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.
