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Abstract 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 ≲ 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 ϵ Eridani, we separately used 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 produced an activity model that reduced the rms scatter in RVs obtained with EXPRES from 4.72 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 allow the stellar inclination and orientation with respect to the debris disk to be definitively 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. 

Study Analysis Group 21 (SAG21) of NASA’s Exoplanet Exploration Program Analysis Group was organized to study the effect of stellar contamination on space-based transmission spectroscopy, a method for studying exoplanetary atmospheres by measuring the wavelength-dependent radius of a planet as it transits its star. Transmission spectroscopy relies on a precise understanding of the spectrum of the star being occulted. However, stars are not homogeneous, constant light sources but have temporally evolving photospheres and chromospheres with inhomogeneities like spots, faculae, plages, granules, and flares. This SAG brought together an interdisciplinary team of more than 100 scientists, with observers and theorists from the heliophysics, stellar astrophysics, planetary science, and exoplanetary atmosphere research communities, to study the current research needs that can be addressed in this context to make the most of transit studies from current NASA facilities like Hubble Space Telescope and JWST. The analysis produced 14 findings, which fall into three science themes encompassing (i) how the Sun is used as our best laboratory to calibrate our understanding of stellar heterogeneities (‘The Sun as the Stellar Benchmark’), (ii) how stars other than the Sun extend our knowledge of heterogeneities (‘Surface Heterogeneities of Other Stars’), and (iii) how to incorporate information gathered for the Sun and other stars into transit studies (‘Mapping Stellar Knowledge to Transit Studies’). In this invited review, we largely reproduce the final report of SAG21 as a contribution to the peer-reviewed literature.