SIMBAD references

Interferometric measurements in the mid-infrared have shown that the sizes of the warm dust distributions in active galactic nuclei (AGN) are consistent with their scaling with the square root of their luminosity. We carry out a more detailed analysis of this size-luminosity relation to investigate which of the general properties of the dusty tori in AGN can be derived from this relation. We are especially interested in the cases, where only a very small number of interferometric measurements are available and the sizes are directly calculated from the measured visibilities assuming a Gaussian brightness distribution. 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≤V≤0.9. The uncertainty in the size estimate depends on the true brightness distribution and is up to a factor of four for the models used in our investigation. 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 (Seyfert 1 case) and edge-on (Seyfert 2 case) tori: the face-on tori should appear significantly more compact for the same luminosity. 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.