GRB 221009A Afterglow from a Shallow Angular Structured Jet

Abstract

Exceptionally bright gamma-ray burst (GRB) afterglows can reveal the angular structure of their jets. GRB jets appear to have a narrow core (of half-opening angle $\theta_c$), beyond which their kinetic energy drops as a power-law with angle $\theta$ from the jet's symmetry axis, $E_{k,\rm iso}(\theta)\propto[1+(\theta/\theta_c)^2]^{-a/2}$. The power-law index $a$ reflects the amount of mixing between the shocked jet and confining medium, which depends on the jet's initial magnetization. Weakly magnetized jets undergo significant mixing, leading to shallow ($a\lesssim2$) angular profiles. We use the exquisite multi-waveband afterglow observations of GRB 221009A to constrain the jet angular structure using a dynamical model that accounts for both the forward and reverse shocks, for a power-law external density profile, $n_{\rm{}ext}\propto{}R^{-k}$. Both the forward-shock emission, that dominates the optical and X-ray flux, and the reverse-shock emission, that produces the radio afterglow, require a jet with a narrow core ($\theta_c\approx0.021$) and a shallow angular structure ($a\approx0.8$) expanding into a stellar wind ($k\approx2$). Moreover, these data appear to favor a small fraction ($\xi_e\approx10^{-2}$) of shock-heated electrons forming a power-law energy distribution in both shocks.