JADES: An Abundance of Ultra-Distant T- and Y-Dwarfs in Deep Extragalactic Data

Ultra-cool T- (T$_{\mathrm{eff}} \approx$ 500 - 1200 K) and Y-dwarfs (T$_{\mathrm{eff}}$ $\lessapprox 500$ K) have historically been found only a few hundred parsecs from the Sun. The sensitivity and wavelength coverage of the NIRCam instrument on board the James Webb Space Telescope offer a unique method for finding low-temperature brown dwarfs in deep extragalactic datasets out to multiple kiloparsecs. Here we report on the selection of a sample of 41 brown dwarf and brown dwarf candidates across the JWST Advanced Deep Extragalactic Survey (JADES) in the GOODS-S and GOODS-N regions. We introduce a new open-source Bayesian tool, the Near-Infrared Fitting for T and Y-dwarfs (\texttt{NIFTY}), to derive effective temperatures, metallicities, and distances from JWST photometry. We find that 31 candidates have fits consistent with T-dwarf temperatures out to 5 - 6 kpc, and 10 candidates have fits consistent with Y-dwarf temperatures out to 1 - 2 kpc. The majority of the sources are best fit with sub-solar metallicity models, consistent with them being subdwarfs in the Milky Way thick disk and halo. We report proper motions for nine brown dwarf candidates (three are newly presented), and calculate the number density of T- and Y-dwarfs as a function of temperature and distance above the Milky Way midplane. We further discuss how Y-dwarfs can serve as contaminants in the search for ultra-high-redshift galaxies. Together, these results demonstrate the power of deep JWST extragalactic imaging to probe the coldest substellar populations far beyond the solar neighborhood, providing new constraints on the Milky Way's structure and brown dwarf demographics.