Orbital Eccentricities Suggest a Gradual Transition from Giant Planets to Brown Dwarfs

To date, hundreds of sub-stellar objects with masses between $1-80\ M_{\rm Jup}$ have been detected orbiting main-sequence stars. The current convention uses the deuterium-burning limit, $M_c \approx 13 M_{\rm Jup}$ to divide this population between giant planets and brown dwarfs. However, this classification heuristic is largely divorced from any formation physics and may not accurately reflect the astrophysical nature of these objects. Previous work has suggested that a transition from ``planet-like'' to ``brown-dwarf-like'' characteristics occurs somewhere in the range $1-10 M_{\rm Jup}$, but precise the crossover mass and whether the transition is gradual or abrupt remains unknown. Here, we explore how the occurrence rate, host star metallicity, and orbital eccentricities vary as a function of mass in a sample of 70 Doppler-detected sub-stellar objects ($0.8 < M_c/M_{\rm Jup} < 80$) from the California Legacy Survey. Our population consists of objects near and beyond the water ice line ($1 < a / \text{AU} < 10$), providing valuable clues to the details of giant planet formation physics at a location in the proto-stellar disk where planet formation efficiency is thought to be enhanced. We find that occurrence rate, host star metallicity, and orbital eccentricity all change gradually across the mass range under consideration, suggesting that ``bottom-up'' core accretion mechanisms and ``top-down'' gravitational instability mechanisms produce objects that overlap in mass. The observed eccentricity distributions could arise either from different formation channels or from post-formation dynamical interactions between massive sub-stellar objects.