Limits on the Optical Brightness of the Epsilon Eridani Dust Ring

The STIS/CCD camera on the {\em Hubble Space Telescope (HST)} was used to take deep optical images near the K2V main-sequence star $\epsilon$ Eridani in an attempt to find an optical counterpart of the dust ring previously imaged by sub-mm observations. Upper limits for the optical brightness of the dust ring are determined and discussed in the context of the scattered starlight expected from plausible dust models. We find that, even if the dust is smoothly distributed in symmetrical rings, the optical surface brightness of the dust, as measured with the {\em HST}/STIS CCD clear aperture at 55 AU from the star, cannot be brighter than about 25 STMAG/"$^2$. This upper limit excludes some solid grain models for the dust ring that can fit the IR and sub-mm data. Magnitudes and positions for $\approx$59 discrete objects between 12.5" to 58" from $\epsilon$ Eri are reported. Most if not all of these objects are likely to be background stars and galaxies.