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Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zonearound Sun-like stars are limited by the effects of stellar variability on thehost star. In particular, suppression of convective blueshift and brightnessinhomogeneities due to photospheric faculae/plage and starspots are thedominant contribution to the variability of such stellar RVs. Gaussian process(GP) regression is a powerful tool for statistically modeling thesequasi-periodic variations. We investigate the limits of this technique using800 days of RVs from the solar telescope on the High Accuracy Radial velocityPlanet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These dataprovide a well-sampled time series of stellar RV variations. Into this dataset, we inject Keplerian signals with periods between 100 and 500 days andamplitudes between 0.6 and 2.4 m s$^{-1}$. We use GP regression to fit theresulting RVs and determine the statistical significance of recovered periodsand amplitudes. We then generate synthetic RVs with the same covarianceproperties as the solar data to determine a lower bound on the observationalbaseline necessary to detect low-mass planets in Venus-like orbits around aSun-like star. Our simulations show that discovering planets with a larger mass($\sim$ 0.5 m s$^{-1}$) using current-generation spectrographs and GPregression will require more than 12 yr of densely sampled RV observations.Furthermore, even with a perfect model of stellar variability, discovering atrue exo-Venus ($\sim$ 0.1 m s$^{-1}$) with current instruments would take over15 yr. Therefore, next-generation spectrographs and better models of stellarvariability are required for detection of such planets.

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar RVs