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

TL;DR

This work addresses whether the boundary between giant planets and brown dwarfs is sharp or gradual by analyzing a homogeneous sample of sub-stellar companions with masses $0.8-80\,M_{\rm Jup}$ at $a\sim 1-10$ AU. The authors apply a hierarchical Bayesian framework to infer the intrinsic eccentricity distribution $f(e)$ across five mass bins, incorporating completeness via injection–recovery and true masses from Hipparcos-Gaia accelerations using Orvara. They find a smooth increase in mean eccentricity from $\langle e\rangle\approx 0.2$ for $1-10\,M_{\rm Jup}$ to $\langle e\rangle\approx 0.5$ for $M_c\gtrsim 13\,M_{\rm Jup}$, with a gradual change in the shape of $f(e)$, suggesting overlapping formation channels. Occurrence rate density declines with mass and metallicity shows no strong correlation, implying both core accretion and gravitational instability contribute across the studied regime. The results argue for a continuum of formation pathways rather than a single dividing line and motivate combining eccentricity with additional observables to separate formation channels.

Abstract

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.

Figures (3)

• Figure 1: Masses and orbital separations of the sub-stellar companions detected by CLS. Black points indicate objects included in our study, whereas gray points are shown for context but not included in our analysis. The colored contours indicate the detection probability for a sub-stellar companion with a given mass and orbital separation and a nominal eccentricity $e=0.2$. The black contour shows the 50% sensitivity line. The red rectangle indicates our chosen parameter space for this study, where completeness is high.
• Figure 2: The eccentricities of sub-stellar objects with star-companion orbital separations $a = 1-10 \text{AU}$ and true masses $M_c = 0.8-80 M_{\mathrm{Jup}}\xspace$. Left panel: Mass vs. eccentricity. Colors correspond to our nominal size bins. There is a clear trend of rising eccentricity with rising mass, with objects below $M=1.6 M_{\mathrm{Jup}}\xspace$ preferring $e \lesssim 0.5$ and objects above $M = 13 M_{\mathrm{Jup}}\xspace$ preferring $e \gtrsim 0.2$. Right panel: Sub-population eccentricity distributions inferred using a hierarchical Bayesian model. Solid lines indicate the median posterior distribution, shaded regions indicate $1\sigma$ confidence intervals, and dashed lines indicated the mean for each subpopulation. There is a smooth transition in the mean eccentricity ${\langle}e{\rangle}$ and the overall shape of the distribution from the lowest mass bin (peaked at $e=0$ and monotonically declining toward zero at $e=1$) to the highest pass bin (nearly uniform over $e$).
• Figure 3: Demographic trends in occurrence rate density, host star metallicity, and orbital eccentricity for sub-stellar objects between $0.8-80M_{\mathrm{Jup}}\xspace$. All three demographic trends display a smooth variation with companion mass. Top panel: Occurrence rate per logarithmic mass bin falls steadily as $M_c$ increases. Middle panel: The relationship between host star metallicity and companion mass is weak-to-nonexistent, but may be weakly anti-correlated. Bottom panel: Mean eccentricity ${\langle}e{\rangle}$ rises steadily as $M_c$ increases.