Constraining the Inclinations of Binary Mergers from Gravitational-wave Observations

Much of the information we hope to extract from the gravitational-wave signatures of compact binaries is only obtainable when we can accurately constrain the inclination of the orbital plane relative to the line of sight. In this paper, we discuss in detail a degeneracy between the measurement of the binary distance and inclination that limits our ability to accurately measure the inclination using gravitational waves alone. This degeneracy is exacerbated by the expected distribution of events in the universe, which leads us to prefer face-on systems at a greater distance. We use a simplified model that only considers the binary distance and orientation and show that this gives comparable results to the full parameter estimates obtained from the binary neutron star merger GW170817. For the advanced LIGO-Virgo network, it is only binaries that are close to edge-on, i.e., with inclinations iota greater than or similar to 75 degrees, that will be distinguishable from face-on systems. Extended networks that have good sensitivity to both gravitational wave polarizations will only be able to constrain the inclination of a face-on binary at a signal-to-noise ratio of 20 to iota less than or similar to 45 degrees. Even for loud signals with signal-to-noise ratios of 100, face-on signals will only be constrained to have inclinations iota less than or similar to 30 degrees . In the absence of observable higher modes or orbital precession, this degeneracy will dominate the mass measurements of binary black hole mergers at cosmological distances.