A Comprehensive Analysis of Text-Book-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 (${\Gamma }_0$), the deceleration radii ($R_{\mathrm{dec}}$), and the magnetic field strength ($B_0$) are log-normal, but the distributions of the isotropic kinetic energy ($E_{\mathrm{k},\mathrm{iso}}$), medium density ($n_0$), and the magnetization parameter (${\sigma }_B\equiv {\epsilon }_B/{\epsilon }_e$) are tentatively bimodal. A tight $R_{\rm dec}\mbox{-}B_{0}\mbox{-}σ_{B}$ relation is found. It infers a universal ${\epsilon }_e{E}_{\mathrm{k},\mathrm{iso}}$ 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 $\log {\theta }_{\mathrm{j},\mathrm{c}}/\mathrm{rad}=-1.51$ (standard deviation $\sigma =0.27$) and $\log (E_{\mathrm{k},\mathrm{j},\mathrm{c}}/\mathrm{erg})=51.78$ ($\sigma =0.54$), respectively. Those GRBs ($19$ GRBs), whose prompt gamma-ray emission is well estimated with broad energy-band observations, satisfy the previously discovered $L_{\gamma ,\mathrm{p},\mathrm{iso}}-E_{\mathrm{p},\mathrm{z}}-{\Gamma }_0$ 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 $\log (M_{\mathrm{fb},\mathrm{c}}/M_{\mathrm{sun}})=-5$ ($\sigma =0.75$).

12 pages, 4 tables, 9 figures. Publication in the Astrophysics Journal (in press)