The Effect of Atmospheric Cooling on 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 the 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 (similar to 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 that the velocity dispersion as a function of spectral type should deviate from the 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 (similar to 1 kpc) 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.