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. 2014.
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 log g = 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 +- 0.1 x 10^-3 pc^-3 and 3.5 +- 0.7 x
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.
