The Effect of Atmospheric Cooling on the Vertical Velocity Dispersion and Density Distribution of Brown Dwarfs

We present a Monte Carlo simulation designed to predict the vertical velocity dispersion of brown dwarfs in the Milky Way. We show that since these stars are constantly cooling, the velocity dispersion has a noticeable trend with spectral type. With realistic assumptions for the initial-mass function, star-formation history, and the cooling models, we show that the velocity dispersion is roughly consistent with what is observed for M dwarfs, decreases to cooler spectral types, and increases again for the coolest types in our study ($\sim$T9). We predict a minimum in the velocity dispersions for L/T transition objects, however the detailed properties of the minimum predominately depend on the star-formation history. Since this trend is due to brown dwarf cooling, we expect the velocity dispersion as a function of spectral type should deviate from constancy around the hydrogen-burning limit. We convert from velocity dispersion to vertical scale height using standard disk models, and present similar trends in disk thickness as a function of spectral type. We suggest that future, wide-field photometric and/or spectroscopic missions may collect sizable samples of distant ($\sim\!1$ kpc) of dwarfs that span the hydrogen-burning limit. As such, we speculate that such observations may provide a unique way of constraining the average spectral type of hydrogen-burning.