The spin-orbit alignment of visual binaries

The angle between the stellar spin-axis and the orbital plane of a stellar or planetary companion has important implications for the formation and evolution of such systems. A study by Hale (1994) found that binaries with separations $a < 30$ au are preferentially aligned while binaries on wider orbits are frequently misaligned. We aim to test the robustness of the Hale (1994) results by reanalysing the sample of visual binaries with measured rotation periods using independently derived stellar parameters and a Bayesian formalism. Our analysis is based on a combination of data from Hale (1994) and newly obtained spectroscopic data from the Hertzsprung SONG telescope, combined with astrometric data from Gaia DR2 and the Washington Double Star Catalog. We combine measurements of stellar radii and rotation periods to obtain stellar rotational velocities $v$. Rotational velocities $v$ are combined with measurements of projected rotational velocities $v\sin i$ to derive posterior probability distributions of stellar inclination angles $i$. We determine line-of-sight projected spin-orbit angles by comparing stellar inclination angles with astrometric orbital inclination angles. We find that the precision of the available data is insufficient to make inferences about the spin-orbit alignment of visual binaries. The data are equally compatible with alignment and misalignment at all orbital separations. We conclude that the previously reported trend that binaries with separations $a < 30$ au are preferentially aligned is spurious. The spin-orbit alignment distribution of visual binaries is unconstrained. Based on simulated observations, we predict that it will be difficult to reach the sufficient precision in $v\sin i$, rotation periods, and orbital inclination required to make robust statistical inferences about the spin-orbit alignment of visual binaries.