The Debris Disk of Solar Analogue $\tau$ Ceti: Herschel Observations and Dynamical Simulations of the Proposed Multiplanet System
$\tau$ Ceti is a nearby, mature G-type star very similar to our Sun, with a massive Kuiper Belt analogue (Greaves et al. 2004) and possible multiplanet system (Tuomi et al. 2013) that has been compared to our Solar System. We present Herschel Space Observatory images of the debris disk, finding the disk is resolved at 70 and 160 microns, and marginally resolved at 250 microns. The Herschel images and infrared photometry from the literature are best modelled using a wide dust annulus with an inner edge between 1-10 AU and an outer edge at ~55 AU, inclined from face-on by 35$\pm$10 degrees, and with no significant azimuthal structure. We model the proposed tightly-packed planetary system of five super-Earths and find that the innermost dynamically stable disk orbits are consistent with the inner edge found by the observations. The photometric modelling, however, cannot rule out a disk inner edge as close to the star as 1 AU, though larger distances produce a better fit to the data. Dynamical modelling shows that the 5 planet system is stable with the addition of a Neptune or smaller mass planet on an orbit outside 5 AU, where the Tuomi et al. analysis would not have detected a planet of this mass.