  Context: Post-Asymptotic Giant Branch (AGB) binaries are surrounded by stable
dusty and gaseous disks similar to the ones around young stellar objects.
Whereas significant effort is spent on modeling observations of disks around
young stellar objects, the disks around post-AGB binaries receive significantly
less attention, even though they pose significant constraints on theories of
disk physics and binary evolution. Aims: We want to examine the structure of
and phenomena at play in circumbinary disks around post-AGB stars. We continue
the analysis of our near-infrared interferometric image of the inner rim of the
circumbinary disk around IRAS08544-4431. We want to understand the physics
governing this inner disk rim. Methods: We use a radiative transfer model of a
dusty disk to reproduce simultaneously the photometry as well as the
near-infrared interferometric dataset on IRAS08544-4431. The model assumes
hydrostatic equilibrium and takes dust settling self-consistently into account.
Results: The best-fit radiative transfer model shows excellent agreement with
the spectral energy distribution up to mm wavelengths as well as with the
PIONIER visibility data. It requires a rounded inner rim structure, starting at
a radius of 8.25 au. However, the model does not fully reproduce the detected
over-resolved flux nor the azimuthal flux distribution of the inner rim. While
the asymmetric inner disk rim structure is likely to be the consequence of
disk-binary interactions, the origin of the additional over-resolved flux
remains unclear. Conclusions: As in young stellar objects, the disk inner rim
of IRAS08544-4431 is ruled by dust sublimation physics. Additional observations
are needed to understand the origin of the extended flux and the azimuthal
perturbation at the inner rim of the disk.
