Planet–Planet Scattering Explains the Mass–Eccentricity Relation of Warm Jupiters

Abstract Warm Jupiters—giant planets with orbital periods of ∼10–365 days—exhibit a positive correlation between mass and eccentricity. We interpret this trend as the outcome of planet–planet scattering, representing a transition from collision-dominated interactions among low-mass planets to ejection-dominated interactions among high-mass planets. This framework has important implications for the origins of warm Jupiters. It suggests that warm Jupiters originate from compact, multiplanet configurations. The dynamical interactions that shape their present-day architectures likely occur near their current semimajor axes, regardless of whether warm Jupiters formed through convergent disk-driven migration or in situ formation. We argue that several observed properties of warm Jupiter systems, including the eccentricity bimodality, the mass–eccentricity relation, and generally low stellar obliquities, can be explained by this picture. We further predict that not only circular warm Jupiters, but also eccentric warm Jupiters, should frequently have additional planetary companions that are detectable through radial velocity observations. Finally, scattering can produce eccentricities high enough to trigger high-eccentricity tidal migration, potentially explaining the emerging population of proto-hot Jupiters on tidal migration tracks.