Too fast to be single: Tidal evolution and photometric identification of stellar and planetary companions

Many stars, including those in binary or multiple systems, exhibit modified rotational evolution due to tidal interactions. While magnetic braking slows rotation in single stars, close binaries experience synchronization from tidal forces, resulting in high spin rates. Thus, fast rotators often signify synchronized binaries or planetary systems. We analyze stellar rotation in the Kepler field to photometrically identify non-single systems. Establishing an initial rotation-temperature relationship for individual stars via young clusters, we confirm our findings through magnitude excess and prior binary star system studies. Stars rotating faster than this relationship display a bimodal distribution in peculiar velocity, indicative of non-single or young stars. Leveraging this, we separate non-single stars when peculiar velocity is measurable, or estimate likelihood for those without. Our method identifies 2229 potential non-single star systems with rotation periods exceeding 3 days. For ultra-fast rotators ($P_{rot} < 3 days$), we compile a catalog of 1518 ultra-short-period binary candidates, often part of hierarchical triples, reinforcing rapid spin's association with multiplicity. Applying our method to planet-host stars uncovers Kepler-1184 as a potential circumbinary system and identifies Kepler-493 and Kepler-957 potentially synchronized by close-in planets, with three others as potential false positives. Analysis of known non-single stars reveals clear tidal effects: period synchronization, orbit circularization, and a minimal pericenter constraint for binaries ($r_p \propto (P_{orb}/P_{rot})^{0.77}$). These findings offer insights into tidal evolution, provide a robust method for identifying stellar multiplicity, and have implications for stellar evolution, binary formation, and exoplanet dynamics.