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.