A Smooth Transition from Giant Planets to Brown Dwarfs from the Radial Occurrence Distribution

TL;DR

By combining decades of radial-velocity measurements from the California Legacy Survey with astrometric accelerations from the Hipparcos-Gaia Catalog, the authors break the $M_c \sin i$ degeneracy to infer true companion masses and orbits for 195 systems. They model companion occurrence as a Poisson process in $(\log M_c, \log a)$ space, accounting for each system's sensitivity and parameter uncertainties, and find a smooth transition between giant planets and brown dwarfs rather than a sharp dividing mass. The results confirm a brown dwarf desert extending to at least $10$ AU and reveal a rise in giant-companion occurrence near the ice line around $1$ AU, with a persistent enhancement up to $\sim 10$ AU. These findings imply overlapping formation channels for planets and brown dwarfs (core accretion and disk instability) and demonstrate the power of RV+astrometry in reconciling dynamical and model masses, with Gaia DR4 expected to sharpen these trends further.

Abstract

Measuring the occurrence rates of celestial objects is a valuable way to study their origins and evolution. Giant planets and brown dwarfs produce large Doppler signatures that are easily detectable by modern instrumentation, and legacy radial velocity (RV) surveys have now achieved full orbital coverage for periods $\lesssim$30 years. However, the Doppler method's sensitivity to companion minimum mass $M_c \sin i$ -- as opposed to true mass $M_c$ -- prevents unambiguous characterization using RVs alone, as purported giant planets may be brown dwarfs or stars on inclined orbits. Here we combined legacy RVs with absolute astrometry to re-fit the orbits of 195 companions from the California Legacy Survey. Nearly 50% (8/18) of the ``brown dwarfs" ($M_c \sin i$=13--80 $M_{Jup}$) we refit had true masses above 80 $M_{Jup}$. We incorporated our orbital posteriors and target sensitivity maps into a Poisson likelihood model to calculate occurrence as a function of true companion mass $M_c$ (0.8--80 $M_{Jup}$) and separation $a$ (0.3--30 AU). The semi-major axis distributions of objects in this range vary smoothly with mass, with Jupiter analogs favoring an abrupt increase in occurrence near 1 AU and brown dwarfs exhibiting a gradual enhancement at wider separations. Marginalized companion occurrence between 1--10 AU decreases smoothly with mass, with brown dwarfs having the lowest occurrence rate: $0.9^{+0.5}_{-0.4}$%. Jupiter analogs are 10 times as common as brown dwarfs per mass interval in this range, demonstrating that the brown dwarf desert extends to 10 AU. The smooth variation in these distributions disfavors a sharp transition mass between ``bottom-up" core accretion and ``top-down" gravitational instability formation mechanisms, and rather suggests that these processes may produce companions in overlapping mass ranges.

Figures (4)

• Figure 1: Left: The masses and semi-major axes of the substellar ($M_c \sin i\xspace \leq 80 \, M_{\mathrm{Jup}}\xspace$) companions reported in the CLS catalog. Orange points show the average $a$ and $M_c \sin i$ fitted, or in some cases quoted, by CLS, while blue points show the average $a$ and $M_c$ refitted in this work. Green borders indicate companions in whose orbital fits we included HGCA astrometry. The color map shows the CLS sensitivity to true mass, averaged over all 719 stars in the survey, with contours indicating sensitivity deciles and the 50% completeness line marked in black. Horizontal green lines mark 13 and 80 $M_{\mathrm{Jup}}$, the traditional brown dwarf mass limits. Right: Our re-fit catalog of 195 CLS companions. Contours enclose 68% of an individual companion's posterior draws. Black rectangles indicate the cells in which we calculated companion occurrence (see Section \ref{['sec:results']}). The completeness map is the same as in the right panel. Note that because the colored markers in the left panel indicate averages, companions with $M_c>80 \, M_{\mathrm{Jup}}\xspace$ may still have significant posterior mass below this limit, and vice versa.
• Figure 2: Radial occurrence rate density distributions for companions between 0.8--80 $M_{\mathrm{Jup}}$, with the highest-mass interval shown in the top panel. We fit each distribution with a log-linear model and a two-level step function. We calculated $\Delta$AIC and $\Delta$BIC values for the best-fit parameters for each model, using a constant model for comparison. In all cases we found that neither model was strongly preferred, though the step function was marginally preferred for companions with $M_c$=0.8--1.6 $M_{\mathrm{Jup}}$, a possible indication that the abundance of planetesimals near the ice line more strongly influences planet formation in this mass interval.
• Figure 3: Marginalized occurrence rate density of CLS companions between 1--10 AU. Companion occurrence decreases log-linearly with increasing mass up to $\sim$20 $M_{\mathrm{Jup}}$, disfavoring a 'cut-off' mass at which companion formation near the ice line abruptly becomes inefficient. We annotate each mass bin with the true occurrence rate, quoting a single value for the range 13--80 $M_{\mathrm{Jup}}$ to facilitate comparison with other studies.
• Figure 4: Occurrence rate density between 0.03-30 AU for companions between 0.8--80 $M_{\mathrm{Jup}}$. Companion occurrence is enhanced beyond 1 AU, and consistent with a decrease beyond 10 AU. A broken power law (solid green) and two-level step function (dotted yellow) fit the distributions comparably well, as measured by their $\Delta$AIC and $\Delta$BIC statistics compared to a constant occurrence rate model. Faded lines show posterior draws for each model. Nearly all steps occur between 0.5 and 1.7 AU.