On the Optical-to-Silicate Extinction Ratio as a Probe of the Dust Size
  in Active Galactic Nuclei
  Dust plays a central role in the unification theory of active galactic nuclei
(AGNs). Whether the dust that forms the torus around an AGN is
tenth-$\mu$m-sized like interstellar grains or much larger has a profound
impact on correcting for the obscuration of the dust torus to recover the
intrinsic spectrum and luminosity of the AGN. Here we show that the ratio of
the optical extinction in the visual band ($A_V$) to the optical depth of the
9.7 $\mu$m silicate absorption feature ($\Delta\tau_{9.7}$) could potentially
be an effective probe of the dust size. The anomalously lower ratio of
$A_V/\Delta\tau_{9.7} \approx 5.5$ of AGNs compared to that of the Galactic
diffuse interstellar medium of $A_V/\Delta\tau_{9.7} \approx 18$ reveals that
the dust in AGN torus could be substantially larger than the interstellar
grains of the Milky Way and of the Small Magellanic Cloud, and therefore, one
might expect a flat extinction curve for AGNs.
