Astronomy & Astrophysics manuscript no. white2v4 c© ESO 2018
November 4, 2018
Trigonometric parallaxes of high velocity halo white dwarf
candidates ?
C. Ducourant1, R. Teixeira2,1, N.C. Hambly3, B. R. Oppenheimer4, M.R.S. Hawkins3, M. Rapaport1, J. Modolo1, and
J.F. Lecampion1
1 Observatoire Aquitain des Sciences de l’Univers, CNRS-UMR 5804, BP 89, 33270 Floirac, France.
2 Instituto de Astronomia, Geofı́sica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226 - Cidade Universitária,
05508-900 São Paulo - SP, Brasil.
3 Scottish Universities Physics Alliance (SUPA), Institute for Astronomy, School of Physics, University of Edinburgh, Royal
Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK.
4 Department of Astrophysics, American Museum of Natural History, 79th Street at Central Park West, New York, NY 10024-5192,
Received / Accepted
ABSTRACT
Context. The status of 38 halo white dwarf candidates identified by Oppenheimer et al. (2001) has been intensively discussed
by various authors. In analyses undertaken to date, trigonometric parallaxes are crucial missing data. Distance measurements are
mandatory to kinematically segregate halo object from disk objects and hence enable a more reliable estimate of the local density of
halo dark matter residing in such objects.
Aims. We present trigonometric parallax measurements for 15 candidate halo white dwarfs (WDs) selected from the Oppenheimer et
al. (2001) list.
Methods. We observed the stars using the ESO 1.56-m Danish Telescope and ESO 2.2-m telescope from August 2001 to July 2004.
Results. Parallaxes with accuracies of 1–2 mas were determined yielding relative errors on distances of ∼ 5% for 6 objects, ∼ 12%
for 3 objects, and ∼ 20% for two more objects. Four stars appear to be too distant (probably farther than 100 pc) to have measurable
parallaxes in our observations.
Conclusions. Distances, absolute magnitudes and revised space velocities were derived for the 15 halo WDs from the Oppenheimer
et al. (2001) list. Halo membership is confirmed unambiguously for 6 objects while 5 objects may be thick disk members and 4
objects are too distant to draw any conclusion based solely on kinematics. Comparing our trigonometric parallaxes with photometric
parallaxes used in previous work reveals an overestimation of distance as derived from photometric techniques. This new data set can
be used to revise the halo white dwarf space density, and that analysis will be presented in a subsequent publication.
Key words. Astrometry : trigonometric parallax – Dark matter – Galaxy : halo – Star : kinematics – white dwarfs.
1. Introduction
In the last decade interest in the very cool, old white dwarf (WD)
halo population has grown. This interest is motivated by the pos-
sibility that these objects could account for a significant fraction
of the baryonic dark matter of our Galaxy. This idea is in accord
with discussions attempting to explain the microlensing events
in the Large Magellanic Cloud in terms of a halo WD popula-
tion – see, for example, Chabrier et al. 1996 and Hansen 1998.
Alcock et al. 1999 suggested that massive compact halo objects
(MACHOs) make up 20 to 100% of the dark matter in the halo,
with MACHOs having typical mass m ∼ 0.5 M�; more recently,
Calchi Novati et al. 2005 find a similar result from pixel lensing
in the line of sight to M31. Hence, in this scenario the search
for, and direct study of, halo WDs can provide constraints on
the fraction of dark matter in the Milk Way that is attributable to
these objects.
Oppenheimer et al. (2001, hereafter OHDHS) identified 38
high proper motion WDs; from their kinematics, the authors
Send offprint requests to: ducourant@obs.u-bordeaux1.fr
? Based on observations collected at the European Southern
Observatory, Chile (067.D-0107, 069.D-0054, 070.D-0028, 071.D-
0005, 072.D-0153, 073.D-0028)
concluded that they were members of a halo population. Since
then an intense discussion concerning the status of these objects
has taken place in the literature. A comprehensive review of
this debate is presented in Hansen and Liebert 2003 where the
conclusion is that the OHDHS interpretation is possibly over-
stated, but that complete conclusions are not possible without
further data. Other studies suggest that the disk and “thick disk”
Galactic populations can be used to explain the great majority
of the objects (Reid 2005, Kilic et al. 2005, Spagna et al. 2004,
Crézé et al. 2004, Holopainen & Flynn 2004, Flynn et al. 2003,
Silvestri et al. 2002). The importance of the high velocity WDs
cannot be understated in other contexts (e.g. the star forma-
tion history of the Galaxy, see also Davies, King & Ritter 2002,
Hansen 2003, Montiero et al. 2006). Moreover, several stud-
ies emphasise the importance of obtaining trigonometric par-
allaxes for candidate halo WDs (Bergeron & Leggett 2002,
Torres et al. 2002, Bergeron 2003). This is especially important
for the coolest WDs, whose spectral energy distributions show
remarkable departures from black–body distributions and which
are proving to be difficult to model accurately (Kowalski 2006,
Gates et al. 2004, Saumon & Jacobson 1999, Hansen 1998). In
the presence of such radical changes to the WD spectrum, the as-
sumption of a monotonic photometric parallax relation (e.g. as
2 C. Ducourant et al.: Parallaxes of halo white dwarf candidates
used in OHDHS) could break down and estimates of intrinsic
space velocities could be in error seriously. Furthermore, a recent
paper (Bergeron et al. 2005) concludes that precise distances are
mandatory to derive accurate kinematics and ages for the puta-
tive halo WDs and in order to derive their evolutionary status.
Aiming to clear up this question, in 2001 we started an ob-
serving program with the ESO 1.56-m Danish and ESO 2.2-m
telescopes to measure the trigonometric parallaxes of these stars.
Trigonometric parallax measurements remain the only direct un-
biased distance determination. They are of great importance in
the debate about the status of cool halo white dwarfs because
they are required to derive precise space velocities and ages
which are used for distinguishing between halo and disk mem-
bership. These trigonometric parallaxes lead to the re-calibration
of photometric distances used until now in this debate and allow
analysis of the cool halo white dwarf population with more con-
fidence. Unfortunately, due to limited observing time, only 15
stars on the OHDHS list have been observed to date. However,
this sub-sample provides important insight into the problem.
2. Observations
Astrometric observations of 15 of the OHDHS list of 38 halo
white dwarf candidates were performed at the ESO 2.2-m tele-
scope equipped with the WFI wide–field mosaic camera (with
0.238 ′′/pixel, a field of view FOV = 34′ × 33′, 4 × 2 mosaic of
2k × 4k CCDs), through the ESO 845 I filter. To reduce astro-
metric distortions and other instrumental effects, only data from
chip 51 (with FOV = 8′× 16′) were used in this work; target stars
were centered in the FOV of this chip.
Four epochs of observation were acquired at maximum
parallactic factor in Right Ascension in November 2002, July
2003, November 2003 and July 2004 with a total of 11 nights of
observations. Two parallactic periods (four observations over 1.5
years) are required, at a minimum, for a unique determination
of the parallax and proper motion. Two preliminary observing
runs were performed at the ESO 1.56-m Danish telescope in
July 2001 and July 2002 but the subsequent closure of the
telescope forced the authors to move the program to the ESO
2.2-m telescope. Data acquired at the Danish telescope were not
included in our final analysis to avoid systematic effects due to
the use of two different telescopes.
To minimize differential colour refraction effects (DCR), ob-
servations were performed around the transit of targets with hour
angles of less than 1 hour. Multiple exposures were taken at
each observation epoch to reduce the astrometric errors and to
estimate the precision of measurements. Exposure times varied
from 100 to 600 seconds depending on the magnitude of the tar-
get. Each field was observed from 20 to 35 times.
3. Astrometric Reduction
3.1. Measurements
Frames were measured using the DAOPHOT II package (Stetson
1987), fitting a PSF. The significance level of a luminosity en-
hancement over the local sky brightness which was regarded as
real was set to 7σ. The PSF routine was used to define a stel-
lar point spread function for each frame. Finally we obtained the
(x, y) measured positions, the internal magnitudes and associated
errors of all stars on each frame. There were typically 300 to 600
stars measured on each frame depending on the exposure time.
From these, a selection on the error in magnitude (ERRMAG)
as derived by the DAOPHOT II software was applied. Any ob-
servation with ERRMAG ≥ 0.15m was rejected. Objects fainter
than 1.5m brighter than a given image’s limiting magnitude were
also rejected from the analysis.
3.2. Cross-Identification
For each of the 15 different fields of view, we selected a “master”
or fiducial image from the set of 20 to 35 images. This master
frame for each object had the deepest limiting magnitude and
highest image quality. For each of the other images for a given
target object, the positions of all stars not rejected by the crite-
ria above were then cross–identified to the master image’s star
positions. Objects not detected on three or more frames were
excluded, yielding 100 to 200 stars in common in each field.
Frames containing less than Nmaster/3 stars in common with the
master frame were removed from the solution (where Nmaster is
the number of stars in the master frame). Note that the master
frame is processed in an identical fashion to the other frames
and is not assumed to be free of errors in the parallax solution.
In other words, the fiducial frames are not taken as an error-free
“truth”, but are simply used as a basis for coordinate transfor-
mations and correlation of star positions that comprise the astro-
metric grid used in the solution.
3.3. Differential Colour Refraction
Atmospheric refraction changes the apparent positions of stars in
ground–based observations and depends on the zenith distance
of the observations. For precision astrometry this effect must be
accounted for, because it can be many tens of milliarcsececonds
at even relatively modest zenith distances. In our case, another
effect becomes important as well, because the atmospheric re-
fraction of our target stars will not be identical to that of the
background stars used for our astrometric reference grid. Our
target stars (WDs) and the background stars (typically main–
sequence G or K stars) have different spectral energy distribu-
tions. Therefore, atmospheric refraction will affect them differ-
ently when observed through a given filter bandpass. This is
called a differential colour refraction (DCR) and is known to
cause spurious parallactic motion Monet et al. 1992. DCR can
affect both the Right Ascension (RA) and Declination of the tar-
get as derived with respect to the field stars. Observations in par-
allax programs are planned to maximize the parallactic factor in
RA so the parallax solution for the target will rely heavily on
the RA measured. Therefore the parallax derived is mainly per-
turbed by the DCR effects in RA which are critically dependent
on the zenith distance of a given observation.
We investigated the impact of such effects on the parallax
of white dwarfs through simulations. Using the usual formula
for atmospheric refraction, a blackbody approximation for white
dwarf and background stellar spectra, the Besançon Galaxy
model for background star characteristics (Robin et al. 1994)
and ESO 845 filter limits, we computed the average differen-
tial colour refraction effects between a white dwarf similar to
those of our list with effective temperatures, Teff , in the range
4000 K to 11000 K (Bergeron et al. 2005, Table 2) and a typical
background star (Teff ∼ 5000 K).
We present in Fig. 1 the effects of DCR in RA for white
dwarfs situated at δ = −30◦, covering the range of temperatures
of our targets. Fig. 1 demonstrates that the impact of DCR effects
were always less than 0.5 mas for observations taken with an
hour angle of less than one hour. Therefore, our observations
C. Ducourant et al.: Parallaxes of halo white dwarf candidates 3
were made specifically so that the hour angle never exceeded
one hour, and DCR corrections were not applied in this work.
Fig. 1. DCR effects in RA between a white dwarf of temperature
Teff and a mean background stars (Teff=5000K) at a Declination
of −30◦ (representative of our sample) for various hour angles of
observation. The DCR effects appear to be always lower than 0.5
mas for observations performed at less than 1 hour from merid-
ian which is the case of the present project. The DCR effects are
then negligible compared with other sources of astrometric error
and were not taken into account in this work.
3.4. Impact of Pixel Scale Errors on Parallax
Proper motions (µx, µy) and trigonometric parallax (πxy) of tar-
gets are determined by comparing the (x, y) measurements ex-
pressed in pixels. A scaling factor S f , the image pixel scale, is
applied to πxy to convert pixel measurements into physical units:
π = S fπxy; d(pc) = π−1, with S f expressed in ′′/pixel.
Derivation of the pixel scale can be achieved through a
cross–correlation between the (x, y) positions of stars on a given
master frame to corresponding values of (α, δ) for the subset of
stars that are also in a reference catalogue. Here we used the
2MASS catalogue (Cutri et al. 2003) to determine the orienta-
tion of the master frame on the sky and for the pixel scale deter-
mination. We selected the 2MASS catalogue as a reference cat-
alogue because of its accuracy and density although we note the
absence of proper motion corrections. Nevertheless the epoch
difference between our observations and the 2MASS catalogue
(3 years) would result in negligible corrections to the catalogue
positions with respect to the catalogue errors.
Errors on the scale so determined, resulting from catalogue
random errors, will produce errors in the distance determination
of the target. It is therefore important to quantify the impact of
the catalogue errors onto the distance of the target.
To measure this impact in the present work, we assumed N
reference stars equally spread over a square detector of side A.
The classical equation relating the (x, y) measurements of a stars
on the frame to its standard coordinates X(α, δ),Y(α, δ) in the
tangent plane to the celestial sphere is (with a similar equation
in the Y coordinate)
X = (ax + by + c)1/F, (1)
where (a,b,c) are the unknown “plate” constants and F the focal
length of the telescope (typically the value indicated in the ref-
erence manual). F is expressed in the same units as (x,y) and A
(pixel, mm). It is then easy to show that a fair approximation of
the variance of the estimation of parameter (a) is given by
�cat, (2)
where �cat is the catalogue precision (expressed in radians).
Similar results can be found in Eichhorn & Williams 1963. We
can express the parallax (in radians) as:
πxy, (3)
σ2π = π
σ2a, σπ =
�cat (4)
with F ∼ 13m, A ∼ 0.03m, we evaluate here σπ ∼ 10−4π. The
impact of the error of the catalogue on the parallax of the target
is far below the measurement errors (typically a few milliarcsec-
onds) and are therefore negligible.
3.5. Global Solution: Relative Parallax
The astrometric reduction of the whole set of data of each
field is performed iteratively through a global central overlap
procedure (Hawkins et al. 1998, Eichhorn 1997) in order to
determine simultaneously the position, the proper motion and
the parallax of each object of the field.
The following condition equations are written for each star
on each of the N frames considered (including the master frame).
These equations relate the measured coordinates to the stellar
astrometric parameters:
X0 + ∆X0 + µX(t − t0) + πFX(t) = a1x(t) + a2y(t) + a3 (5)
Y0 + ∆Y0 + µY (t − t0) + πFY (t) = b1x(t) + b2y(t) + b3 (6)
where (X0,Y0) are the known standard coordinate of the star at
the epoch t0 of the master frame, and (x(t), y(t)) its measured
coordinates on the frame (epoch t) to be transformed into the
master frame system. ∆X0, ∆Y0, µX , µY and π are the unknown
stellar astrometric parameters: (∆X0, ∆Y0) yield correction of the
standard coordinates of the star on the master frame, (µX , µY ) are
the projected proper motion in RA ∗cos(δ) and Dec, and π is the
parallax. Coefficients (ai, bi) are the unknown frame parameters
which describe the transformation to the master frame system.
(FX , FY ) are the parallax factors in standard coordinates. The
unknowns of this large over–determined system of equations are
the stellar astrometric parameters of each object, and the trans-
formation coefficients of each of the N frames considered. The
system of equations is singular and therefore the derived solution
is not unique; any solution will depend on the starting point of
the iterations. The usual technique to obtain a particular solution
is to introduce a set of constraints that the solution must satisfy.
In this work we chose to set strictly to zero the mean parallax of
the reference stars.
We used a Gauss–Seidel type iterative method to solve the
set of equations. At the first iteration all stellar parameters are
assumed null, we then computed the plate constants which are
4 C. Ducourant et al.: Parallaxes of halo white dwarf candidates
injected into the system of equations to derive the stellar param-
eters. These results are then used as the starting point of the fol-
lowing iteration. The iterative procedure converges usually at the
second or third iteration. A test of elimination at 3σ is applied to
remove poor observations either in the master frame fit or in the
stellar parameters fit. The stellar parameters fit equations have
been weighted by the mean residual of the master frame fit. This
weighting represents the quality of the measurements. The stars
used for the master frame fit are called here reference stars.
We applied this global treatment to the various observations
of the 15 fields observed and we derived for the targets a proper
motion and parallax with associated variances.
3.6. Conversion from Relative to Absolute Parallax
The parallaxes that we derived for our targets are relative to the
reference stars (for which we used the constraint
π = 0), sup-
posed placed at infinite distance. In fact these reference stars are
at a finite distance from Sun. We must therefore correct the rela-
tive parallax of the target from an estimate of the mean distance
of the reference stars to obtain the absolute parallax of the target.
The choice we made to keep as many reference stars as possible
in our calculation is interesting because statistically faint stars
have smaller parallax and require smaller correction.
There are several ways to estimate the mean distance of
reference stars: statistical methods relying on a model of the
Galaxy; spectroscopic parallax; and photometric parallax. For
the corrections from relative parallax to absolute parallax we
used a statistical method relying on simulations using the
Besançon Galaxy model (Robin et al. 1994) to derive the theo-
retical mean distance of reference stars. A simulation of each ob-
served field was performed, providing catalogues of distance and
apparent magnitude of simulated stars. We computed in these
catalogues mean distances and associated dispersion in magni-
tude bins of 0.2 mag, establishing a table of theoretical distances
with respect to apparent magnitude. Then we considered our ob-
served fields and we computed the weighted mean parallax and
associated dispersion of our reference stars using the theoretical
table. Finally we added this mean parallax of reference stars to
the relative parallax of our target leading to the absolute parallax
of the white dwarfs.
We give in Table 1 the relative to absolute corrections in mil-
liarcseconds as found from the Besançon Galaxy model in each
of the field treated.
4. Results
4.1. Distances of Halo White Dwarf Candidates
We present in Table 2 the proper motions and absolute parallaxes
of the fifteen halo white dwarf candidates as derived from this
work together with their absolute magnitude MV computed using
CCD V magnitudes from Bergeron et al. (2005).
One notices that WD2326–272, LP586–51, LP588–37, and
WD2324–595 are too distant to have a measurable parallax.
Eleven objects are at distances ranging from 19 pc to 90 pc from
the Sun. The parallax errors are about 1–2 mas corresponding
to relative precisions of 5 to 20%. WD2214–390, which is the
closest and brightest object, has a σπ = 2.6 mas. This poor pre-
cision is due to the short exposure time used to avoid saturation
problems and corresponding lower signal–to–noise ratio.
We present in Figs 8 and ?? the positions (empty circles),
their weighted mean (filled circles) and associated error bars at
Table 1. Relative to absolute corrections ∆π and associated
RMS (σ) as found from the Besançon Galaxy model in the
Galactic direction (l,b) together with number of reference stars
(N*) in magnitude interval [Jmin,Jmax].
Target l b ∆π σ N* Jmin Jmax
[◦] [◦] [mas] [mag]
WD2214-390 2.79 -55.37 1.3 0.3 38 13.1 16.2
WD2242-197 40.01 -59.42 1.0 0.3 97 14.0 18.4
WD2259-465 344.30 -60.62 1.1 0.2 83 13.6 18.0
LHS542 72.40 -59.70 1.2 0.3 42 13.4 17.0
WD2324-595 321.83 -54.34 1.1 0.2 62 13.3 17.0
WD2326-272 27.66 -71.06 1.3 0.4 80 14.2 18.7
LHS4033 90.24 -61.96 1.3 0.2 39 14.2 16.5
LHS4041 351.44 -74.66 1.4 0.3 37 13.5 16.2
LHS4042 6.55 -76.61 1.5 0.4 38 13.3 16.6
WD0045-061 118.54 -68.96 1.5 0.3 54 13.5 17.7
F351-50 314.26 -83.50 0.3 0.2 53 14.1 18.1
LP586-51 128.88 -63.30 1.3 0.3 47 14.1 17.4
WD0135-039 149.30 -64.53 1.3 0.2 82 14.4 19.0
LP588-37 150.44 -61.52 1.4 0.2 57 13.6 17.7
LHS147 178.72 -73.56 1.5 0.3 43 13.4 16.8
each epoch of observation, together with the fitted path for the
eleven most significant parallaxes, where π/σπ ≥ 4.
4.2. Comparison with Published Distances
We have compared our results with available data from the lit-
erature, employing both trigonometric and photometric paral-
laxes measured previously. We give in Table 3 the comparison
with published trigonometric parallaxes and in Figure 2 a com-
parison of the parallaxes derived in this work with photomet-
ric parallaxes (from OHDHS, where photometric parallax errors
were 20%). Parameters of a weighted linear fit between pho-
tometric and trigonometric parallaxes are: πtrig = a.πphot + b
with a = 1.08+/-0.08 and b = 3.21+/-1.56 [mas] with a reduced
χ2 =8.06.
Table 3. Comparison of trigonometric parallaxes from this
work (πThiswork) with published data (πext) for LHS 147
(Van Altena et al. 1995), LHS 4033 (Dahn et al. 2004) and LHS
542 (Bergeron et al. 2005).
Target πThiswork πext ∆π
[mas] [mas] [mas]
LHS 542 29.6 +/- 1.8 32.2 +/- 3.7 2.6
LHS 147 14.8 +/- 1.8 14.0 +/- 9.2 –0.8
LHS 4033 30.1 +/-1.8 33.9 +/- 0.6 3.8
Our parallaxes are in excellent agreement with the 3 pre-
viously published trigonometric parallaxes, within the errors
(which are considerably smaller in two cases than published val-
ues). In Fig. 2 one notices a clear systematic tendency of pho-
tometric parallaxes to be underestimated. This overestimation of
OHDHS distances is of importance in the calculation of WD
kinematics and space density.
C. Ducourant et al.: Parallaxes of halo white dwarf candidates 5
Table 2. Proper motion and absolute parallaxes of the fifteen halo white dwarf candidates, where µα∗ = µαcos(δ) and σµ=σµα∗=σµδ ;
π and σπ are the parallax and its precision, Dist the derived distance in parsec and MV the absolute magnitude. No value is given
for Dist and Mv when the parallax is not better than 3 σ. N* is the number of reference stars and Nf the Number of frames. Dphot
is the photometric distance from OHDHS and V is extracted from Bergeron et al. (2005) when available, otherwise (cases marked
by an asterix) it comes from Salim et al. (2004). Note that LHS 4041 is in the OHDHS sample, but is not listed in OHDHS Table 1
(see Table 4 of Salim et al. 2004)
Name α δ Epoch V µα∗ µδ σµ π σπ Dist Mv N* Nf Dphot
[J2000] [yr] [mag] [mas/yr] [mas] [pc] [mag] [pc]
WD2214–390 22 14 34.727 –38 59 07.05 2003.5 15.92 1009 –350 2.9 53.5 2.6 19 14.78 38 28 24
WD2242–197 22 41 44.252 –19 40 41.41 2003.5 19.74 359 +48 3.1 11.1 2.3 90 14.89 97 27 117
WD2259–465 22 59 06.633 –46 27 58.86 2002.9 19.56 402 –153 1.8 22.7 1.3 44 16.49 83 32 71
LHS542 23 19 09.518 –06 12 49.92 2003.5 18.15 –615 –1576 1.8 29.6 1.8 34 15.58 42 33 42
WD2324–595 23 24 10.165 –59 28 07.95 2003.5 16.79 136 –562 1.8 (3.1) 1.5 —- —- 62 25 58
WD2326–272 23 26 10.718 –27 14 46.68 2002.9 ∗19.92 574 –85 2.7 (6.2) 2.4 —- —- 80 17 108
LHS4033 23 52 31.941 –02 53 11.76 2002.9 16.98 631 298 2.5 30.1 1.8 33 14.38 39 26 63
LHS4041 23 54 18.793 –36 33 54.60 2002.9 ∗15.46 21 –662 1.8 13.4 1.5 75 11.10 37 27 59
LHS4042 23 54 35.034 –32 21 19.44 2003.5 17.41 421 –37 2.2 13.9 1.8 72 13.13 38 25 85
WD0045–061 00 45 06.325 –06 08 19.65 2002.9 18.26 111 –668 1.9 30.1 1.9 33 15.59 54 27 44
F351–50 00 45 19.695 –33 29 29.46 2003.5 19.01 1820 –1476 2.1 28.3 1.4 35 16.63 53 34 37
LP586–51 01 02 07.181 –00 33 01.82 2002.9 18.18 350 –118 3.6 (2.4) 2.7 —- —- 47 24 120
WD0135–039 01 35 33.685 –03 57 17.90 2002.9 19.68 456 –180 3.4 13.3 2.9 75 15.26 82 21 146
LP588–37 01 42 20.770 –01 23 51.38 2002.9 ∗18.50 112 –328 3.4 (1.4) 4.5 —- —- 57 17 120
LHS147 01 48 09.120 –17 12 14.08 2002.9 17.62 –115 –1094 2.1 14.8 1.8 68 13.46 43 29 71
Fig. 2. Comparison of parallaxes derived in this work with pho-
tometric parallaxes from OHDHS (errors are assumed 20% for
πphot). Parameters of a weighted linear regression (diagonal line)
between both types of parallaxes are π = 1.08πphot + 3.21 [mas]
with a reduced χ2 = 8.06. The photometric distances are sys-
tematically larger than the astrometric ones.
4.3. Proper Motions
We have compared the proper motions derived here with the
OHDHS proper motions in order to check wether some system-
atic effects could affect our proper motions derived on a 1.5 yr
time span and, as a result, our parallaxes. We present this com-
parison in Fig. 3 and Fig. 4. Error bars are drawn in both co-
ordinates but since the present work has much higher precision
than the photographic astrometry, the error bars in x are not vis-
ible. The slope of a linear regression between proper motions in
α cos(δ) derived in this work with the OHDHS proper motions
is 1.04 ± 0.02 with a reduced χ2 = 3.7. The equivalent linear
fit in proper motions in Declination has a slope of 1.01 ± 0.02
with a reduced χ2 = 0.7. For F351-50 (the largest error bars in
both figures), the accordance in RA and Dec proper motions is
not good. This is due to a known problem of contamination by
a background galaxy of the Schmidt plate measurements used
in the OHDHS work. Nevertheless the accordance is within 2σ.
These comparisons show excellent agreement between both sets
of proper motions, and argue against any systematic effects from
the present work.
4.4. Space Velocities
We derived the Galactic space velocities U, V, W
(Johnson and Soderblom 1987) for the white dwarfs using
the distances and proper motions measured here together with
radial velocities from Salim et al. 2004 (data available for 9
of the 15 white dwarfs treated here). Salim’s observed radial
velocities were corrected for a mean gravitational redshift of
+28km/s as suggested by the authors in their paper except in
the case of the very massive white dwarf LHS4033 were the
correction was taken from Dahn et al. 2004. U is radial toward
the Galactic center, V is in the direction of rotation and W
perpendicular to the Galactic disk. U,V and W were corrected
for the Sun’s peculiar velocity (Mihalas and Binney (1981)).
When no radial velocity was available from other studies, we
assumed Vr = 0 km/s. This approximation is acceptable due to
its minor impact on U,V velocities since the targets are located
6 C. Ducourant et al.: Parallaxes of halo white dwarf candidates
Fig. 3. Comparison of proper motions in RA cos(δ) with the
OHDHS proper motions. Error bars are drawn in both coordi-
nates but since the present work has much higher precision than
the photographic astrometry, error bars in abscissae are not visi-
ble. The slope of a linear regression (dotted line) is 1.04 ± 0.02
indicating good accordance between both proper motion data
sets with a reduced χ2 = 3.7.
close to South Galactic Cap (the effect was investigated in
OHDHS and shown to be negligible).
We present in Figure 5 the distribution of velocities in
the Galactic plane together with the velocity dispersion for
the disk (right most)(1, 2 and 3 σ), thick disk (middle)(1,
2 and 3 σ)( Fuhrmann 2004) and halo (left) (1 and 2σ)
(Chiba and Beers 2000) and in Figure 6 the component of mo-
tion perpendicular to the Galactic plane. These two figures con-
cern the 11 objects with parallax measured at the 4σ level or
better.
In Fig. 5 one notices that 4 of the 11 studied WDs have a
velocity incompatible at the 3σ level with the kinematic of the
disk and of the thick disk and that 6 of them are incompatible at a
2σ level. No star lies within the 1σ ellipse of the disk, primarily
because of selection effects in the original proper motion survey
that OHDHS based is based upon Hambly et al. 2005.
Obviously the choice of the center and dispersions of halo,
thick disk and disk ellipses is critical to classify objects as be-
longing to a particular population. We adopted recent values
which are in in the range of the values cited by Reid 2005
in his review: Disk (Fuhrmann 2004) : (U,V) = (7.7, −18.1)
km/s, (σU , σV ) = (42.6, 22.6) km/s; thick disk (Fuhrmann 2004):
(U, V) = (-18, −63) km/s, (σU , σV ) = (58, 41) km/s; halo
(Chiba and Beers 2000): (U,V) = (0, −180) km/s, (σU , σV ) =
(141, 106) km/s.
5. Discussion
As discussed above, OHDHS sparked a lively debate about
whether stellar remnants contribute to a significant fraction of
the baryonic component of the putative dark matter halo of our
Galaxy. The main criticisms have concerned interpretation, and
we do not address those here. However, the photographic pho-
Fig. 4. Comparison of proper motions in Declination derived
in this work with the OHDHS proper motions. Error bars are
drawn in both coordinates but since the present work has much
higher precision than the photographic astrometry, error bars in
abscissae are not visible. The slope of a linear regression (dotted
line) is 1.01 ± 0.02 indicating a good accordance between both
proper motion data sets with a reduced χ2 = 0.7.
tometry and use of a single photometric parallax relation are also
potential sources of systematic error. Both Salim et al. (2004)
and Bergeron et al. (2005) have shown that the original photom-
etry presented in OHDHS was as accurate as could be expected.
Here, we address the question of the accuracy of photometric
parallaxes directly via trigonometric determination of distances.
In Fig. 2 we compare the trigonometric parallaxes derived
here with the OHDHS photometric parallaxes. Parameters of a
weighted linear regression between both types of parallaxes are
π = 1.08 πphot + 3.21 with a reduced χ2 = 8.06. A clear under-
estimation of photometric parallaxes is visible in this figure with
only one point below the diagonal and three points more than
3σ above the relation. With the usual caveat of small number
statistics, this indicates some level of non–Gaussian scatter, or
at least a mean value for the relation that is not coincident with
π = πphot. The photometric parallax overestimates the distance.
This leads, of course, to an overestimation of tangential space
velocities based on proper motion and distance (as an aside, we
note that the quoted photometric parallax errors of 20% were
conservatively overestimated by OHDHS).
It is interesting to note that the mass distribution of hot
(Teff > 12, 000 K) DA WDs is not Gaussian and has a broad
tail on the high mass side (Należyty et al. 2005). Given that ra-
dius r ∝ m−1/3 for WDs, we would expect photometric paral-
laxes to tend to overestimate rather than underestimate distances
since some of the sample may have higher than average mass,
and correspondingly smaller radii, placing them nearer to the
Sun than typical objects of the same colour. Adding in a sprin-
kling of higher mass WDs with helium–dominated atmospheres
will introduce further systematic overestimation of distances. It
is almost certainly the case that the discrepant photometric par-
allaxes for WD2259–465 and WD0135–039 are caused by these
effects; indeed, this has been shown to be the case for LHS 4033
C. Ducourant et al.: Parallaxes of halo white dwarf candidates 7
Fig. 5. Distribution of velocities in the Galactic plane to-
gether with the velocity dispersion for the disk (right most)(1,
2 and 3 σ), thick disk (middle)(1, 2 and 3 σ)( Fuhrmann 2004)
and halo (left) (1 and 2σ) (Chiba and Beers 2000). Filled
squares correspond to objects with a measured radial velocity
(Salim et al. 2004) while open circles correspond to objects with
no Vr measurement. Only objects with parallax measured at the
4σ level or better are plotted.
which has a mass m ∼ 1.3 M� (Dahn et al. 2004). On the other
hand, the low–mass side of the mass distribution is by no means
perfectly Gaussian (e.g. due to low-mass, helium–core white
dwarfs formed in close binaries). Moreover, any overestimation
in distance leads to a corresponding underestimate of space den-
sity using the 1/Vmax technique. So the interpretation of the re-
sults from this relatively small sub–sample is rather complicated,
and it is only through detailed simulations compared with much
larger samples that significant progress is likely to be made con-
cerning the question of the kinematic population of such objects.
From the comparison of trigonometric and photometric
parallaxes (Fig. 2) we recalibrated photometric distances of
the original OHDHS sample and, using radial velocities from
Salim et al. 2004, we derived their associated recalibrated space
velocities. We present the recalibrated UV plane for the entire
OHDHS sample in Fig. 7.
When compared to Fig. 3 of OHDHS, the number of halo
objects has diminished. From the 38 original OHDHS halo can-
didates, 16 appear compatible with a halo status based on a 2σ
cut with the disk and thick disk velocity distributions (a 3σ cut
would reduce this number to 7), the remaining objects being now
located within the disk and thick disk 2 sigma ellipses. In the lit-
erature there is a large spread of the proposed values to charac-
terise the thick disk and halo populations in terms of kinematics.
For instance in Reid 2005 the velocity dispersions for thick disk
vary from 50 to 69 km/s in the U direction and from 39 to 58
km/s in the V direction. Even the center of velocity ellipsoid
varies from –30 to –63 km/s in the < V > coordinate from one
author to another. All this makes it very difficult to separate ob-
jects into halo and thick disk populations and requires a more
detailed analysis which is beyond the scope of the present paper.
Fig. 6. Component of motion perpendicular to the Galactic
plane (W) as function of
U2 + V2. Only objects with paral-
lax measured at the 4σ level or better and with available radial
velocity (Salim et al. 2004) arre plotted. The vertical line is the
OHDHS
U2 + V2 = 94 km/s cut.
The conclusions of OHDHS about local halo WD density
must be now reanalysed since the volume explored by their sur-
vey has changed (re-calibrated distances) and the number of halo
candidates has also changed. This will be the subject of a forth-
coming paper.
6. Acknowledgements
The authors wish to thank G. Daigne for helpful comments and
CAPES/COFECUB, FAPESP organizations and INR for sup-
porting the project.
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C. Ducourant et al.: Parallaxes of halo white dwarf candidates 9
Fig. 8. Observations along the fitted path expressed in mas.
	Introduction
	Observations
	Astrometric Reduction
	Measurements
	Cross-Identification
	Differential Colour Refraction
	Impact of Pixel Scale Errors on Parallax
	Global Solution: Relative Parallax
	Conversion from Relative to Absolute Parallax
	Results
	Distances of Halo White Dwarf Candidates
	Comparison with Published Distances
	Proper Motions
	Space Velocities
	Discussion
	Acknowledgements

  The status of 38 halo white dwarf candidates identified by Oppenheimer et al.
(2001) has been intensively discussed by various authors. In analyses
undertaken to date, trigonometric parallaxes are crucial missing data. Distance
measurements are mandatory to kinematically segregate halo object from disk
objects and hence enable a more reliable estimate of the local density of halo
dark matter residing in such objects.
  We present trigonometric parallax measurements for 15 candidate halo white
dwarfs (WDs) selected from the Oppenheimer et al. (2001) list. We observed the
stars using the ESO 1.56-m Danish Telescope and ESO 2.2-m telescope from August
2001 to July 2004. Parallaxes with accuracies of 1--2 mas were determined
yielding relative errors on distances of $\sim5$% for 6 objects, $\sim12$% for
3 objects, and $\sim20$% for two more objects. Four stars appear to be too
distant (probably farther than 100 pc) to have measurable parallaxes in our
observations. Distances, absolute magnitudes and revised space velocities were
derived for the 15 halo WDs from the Oppenheimer et al. (2001) list. Halo
membership is confirmed unambiguously for 6 objects while 5 objects may be
thick disk members and 4 objects are too distant to draw any conclusion based
solely on kinematics. Comparing our trigonometric parallaxes with photometric
parallaxes used in previous work reveals an overestimation of distance as
derived from photometric techniques. This new data set can be used to revise
the halo white dwarf space density, and that analysis will be presented in a
subsequent publication.

Introduction
In the last decade interest in the very cool, old white dwarf (WD)
halo population has grown. This interest is motivated by the pos-
sibility that these objects could account for a significant fraction
of the baryonic dark matter of our Galaxy. This idea is in accord
with discussions attempting to explain the microlensing events
in the Large Magellanic Cloud in terms of a halo WD popula-
tion – see, for example, Chabrier et al. 1996 and Hansen 1998.
Alcock et al. 1999 suggested that massive compact halo objects
(MACHOs) make up 20 to 100% of the dark matter in the halo,
with MACHOs having typical mass m ∼ 0.5 M�; more recently,
Calchi Novati et al. 2005 find a similar result from pixel lensing
in the line of sight to M31. Hence, in this scenario the search
for, and direct study of, halo WDs can provide constraints on
the fraction of dark matter in the Milk Way that is attributable to
these objects.
Oppenheimer et al. (2001, hereafter OHDHS) identified 38
high proper motion WDs; from their kinematics, the authors
Send offprint requests to: ducourant@obs.u-bordeaux1.fr
? Based on observations collected at the European Southern
Observatory, Chile (067.D-0107, 069.D-0054, 070.D-0028, 071.D-
0005, 072.D-0153, 073.D-0028)
concluded that they were members of a halo population. Since
then an intense discussion concerning the status of these objects
has taken place in the literature. A comprehensive review of
this debate is presented in Hansen and Liebert 2003 where the
conclusion is that the OHDHS interpretation is possibly over-
stated, but that complete conclusions are not possible without
further data. Other studies suggest that the disk and “thick disk”
Galactic populations can be used to explain the great majority
of the objects (Reid 2005, Kilic et al. 2005, Spagna et al. 2004,
Crézé et al. 2004, Holopainen & Flynn 2004, Flynn et al. 2003,
Silvestri et al. 2002). The importance of the high velocity WDs
cannot be understated in other contexts (e.g. the star forma-
tion history of the Galaxy, see also Davies, King & Ritter 2002,
Hansen 2003, Montiero et al. 2006). Moreover, several stud-
ies emphasise the importance of obtaining trigonometric par-
allaxes for candidate halo WDs (Bergeron & Leggett 2002,
Torres et al. 2002, Bergeron 2003). This is especially important
for the coolest WDs, whose spectral energy distributions show
remarkable departures from black–body distributions and which
are proving to be difficult to model accurately (Kowalski 2006,
Gates et al. 2004, Saumon & Jacobson 1999, Hansen 1998). In
the presence of such radical changes to the WD spectrum, the as-
sumption of a monotonic photometric parallax relation (e.g. as
2 C. Ducourant et al.: Parallaxes of halo white dwarf candidates
used in OHDHS) could break down and estimates of intrinsic
space velocities could be in error seriously. Furthermore, a recent
paper (Bergeron et al. 2005) concludes that precise distances are
mandatory to derive accurate kinematics and ages for the puta-
tive halo WDs and in order to derive their evolutionary status.
Aiming to clear up this question, in 2001 we started an ob-
serving program with the ESO 1.56-m Danish and ESO 2.2-m
telescopes to measure the trigonometric parallaxes of these stars.
Trigonometric parallax measurements remain the only direct un-
biased distance determination. They are of great importance in
the debate about the status of cool halo white dwarfs because
they are required to derive precise space velocities and ages
which are used for distinguishing between halo and disk mem-
bership. These trigonometric parallaxes lead to the re-calibration
of photometric distances used until now in this debate and allow
analysis of the cool halo white dwarf population with more con-
fidence. Unfortunately, due to limited observing time, only 15
stars on the OHDHS list have been observed to date. However,
this sub-sample provides important insight into the problem.
2. Observations
Astrometric observations of 15 of the OHDHS list of 38 halo
white dwarf candidates were performed at the ESO 2.2-m tele-
scope equipped with the WFI wide–field mosaic camera (with
0.238 ′′/pixel, a field of view FOV = 34′ × 33′, 4 × 2 mosaic of
2k × 4k CCDs), through the ESO 845 I filter. To reduce astro-
metric distortions and other instrumental effects, only data from
chip 51 (with FOV = 8′× 16′) were used in this work; target stars
were centered in the FOV of this chip.
Four epochs of observation were acquired at maximum
parallactic factor in Right Ascension in November 2002, July
2003, November 2003 and July 2004 with a total of 11 nights of
observations. Two parallactic periods (four observations over 1.5
years) are required, at a minimum, for a unique determination
of the parallax and proper motion. Two preliminary observing
runs were performed at the ESO 1.56-m Danish telescope in
July 2001 and July 2002 but the subsequent closure of the
telescope forced the authors to move the program to the ESO
2.2-m telescope. Data acquired at the Danish telescope were not
included in our final analysis to avoid systematic effects due to
the use of two different telescopes.
To minimize differential colour refraction effects (DCR), ob-
servations were performed around the transit of targets with hour
angles of less than 1 hour. Multiple exposures were taken at
each observation epoch to reduce the astrometric errors and to
estimate the precision of measurements. Exposure times varied
from 100 to 600 seconds depending on the magnitude of the tar-
get. Each field was observed from 20 to 35 times.
3. Astrometric Reduction
3.1. Measurements
Frames were measured using the DAOPHOT II package (Stetson
1987), fitting a PSF. The significance level of a luminosity en-
hancement over the local sky brightness which was regarded as
real was set to 7σ. The PSF routine was used to define a stel-
lar point spread function for each frame. Finally we obtained the
(x, y) measured positions, the internal magnitudes and associated
errors of all stars on each frame. There were typically 300 to 600
stars measured on each frame depending on the exposure time.
From these, a selection on the error in magnitude (ERRMAG)
as derived by the DAOPHOT II software was applied. Any ob-
servation with ERRMAG ≥ 0.15m was rejected. Objects fainter
than 1.5m brighter than a given image’s limiting magnitude were
also rejected from the analysis.
3.2. Cross-Identification
For each of the 15 different fields of view, we selected a “master”
or fiducial image from the set of 20 to 35 images. This master
frame for each object had the deepest limiting magnitude and
highest image quality. For each of the other images for a given
target object, the positions of all stars not rejected by the crite-
ria above were then cross–identified to the master image’s star
positions. Objects not detected on three or more frames were
excluded, yielding 100 to 200 stars in common in each field.
Frames containing less than Nmaster/3 stars in common with the
master frame were removed from the solution (where Nmaster is
the number of stars in the master frame). Note that the master
frame is processed in an identical fashion to the other frames
and is not assumed to be free of errors in the parallax solution.
In other words, the fiducial frames are not taken as an error-free
“truth”, but are simply used as a basis for coordinate transfor-
mations and correlation of star positions that comprise the astro-
metric grid used in the solution.
3.3. Differential Colour Refraction
Atmospheric refraction changes the apparent positions of stars in
ground–based observations and depends on the zenith distance
of the observations. For precision astrometry this effect must be
accounted for, because it can be many tens of milliarcsececonds
at even relatively modest zenith distances. In our case, another
effect becomes important as well, because the atmospheric re-
fraction of our target stars will not be identical to that of the
background stars used for our astrometric reference grid. Our
target stars (WDs) and the background stars (typically main–
sequence G or K stars) have different spectral energy distribu-
tions. Therefore, atmospheric refraction will affect them differ-
ently when observed through a given filter bandpass. This is
called a differential colour refraction (DCR) and is known to
cause spurious parallactic motion Monet et al. 1992. DCR can
affect both the Right Ascension (RA) and Declination of the tar-
get as derived with respect to the field stars. Observations in par-
allax programs are planned to maximize the parallactic factor in
RA so the parallax solution for the target will rely heavily on
the RA measured. Therefore the parallax derived is mainly per-
turbed by the DCR effects in RA which are critically dependent
on the zenith distance of a given observation.
We investigated the impact of such effects on the parallax
of white dwarfs through simulations. Using the usual formula
for atmospheric refraction, a blackbody approximation for white
dwarf and background stellar spectra, the Besançon Galaxy
model for background star characteristics (Robin et al. 1994)
and ESO 845 filter limits, we computed the average differen-
tial colour refraction effects between a white dwarf similar to
those of our list with effective temperatures, Teff , in the range
4000 K to 11000 K (Bergeron et al. 2005, Table 2) and a typical
background star (Teff ∼ 5000 K).
We present in Fig. 1 the effects of DCR in RA for white
dwarfs situated at δ = −30◦, covering the range of temperatures
of our targets. Fig. 1 demonstrates that the impact of DCR effects
were always less than 0.5 mas for observations taken with an
hour angle of less than one hour. Therefore, our observations
C. Ducourant et al.: Parallaxes of halo white dwarf candidates 3
were made specifically so that the hour angle never exceeded
one hour, and DCR corrections were not applied in this work.
Fig. 1. DCR effects in RA between a white dwarf of temperature
Teff and a mean background stars (Teff=5000K) at a Declination
of −30◦ (representative of our sample) for various hour angles of
observation. The DCR effects appear to be always lower than 0.5
mas for observations performed at less than 1 hour from merid-
ian which is the case of the present project. The DCR effects are
then negligible compared with other sources of astrometric error
and were not taken into account in this work.
3.4. Impact of Pixel Scale Errors on Parallax
Proper motions (µx, µy) and trigonometric parallax (πxy) of tar-
gets are determined by comparing the (x, y) measurements ex-
pressed in pixels. A scaling factor S f , the image pixel scale, is
applied to πxy to convert pixel measurements into physical units:
π = S fπxy; d(pc) = π−1, with S f expressed in ′′/pixel.
Derivation of the pixel scale can be achieved through a
cross–correlation between the (x, y) positions of stars on a given
master frame to corresponding values of (α, δ) for the subset of
stars that are also in a reference catalogue. Here we used the
2MASS catalogue (Cutri et al. 2003) to determine the orienta-
tion of the master frame on the sky and for the pixel scale deter-
mination. We selected the 2MASS catalogue as a reference cat-
alogue because of its accuracy and density although we note the
absence of proper motion corrections. Nevertheless the epoch
difference between our observations and the 2MASS catalogue
(3 years) would result in negligible corrections to the catalogue
positions with respect to the catalogue errors.
Errors on the scale so determined, resulting from catalogue
random errors, will produce errors in the distance determination
of the target. It is therefore important to quantify the impact of
the catalogue errors onto the distance of the target.
To measure this impact in the present work, we assumed N
reference stars equally spread over a square detector of side A.
The classical equation relating the (x, y) measurements of a stars
on the frame to its standard coordinates X(α, δ),Y(α, δ) in the
tangent plane to the celestial sphere is (with a similar equation
in the Y coordinate)
X = (ax + by + c)1/F, (1)
where (a,b,c) are the unknown “plate” constants and F the focal
length of the telescope (typically the value indicated in the ref-
erence manual). F is expressed in the same units as (x,y) and A
(pixel, mm). It is then easy to show that a fair approximation of
the variance of the estimation of parameter (a) is given by
�cat, (2)
where �cat is the catalogue precision (expressed in radians).
Similar results can be found in Eichhorn & Williams 1963. We
can express the parallax (in radians) as:
πxy, (3)
σ2π = π
σ2a, σπ =
�cat (4)
with F ∼ 13m, A ∼ 0.03m, we evaluate here σπ ∼ 10−4π. The
impact of the error of the catalogue on the parallax of the target
is far below the measurement errors (typically a few milliarcsec-
onds) and are therefore negligible.
3.5. Global Solution: Relative Parallax
The astrometric reduction of the whole set of data of each
field is performed iteratively through a global central overlap
procedure (Hawkins et al. 1998, Eichhorn 1997) in order to
determine simultaneously the position, the proper motion and
the parallax of each object of the field.
The following condition equations are written for each star
on each of the N frames considered (including the master frame).
These equations relate the measured coordinates to the stellar
astrometric parameters:
X0 + ∆X0 + µX(t − t0) + πFX(t) = a1x(t) + a2y(t) + a3 (5)
Y0 + ∆Y0 + µY (t − t0) + πFY (t) = b1x(t) + b2y(t) + b3 (6)
where (X0,Y0) are the known standard coordinate of the star at
the epoch t0 of the master frame, and (x(t), y(t)) its measured
coordinates on the frame (epoch t) to be transformed into the
master frame system. ∆X0, ∆Y0, µX , µY and π are the unknown
stellar astrometric parameters: (∆X0, ∆Y0) yield correction of the
standard coordinates of the star on the master frame, (µX , µY ) are
the projected proper motion in RA ∗cos(δ) and Dec, and π is the
parallax. Coefficients (ai, bi) are the unknown frame parameters
which describe the transformation to the master frame system.
(FX , FY ) are the parallax factors in standard coordinates. The
unknowns of this large over–determined system of equations are
the stellar astrometric parameters of each object, and the trans-
formation coefficients of each of the N frames considered. The
system of equations is singular and therefore the derived solution
is not unique; any solution will depend on the starting point of
the iterations. The usual technique to obtain a particular solution
is to introduce a set of constraints that the solution must satisfy.
In this work we chose to set strictly to zero the mean parallax of
the reference stars.
We used a Gauss–Seidel type iterative method to solve the
set of equations. At the first iteration all stellar parameters are
assumed null, we then computed the plate constants which are
4 C. Ducourant et al.: Parallaxes of halo white dwarf candidates
injected into the system of equations to derive the stellar param-
eters. These results are then used as the starting point of the fol-
lowing iteration. The iterative procedure converges usually at the
second or third iteration. A test of elimination at 3σ is applied to
remove poor observations either in the master frame fit or in the
stellar parameters fit. The stellar parameters fit equations have
been weighted by the mean residual of the master frame fit. This
weighting represents the quality of the measurements. The stars
used for the master frame fit are called here reference stars.
We applied this global treatment to the various observations
of the 15 fields observed and we derived for the targets a proper
motion and parallax with associated variances.
3.6. Conversion from Relative to Absolute Parallax
The parallaxes that we derived for our targets are relative to the
reference stars (for which we used the constraint
π = 0), sup-
posed placed at infinite distance. In fact these reference stars are
at a finite distance from Sun. We must therefore correct the rela-
tive parallax of the target from an estimate of the mean distance
of the reference stars to obtain the absolute parallax of the target.
The choice we made to keep as many reference stars as possible
in our calculation is interesting because statistically faint stars
have smaller parallax and require smaller correction.
There are several ways to estimate the mean distance of
reference stars: statistical methods relying on a model of the
Galaxy; spectroscopic parallax; and photometric parallax. For
the corrections from relative parallax to absolute parallax we
used a statistical method relying on simulations using the
Besançon Galaxy model (Robin et al. 1994) to derive the theo-
retical mean distance of reference stars. A simulation of each ob-
served field was performed, providing catalogues of distance and
apparent magnitude of simulated stars. We computed in these
catalogues mean distances and associated dispersion in magni-
tude bins of 0.2 mag, establishing a table of theoretical distances
with respect to apparent magnitude. Then we considered our ob-
served fields and we computed the weighted mean parallax and
associated dispersion of our reference stars using the theoretical
table. Finally we added this mean parallax of reference stars to
the relative parallax of our target leading to the absolute parallax
of the white dwarfs.
We give in Table 1 the relative to absolute corrections in mil-
liarcseconds as found from the Besançon Galaxy model in each
of the field treated.
4. Results
4.1. Distances of Halo White Dwarf Candidates
We present in Table 2 the proper motions and absolute parallaxes
of the fifteen halo white dwarf candidates as derived from this
work together with their absolute magnitude MV computed using
CCD V magnitudes from Bergeron et al. (2005).
One notices that WD2326–272, LP586–51, LP588–37, and
WD2324–595 are too distant to have a measurable parallax.
Eleven objects are at distances ranging from 19 pc to 90 pc from
the Sun. The parallax errors are about 1–2 mas corresponding
to relative precisions of 5 to 20%. WD2214–390, which is the
closest and brightest object, has a σπ = 2.6 mas. This poor pre-
cision is due to the short exposure time used to avoid saturation
problems and corresponding lower signal–to–noise ratio.
We present in Figs 8 and ?? the positions (empty circles),
their weighted mean (filled circles) and associated error bars at
Table 1. Relative to absolute corrections ∆π and associated
RMS (σ) as found from the Besançon Galaxy model in the
Galactic direction (l,b) together with number of reference stars
(N*) in magnitude interval [Jmin,Jmax].
Target l b ∆π σ N* Jmin Jmax
[◦] [◦] [mas] [mag]
WD2214-390 2.79 -55.37 1.3 0.3 38 13.1 16.2
WD2242-197 40.01 -59.42 1.0 0.3 97 14.0 18.4
WD2259-465 344.30 -60.62 1.1 0.2 83 13.6 18.0
LHS542 72.40 -59.70 1.2 0.3 42 13.4 17.0
WD2324-595 321.83 -54.34 1.1 0.2 62 13.3 17.0
WD2326-272 27.66 -71.06 1.3 0.4 80 14.2 18.7
LHS4033 90.24 -61.96 1.3 0.2 39 14.2 16.5
LHS4041 351.44 -74.66 1.4 0.3 37 13.5 16.2
LHS4042 6.55 -76.61 1.5 0.4 38 13.3 16.6
WD0045-061 118.54 -68.96 1.5 0.3 54 13.5 17.7
F351-50 314.26 -83.50 0.3 0.2 53 14.1 18.1
LP586-51 128.88 -63.30 1.3 0.3 47 14.1 17.4
WD0135-039 149.30 -64.53 1.3 0.2 82 14.4 19.0
LP588-37 150.44 -61.52 1.4 0.2 57 13.6 17.7
LHS147 178.72 -73.56 1.5 0.3 43 13.4 16.8
each epoch of observation, together with the fitted path for the
eleven most significant parallaxes, where π/σπ ≥ 4.
4.2. Comparison with Published Distances
We have compared our results with available data from the lit-
erature, employing both trigonometric and photometric paral-
laxes measured previously. We give in Table 3 the comparison
with published trigonometric parallaxes and in Figure 2 a com-
parison of the parallaxes derived in this work with photomet-
ric parallaxes (from OHDHS, where photometric parallax errors
were 20%). Parameters of a weighted linear fit between pho-
tometric and trigonometric parallaxes are: πtrig = a.πphot + b
with a = 1.08+/-0.08 and b = 3.21+/-1.56 [mas] with a reduced
χ2 =8.06.
Table 3. Comparison of trigonometric parallaxes from this
work (πThiswork) with published data (πext) for LHS 147
(Van Altena et al. 1995), LHS 4033 (Dahn et al. 2004) and LHS
542 (Bergeron et al. 2005).
Target πThiswork πext ∆π
[mas] [mas] [mas]
LHS 542 29.6 +/- 1.8 32.2 +/- 3.7 2.6
LHS 147 14.8 +/- 1.8 14.0 +/- 9.2 –0.8
LHS 4033 30.1 +/-1.8 33.9 +/- 0.6 3.8
Our parallaxes are in excellent agreement with the 3 pre-
viously published trigonometric parallaxes, within the errors
(which are considerably smaller in two cases than published val-
ues). In Fig. 2 one notices a clear systematic tendency of pho-
tometric parallaxes to be underestimated. This overestimation of
OHDHS distances is of importance in the calculation of WD
kinematics and space density.
C. Ducourant et al.: Parallaxes of halo white dwarf candidates 5
Table 2. Proper motion and absolute parallaxes of the fifteen halo white dwarf candidates, where µα∗ = µαcos(δ) and σµ=σµα∗=σµδ ;
π and σπ are the parallax and its precision, Dist the derived distance in parsec and MV the absolute magnitude. No value is given
for Dist and Mv when the parallax is not better than 3 σ. N* is the number of reference stars and Nf the Number of frames. Dphot
is the photometric distance from OHDHS and V is extracted from Bergeron et al. (2005) when available, otherwise (cases marked
by an asterix) it comes from Salim et al. (2004). Note that LHS 4041 is in the OHDHS sample, but is not listed in OHDHS Table 1
(see Table 4 of Salim et al. 2004)
Name α δ Epoch V µα∗ µδ σµ π σπ Dist Mv N* Nf Dphot
[J2000] [yr] [mag] [mas/yr] [mas] [pc] [mag] [pc]
WD2214–390 22 14 34.727 –38 59 07.05 2003.5 15.92 1009 –350 2.9 53.5 2.6 19 14.78 38 28 24
WD2242–197 22 41 44.252 –19 40 41.41 2003.5 19.74 359 +48 3.1 11.1 2.3 90 14.89 97 27 117
WD2259–465 22 59 06.633 –46 27 58.86 2002.9 19.56 402 –153 1.8 22.7 1.3 44 16.49 83 32 71
LHS542 23 19 09.518 –06 12 49.92 2003.5 18.15 –615 –1576 1.8 29.6 1.8 34 15.58 42 33 42
WD2324–595 23 24 10.165 –59 28 07.95 2003.5 16.79 136 –562 1.8 (3.1) 1.5 —- —- 62 25 58
WD2326–272 23 26 10.718 –27 14 46.68 2002.9 ∗19.92 574 –85 2.7 (6.2) 2.4 —- —- 80 17 108
LHS4033 23 52 31.941 –02 53 11.76 2002.9 16.98 631 298 2.5 30.1 1.8 33 14.38 39 26 63
LHS4041 23 54 18.793 –36 33 54.60 2002.9 ∗15.46 21 –662 1.8 13.4 1.5 75 11.10 37 27 59
LHS4042 23 54 35.034 –32 21 19.44 2003.5 17.41 421 –37 2.2 13.9 1.8 72 13.13 38 25 85
WD0045–061 00 45 06.325 –06 08 19.65 2002.9 18.26 111 –668 1.9 30.1 1.9 33 15.59 54 27 44
F351–50 00 45 19.695 –33 29 29.46 2003.5 19.01 1820 –1476 2.1 28.3 1.4 35 16.63 53 34 37
LP586–51 01 02 07.181 –00 33 01.82 2002.9 18.18 350 –118 3.6 (2.4) 2.7 —- —- 47 24 120
WD0135–039 01 35 33.685 –03 57 17.90 2002.9 19.68 456 –180 3.4 13.3 2.9 75 15.26 82 21 146
LP588–37 01 42 20.770 –01 23 51.38 2002.9 ∗18.50 112 –328 3.4 (1.4) 4.5 —- —- 57 17 120
LHS147 01 48 09.120 –17 12 14.08 2002.9 17.62 –115 –1094 2.1 14.8 1.8 68 13.46 43 29 71
Fig. 2. Comparison of parallaxes derived in this work with pho-
tometric parallaxes from OHDHS (errors are assumed 20% for
πphot). Parameters of a weighted linear regression (diagonal line)
between both types of parallaxes are π = 1.08πphot + 3.21 [mas]
with a reduced χ2 = 8.06. The photometric distances are sys-
tematically larger than the astrometric ones.
4.3. Proper Motions
We have compared the proper motions derived here with the
OHDHS proper motions in order to check wether some system-
atic effects could affect our proper motions derived on a 1.5 yr
time span and, as a result, our parallaxes. We present this com-
parison in Fig. 3 and Fig. 4. Error bars are drawn in both co-
ordinates but since the present work has much higher precision
than the photographic astrometry, the error bars in x are not vis-
ible. The slope of a linear regression between proper motions in
α cos(δ) derived in this work with the OHDHS proper motions
is 1.04 ± 0.02 with a reduced χ2 = 3.7. The equivalent linear
fit in proper motions in Declination has a slope of 1.01 ± 0.02
with a reduced χ2 = 0.7. For F351-50 (the largest error bars in
both figures), the accordance in RA and Dec proper motions is
not good. This is due to a known problem of contamination by
a background galaxy of the Schmidt plate measurements used
in the OHDHS work. Nevertheless the accordance is within 2σ.
These comparisons show excellent agreement between both sets
of proper motions, and argue against any systematic effects from
the present work.
4.4. Space Velocities
We derived the Galactic space velocities U, V, W
(Johnson and Soderblom 1987) for the white dwarfs using
the distances and proper motions measured here together with
radial velocities from Salim et al. 2004 (data available for 9
of the 15 white dwarfs treated here). Salim’s observed radial
velocities were corrected for a mean gravitational redshift of
+28km/s as suggested by the authors in their paper except in
the case of the very massive white dwarf LHS4033 were the
correction was taken from Dahn et al. 2004. U is radial toward
the Galactic center, V is in the direction of rotation and W
perpendicular to the Galactic disk. U,V and W were corrected
for the Sun’s peculiar velocity (Mihalas and Binney (1981)).
When no radial velocity was available from other studies, we
assumed Vr = 0 km/s. This approximation is acceptable due to
its minor impact on U,V velocities since the targets are located
6 C. Ducourant et al.: Parallaxes of halo white dwarf candidates
Fig. 3. Comparison of proper motions in RA cos(δ) with the
OHDHS proper motions. Error bars are drawn in both coordi-
nates but since the present work has much higher precision than
the photographic astrometry, error bars in abscissae are not visi-
ble. The slope of a linear regression (dotted line) is 1.04 ± 0.02
indicating good accordance between both proper motion data
sets with a reduced χ2 = 3.7.
close to South Galactic Cap (the effect was investigated in
OHDHS and shown to be negligible).
We present in Figure 5 the distribution of velocities in
the Galactic plane together with the velocity dispersion for
the disk (right most)(1, 2 and 3 σ), thick disk (middle)(1,
2 and 3 σ)( Fuhrmann 2004) and halo (left) (1 and 2σ)
(Chiba and Beers 2000) and in Figure 6 the component of mo-
tion perpendicular to the Galactic plane. These two figures con-
cern the 11 objects with parallax measured at the 4σ level or
better.
In Fig. 5 one notices that 4 of the 11 studied WDs have a
velocity incompatible at the 3σ level with the kinematic of the
disk and of the thick disk and that 6 of them are incompatible at a
2σ level. No star lies within the 1σ ellipse of the disk, primarily
because of selection effects in the original proper motion survey
that OHDHS based is based upon Hambly et al. 2005.
Obviously the choice of the center and dispersions of halo,
thick disk and disk ellipses is critical to classify objects as be-
longing to a particular population. We adopted recent values
which are in in the range of the values cited by Reid 2005
in his review: Disk (Fuhrmann 2004) : (U,V) = (7.7, −18.1)
km/s, (σU , σV ) = (42.6, 22.6) km/s; thick disk (Fuhrmann 2004):
(U, V) = (-18, −63) km/s, (σU , σV ) = (58, 41) km/s; halo
(Chiba and Beers 2000): (U,V) = (0, −180) km/s, (σU , σV ) =
(141, 106) km/s.
5. Discussion
As discussed above, OHDHS sparked a lively debate about
whether stellar remnants contribute to a significant fraction of
the baryonic component of the putative dark matter halo of our
Galaxy. The main criticisms have concerned interpretation, and
we do not address those here. However, the photographic pho-
Fig. 4. Comparison of proper motions in Declination derived
in this work with the OHDHS proper motions. Error bars are
drawn in both coordinates but since the present work has much
higher precision than the photographic astrometry, error bars in
abscissae are not visible. The slope of a linear regression (dotted
line) is 1.01 ± 0.02 indicating a good accordance between both
proper motion data sets with a reduced χ2 = 0.7.
tometry and use of a single photometric parallax relation are also
potential sources of systematic error. Both Salim et al. (2004)
and Bergeron et al. (2005) have shown that the original photom-
etry presented in OHDHS was as accurate as could be expected.
Here, we address the question of the accuracy of photometric
parallaxes directly via trigonometric determination of distances.
In Fig. 2 we compare the trigonometric parallaxes derived
here with the OHDHS photometric parallaxes. Parameters of a
weighted linear regression between both types of parallaxes are
π = 1.08 πphot + 3.21 with a reduced χ2 = 8.06. A clear under-
estimation of photometric parallaxes is visible in this figure with
only one point below the diagonal and three points more than
3σ above the relation. With the usual caveat of small number
statistics, this indicates some level of non–Gaussian scatter, or
at least a mean value for the relation that is not coincident with
π = πphot. The photometric parallax overestimates the distance.
This leads, of course, to an overestimation of tangential space
velocities based on proper motion and distance (as an aside, we
note that the quoted photometric parallax errors of 20% were
conservatively overestimated by OHDHS).
It is interesting to note that the mass distribution of hot
(Teff > 12, 000 K) DA WDs is not Gaussian and has a broad
tail on the high mass side (Należyty et al. 2005). Given that ra-
dius r ∝ m−1/3 for WDs, we would expect photometric paral-
laxes to tend to overestimate rather than underestimate distances
since some of the sample may have higher than average mass,
and correspondingly smaller radii, placing them nearer to the
Sun than typical objects of the same colour. Adding in a sprin-
kling of higher mass WDs with helium–dominated atmospheres
will introduce further systematic overestimation of distances. It
is almost certainly the case that the discrepant photometric par-
allaxes for WD2259–465 and WD0135–039 are caused by these
effects; indeed, this has been shown to be the case for LHS 4033
C. Ducourant et al.: Parallaxes of halo white dwarf candidates 7
Fig. 5. Distribution of velocities in the Galactic plane to-
gether with the velocity dispersion for the disk (right most)(1,
2 and 3 σ), thick disk (middle)(1, 2 and 3 σ)( Fuhrmann 2004)
and halo (left) (1 and 2σ) (Chiba and Beers 2000). Filled
squares correspond to objects with a measured radial velocity
(Salim et al. 2004) while open circles correspond to objects with
no Vr measurement. Only objects with parallax measured at the
4σ level or better are plotted.
which has a mass m ∼ 1.3 M� (Dahn et al. 2004). On the other
hand, the low–mass side of the mass distribution is by no means
perfectly Gaussian (e.g. due to low-mass, helium–core white
dwarfs formed in close binaries). Moreover, any overestimation
in distance leads to a corresponding underestimate of space den-
sity using the 1/Vmax technique. So the interpretation of the re-
sults from this relatively small sub–sample is rather complicated,
and it is only through detailed simulations compared with much
larger samples that significant progress is likely to be made con-
cerning the question of the kinematic population of such objects.
From the comparison of trigonometric and photometric
parallaxes (Fig. 2) we recalibrated photometric distances of
the original OHDHS sample and, using radial velocities from
Salim et al. 2004, we derived their associated recalibrated space
velocities. We present the recalibrated UV plane for the entire
OHDHS sample in Fig. 7.
When compared to Fig. 3 of OHDHS, the number of halo
objects has diminished. From the 38 original OHDHS halo can-
didates, 16 appear compatible with a halo status based on a 2σ
cut with the disk and thick disk velocity distributions (a 3σ cut
would reduce this number to 7), the remaining objects being now
located within the disk and thick disk 2 sigma ellipses. In the lit-
erature there is a large spread of the proposed values to charac-
terise the thick disk and halo populations in terms of kinematics.
For instance in Reid 2005 the velocity dispersions for thick disk
vary from 50 to 69 km/s in the U direction and from 39 to 58
km/s in the V direction. Even the center of velocity ellipsoid
varies from –30 to –63 km/s in the < V > coordinate from one
author to another. All this makes it very difficult to separate ob-
jects into halo and thick disk populations and requires a more
detailed analysis which is beyond the scope of the present paper.
Fig. 6. Component of motion perpendicular to the Galactic
plane (W) as function of
U2 + V2. Only objects with paral-
lax measured at the 4σ level or better and with available radial
velocity (Salim et al. 2004) arre plotted. The vertical line is the
OHDHS
U2 + V2 = 94 km/s cut.
The conclusions of OHDHS about local halo WD density
must be now reanalysed since the volume explored by their sur-
vey has changed (re-calibrated distances) and the number of halo
candidates has also changed. This will be the subject of a forth-
coming paper.
6. Acknowledgements
The authors wish to thank G. Daigne for helpful comments and
CAPES/COFECUB, FAPESP organizations and INR for sup-
porting the project.
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C. Ducourant et al.: Parallaxes of halo white dwarf candidates 9
Fig. 8. Observations along the fitted path expressed in mas.
	Introduction
	Observations
	Astrometric Reduction
	Measurements
	Cross-Identification
	Differential Colour Refraction
	Impact of Pixel Scale Errors on Parallax
	Global Solution: Relative Parallax
	Conversion from Relative to Absolute Parallax
	Results
	Distances of Halo White Dwarf Candidates
	Comparison with Published Distances
	Proper Motions
	Space Velocities
	Discussion
	Acknowledgements
