Direct Imaging for the Debris Disk around $\epsilon$ Eridani with the Cool-Planet Imaging Coronagraph

We analyze the inner debris disk around $\epsilon$ Eridani using simulated observations with the Cool-Planet Imaging Coronagraph (CPI-C). Using the radiative transfer code MCFOST, we generate synthetic scattered-light images and spectral energy distributions for three disk models that differ in inclination and radial extent, and compare these results with the anticipated performance of CPI-C. CPI-C can resolve disk structures down to $\sim$3 au, offering substantially finer spatial resolution than existing HST/STIS and Spitzer/IRS observations. Recovered inclinations and radial extents closely match the input models, constraining the disk geometry and informing potential planet-disk interactions in the $\epsilon$ Eri system. Although the cold Jupiter-like planet $\epsilon$ Eri b is not detected in our simulations, polarimetric methods may enable detection of its reflected light. These results highlight the capability of next-generation coronagraphs to probe cold dust in nearby planetary systems.