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Direct Detection of Galactic Halo Dark Matter

The Milky Way Galaxy contains a large, spherical component which is believed to harbor a substantial amount of unseen matter. Recent observations indirectly suggest that as much as half of this ``dark matter'' may be in the form of old, very cool white dwarfs, the remnants of an ancient population of stars as old as the Galaxy itself. We conducted a survey to find faint, cool white dwarfs with large space velocities, indicative of their membership in the Galaxy's spherical halo component. The survey reveals a substantial, directly observed population of old white dwarfs, too faint to be seen in previous surveys. This newly discovered population accounts for at least 2% of the halo dark matter. It provides a natural explanation for the indirect observations, and represents a direct detection of Galactic halo dark matter.


Observations
Our survey used digitized, photographic plates in the R59F and B J passbands from the SuperCOSMOS Sky Survey (12)(13)(14). R59F and B J roughly correspond to optical wavelengths of 0.59 and 0.45 µm respectively. We searched for objects with proper motions, µ, between 0.33 and 10.00 ′′ year −1 as faint as R59F = 19.8, using plates near the South Galactic Cap (SGC) at three epochs in each field. The SGC plates comprise 196 fields (15). The non overlapping area of each field is 25 square degrees. Hence, the area of our survey is 4900 square degrees, or about 12% of the sky. Because of image blending problems and large halos of scattered light around bright stars, the actual area surveyed is 4165 square degrees, or 10% of the sky. This is several times larger than the areas searched in two previous surveys (3,16). At the very faint end of our sample, we found many objects not included in the Luyten catalogs of proper motion stars (17), primarily because Luyten's survey in the Southern Hemisphere did not attempt to find objects as faint as those we have found. These previously undetected stars are the principal members of our sample of halo white dwarfs.
We used the technique of reduced proper motion (RPM) (18,19) to identify white dwarfs by their subluminosity in comparison to main-sequence stars and their high intrinsic space motions. RPM is defined as H R = R59F + 5 log µ + 5, and is an estimate of the absolute magnitude based on the proper motion, µ, in arcseconds per year. We selected all 126 objects in the RPM diagram ( Fig. 1) having either H R > 22.5 or lying in the subluminous regions as potential halo white dwarfs. Sixty-three of these were previously cataloged (12,20). Of these 63 known, high-proper-motion stars, 29 had no published spectroscopic follow-up. This yielded an observing list of 92 stars for follow-up, including 63 new discoveries.
Over four nights (11 to 14 October 2000) at the Cerro Tololo Interamerican Observatory's V. M. Blanco 4-m Telescope, we obtained spectra in the wavelength range 0.48 to 0.98 µm for 69 of the 92 candidates (filled symbols in Fig. 1). We inspected the spectra within minutes of collecting the data, so we were able to discern by the middle of the second night which types of objects populated which parts of the RPM diagram ( Fig. 1). For example, as expected, we found only white dwarfs with Hα features on the far left of the subluminous sequence. Dwarf and subdwarf M-type stars are restricted to the right, which is also the bottom of the main sequence. We concentrated our observing resources on the cool objects, which occupy the lower part of the subluminous sequence. Of the 69 candidate objects observed, 16 are M-dwarfs or M-subdwarfs, 2 are hot He white dwarfs, 13 are white dwarfs with Hα features, and 38 are new cool white dwarfs (Fig. 2a), a few of which are probably cooler than WD0346+246, the prototypical ultracool white dwarf, which exhibits the H 2 opacity (2,7,21,22).
Two of the 38 new cool white dwarfs have unusual spectra (Fig. 2b). One, LHS 1402, has a spectrum very similar to those of the peculiar stars LHS 3250 (5, 7) and SDSS 1337+00 (6), but with a steeper slope toward longer wavelengths, suggesting a cooler temperature. The other object, WD2356−209, possesses a bizarre spectrum, incomparable to any other known object. We reanalyzed the data on this object several times and found no evidence for residual instrumental effects.

White Dwarfs in the Galactic Halo
The 38 cool white dwarfs in our sample show no spectral lines (e.g., Fig. 2a), preventing determination of their radial velocities. Nevertheless, we can estimate their space motions from the tangential velocity, v tan = µd, where µ is the proper motion and d is the distance between each star and Earth. To estimate distances, we used a photometric parallax relation derived from a linear least-squares fit to the cool white dwarf sample of Bergeron, Ruiz, and Leggett (23), supplemented by the ultracool WD0346+246, yielding the absolute magnitude in the B J filter, M B J = 12.73 + 2.58(B J − R59F ). Our calculations of the spectra of very cool white dwarfs also show a linear relation between M B J and B J − R59F . The color turnoff in B J − R59F due to collision-induced absorption by H 2 molecules in the pure hydrogen atmospheres becomes apparent in B J − R59F only at effective temperatures below 2500 K. The distances derived by this method are listed in Table 1. The scatter of the data around the least-squares fit results in a 20% uncertainty in our distance estimates. For LHS 147 and LHS 542, the only stars in Table 1 with measured distances (16,24), our estimates and the measured distances agree within 1 and 20%, respectively.
In order to use the velocities of the stars as an indicator of membership in the Galactic Halo, we transformed v tan into the components U, V , and W , in galactic coordinates. U is radial away from the Galactic center, V is in the direction of rotation, whereas W is perpendicular to the Galactic disk. The calculations used to derive these velocities take into account the deviation of the velocity of the Sun with respect to the average velocity of nearby stars in the Galactic disk. Because our survey was centered around the SGC, our observations are most sensitive to the U and V velocities (Fig. 3). Therefore, the most reasonable assumption is that W is zero for all of our stars. Zero is also the average value of W for all stars in the Milky Way. The point where U, V , and W are all equal to zero defines the so-called "local standard of rest," a frame of reference which is rotating in the disk about the Galactic center at the average rotation velocity of the disk near the Sun. Halo objects, because they have an isotropic velocity distribution with little or no overall rotation, should lag behind the local standard of rest with a distribution centered near V = −220 km s −1 , because the local standard of rest orbits the Galaxy at 220 km s −1 (25).
Our survey contains 38 stars that unambiguously possess halo kinematics (Fig. 3). We selected a sample of halo stars by accepting all objects whose velocities exceed the 2σ = 94 km s −1 velocity dispersion for the old disk stars (25). Our velocity cut excludes some halo stars with lower velocities, but permits only minimal contamination of the sample by disk stars. By choosing stars above 2σ = 94 km s −1 , we excluded 95% of the disk stars.
Furthermore, if a portion of our sample contains binary stars [the fraction of white dwarfs that are in white dwarf-white dwarf pairs is between 2 and 20% (26)], we expect that the velocity distribution of halo stars (Fig. 3) will be biased toward the point (V, U) = (0, 0). This is because we assumed that all of the stars are solitary in our estimate of distance. For those that are actually binary, we underestimated the intrinsic luminosity by, at most, a factor of 2 and the distance by a factor of √ 2. Therefore the values of U and V are underestimated by the same factor of √ 2. This bias is apparent in our sample (Fig. 3), implying that while we may have included a few disk stars in our sample, we may also have excluded a few binary halo stars. Because we searched for stars having µ > 0.33 ′′ year −1 there is a lack of stars with very low space motions. Furthermore, because of large differences in the epochs of the plates, an object with a proper motion above 3 ′′ year −1 will have a displacement of at least 30 ′′ between the plates. This compromises the detection of objects with extremely high space motions: even though we searched for objects having annual motions of up to 10 ′′ , our survey probably had less than a 10% chance of finding very faint stars moving by 3 ′′ year −1 or more. These biases against stars with very low and very high space motions result in the dearth of points within 50 km s −1 of the point (U, V ) = (0, 0) and the paucity of points at the extreme left of the UV velocity diagram (Fig. 3). Therefore, we underestimated the numbers of halo white dwarfs, and we measured a lower limit to the space density of these objects.
The subset of objects with velocities outside the 2σ velocity dispersion of the old disk stars (Fig. 3) contains 24 cool white dwarfs and 14 white dwarfs with Hα features (Table 1). An initial estimate of the space density of these objects is obtained using only the 12 coolest white dwarfs, whose average absolute magnitude, M R59F , is 16. With the survey depth of 19.8 and the survey area, a rough volume is computed yielding a space density of 2 × 10 −4 pc −3 , or 1.
To obtain a more precise estimate of the space density of all 38 of the halo white dwarfs in our survey, we used the 1/V max technique (27), which determines the maximum volume, V max , in which the survey could have found each star, given the brightness detection limit. The sum of 1/V max for all of the stars in the sample is the number density. Because our survey was limited to stars brighter than R59F lim = 19.8, we have computed V max using the absolute R59F magnitudes, M R59F , implied by the distances inferred above.
V max = (4/3)πd 3 max Ω/(4π) pc 3 (1) Here, Ω is the surveyed area in steradians, and d max , the maximum distance in parsecs (pc) that determines V max , is the minimum of the two following relations.
(3) The number density derived in this manner is 1.8 × 10 −4 pc −3 . Using 0.6 M ⊙ as the average white dwarf mass in the halo (28), the local space density of halo white dwarfs is 1.1 × 10 −4 M ⊙ pc −3 . However, our survey is not complete to the R59F = 19.8 level. A measure of the uniformity of our sample is given by the average value of V /V max , where V is the volume of space given by the distance to the given star and the survey area. In the case of this survey, the average of V /V max is 0.46. For a sample distributed uniformly in space, this value should be 0.5. An average of V /V max = 0.5 is found for R59F = 19.7, indicating that all stars brighter than 19.7, with the proper motion constraint mentioned above, were found in the survey. Recalculating the space density using R59F lim = 19.7 yields 1.3 × 10 −4 M ⊙ pc −3 .
The density of white dwarfs in the halo predicted from the subdwarf star counts and a standard initial mass function is 1.3×10 −5 M ⊙ pc −3 (29), which is ten times smaller than the value we calculate. This means that star formation in the early Galaxy must have favored higher-mass stars that would evolve into the white dwarfs we are detecting now. At the same time, this early star formation must have under produced the low-mass subdwarfs relative to the more recent star formation processes observed in the disk (4).
The estimated density of halo dark matter near the Sun is approximately 8×10 −3 M ⊙ pc −3 (30). Thus, the population we have detected accounts for about 2% of the local dark matter. We treat this number as a lower limit for the reasons discussed above and because it appears that we have not probed the entire range of intrinsic luminosities of these objects. Indeed, the number density as a function of M R59F suggests that we are only detecting the rising power law of the luminosity function and have not seen any indication of the expected turnover due to the finite life time of the halo white dwarf population (31). This means that there may be an undetected, larger population of even fainter and cooler white dwarfs in the halo.

Discussion
Microlensing experiments have indirectly revealed a population of massive, compact objects in the line of sight to the Large Magellanic Cloud. The Massive Compact Halo Object project (MACHO) (1) estimates that these compact objects contribute between 8 and 50% of the local halo dark matter at the 95% confidence level, and the inferred lens mass suggests that they are white dwarfs. The similar Expérience pour la Recherche d'Objets Sombres project (EROS) places a strong upper limit of 35% for such objects (32). Because the halo white dwarf space density that we derive from our survey represents a lower limit and is consistent with the two measurements mentioned above, the population of white dwarfs with halo kinematics that we have discovered provides a natural explanation for the microlensing results.
A number of the white dwarfs revealed in this survey may be cooler than any other white dwarf previously known. There are at least three objects ( Table 1) that are comparable in temperature to WD0346+246 (7), representing a doubling of the number of ultracool white dwarfs known. The nature of cool white dwarfs can be discussed on the basis of their positions in color-color diagrams. Although a combination of optical and infrared colors is necessary at these low effective temperatures (7,23), for now, we must contend with the limited spectral coverage of photographic plates for this sample. The comparison of B J , R59F , and I N (a bandpass centered on 0.8 µm) colors is a poor diagnostic of atmospheric composition for effective temperatures, T eff , greater than 3500 K (Fig. 4). Given the large photometric error bars, there is little that distinguishes the colors of these stars from a sample of cool white dwarfs with disk kinematics (33).
Stars with B J −R59F ∼ < 1.2 are relatively warm, with T eff ∼ > 5000 K (except for the strange stars LHS 3250, SDSS 1337+00 and LHS 1402). They are also the most luminous and most distant stars in the sample (Table 1). Although it is not possible to guess the atmospheric composition of any of these stars from the present data, we point out that the sample may contain a few unusual objects, in addition to the peculiar LHS 1402 and WD2356−209 (Fig.  2b). Other inferences, however, can be made from the photographic color-color diagram (Fig.  4), using stars previously studied. LHS 542 has a pure He atmosphere and T eff = 4747 K (24). WD0346+246 and F351−50 are similar to each other with predominantly He atmospheres, a very small admixture of H, and T eff of ∼ 3750 K and ∼ 3500 K, respectively (7). The most extreme star of the sample, and also the faintest, is WD0351−564 with B J − R59F = 1.98. The stars with B J − R59F > 1.6 (WD0351−564, WD0205−053 and WD0345−362) may have either pure He atmospheres with T eff > 4000 K or, more interestingly, be other examples of very cool white dwarfs with He atmospheres polluted by a small amount of H, like WD0346+246. The stars most likely to have pure H atmospheres residing below the color turnoff due to strong H 2 collision-induced opacity are WD0135−546, WD0340−330, and, perhaps, WD0351−564.
We still do not understand the nature of the three strange objects LHS 3250, LHS 1402, and SDSS 1337+00 (5-7), all of which lie at R59F − I N colors near −0.5 (well outside of Fig. 4). The kinematics of these stars, with the exception of LHS 1402, suggest that they may be disk objects. Although they are certainly cool white dwarfs, we know neither their effective temperatures nor their atmospheric compositions. They may represent another, perhaps unusual, stage in the spectral evolution of cool white dwarfs.
The direct detection of a significant white dwarf halo population opens promising avenues of investigation. Besides the opportunity to study individual white dwarfs that are older and cooler than any known so far, dedicated studies of this population of stellar remnants will bear directly on the ancient history of the Galaxy. For instance, a determination of the luminosity function of halo white dwarfs and a characterization of the low luminosity cutoff will reveal the age of the first generation of halo stars, lead to a determination of its initial mass function, and provide strong constraints on formation scenarios of the Galaxy. The interpretation of observations of young galaxies at high redshifts will benefit from a better understanding of the early history of our Galaxy. Finally, the complete characterization of this new stellar population will reveal whether it is responsible for the microlensing.   (20), who classify this object as "cool no Hα", and F351-50 was discovered by Ibata et al.    Table 1 are indicated. None of the fine features are real.  composition on a T eff = 3500 K model, with the number ratio of He to H ranging from 0 to 10 7 (7). All models have log g(cm s −2 )= 8. As a basis for comparison, three stars whose spectra have been studied in greater detail (3,7) are labeled. WD0346+246 is not part of our survey and is shown here for comparison.