Modeling the Infrared Reverberation Response of the Circumnuclear Dusty
  Torus in AGNs: An Investigation of Torus Response Functions
  The size and structure of the dusty circumnuclear torus in active galactic
nuclei (AGN) can be investigated by analyzing the temporal response of the
torus's infrared (IR) dust emission to variations in the AGN
ultraviolet/optical luminosity. This method, reverberation mapping, is
applicable over a wide redshift range, but the IR response is sensitive to
several poorly constrained variables relating to the dust distribution and its
illumination, complicating the interpretation of measured reverberation lags.
We have used an enhanced version of our torus reverberation mapping code
(TORMAC) to conduct a comprehensive exploration of the torus response functions
at selected wavelengths, for the standard interstellar medium grain
composition. The shapes of the response functions vary widely over the
parameter range covered by our models, with the largest variations occurring at
shorter wavelengths ($\leq 4.5\,\mu$m). The reverberation lag, quantified as
the response-weighted delay (RWD), is most affected by the radial depth of the
torus, the steepness of the radial cloud distribution, the degree of anisotropy
of the AGN radiation field, and the volume filling factor. Nevertheless, we
find that the RWD provides a reasonably robust estimate, to within a factor of
$\sim 3$, of the luminosity-weighted torus radius, confirming the basic
assumption underlying reverberation mapping. However, overall, the models
predict radii at $2.2\,\mu$m that are a typically factor of $\sim 2$ larger
than those derived from K-band reverberation mapping. This is likely an
indication that the innermost region of the torus is populated by clouds
dominated by large graphite grains.
