Constraining the ejecta for the nonthermal emission from GW170817

We consider a simple model for the nonthermal emission from GW170817, in which a quasi-spherical ejecta is released in the merger event, with the kinetic energy distributed over the momentum as $E(>\gamma\beta)\propto(\gamma\beta)^{-k}$. The ejecta drives a shock into the medium and gives rise to synchrotron radiation. Using multi-band observations we constrain that $k\approx6.7$; (assuming medium density of $\sim10^{-2}\rm cm^{-3}$ and postshock magnetic field carries a fraction $10^{-5}-10^{-3}$ of the postshock internal energy) the total kinetic energy is $(0.3-5)\times10^{51}$erg; the slowest ejecta velocity is $\sim(0.7-0.8)c$; and the fastest ejecta has a Lorentz factor of $\sim4-7$. We conclude that the sub-relativistic dynamical ejecta responsible to the kilonova cannot produce the nonthermal emission. The co-existence of the nonthermal and thermal kilonova emission implies that two corresponding ejecta are ejected at different angles.