Disk Contamination in a Sample of Proper Motion Selected Halo Stars a Comment on Direct Detection of Galactic Halo Dark Matter, B.a. Oppenheimer Et Al. 2001, Science

submitted as a Technical Comment to Science Sir: I am writing in comment to the recent survey by Oppenheimer et al [1]. This survey finds 34 high velocity white dwarfs, and concludes that these white dwarfs form a component of dark matter, representing 3% of the local mass of the halo. This survey is similar to the Luyten survey [2], covering 10% of the sky whereas Luyten covers 2/3 of the sky, but this survey goes somewhat deeper. It covers about 2/3 the volume of the Luyten survey, ignoring the proper motion limits. The authors are sensitive to a similar range of proper motions to Luyten, though the range of velocities is not the same since the Oppenheimer et al. survey will see objects to a larger distance, and hence a larger velocity. Since the surveys are so similar, it is surprising that the results are so different. However , closer examination shows that the results are not different. A further analysis of the Luyten survey including trigonometric paral-lax [3] shows that roughly half Luyten's white dwarfs have velocities greater than 94 km s −1 , as is true for Oppenheimer et al's. Whereas these objects were classified as disk or thick disk dwarfs by [3], they are classified as Halo objects by Oppenheimer et al. In both surveys, these stars are the high velocity Gaussian tail of the disk population. The density of halo main sequence stars is about 1/600 the density of disk stars. The authors claim that their cut at 94 km/sec will eliminate 95% of the disk population, but this means that the remaining 5% of the disk dwarfs should still outnumber the halo dwarfs by 30 to 1. The problem is even worse since this is a proper motion limited survey. Such a survey obviously selects for the highest velocity stars, thus the typical velocity of a proper motion limited survey will be higher than in the underlying population. A quick Monte Carlo simulation shows that the mean velocity in a proper motion limited survey is about twice that of the underlying population. Thus, the 94 km/sec threshold is actually a 1 σ cutoff, and we expect a fair fraction of detected disk stars pass this threshold. This is born out by examining figure 3 of Oppenheimer et al. which shows that most of the white dwarfs in the sample are rotating around the galaxy …