ar X iv : a st ro - p h / 01 04 25 5 v 4 1 2 Ju n 20 01 White Dwarfs and Dark Matter Accepted for publication as a Technical

Based upon the identification of 38 white dwarfs with halo kinematics, in a survey covering 10% of the sky near the south Galactic pole, Oppenheimer et al. (1) argue that at least 2% of the dark matter in the Galaxy has now been detected directly. Put into context, the Oppenheimer et al. result implies that the stellar remnant mass of the halo may be comparable to that of the entire disk of our Galaxy. If true, this finding has crucial consequences for understanding the formation and evolution of the Milky Way. Careful examination of the Oppenheimer et al. results leads us to conclude that they have overestimated the density of white dwarfs with halo kinematics. Oppenheimer et al. derive their local white dwarf density n via the 1/V max technique (2). The equation that applies for a survey covering 10% of the sky is n = 38 i=1 V −1 i,max ≈ 2.4 d −3 i,max pc −3 where V max represents the maximum volume in which the survey could have found each of the 38 white dwarfs listed in Table 1 of (1) and d max is the distance in parsecs which determines V max. Oppenheimer et al. considered two relations for d max , one depending upon the limiting magnitude of the survey R59F lim and the luminosities M i,R59F of each of the 38 white dwarfs, and one depending upon the inferred distance d and observed proper motion µ. Using equation 1 and the 38 white dwarfs in their sample, Oppenheimer et al. derived a white dwarf number density n=1.8×10 −4 pc −3. We rederived n, employing the above relation, the data tabulated in their Table 1, and the identical d i,max criteria used in their analysis, and found n=1.54×10 −4 pc −3. Moreover, Oppenheimer et al. assumed a typical white dwarf mass of 0.6 M ⊙ , which in combination with their derived number density, resulted in a local mass density of 1.1×10 −4 pc −3 M ⊙ pc −3. By contrast, in metal-poor systems such as globular clusters-which would be expected to mimic to some degree the patterns in the Galactic halo proper-the typical white dwarf mass is 0.51±0.03 M ⊙ (3). That average mass, combined with our recalculated number density, results in a local white dwarf mass density of 0.79×10 −4 M ⊙ pc −3 , 30% below that found by Oppenheimer et al. …