3D modelling of clumpy PDRs - Understanding the Orion Bar stratification

Aims. We aim to construct a self-consistent numerical PDR model to simulate full spectral cubes of line emission from arbitrary PDRs in three dimensions (3D). The model is to reproduce the intensity of the main cooling lines from the Orion Bar PDR and the observed layering structure of the different transitions. Methods. Using a fractal description of the ISM combined with the KOSMA-{\tau} PDR model, we build up a 3D compound, made of voxels ("3D pixels"), resembling the internal structure of a PDR. Each voxel contains "clumps" mimicking the fractal ISM. The local FUV field strength is calculated self-consistently for each voxel. Line emissivities and opacities of individual clumps, provided by the KOSMA-{\tau} PDR model, are used to calculate voxel-averaged emissivities and opacities that are finally used to simulate full spectral cubes computing the radiative transport through the compound. To test the new model we try to simulate the structure of the Orion Bar PDR and compare the results to observations from HIFI/Herschel and from the Caltech Submillimetre Observatory (CSO). Results. Our model is able to qualitatively reproduce the line intensities and the observed stratification of the emission structure in the various tracers based on the representation of the Orion Bar PDR by a clumpy edge-on cavity wall. In contrast, the model of a convex filament can be ruled out. In the cavity wall, a large fraction of the total mass needs to be contained in clumps. The mass of the interclump medium is constrained by the FUV penetration. Furthermore, the stratification profile cannot be reproduced by a model having the same amount of clump and interclump mass in each voxel, but dense clumps have to be removed from the PDR surface to reproduce the observed intensities and spatial structure.