Afterglow constraints on the viewing angle of binary neutron star mergers and determination of the Hubble constant

Abstract

One of the key properties of any binary is its viewing angle (i.e., inclination), ${\theta }_{\mathrm{obs}}$. 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, $H_0$. The opening angle of the jet that these mergers launch, ${\theta }_j$, 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 ${\theta }_{\mathrm{obs}}/{\theta }_j$ based on the afterglow light curve and show that this is the only quantity that can be determined from the light curve alone. Namely, it is impossible to determine each of the angles separately without additional information. 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 ${\theta }_{\mathrm{obs}}$ and ${\theta }_j$, the most useful is a VLBI measurement of the afterglow image superluminal motion. An alternative is an identification of the afterglow transition to the sub-relativistic 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 $H_0$ 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 $H_0$ in each one of these events, possibly to a level of 4-5\%. A minority of the mergers with high precision measurements of this kind may dominate in the future the precision in which $H_0$ will be measured using this method.

Accepted for publication in ApJ

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• HERMES: Gamma Ray Burst and Gravitational Wave counterpart hunter
• Impact of weak lensing on bright standard siren analyses
• Predicting Short-duration GRB Rates in the Advanced LIGO Volume
• Investigating the detection rates and inference of gravitational-wave and radio emission from black hole neutron star mergers
• Data-driven approach for modeling the temporal and spectral evolution of kilonova systematic uncertainties
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• Accurate flux calibration of GW170817: is the X-ray counterpart on the rise?
• Weak lensing of bright standard sirens: prospects for ${\sigma }_8$
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• Are Interactions with Neutron Star Merger Winds Shaping the Jets?