Study of the sub-AU disk of the Herbig B[e] star HD 85567 with near-infrared interferometry

Context: The structure of the inner disk of Herbig Be stars is not well understood. The continuum disks of several Herbig Be stars have inner radii that are smaller than predicted by models of irradiated disks with optically thin holes. Aims: We study the size of the inner disk of the Herbig B[e] star HD 85567 and compare the model radii with the radius suggested by the size-luminosity relation. Methods: The object was observed with the AMBER instrument of the Very Large Telescope Interferometer. We obtained K-band visibilities and closure phases. These measurements are interpreted with geometric models and temperature-gradient models. Results: Using several types of geometric star-disk and star-disk-halo models, we derived inner ring-fit radii in the K band that are in the range of 0.8 - 1.6 AU. Additional temperature-gradient modeling resulted in an extended disk with an inner radius of $0.67^{+0.51}_{-0.21}$ AU, a high inner temperature of $2200^{+750}_{-350}$ K, and a disk inclination of $53^{+15}_{-11}$$^\circ$. Conclusions: The derived geometric ring-fit radii are approximately 3 - 5 times smaller than that predicted by the size-luminosity relation. The small geometric and temperature-gradient radii suggest optically thick gaseous material that absorbs stellar radiation inside the dust disk.