The afterglow emission from a stratified jet in GRB 170817A

The afterglow of GRB 170817A has been detected for more than three years, but the origin multi-band light curves remains under debate. A classical top-hat jet model is faced with difficulties in producing a shallow rise as observed $(F_{\nu} \propto T^{0.8})$. Here we reconsider stratified ejecta energy profile $E(>\Gamma \beta)=E_0(\Gamma \beta)^{-k}$ burst, where $\Gamma$ and $\beta$ are Lorentz factor speed ejecta, respectively. $k$ power-law slope profile. We consider collimated into jets. Two kinds evolutions investigated, including lateral-spreading non-lateral-spreading jet. fit curves, X-ray data at one thousand days post-burst, find that both models spreading non-spreading jets can well, angular size source apparent velocity flux centroid beyond observation limits, while meets limits. Some best-fit parameters model, such number density circumburst medium $\sim10^{-2}$ cm$^{-3}$ total kinetic $E \sim 4.8\times 10^{51}$ erg, also appear plausible. $k 7.1$. Our results suggest may arise from lateral not significant.