On the Eccentricity Distribution and Tidal Evolution of Transiting Brown Dwarfs

Brown dwarfs on short-period orbits populate an intermediate regime between hot Jupiters and tight stellar binaries, lying at the intersection of possible evolutionary avenues. Their orbital eccentricities retain the dynamical imprint of both their formation pathways and any subsequent tidal evolution, providing a diagnostic for whether such objects formed in situ at small separations or were driven inward from higher-eccentricity orbits shaped by tidal dissipation. Using a hierarchical Bayesian framework, we characterise the orbital eccentricity distribution of transiting brown dwarfs. Short-period brown dwarfs ($P < 16$ days) are well represented by a Beta distribution with $\alpha < 1$ and $\beta > 1$, indicating a population concentrated at low eccentricities, whereas longer-period brown dwarfs ($P \geq 16$ days) display $\alpha,~\beta > 1$ and therefore occupy a more dynamically excited regime. This difference in eccentricity distributions likely reflects corresponding differences in the populations' eccentricity-damping timescales: close-in systems may evolve toward circular orbits on relatively short timescales, whilst wider companions experience negligible tidal processing over their lifetimes. Assuming that the full set of transiting brown dwarfs stems from a single primordial eccentricity distribution, {we constrain the typical brown dwarf tidal quality factor to $\mathcal{Q}_{\rm BD} = 10^{8.1\pm1.0}$ when neglecting the influence of tides raised on the host star, or $\mathcal{Q}_{\rm BD} = 10^{7.1\pm0.3}$ and $\mathcal{Q}_{\star} = 10^{6.0\pm0.1}$ when they are included.