The Brown-dwarf Desert Persists as a Mass-ratio Desert around Low-mass Stars

TL;DR

Brown-dwarf companions around Sun-like stars show a desert in mass ratio, and this study tests whether a similar mass-ratio desert exists around low-mass microlensing hosts ($0.05$--$0.8\,M_\odot$). The authors analyze homogeneous MOA-II (2007–2012) and KMTNet (2016–2019) microlensing samples, model detection sensitivities, and fit a mass-ratio distribution while accounting for degeneracies and incompleteness. They identify a statistically significant desert at $0.02 \lesssim q \lesssim 0.05$ with an upper truncation near $q \simeq 0.02$ and a pile-up near $q \simeq 0.05$, and find a giant-planet occurrence density of $5.8\pm0.8$\% per decade of projected separation near $2$--$3$ au. Extrapolating the fitted distribution to the desert range would predict many more detections than observed (e.g., about $27^{+7}_{-6}$ vs $3$), leading to a rejection of a single power-law explanation at $>3\sigma$, which supports a real, sharp mass-ratio boundary and a scale-invariant formation picture across stellar masses.

Abstract

Sun-like stars are known to host a paucity of brown dwarf companions at close separations. Direct imaging surveys of intermediate-mass stars have suggested that the brown dwarf desert may be fundamentally a feature in the mass ratio. Microlensing surveys provide a unique opportunity to investigate the nature of this desert around low mass stars, as microlensing hosts have typical masses of 0.05-0.8 $M_\odot$. Here, we perform a statistical analysis of homogeneously selected binary-lens microlensing events in the literature, and identify a companion mass-ratio desert at $0.02\lesssim q\lesssim0.05$ and projected separations around 1-5 au. We derive a statistically significant truncation to the giant-planet mass-ratio distribution at $q\simeq0.02$, above which the occurrence rate density drops by approximately an order of magnitude. Due to the possibility that the small number of detected companions in this desert orbit white dwarfs, this mass-ratio desert may be closer to being completely dry around main-sequence stars. Below this desert, we derive a giant-planet ($q>4\times10^{-4}$) occurrence rate density of $5.8\pm0.8$% per decade of projected separation. Our analysis furthers the hypothesis that the brown dwarf desert is fundamentally a feature in the mass ratio, separating distinct populations of planetary and non-planetary companions that are likely formed via core accretion and gravitational instability, respectively. The persistence of this desert across stellar types suggests that both gas-giant planets and sub-stellar companions form in a scale-invariant fashion, with planets growing to a maximum of approximately 2% their host masses.

Figures (3)

• Figure 1: Cumulative number of detected microlensing companions with mass ratios smaller than each value on the horizontal axis, shown on a logarithmic scale. Events with severe degeneracies in the mass ratio are excluded from this plot. The gray shade indicates a dearth of detections between mass ratios of $0.017<q<0.047$.
• Figure 2: Mass-ratio distribution of microlensing companions from the KMTNet (2016--2019) and MOA-II (2007-2012) survey samples, extended out to $q=0.047$. The black points (left axis) show occurrence rate densities in bins of the mass ratio, shown as the posterior median and 16--84 percentile interval under a Jeffreys prior. The solid orange line represents the best power-law fit over $-3.4<\log(q)<-1.75$, with the shaded region indicating the $1\sigma$ confidence interval. The light shade shows extrapolation to the mass-ratio desert. The histogram (right axis) shows the number of detections in each bin.
• Figure 3: Corner plot illustrating the posterior distribution of the power-law mass-ratio function fitted to the combined KMTNet and MOA-II samples ($-3.4<\log(q)<-1.75$), with the upper truncation value $q_{\rm max}>0.017$ as a free parameter. Contours show the 1/2/3-$\sigma$ regions, with vertical lines in the 1D marginal plots showing the 16/50/84 percentiles. The parameter values differ from Equations 4--5, which adopted a fixed $q_{\rm max}=0.017$.