EXPRES. III. Revealing the Stellar Activity Radial Velocity Signature of $\epsilon$ Eridani with Photometry and Interferometry

The distortions of absorption line profiles caused by photospheric brightness variations on the surfaces of cool, main-sequence stars can mimic or overwhelm radial velocity (RV) shifts due to the presence of exoplanets. The latest generation of precision RV spectrographs aims to detect velocity amplitudes $\lesssim 10$ cm s$^{-1}$, but requires mitigation of stellar signals. Statistical techniques are being developed to differentiate between Keplerian and activity-related velocity perturbations. Two important challenges, however, are the interpretability of the stellar activity component as RV models become more sophisticated, and ensuring the lowest-amplitude Keplerian signatures are not inadvertently accounted for in flexible models of stellar activity. For the K2V exoplanet host $\epsilon$ Eridani, we separately use ground-based photometry to constrain Gaussian processes for modeling RVs and TESS photometry with a light-curve inversion algorithm to reconstruct the stellar surface. From the reconstructions of TESS photometry, we produce an activity model, which reduces the rms scatter in RVs obtained with EXPRES from 4.72 m s$^{-1}$ to 1.98 m s$^{-1}$. We present a pilot study using the CHARA Array and MIRC-X beam combiner to directly image the starspots seen in the TESS photometry. With the limited phase coverage, our spot detections are marginal with current data but a future dedicated observing campaign should allow for imaging, as well as the stellar inclination and orientation with respect to its debris disk to be definitely determined. This work shows that stellar surface maps obtained with high cadence, time-series photometric and interferometric data can provide the constraints needed to accurately reduce RV scatter.