Using photometry of NGC 1097 from the Herschel PACS (Photodetector Array Camera and Spectrometer) instrument, we study the resolved properties of thermal dust continuum emission from a circumnuclear starburst ring with a radius ~ 900 pc. These observations are the first to resolve the structure of a circumnuclear ring at wavelengths that probe the peak (i.e. lambda ~ 100 micron) of the dust spectral energy distribution. The ring dominates the far-infrared (far-IR) emission from the galaxy - the high angular resolution of PACS allows us to isolate the rings contribution and we find it is responsible for 75, 60 and 55% of the total flux of NGC 1097 at 70, 100 and 160 micron, respectively. We compare the far-IR structure of the ring to what is seen at other wavelengths and identify a sequence of far-IR bright knots that correspond to those seen in radio and mid-IR images. The mid- and far-IR band ratios in the ring vary by less than +/- 20% azimuthally, indicating modest variation in the radiation field heating the dust on ~ 600 pc scales. We explore various explanations for the azimuthal uniformity in the far-IR colors of the ring including a lack of well-defined age gradients in the young stellar cluster population, a dominant contribution to the far-IR emission from dust heated by older (> 10 Myr) stars and/or a quick smoothing of local enhancements in dust temperature due to the short orbital period of the ring. Finally, we improve previous limits on the far-IR flux from the inner ~ 600 pc of NGC 1097 by an order of magnitude, providing a better estimate of the total bolometric emission arising from the active galactic nucleus and its associated central starburst.
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