The emission and distribution of dust of the torus of NGC 1068

We present observations of NGC 1068 covering the $19.7-53.0$ $\mu$m wavelength range using FORCAST and HAWC+ onboard SOFIA. Using these observations, high-angular resolution infrared (IR) and sub-mm observations, we find an observational turn-over of the torus emission in the $30-40$ $\mu$m wavelength range with a characteristic temperature of $70-100$ K. This component is clearly different from the diffuse extended emission in the narrow line and star formation regions at 10-100 $\mu$m within the central 700 pc. We compute $2.2-432$ $\mu$m 2D images using the best inferred \textsc{clumpy} torus model based on several nuclear spectral energy distribution (SED) coverages. We find that when $1-20$ $\mu$m SED is used, the inferred result gives a small torus size ($<4$ pc radius) and a steep radial dust distribution. The computed torus using the $1-432$ $\mu$m SED provides comparable torus sizes, $5.1^{+0.4}_{-0.4}$ pc radius, and morphology to the recently resolved 432 $\mu$m ALMA observations. This result indicates that the $1-20$ $\mu$m wavelength range is not able to probe the full extent of the torus. The characterization of the turn-over emission of the torus using the $30-60$ $\mu$m wavelength range is sensitive to the detection of cold dust in the torus. The morphology of the dust emission in our 2D image at 432 $\mu$m is spatially coincident with the cloud distribution, while the morphology of the emission in the $1-20$ $\mu$m wavelength range shows an elongated morphology perpendicular to the cloud distribution. We find that our 2D \textsc{clumpy} torus image at 12 $\mu$m can produce comparable results to those observed using IR interferometry.