  We find, using high resolution numerical relativistic simulations, that the
tail of the dynamical ejecta of neutron star mergers extends to mildly
relativistic velocities faster than $0.7c$. The kinetic energy of this fast
tail is $\sim 10^{47}$--$10^{49}$ erg, depending on the neutron star equation
of state and on the binary masses. The synchrotron flare arising from the
interaction of this fast tail with the surrounding ISM can power the observed
non-thermal emission that followed GW170817, provided that the ISM density is
$\sim 10^{-2}\,{\rm cm^{-3}}$, the two neutron stars had roughly equal masses
and the neutron star equation of state is soft (small neutron star radii). One
of the generic predictions of this scenario is that the cooling frequency
crosses the X-ray band on a time scale of a few months to a year, leading to a
cooling break in the X-ray light curve. If this dynamical ejecta scenario is
correct, we expect that the synchrotron radio flare from the ejecta that have
produced the macronova/kilonova emission will be observable on time scales of
$10^3$ to $10^5$ days. Further multi-frequency observations will confirm or
rule out this dynamical ejecta scenario.
