Constraining Brown Dwarf Desert Formation Mechanisms Through Bayesian Statistical Comparison of Observed and Simulated Populations

Abstract

We present a comprehensive Bayesian statistical analysis of brown dwarf companions to investigate the physical mechanisms responsible for the observed ``brown dwarf desert'' -- the notable paucity of brown dwarf companions at orbital separations $<$5~AU. Using a carefully vetted sample of 88 confirmed brown dwarf companions from the \texttt{exoplanet.eu} catalog with masses 13--80~$\mjup$ and semi-major axes 0.1--5.0~AU, we employ Markov Chain Monte Carlo (MCMC) optimization and two-dimensional Kolmogorov-Smirnov tests to compare observed orbital and mass distributions with three theoretical formation scenarios: (A) Type II disk-driven migration, (B) core accretion with mass-dependent survival, and (C) dynamical scattering from wide orbits. Our analysis spans 4-parameter models for each scenario, with proper posterior distributions quantifying parameter uncertainties and correlations. The disk migration model provides statistically superior fits (2D KS $p = 0.18$), with optimal parameters $\log_{10}ν= -6.47^{+0.42}_{-0.31}$, $σ_ν= 0.34^{+0.23}_{-0.17}$, $t_{\rm disk} = 1.66^{+1.24}_{-0.84}$~Myr, and $M_{\rm gap} = 12.0^{+4.7}_{-8.3}~\mjup$, consistent with Type II migration theory. The dynamical scattering model achieves intermediate performance ($p = 0.08$), while core accretion scenarios show poor agreement ($p < 0.001$) despite theoretical sophistication. Occurrence rate analysis reveals the desert region (0.1--5~AU) is depleted by a factor of $\approx$1.6 relative to wide separations ($>$5~AU), a constraint successfully reproduced only by the migration model. Our results provide quantitative evidence that brown dwarfs form at wide separations (10--30~AU) through disk fragmentation and undergo limited Type II migration to reach observed close-in locations, with migration naturally halting near 1~AU through gap-opening processes.

Figures (6)

• Figure 1: Comprehensive diagnostics for the brown dwarf sample used in this analysis. Top row: (Left) Mass distribution showing bimodal structure with split at $\approx$42.5 $M_{\rm Jup}$Ma2014. (Middle) Separation distribution clearly exhibiting the desert signature with suppression at $<$1 AU. (Right) Mass versus separation showing no strong correlation but clear desert boundary. Bottom row: (Left) Cumulative distribution function (CDF) for semi-major axis, showing characteristic desert shape. (Middle) CDF for mass distribution. (Right) Occurrence rate per logarithmic separation bin, demonstrating factor of $\approx$1.6 depletion in desert region (0.1--5 AU) relative to wide separations ($>$5 AU). Note that the comparison is based on the full dataset and not solely on the plotted bins.
• Figure 2: MCMC posterior distributions for the Type II disk migration model. Corner plot shows 1D marginalized posteriors (diagonal) and 2D joint posteriors (off-diagonal) for the four model parameters. Dashed vertical lines indicate 16th, 50th, and 84th percentiles. The optimal viscosity $\log_{10}\nu = -6.47^{+0.42}_{-0.31}$ is consistent with MRI-driven turbulence in protoplanetary disks. The disk lifetime $t_{\rm disk} = 1.66^{+1.24}_{-0.84}$ Myr agrees with observed disk dissipation timescales. Note the strong correlation between $\log_{10}\nu$ and $t_{\rm disk}$, indicating degeneracy between fast migration over short times versus slow migration over longer periods.
• Figure 3: MCMC posterior distributions for the core accretion model. The steep mass function slope ($\alpha = 2.10$) and low cutoff mass ($M_{\rm cutoff} = 13.00~M_{\rm Jup}$) indicate the model struggles to produce sufficient high-mass brown dwarfs. The narrow, well-constrained posteriors reflect the model's inability to fit observations regardless of parameter values. Despite sophisticated physics, this model achieves poor statistical agreement ($p < 0.001$), confirming that core accretion cannot efficiently form brown dwarfs at the observed masses and separations.
• Figure 4: MCMC posterior distributions for the dynamical scattering model. The low scattering probabilities ($p_{\rm low} = 0.045$, $p_{\rm high} = 0.064$) indicate only $\approx$5% of wide brown dwarfs undergo significant orbital evolution. The mass split at $M_{\rm split} = 43.0~M_{\rm Jup}$ closely matches the observed bimodal mass distribution boundary. The model achieves intermediate statistical performance ($p = 0.08$), suggesting dynamical processes contribute meaningfully but cannot fully explain the brown dwarf desert.
• Figure 5: Comparison of observed and simulated brown dwarf distributions in $(a, M)$ space. Each panel shows observed data (points with error bars) overlaid on simulated populations (contours show the two-dimensional probability density of the simulated population in semi-major axis and mass) for optimal parameters from MCMC. Left: Disk migration model successfully reproduces both orbital and mass structure. Middle: Core accretion model severely underproduces brown dwarfs, particularly at wide separations and high masses. Right: Formation bias model captures mass bimodality but shows excessive concentration at specific separations.