Absolute Proper Motions to B ~ 22.5. IV. Faint, Low-Velocity White Dwarfs and the White Dwarf Population Density Law

The reduced proper-motion diagram (RPMD) for a complete sample of 819 faint (B ≤ 22.5) stars with high-accuracy proper motions (σμ ~ 1 mas yr-1) in an area of 0.3 deg2 in the north Galactic pole field SA 57 is investigated. Eight stars with very large reduced proper motions are identified as faint white dwarf candidates. On the basis of larger than 6 σ measured proper motions and the lack of photometric variability over a 20 yr baseline, we discriminate these white dwarf candidates from the several times more numerous quasi-stellar objects (QSOs), which can potentially occupy a similar location in the RPMD. For comparison, less than 4 σ proper motions and photometric variability are found in all but one of 35 spectroscopically confirmed QSOs in the same field. While spectroscopic confirmation of their status as white dwarfs is a necessary, but difficult, outstanding task, we discuss the implausibility that these stars could be any kind of survey contaminant. High-quality proper motions lend confidence in our ability to separate white dwarfs from subdwarfs in the RPMD. If bona fide white dwarfs, the eight candidates found here represent a portion of the white dwarf population that hitherto has remained uninvestigated by previous surveys by virtue of the faint magnitudes and low proper motions of the stars. This faint, low-velocity sample represents an increase in the white dwarf sky surface density to B = 22.5 by an order of magnitude than that found in the previously most complete surveys to this depth. However, because the majority of the stars discovered here are at projected distances of more than a disk scale height above the Galactic midplane, their existence does not affect significantly the typical estimates of the local white dwarf density. On the other hand, as distant white dwarf candidates with low, typically thin-disk-like transverse velocities (<40 km s-1), the newly discovered stars suggest a disk white dwarf scale height larger than the values of 250-350 pc typically assumed in assessments of the local white dwarf density (and thought to characterize the Galactic old thin disk in stellar population models). Both a ⟨V/Vmax⟩ and a more complex maximum-likelihood analysis of the spatial distribution of our likely thin-disk white dwarfs yield scale heights of 400-600 pc while at the same time giving a reasonable match to the local white dwarf volume density found in other surveys (although this good match is a result of the dominance of the one relatively nearby white dwarf in the 1/Vmax density calculation). A high scale height persists even if the relatively small sample is pruned of any potential thick-disk or halo white dwarfs. While our work is not optimized toward the study of halo white dwarfs as potential MACHO objects, our results do have interesting implications for this hypothesis. We can place some direct constraints (albeit weak ones) on the contribution of halo white dwarfs to the dark matter of the Galaxy. Moreover, the elevated scale height that we measure for the thin disk could alter the interpretation of microlensing results to the extent of making white dwarfs untenable as the dominant MACHO contributor.