The Transition from Giant Planets to Brown Dwarfs beyond 1 au from the Stellar Metallicity Distribution

TL;DR

The paper addresses how to distinguish giant-planet and brown-dwarf formation pathways by examining how host-star metallicity depends on companion mass in 1–50 au. It employs a homogeneous California Legacy Survey dataset and a hierarchical Bayesian framework to infer a mass-dependent transition in the stellar metallicity distribution, using posterior companion masses $M_{c, {\rm post}}$ and host metallicities ${\rm [Fe/H]}$ with uncertainties. The analysis yields a transition at $\gamma = 27_{-8}^{+12} \, M_{\rm Jup}$, with low-mass companions forming around metal-rich hosts (${\rm [Fe/H]} = 0.17 \pm 0.12$ dex) and high-mass companions around near-solar or sub-solar metallicities (${\rm [Fe/H]} = -0.03 \pm 0.10$ dex); it strongly disfavors a transition at $\le 10 \, M_{\rm Jup}$. These findings inform formation theories—supporting a metallicity-enhanced core accretion channel for lower-mass companions and a less metallicity-dependent pathway for higher-mass objects—and demonstrate a rigorous population-level approach to disentangle formation mechanisms.

Abstract

Giant planets and brown dwarfs are thought to form via a combination of pathways, including bottom-up mechanisms in which gas is accreted onto a solid core and top-down mechanisms in which gas collapses directly into a gravitationally-bound object. One can distinguish the prevalence of these mechanisms using host star metallicities. Bottom-up formation thrives in metal-rich environments, whereas top-down formation is weakly dependent on ambient metal content. Using a hierarchical Bayesian model and the results of the California Legacy Survey (CLS), a low-bias and homogeneously analyzed radial velocity survey, we find evidence for a transition in the stellar metallicity distribution at a companion mass of $γ= 27_{-8}^{+12} \, M_{\rm Jup}$ for companions with orbital separations between $1-50$ au. Companions below and above this threshold tend to orbit stars with higher ($\rm{[Fe/H]} = 0.17 \pm 0.12$ dex) and lower ($\rm{[Fe/H]} = -0.03 \pm 0.10$ dex) metallicities, respectively. Previous studies of relatively close-in companions reported evidence of a lower transition mass of $\leq 10 \, {\rm M_{\rm Jup}}$. When applied to the CLS sample, our model predicts the probability of a transition in the stellar metallicity distribution at or below $10 \, { M_{\rm Jup}}$ to be $< 1 \%$. We compare our results to estimates of $γ$ gleaned from other observational metrics and discuss implications for planet formation theory.

Figures (2)

• Figure 1: Visualization of the sample of CLS systems analyzed in this paper. The top two panels are histograms of the masses (top left) and effective temperatures (top right) of the stars in the sample. The bottom two panels show the distribution of systems in the orbital separation -- companion mass plane (bottom left) and the companion mass -- stellar metallicity plane (bottom right).
• Figure 2: Plate diagram illustrating our HBM framework. Latent parameters (white) and observed parameters (grey) are located inside the box. The latent and observed parameters, indexed via the superscript $j$, have $N$ members corresponding to the number of systems in the sample. Hyperparameters (green) are located outside the box. The model parameters are as follows: companion mass between which the stellar metallicity distributions transition ($\gamma$), low-mass population metallicity distribution mean ($C_1$), low-mass population metallicity distribution standard deviation ($S_1$), high-mass population metallicity distribution mean ($C_2$), high-mass population metallicity distribution standard deviation ($S_2$), companion mass posterior distribution ($M_{c, {\rm post}}^j$), observed stellar metallicity (${\rm [Fe/H]}_o^j$), and the uncertainty of the observed stellar metallicity ($\sigma_{{\rm [Fe/H]}_o^j}$).