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Abstract Kepler-51 is a ≲1 Gyr old Sun-like star hosting three transiting planets with radii ≈6–9R_⊕and orbital periods ≈45–130 days. Transit timing variations (TTVs) measured with past Kepler and Hubble Space Telescope (HST) observations have been successfully modeled by considering gravitational interactions between the three transiting planets, yielding low masses and low mean densities (≲0.1 g cm⁻³) for all three planets. However, the transit time of the outermost transiting planet Kepler-51d recently measured by the James Webb Space Telescope 10 yr after the Kepler observations is significantly discrepant from the prediction made by the three-planet TTV model, which we confirmed with ground-based and follow-up HST observations. We show that the departure from the three-planet model is explained by including a fourth outer planet, Kepler-51e, in the TTV model. A wide range of masses (≲M_Jup) and orbital periods (≲10 yr) are possible for Kepler-51e. Nevertheless, all the coplanar solutions found from our brute-force search imply masses ≲10M_⊕for the inner transiting planets. Thus, their densities remain low, though with larger uncertainties than previously estimated. Unlike other possible solutions, the one in which Kepler-51e is around the 2:1 mean motion resonance with Kepler-51d implies low orbital eccentricities (≲0.05) and comparable masses (∼5M_⊕) for all four planets, as is seen in other compact multiplanet systems. This work demonstrates the importance of long-term follow-up of TTV systems for probing longer-period planets in a system. 

Abstract The Kepler and TESS missions have demonstrated that planets are ubiquitous. However, the success of these missions heavily depends on ground-based radial velocity (RV) surveys, which combined with transit photometry can yield bulk densities and orbital properties. While most Kepler host stars are too faint for detailed follow-up observations, TESS is detecting planets orbiting nearby bright stars that are more amenable to RV characterization. Here, we introduce the TESS-Keck Survey (TKS), an RV program using ∼100 nights on Keck/HIRES to study exoplanets identified by TESS. The primary survey aims are investigating the link between stellar properties and the compositions of small planets; studying how the diversity of system architectures depends on dynamical configurations or planet multiplicity; identifying prime candidates for atmospheric studies with JWST; and understanding the role of stellar evolution in shaping planetary systems. We present a fully automated target selection algorithm, which yielded 103 planets in 86 systems for the final TKS sample. Most TKS hosts are inactive, solar-like, main-sequence stars (4500 K ≤ T eff <6000 K) at a wide range of metallicities. The selected TKS sample contains 71 small planets ( R p ≤ 4 R ⊕ ), 11 systems with multiple transiting candidates, six sub-day-period planets and three planets that are in or near the habitable zone ( S inc ≤ 10 S ⊕ ) of their host star. The target selection described here will facilitate the comparison of measured planet masses, densities, and eccentricities to predictions from planet population models. Our target selection software is publicly available and can be adapted for any survey that requires a balance of multiple science interests within a given telescope allocation.