The evolved circumbinary disk of AC Herculis: A radiative transfer, interferometric, and mineralogical study

Context. Many post-asymptotic giant branch (post-AGB) stars in binary systems have an infrared (IR) excess arising from a dusty circumbinary disk. The disk formation, current structure, and further evolution are, however, poorly understood. Aims. We aim to constrain the structure of the circumstellar material around the post-AGB binary and RV Tauri pulsator AC Her. We want to constrain the spatial distribution of the amorphous and of the crystalline dust. Methods. We present very high-quality mid-IR interferometric data that were obtained with the MIDI/VLTI instrument. We analyze the MIDI visibilities and differential phases in combination with the full spectral energy distribution, using the MCMax radiative transfer code, to find a good structure model of AC Her's circumbinary disk. We include a grain size distribution and midplane settling of dust self-consistently in our models. The spatial distribution of crystalline forsterite in the disk is investigated with the mid-IR features, the 69 μm band and the 11.3 μm signatures in the interferometric data. Results. All the data are well fitted by our best model. The inclination and position angle of the disk are precisely determined at i = 50 ± 8° and PA = 305 ± 10°. We firmly establish that the inner disk radius is about an order of magnitude larger than the dust sublimation radius. The best-fit dust grain size distribution shows that significant grain growth has occurred, with a significant amount of mm-sized grains now being settled to the midplane of the disk. A large total dust mass ≤10^-3 M⊙ is needed to fit the mm fluxes. By assuming α_turb = 0:01, a good fit is obtained with a small grain size power law index of 3.25, combined with a small gas/dust ratio ≤10. The resulting gas mass is compatible with recent estimates employing direct gas diagnostics. The spatial distribution of the forsterite is diferent from the amorphous dust, as more warm forsterite is needed in the surface layers of the inner disk. Conclusions. The disk in the ACHer system is in a very evolved state, as shown by its small gas/dust ratio and large inner hole. Mid-IR interferometry ofers unique constraints, complementary to mid-IR features, for studying the mineralogy in disks. A better uv coverage is needed to constrain in detail the distribution of the crystalline forsterite in the disk of ACHer, but we find strong similarities with the protoplanetary disk HD 100546.