The Degree of Alignment between Circumbinary Disks and Their Binary Hosts

All 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 theta between disk and binary cannot be directly measured because relative nodal angles are unknown, the near coincidence of i(disk) and i(*) suggests that theta 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 theta < 3 degrees .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 10(5) 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.