Three-dimensional Orbit of AC Her Determined: Binary-induced Truncation Cannot Explain the Large Cavity in This Post-AGB Transition Disk

Some evolved binaries, namely post-asymptotic giant branch (AGB) binaries, are surrounded by stable and massive circumbinary disks similar to protoplanetary disks found around young stars. Around 10% of these disks are transition disks: they have a large inner cavity in the dust. Previous interferometric measurements and modeling have ruled out these cavities being formed by dust sublimation and suggested that they are due to massive circumbinary planets that trap dust in the disk and produce the observed depletion of refractory elements on the surfaces of the post-AGB stars. In this study, we test an alternative scenario in which the large cavities could be due to dynamical truncation from the inner binary. We performed near-infrared interferometric observations with the CHARA Array on the archetype of such a transition disk around a post-AGB binary: AC Her. We detect the companion at ten epochs over 4 yr and determine the three-dimensional orbit using these astrometric measurements in combination with a radial velocity time series. This is the first astrometric orbit constructed for a post-AGB binary system. We derive the best-fit orbit with a semimajor axis of 2.01 ± 0.01 mas (2.83 ± 0.08 au), inclination (142.9 ± 1.1)°, and longitude of the ascending node (155.1 ± 1.8)°. We find that the theoretical dynamical truncation and dust sublimation radii are at least ~3× smaller than the observed inner disk radius (~21.5 mas or 30 au). This strengthens the hypothesis that the origin of the cavity is due to the presence of a circumbinary planet.