Lower-mass giant planets (1–3 Jupiter masses) usually form by core accretion, their orbit eccentricity is less. Brown dwarfs (mass> 13 Jupiter mass) have high eccentricity, they are formed by gravitational instability. The eccentricity changes slowly and smoothly with mass.
Radial velocity with Hipparcos + Gaia Astrometric accelerations astrometry is used here which gives the tilt of the orbit. That allows them to measure the actual masses.
Low-mass giant planets are common. As mass increases, planets become rarer
So occurrence rate decreases smoothly with mass increase.
The giant planets and brown dwarfs do not form two separate, sharply divided populations. Instead, their properties—eccentricity, occurrence rate, and host star metallicity—change continuously and gradually as mass increases from about 1 to 80 Jupiter masses. Eccentricity rises steadily, indicating a transition from core-accretion formation to gravitational-instability processes, but this shift is smooth rather than abrupt.
Hierarchical Bayesian Modeling of Eccentricity Distributions is used in the article.
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