Spitzer Space Telescope Measurements of Dust Reverberation Lags in the
  Seyfert 1 Galaxy NGC 6418
  We present results from a fifteen-month campaign of high-cadence (~ 3 days)
mid-infrared Spitzer and optical (B and V ) monitoring of the Seyfert 1 galaxy
NGC 6418, with the objective of determining the characteristic size of the
dusty torus in this active galactic nucleus (AGN). We find that the 3.6 $\mu$m
and 4.5 $\mu$m flux variations lag behind those of the optical continuum by
$37.2^{+2.4}_{-2.2}$ days and $47.1^{+3.1}_{-3.1}$ days, respectively. We
report a cross-correlation time lag between the 4.5 $\mu$m and 3.6 $\mu$m flux
of $13.9^{+0.5}_{-0.1}$ days. The lags indicate that the dust emitting at 3.6
$\mu$m and 4.5 $\mu$m is located at a distance of approximately 1 light-month
(~ 0.03 pc) from the source of the AGN UV-optical continuum. The reverberation
radii are consistent with the inferred lower limit to the sublimation radius
for pure graphite grains at 1800 K, but smaller by a factor of ~ 2 than the
corresponding lower limit for silicate grains; this is similar to what has been
found for near-infrared (K-band) lags in other AGN. The 3.6 and 4.5 $\mu$m
reverberation radii fall above the K-band $\tau \propto L^{0.5}$
size-luminosity relationship by factors $\lesssim 2.7$ and $\lesssim 3.4$,
respectively, while the 4.5 $\mu$m reverberation radius is only 27% larger than
the 3.6 $\mu$m radius. This is broadly consistent with clumpy torus models, in
which individual optically thick clouds emit strongly over a broad wavelength
range.
