2019ApJ...883...22C

All four circumbinary (CB) protoplanetary disks orbiting short-period (P < 20 days) double-lined spectroscopic binaries (SB2s)-a group that includes UZ Tau E, for which we present new Atacama Large Millimeter/Submillimeter Array data-exhibit sky-plane inclinations i_disk that match, to within a few degrees, the sky-plane inclinations i_* of their stellar hosts. Although for these systems the true mutual inclinations θ between disk and binary cannot be directly measured because relative nodal angles are unknown, the near coincidence of i_disk and i_* suggests that θ is small for these most compact of systems. We confirm this hypothesis using a hierarchical Bayesian analysis, showing that 68% of CB disks around short-period SB2s have θ < 3.°0. Near coplanarity of CB disks implies near coplanarity of CB planets discovered by Kepler, which in turn implies that the occurrence rate of close-in CB planets is similar to that around single stars. By contrast, at longer periods ranging from 30 to 10⁵ days (where the nodal degeneracy can be broken via, e.g., binary astrometry), CB disks exhibit a wide range of mutual inclinations, from coplanar to polar. Many of these long-period binaries are eccentric, as their component stars are too far separated to be tidally circularized. We discuss how theories of binary formation and disk-binary gravitational interactions can accommodate all these observations.