A DEEP PROPER MOTION CATALOG WITHIN THE SLOAN DIGITAL SKY SURVEY FOOTPRINT. II. THE WHITE DWARF LUMINOSITY FUNCTION

A catalog of 8472 white dwarf (WD) candidates is presented, selected using reduced proper motions from the deep proper motion catalog of Munn et al. Candidates are selected in the magnitude range $16<r<21.5$ over 980 square degrees, and $16<r<21.3$ over an additional 1276 square degrees, within the Sloan Digital Sky Survey (SDSS) imaging footprint. Distances, bolometric luminosities, and atmospheric compositions are derived by fitting SDSS ugriz photometry to pure hydrogen and helium model atmospheres (assuming surface gravities $logg=8$). The disk white dwarf luminosity function (WDLF) is constructed using a sample of 2839 stars with $5.5<M_{bol}<17$, with statistically significant numbers of stars cooler than the turnover in the luminosity function. The WDLF for the halo is also constructed, using a sample of 135 halo WDs with $5<M_{bol}<16$. We find space densities of disk and halo WDs in the solar neighborhood of $5.5\pm 0.1\times {10}^{-3}{pc}^{-3}$ and $3.5\pm 0.7\times {10}^{-5}{pc}^{-3}$, respectively. We resolve the bump in the disk WDLF due to the onset of fully convective envelopes in WDs, and see indications of it in the halo WDLF as well.