Afterglow Constraints on the Viewing Angle of Binary Neutron Star Mergers and Determination of the Hubble Constant

One of the key properties of any binary is its viewing angle (i.e., inclination), θ_obs. In binary neutron star (BNS) mergers it is of special importance due to the role that it plays in the measurement of the Hubble constant, H₀. The opening angle of the jet that these mergers launch, θ_j, is also of special interest. Following the detection of the first BNS merger, GW170817, there were numerous attempts to estimate these angles using the afterglow light curve, finding a wide range of values. Here we provide a simple formula for the ratio θ_obs/θ_j based on the afterglow light curve and show that this is the only quantity that can be determined from the light curve alone. Our result explains the inconsistency of the values found by the various studies of GW170817 that were largely driven by the different priors taken in each study. Among the additional information that can be used to estimate θ_obs and θ_j, the most useful is a VLBI measurement of the afterglow image superluminal motion. An alternative is an identification of the afterglow transition to the subrelativistic phase. These observations are possible only for mergers observed at small viewing angles, whose afterglow is significantly brighter than the detector's threshold. We discuss the implications of these results to measurements of H₀ using GW observations. We show that while the viewing angle will be measured only in a small fraction of future BNS mergers, it can significantly reduce the uncertainty in H₀ in each one of these events, possibly to a level of 4%-5%.