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

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 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 (υ) = -6.47 (+0.42)(-0.31), (\sigma {\nu }) = 0.34(-0.17)^(+0.23), t_disk = 1.66 (-0.84)^(+1.24) Myr, and Mgap = 12.0_(-8.3)^(+4.7) 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 ≈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.