Measuring the viewing angle of GW170817 with electromagnetic and gravitational waves

The joint detection of gravitational waves (GWs) and electromagnetic (EM) radiation from the binary neutron star merger GW170817 ushered in a new era of multi-messenger astronomy. Joint GW-EM observations can be used to measure the parameters of the binary with better precision than either observation alone. Here, we use joint GW-EM observations to measure the viewing angle of GW170817, the angle between the binary's angular momentum and the line of sight. We combine a direct measurement of the distance to the host galaxy of GW170817 (NGC 4993) of $40.7\pm 2.36$ Mpc with the Laser Interferometer Gravitational-wave Observatory (LIGO)/Virgo GW data and find that the viewing angle is $32^{+10}_{-13}\,\pm 1.7$ degrees (90% confidence, statistical, and systematic errors). We place a conservative lower limit on the viewing angle of $\ge 13^\circ$, which is robust to the choice of prior. This measurement provides a constraint on models of the prompt $\gamma$-ray and radio/X-ray afterglow emission associated with the merger; for example, it is consistent with the off-axis viewing angle inferred for a structured jet model. We provide for the first time the full posterior samples from Bayesian parameter estimation of LIGO/Virgo data to enable further analysis by the community.