THE WHITE DWARFS WITHIN 20 PARSECS OF THE SUN: KINEMATICS AND STATISTICS

The population of local white dwarfs (WDs) is astrophysically important for a number of reasons. First, from complete samples, it offers an excellent probe of the coolest, least luminous (oldest) component of the overall white dwarf population. Second, it samples the mix of stellar populations that evolve into the different spectroscopic subtypes in the immediate vicinity of the Sun. Third, it provides a unique way of measuring the local space density and mass density of white dwarfs which are currently of critical interest because: (1) they represent a history of star formation and stellar evolution in the Galactic plane; (2) the luminosity function of these stars can be used to place a lower limit on the age of the Galactic disk (Liebert 1988; Oswalt et al. 1996); (3) cool white dwarfs have been suggested as the origin of the MACHO lensing objects seen in lensing surveys (Oppenheimer et al. 2001; Kawaler 1996); and (4) they are important to understanding the overall mass density of the Galactic plane (Bahcall 1984).

Recently, Holberg et al. (2008, hereafter, LS08) completed a detailed survey of the local population of white dwarfs lying within 20 pc of the Sun which they estimated to be 80% complete. Their sample contained 124 individual degenerate stars, including both members of four unresolved double degenerate binaries, one of which was a suspected new double degenerate binary (WD0423+120). Since the publication of LS08, we have added seven additional white dwarfs to the 20 pc sample, bringing the present total to 131 degenerate stars. Two of these additional stars are close Sirius-like companions to nearby K stars (Holberg 2009), GJ86 (WD0208−510), and HD27442 (WD0415−594), discovered during exoplanet investigations (see Mugrauer & Neuhäuser 2005 and Chauvin et al. 2007, respectively). Of the remaining five single white dwarfs, three stars, WD0011−721, WD0708−670, and WD1116−470, are from Subasavage et al. (2008), and one star, WD1315−781, is from Subasavage et al. (2009). We have excluded one interesting high-velocity star, WD1339−340. Lepine et al. (2005) noted that this star had a space motion of 313 km s⁻¹ relative to the Sun based on an assumed distance of 18 pc. Holberg et al. (2008) determined that WD1339−340 has an estimated distance of 21.2 ± 3.5 pc placing it formally outside the limits of our 20 pc sample. Nevertheless, this star has a finite probability of being within 20 pc.

Including the new stars in the local sample of 129 white dwarfs within 20 pc, yields a revised white dwarf space density of (4.9 ± 0.5) × 10⁻³ pc⁻³. The corresponding mass density is (3.3 ± 0.3) × 10⁻³ M_☉ pc⁻³. The completeness of the sample, however, remains at 80% since the addition of the companion of GJ86 (at 10.8 pc) contributes to the number of white dwarfs within 13 pc upon which the stellar density is based.

In this work, we use the enlarged local sample to examine the kinematical properties, distribution of spectroscopic subtypes, and stellar population subcomponents of the white dwarfs sampled in this volume of space around the Sun.

Table 1 presents the sample of white dwarfs within 20 pc of the Sun. The basic observational data from which space motions have been computed are given in Table 1, which contains by column: (1) the WD number; (2) the coordinates (R.A. and decl. are in decimal degrees); (3) DIST (distance in parsecs); (4) PM (proper motion in arcsec yr⁻¹); (5) P.A. (position angle in degrees); and (6) the method of distance determination, denoted by p for trigonometric parallax, s for spectrophotometric distances, and a for a weighted average of the parallax and photometric distances according to their respective uncertainties. Distance estimates are taken from LS08 which are based on both trigonometric parallaxes and spectrophotometric distances. Whenever possible, preference was given to trigonometric parallax distances. In LS08, the photometric distances were computed based upon spectroscopic and photometric measurements using the techniques described in Holberg et al. (2008).

Proper motions are taken from the McCook and Sion Catalog, or where available, were determined from NOMAD. Radial velocities were available from the literature for approximately 50% of our sample, and correspond either to direct measurements of the white dwarf or the system velocities or radial velocities of the main-sequence companions. For radial velocities derived from individual white dwarfs, corrections for the gravitational redshift have been made based on the individual masses and radii of each star. These mass and radius determinations were interpolated from within the synthetic photometric tables described in Holberg & Bergeron (2006) and were based on temperatures and gravities given in LS08.

Using the spectral types given in LS08 and revised by Holberg (2009), we summarize the percentage breakdown of spectral subtypes among the 20 pc sample of local white dwarfs in Table 2. As expected, the DA stars dominate the sample with the other spectral groups having roughly the same percentages as the proper-motion-selected white dwarf sample as a whole.

The DAZ stars which exhibit photospheric metal lines due to accreted metals are counted separately from the "pure" DA stars in the 20 pc sample. The 11 DAZ stars within 20 pc account for 8% of the local sample while the DZ stars, which have helium-rich atmospheres account for 7% of the 20 pc sample. There is only one DB star within 20 parsecs, the cool DBQZ star LDS678A while the DQ stars, which exhibit molecular and atomic carbon, account for 9%.

The value of the total DA to non-DA ratio of the 20 pc sample, obtained here, is 1.6. This ratio holds important astrophysical significance since the competition between accretion, diffusion, and convective mixing controls and/or modifies the flow of elements in a high gravity atmosphere and hence determines what elements are spectroscopically detected at the surface (Strittmatter & Wickramasinghe 1971). The value of the ratio obtained here is expected for a sample dominated by cool degenerates since earlier observational studies showed that there is a gradual reduction of this ratio from 4:1 for white dwarfs hotter than 20,000 K down to roughly 1:1 for the coolest degenerates below 10,000 K (Sion 1984; Greenstein 1986). This transformation in the DA/non-DA ratio occurs when mixing by deepening envelope convection increasingly transforms DA white dwarfs with sufficiently thin surface H layers into non-DA stars (Sion 1984; Greenstein 1986, and references therein). However, DA stars begin their cooling evolution with a range of hydrogen layer masses. Those with thick hydrogen layers may not transform via convective mixing and dilution and will remain DA until the Balmer lines fade below 5000 K while DA stars with sufficiently thin hydrogen layers should undergo transformation to non-DA stars as the deepening H convection reaches the deeper, more massive underlying helium convection zone. Thus, some cooling DA stars may transform to DZ stars when the hydrogen is mixed downward and diluted by the deepening helium convection. Such an object would be classified DZA and may owe their observed H abundances to convective mixing and dilution instead of accretion.

For the local white dwarfs with sufficient kinematical information (photometric or trigonometric parallax, proper motion, position angle), we have computed the vector components of the space motion U, V, and W relative to the Sun in a right-handed system following Wooley et al. (1970) where U is measured positive in the direction of the Galactic anti-center, V is measured positive in the direction of the Galactic rotation, and W is measured positive in the direction of the north Galactic pole.

The space motions were calculated in two ways: (1) using any known radial velocities for 55 of the 129 stars in the 20 pc sample and (2) by assuming zero radial velocity for the entire sample. Also calculated were the average velocity, velocity dispersions, and standard errors for the entire sample of 129 WDs and for each spectroscopic subclass separately. We found relatively little kinematical difference among the samples if we used the 55 available radial velocities and the sample with the assumption of zero radial velocity. This finding is consistent with earlier studies (Silvestri et al. 2002; Pauli et al. 2003, 2006) which reported little difference in the kinematical results with or without the inclusion of radial velocities.

Table 3 lists by column: the WD number, the white dwarf spectral type, U-component, V-component, W-component, and T, the total space velocity. All velocities are expressed in km s⁻¹. At the end of the tabulation of individual white dwarf motions, we have listed the average velocity in each of the three vector components and in the total motion, T, for the white dwarfs within 20 pc, the velocity dispersion in each average velocity component, and the standard error in each velocity component.

In order to try to assign stellar population membership, it is useful to compare the distribution of space velocities of the 20 parsec sample with other analyses in which the assignment of population membership is on a secure footing. Since the population membership of main-sequence stars, unlike white dwarfs, is assigned with chemical abundance data as well as kinematical characteristics, it is illuminating to compare the distribution of white dwarfs in the UV velocity plane for the 20 pc sample with the velocity distribution (velocity ellipses) of a well-studied sample of main-sequence stars. In Figure 1, we have displayed the U versus V space velocity diagram for the 20 pc sample of white dwarfs with the assumption of zero radial velocity relative to three velocity ellipses for main-sequence stars (Chiba & Beers 2000; see also Kawka & Vennes 2006). In the diagram, we have displayed the 2σ velocity ellipse contour (solid line) of the thin disk component, the 2σ ellipse of the thick disk component (short-dashed line), and the 1σ contour of the halo component (long-dashed line).

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Examining Table 3, if we take T>150 km s⁻¹ as the lower cutoff for halo space motions, then at first glance, six stars or 4% of the total sample could be considered likely candidates for the halo population subcomponent. However, the assignment of white dwarfs to the halo population subcomponent cannot be made on the basis of space motions alone. The candidate white dwarfs must also have total stellar ages that are of order 12 billion years or older. In Table 4, we have tabulated the cooling ages of the white dwarfs in the 20 pc sample in descending order of decreasing age. The cooling ages listed in Table 4 have been interpolated from the photometric grid of P. Bergeron⁴. Hence, when we take into account the total stellar ages of each of the six stars in Table 3 with T>150 km s⁻¹, then we conclude that based upon their space motions together with their total stellar ages, no clear evidence of halo white dwarfs has been found among the white dwarfs within 20 pc of the Sun.

If we take the range of total velocities 60 < T < 150 km s⁻¹ to be the range of space motions of the thick disk subcomponent and if we take total motions less than 60 km s⁻¹ to be characteristic of the thin disk, then, at first glance, 28 white dwarfs (21% of the 20 pc sample) in Table 1 could potentially belong to the thick disk with the vast majority of stars (79%) belonging to the thin disk. However, distinguishing thin disk from thick disk members is a daunting task which involves far more than simply using space motions alone. Napiwotzki (2009) has already noted that it is not possible to uniquely identify thick disk stars from thin disk stars based on space motions in the U–V plane alone or even with all three vector components available. This is because the space motions of these thin and thick disk populations overlap. Napiwotzki (2006) used Monte Carlo simulations of the two populations to estimate the relative contribution of the two populations to his observed sample. Thus, in the range 60 km s⁻¹ <vtan < 150 km s⁻¹, it is not possible to uniquely identify bona fide thick disk stars without considering their total stellar ages as well as applying a Galactic model as was done by Pauli et al. (2006). Star formation in the thick disk ended more than 10 billion years ago. It is clear that white dwarfs which are the descendants of the thick disk population should have large velocity dispersions similar to those given by Chiba & Beers (2000) for the thick disk while having lower than average masses since they are the descendants of low mass progenitors (Napiwotzki 2009). The velocity dispersions, σ(U), σ(V), and σ(W) of the entire 20 pc sample lies below the boundary line for thick disk membership which is defined by Chiba & Beers (2000) to be σ(U) = 46 km s⁻¹, σ(V) =  50 km s⁻¹, and σ(W) =  35 km s⁻¹.

This conclusion about the absence of genuine thick disk members in the 20 pc sample is supported by Silvestri et al.'s (2002) study of 116 common proper-motion binaries with white dwarf plus M dwarf components. Their wide binary pairs gave them at least three independent parameters related to stellar population subcomponent membership: (1) abundance; (2) intrinsic radial velocity; and (3) age (from chromospheric activity, main sequence fitting, etc.). They present kinematics plots (see their Figures 4 and 5) of their wide binary pairs which indicate by comparison with our Figure 1 that there are few, if any, halo or thick disk objects in the local 20 pc WD sample. Our local sample has a far smaller velocity dispersion than the Silvestri et al. (2002) sample.

Even in much larger samples of white dwarfs such as the Pauli et al. (2003, 2006) SN Ia Progenitor surveY (SPY), there are relatively few genuine halo and thick disk candidates. For example, in their sample of 398 white dwarfs which effectively constituted a magnitude-limited sample, they examined both the UVW space motions and the Galactic orbits of their stars. They found that only 2% of their sample kinematically belonged to the halo and 7% to the thick disk.

Other explanations for high-velocity white dwarfs exist. For example, Rappaport et al. (1994) and Davies et al. (2001) have shown that Type II supernovae may disrupt binaries with orbital periods in the range of 0.3–2 days, yielding single stars whose space velocities are similar to their original presupernova orbital velocities, V_orb. Thus, a population of high-velocity white dwarfs can be expected to arise from within the thin disk component of the Galactic disk, at least from this mechanism. High-velocity stars may also arise from much wider binary pairs (see Kawka et al. 2006).

In Table 5, we have tabulated the velocity statistics broken down by spectral subgroup. By column is listed: (1) the spectroscopic subgroup; (2) N, the number of white dwarfs of a given spectral type; (3) the vector components of velocity U,  V, andW and the total motion T; (4) the average velocity in each component; (5) the velocity dispersion of each component; and (6) the error in each component. The motions of individual spectroscopic subgroups, as seen in Table 5, differ little from each other although compared with the size of the DA sample, the non-DA groups are relatively small in number. The only subgroup of white dwarfs differing significantly at least from the non-DA subgroups are the magnetic white dwarfs, which have significantly lower space velocities. Here again, caution is advised because there are only 16 magnetic degenerates with known space motions within 20 parsecs of the Sun. Nonetheless, the trend is in the direction expected from earlier kinematical evidence (Sion et al. 1988; Anselowitz et al. 1999) that they are the progeny of more massive stars. We find a smaller fraction of magnetic white dwarfs, 12%, of the 20 pc sample than Kawka & Vennes (2006) who found 20% magnetics within 13 pc of the Sun. However, given the quoted uncertainty in the percentage of magnetic degenerates in their sample and the lower completeness of the 20 pc sample, we cannot attach any significance to the differences at the present time.

Finally, although the number of stars in each non-DA spectroscopic subgroup may be too small for a statistically significant comparison, it appears that the magnetic white dwarfs have significantly lower velocities and velocity dispersions than the non-DA spectral types. However, magnetic white dwarfs closely resemble the kinematical properties of the DA white dwarfs within 20 pc.

We have attempted to fully characterize the white dwarfs within 20 pc of the Sun since LS08. By adding six new objects within 20 pc, there is now a total of 129 individual degenerate stars. Three of the added objects are from Subasavage et al. (2008), one object is from Subasavage et al. (2009), and two are in wide binaries (Holberg 2009). The completeness of the 20 pc sample remains at 80%. Based upon the sample of white dwarfs within 13 pc which is likely 100% complete, the local space density of white dwarfs has been revised to (4.9 ± 0.5) × 10⁻³ pc⁻³.

In this volume-limited sample, every major white dwarf spectral type (DA, DC, DQ, DZ, DH/DP) is found except for the pure DB and DO stars. There is, however, one cool, hybrid DB, the DBQZ star LDS678A within 20 pc. Based upon their individual space motions, velocity averages, velocity dispersions, and total stellar ages, the 20 pc sample of white dwarfs overwhelmingly consists of members of the thin disk population. There is no clear evidence of either halo population white dwarfs or bona fide thick disk members. It also appears that the magnetic white dwarfs have significantly lower velocities and lower velocity dispersions than the non-DA spectral types but similar velocity dispersions to the DA stars with 20 pc.

We have taken a census of DAZ and helium-rich DZ stars within 20 pc of the Sun. The DAZ stars which exhibit accreted metals and which have shorter diffusion timescales than non-DA stars, have been counted separately from the "pure" DA stars in our statistics. However, we note that there are 11 such objects or 8% of the local white dwarfs within 20 pc. Because of their short diffusion timescales, they must be accreting presently or in the very recent past. This fact coupled with the complete lack of any local interstellar clouds of sufficient density (Aannestad & Sion 1985; Aannestad et al. 1993) implies they must be accreting from circumstellar material. This has been confirmed by the detection with Spitzer Space Telescope of debris disks around several DAZ stars (Farihi et al. 2009, and references therein). The accretion rates required to explain their observed metal abundances are as little as 3 × 10⁸ g s⁻¹.

The helium-rich DZ stars which typically exhibit calcium and magnesium in the optical spectra account for 7% of the 20 pc sample. They have much longer diffusion timescales (and deeper convection zones) than DAs. As cooling helium-rich white dwarfs cool below 12,000 K, helium lines can no longer be detected. Since H is the lightest element, it tends to float up to the upper layers of the photosphere. Those DZs with detected H, known as DZA stars, may also have accreted H and metals from the interstellar medium or from circumstellar debris disks. However, DZ stars contain less hydrogen in their atmospheres than what is expected if the accreted material had a solar composition. Thus, the hydrogen accretion rate must be reduced relative to that of metals in order to account for the relatively low hydrogen abundances (with respect to heavier elements) observed in DZ stars (Dufour et al. 2007). While the Dupuis et al. (1993) two-phase model of interstellar accretion onto white dwarfs cannot be ruled out completely, the cooler DZ stars do not have the strong UV radiation field needed to ionize accreting H so that a weakly magnetic, slowly rotating DZ would avoid H accretion by the propellor mechanism.

Despite the detection of debris/dust disks around some but not all metal polluted white dwarfs observed by Spitzer, it appears highly probable that virtually all of the DAZ stars owe their metals to circumstellar accretion. Thus, from our 20 pc census of white dwarfs, if we consider only the DAZ stars, then we estimate a lower limit percentage of at least 8% of the white dwarfs within 20 parsecs of the Sun that probably have circumstellar material (debris disks) around them. Insofar as we can regard the DAZ white dwarfs as probes of their circumstellar environments, then this would suggest a high probability that at least the same percentage should have asteroid-like minor planets and possibly even terrestrial-like rocky metallic planets. Indeed one local white dwarf G29−38 (WD2326+049) in our 20 pc sample is known to have a dusty debris disk (Zuckerman & Becklin 1987) while three white dwarfs in our 20 pc sample are in systems with confirmed extrasolar planets, WD0208−510 (K1V + DA10), WD0415−594 (K2IV + DA3.8), and WD1620−391 (G2V + DA2), although the planets in the latter three systems do not orbit the white dwarf. Furthermore, if we suppose that the DZ stars, including the DZA stars (but see Section 2), have also accreted circumstellar material (have debris disks), then summing the DZ stars with the DAZ stars, we speculate that at least 15% of the white dwarfs within 20 pc of the Sun have circumstellar debris disks with rocky, metallic debris.

We have excluded the DQ stars from this estimate. While it is possible that the DQ white dwarfs may accrete from circumstellar or even interstellar matter, we do not include them in our estimate because we regard it more likely that the source of their photospheric carbon is either due to convective mixing (Dufour et al. 2005, and references therein) or is primordial (Dufour et al. 2007). Indeed, only one DQ has been found to have atmospheric hydrogen (G99−37). Accreted metals are also easier to hide in DQ atmospheres due to the increased opacity provided by carbon.

We are grateful to an anonymous referee for numerous helpful suggestions and comments. This work was supported by NSF grant AST05-07797 to the University of Arizona, Villanova University, and the Florida Institute of Technology. Participation by TDO was also supported by NSF grant AST-0807919 to FIT.