Hiding Dust Around $\epsilon$ Eridani
With a Jupiter-like exoplanet and a debris disk with both asteroid and Kuiper belt analogs, $\epsilon$ Eridani has a fascinating resemblance to our expectations for a young Solar System. We present a deep HST/STIS coronographic dataset using eight orbit visits and the PSF calibrator $\delta$ Eridani. While we were unable to detect the debris disk, we place stringent constraints on the scattered light surface brightness of $\sim 4 \, \mu Jy/arcsec^{2}$. We combine this scattered light detection limit with a reanalysis of archival near and mid-infrared observations and a dynamical model of the full planetary system to refine our model of the $\epsilon$ Eridani debris disk components. Radiative transfer modeling suggests an asteroid belt analog inside of 3 au, an intermediate disk component in the 6 - 37 au region and a Kuiper belt analog co-located with the narrow belt observed in the millimeter (69 au). Modeling also suggests a large minimum grain size requiring either very porous grains or a suppression of small grain production, and a radially stratified particle size distribution. The inner disk regions require a steep power law slope ($s^{-3.8}$ where $s$ is the grain size) weighted towards smaller grains and the outer disk prefers a shallower slope ($s^{-3.4}$) with a minimum particle size of $> 2 \, \mu m$. These conclusions will be enhanced by upcoming coronographic observations of the system with the James Webb Space Telescope, which will pinpoint the radial location of the dust belts and further diagnose the dust particle properties.