Interferometric measurements in the mid-infrared have shown that the sizes of the warm dust distributions in active galactic nuclei are consistent with their scaling with the square root of their luminosity. We carry out a more detailed analysis of t
his size-luminosity relation to investigate which of the general properties of the dusty tori in active galactic nuclei can be derived from this relation. We improve the accuracy of the size-luminosity relation by adding a few additional size measurements from more recent interferometric observations and compare the measured sizes to those derived from hydrodynamical and radiative transfer models of AGN tori. We find that a Gaussian approximation yields a reasonable estimate of the size of the brightness distribution, as long as the visibilities are within 0.2 {leg} V {leg} 0.9. The size estimates derived from the models are consistent with those determined from the measurements. However, the models predict a significant offset between the sizes derived for face-on and edge-on tori. This offset is not observed in the current data, probably because of the large uncertainties and low statistics of the present interferometric measurements. Furthermore, we find a ratio of the mid- to near-infrared sizes of approximately 30, whereas the first probes the body of the torus and the second is an estimate of the inner rim. The size-luminosity relation of AGN tori using Gaussian size estimates is a very simple and effective tool to investigate the internal structure and geometry of AGN tori and obtain constraints on the differences between type 1 and type 2 AGN. However, to fully exploit the possibilities of investigating the nuclear distributions of gas and dust in AGN using this size-luminosity relation, more accurate interferometric measurements of a larger sample of AGN are needed.
We investigate the evolution of dusty gas clouds falling into the centre of an active Seyfert nucleus. Two-dimensional high-resolution radiation hydrodynamics simulations are performed to study the fate of single clouds and the interaction between tw
o clouds approaching the Active Galactic Nucleus. We find three distinct phases of the evolution of the cloud: (i) formation of a lenticular shape with dense inner rim caused by the interaction of gravity and radiation pressure (the lense phase), (ii) formation of a clumpy sickle-shaped structure as the result of a converging flow (the clumpy sickle phase) and (iii) a filamentary phase caused by a rapidly varying optical depth along the sickle. Depending on the column density of the cloud, it will either be pushed outwards or its central (highest column density) parts move inwards, while there is always some material pushed outwards by radiation pressure effects. The general dynamical evolution of the cloud can approximately be described by a simple analytical model.
