We report deep Chandra, HST and VLA observations of the binary neutron star event GW170817 at $t<160$ d after merger. These observations show that GW170817 has been steadily brightening with time and might have now reached its peak, and constrain the emission process as non-thermal synchrotron emission where the cooling frequency $ u_c$ is above the X-ray band and the synchrotron frequency $ u_m$ is below the radio band. The very simple power-law spectrum extending for eight orders of magnitude in frequency enables the most precise measurement of the index $p$ of the distribution of non-thermal relativistic electrons $N(gamma)propto gamma^{-p}$ accelerated by a shock launched by a NS-NS merger to date. We find $p=2.17pm0.01$, which indicates that radiation from ejecta with $Gammasim3-10$ dominates the observed emission. While constraining the nature of the emission process, these observations do emph{not} constrain the nature of the relativistic ejecta. We employ simulations of explosive outflows launched in NS ejecta clouds to show that the spectral and temporal evolution of the non-thermal emission from GW170817 is consistent with both emission from radially stratified quasi-spherical ejecta traveling at mildly relativistic speeds, emph{and} emission from off-axis collimated ejecta characterized by a narrow cone of ultra-relativistic material with slower wings extending to larger angles. In the latter scenario, GW170817 harbored a normal SGRB directed away from our line of sight. Observations at $tle 200$ days are unlikely to settle the debate as in both scenarios the observed emission is effectively dominated by radiation from mildly relativistic material.
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