What does a typical full disc around a post-AGB binary look like?

Context. Stable circumbinary discs around evolved post-asymptotic giant branch (post-AGB) binary systems composed of gas and dust show many similarities with protoplanetary discs around young stellar objects. These discs can provide constraints on both binary evolution and the formation of macrostructures within circumstellar discs. Here we focus on one post-AGB binary system: IRAS 08544-4431. Aims. We aim to refine the physical model of IRAS 08544-4431 with a radiative transfer treatment and continue the near-infrared and mid-infrared interferometric analysis covering the H, K, L, and N bands. Results from geometric modelling of these data in our previous study constrain the shape of the inner rim of the disc and its radial dust structure. We aim to capture the previously detected amount of over-resolved flux and the radial intensity profile at and beyond the inner dust disc rim to put constraints on the physical processes in the inner disc regions. Methods. We used a three-dimensional Monte Carlo radiative transfer code to investigate the physical structure of the disc by reproducing both the photometry and the multi-wavelength infrared interferometric dataset. We first performed a parametric study to explore the effect of the individual parameters and selected the most important parameters, which were then used in a thorough grid search to fit the structural characteristics. We developed a strategy to identify the models that were best able to reproduce our extensive multi-wavelength dataset. Results. We find a family of models that successfully fit the infrared photometric and interferometric data in all bands. These models show a flaring geometry with efficient settling. Larger grains are present in the inner disc as probed by our infrared interferometric observations. Some over-resolved flux component was recovered in all bands, but the optimised models still fall short in explaining all the over-resolved flux. This suggests that another dusty structure within the system that is not included in our models plays a role. The structure of this over-resolved component is unclear, but it has a colour temperature between 1400 and 3600 K. Conclusions. Multi-wavelength infrared interferometric observations of circumstellar discs allow the inner disc regions to be studied in unprecedented detail. The refined physical models can reproduce most of the investigated features, including the photometric characteristics, the radial extent, and the overall shape of the visibility curves. Our multi-wavelength interferometric observations combined with photometry show that the disc around IRAS 08544-4431 is similar to protoplanetary discs around young stars with similar dust masses and efficient dust growth. The resulting disc geometry is capable of reproducing part of the over-resolved flux, but to fully reproduce the over-resolved flux component, an additional component is needed. Multi-scale high-angular-resolution analysis combining VLTI, VLT/SPHERE, and ALMA data is needed to fully define the structure of the system