On the size-luminosity relation of AGN dust tori in the mid-infrared
  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 this 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.
