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 $k\approx 6.7$; (assuming medium density of $\sim10^{-2}\rm cm^{-3}$andpostshockmagneticfieldcarriesafraction$10^{-5}-10^{-3}$ of the postshock internal energy) the total kinetic energy is $(0.3-5)\times {10}^{51}$erg; the slowest ejecta velocity is $\sim (0.7-0.8)c$; and the fastest ejecta has a Lorentz factor of $\sim 4-7$. 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.