Utilizing Photometry from Multiple Sources to Mitigate Stellar Variability in Precise Radial Velocities: A Case Study of Kepler-21

We present a new analysis of Kepler-21, the brightest (V = 8.5) Kepler system with a known transiting exoplanet, Kepler-21 b. Kepler-21 b is a radius valley planet ($R = 1.6\pm 0.2 R_{\oplus}$) with an Earth-like composition (8.38$\pm$1.62 g/cc), though its mass and radius fall in the regime of possible "water worlds." We utilize new Keck/HIRES and WIYN/NEID radial velocity (RV) data in conjunction with Kepler and TESS photometry to perform a detailed study of activity mitigation between photometry and RVs. We additionally refine the system parameters, and we utilize Gaia astrometry to place constraints on a long-term RV trend. Our activity analysis affirms the quality of Kepler photometry for removing correlated noise from RVs, despite its temporal distance, though we reveal some cases where TESS may be superior. Using refined orbital parameters and updated composition curves, we rule out a ``water world" scenario for Kepler-21 b, and we identify a long period super-Jupiter planetary candidate, Kepler-21 (c).