (standard deviation σ = 0.27) and log ( E k , 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 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 log ( M fb , c / M ☉ ) = − 5 ( σ = 0.75).
Zhang et al. (Sun,) studied this question.