Beyond the Local Volume I: Surface Densities of Ultracool Dwarfs in Deep HST/WFC3 Parallel Fields

Ultracool dwarf stars and brown dwarfs provide a unique probe of large-scale Galactic structure and evolution; however, until recently spectroscopic samples of sufficient size, depth, and fidelity have been unavailable. Here, we present the identification of 164~M7--T9 ultracool dwarfs in 0.6~deg$^2$ of deep, low-resolution, near-infrared spectroscopic data obtained with the \textit{Hubble Space Telescope} Wide Field Camera 3 instrument as part of the WFC3 Infrared Spectroscopic Parallel Survey and the 3D-HST survey. We describe the methodology by which we isolate ultracool dwarf candidates from over 200,000 spectra, and show that selection by machine learning classification is superior to spectral index-based methods in terms of completeness and contamination. We use the spectra to accurately determine classifications and spectrophotometric distances, the latter reaching to $\sim$2~kpc for L dwarfs and $\sim$400~pc for T dwarfs.