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THE ASTROPHYSICAL JOURNAL, 517 : 399õ415, 1999 May 20
1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.
(
A COMPARATIVE STUDY OF THE MASS DISTRIBUTION OF EXTREME­ULTRAVIOLETõSELECTED
WHITE DWARFS1
R. NAPIWOTZKI
Dr. Remeis­Sternwarte, Sternwartstrasse 7, 96049 Bamberg, Germany ; ai23=sternwarte.uni­erlangen.de
PAUL J. GREEN
Harvard­Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 ; pgreen=cfa.harvard.edu
AND
REX A. SAFFER
Department of Astronomy and Astrophysics, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085 ; sa+er=ast.vill.edu
Received 1998 June 4 ; accepted 1998 December 28
ABSTRACT
We present new determinations of e+ective temperature, surface gravity, and masses for a sample of 46
hot DA white dwarfs selected from the Extreme Ultraviolet Explorer (EUV E) and ROSAT Wide Field
Camera bright source lists in the course of a near­infrared survey for low­mass companions. Our
analysis, based on hydrogen non­LTE model atmospheres, provides a map of LTE correction vectors,
which allow a thorough comparison with previous LTE studies. We ïnd that previous studies underesti­
mate both the systematic errors and the observational scatter in the determination of white dwarf
parameters obtained via ïts to model atmospheres. The structure of very hot or low­mass white dwarfs
depends sensitively on their history. To compute white dwarf masses, we thus use theoretical mass­radius
relations that take into account the complete evolution from the main sequence. We ïnd a peak mass of
our white dwarf sample of 0.59 in agreement with the results of previous analyses. However, we do
M _ ,
not conïrm a trend of peak mass with temperature reported in two previous analyses. Analogous to
other EUV­selected samples, we note a lack of low­mass white dwarfs and a large fraction of massive
white dwarfs. Only one white dwarf is likely to have a helium core. While the lack of helium white
dwarfs in our sample can be easily understood from their high cooling rate, and therefore low detection
probability in our temperature range, this is not enough to explain the large fraction of massive white
dwarfs. This feature very likely results from a decreased relative sample volume for low­mass white
dwarfs caused by interstellar absorption in EUV­selected samples.
Subject headings : binaries : close õ stars : atmospheres õ stars : evolution õ ultraviolet : stars õ
white dwarfs
1. INTRODUCTION
UV observations of EUV­detected stars have revealed
the presence of about 15 hot white dwarf (WD) companions
to bright stars in noninteracting binary systems (see, e.g.,
Burleigh, Barstow, & Fleming 1997). At optical wave­
lengths, these WDs are hidden because of their close prox­
imity to much more luminous companions, which are
main­sequence (spectral type K or earlier) or evolved stars.
A fascinating variety of objects are known or proposed to
contain WD stars in interacting binary systems. A partial
list includes novae, cataclysmic variables, symbiotic stars,
Ba and CH giants, Feige 24 type systems, and dwarf carbon
stars (Green & Margon 1994). These systems o+er great
insights to evolution and dynamical processes in binaries.
A number of interacting binary systems where the WD is
the primary (i.e., optically brightest) star have also been
found among EUV­detected systems (e.g., six close, inter­
acting WD/red dwarf binaries by Vennes & Thorstensen
1994). Optical or ultraviolet spectral observations are most
commonly used to detect companions to WD primaries by
searching for (1) the presence of narrow Balmer line emis­
sion overlying the broad smooth Balmer absorption of the
WD, (2) a composite WD plus main sequence spectrum, or
1 Spectral observations reported here were obtained with the Multiple
Mirror Telescope, a joint facility of the University of Arizona and the
Smithsonian Institution, and with the Bok telescope at the Steward Obser­
vatory of the University of Arizona.
(3) radial velocity (RV) variations. However, only WDs with
very close or intrinsically active companions will be found
by case (1). For hot WD systems, composite spectra (case
[2]) are only expected to be visible if the companionîs spec­
tral type is early enough. RV variations (case [3]) require
multiple observations at high spectral resolution, and detec­
tion strongly favors close and/or massive companions.
All of the discoveries mentioned above have been strong­
ly dominated by these selection e+ects, with companions
biased to earlier types than predicted by the simulations of
deKool & Ritter (1993) and others. Scaling from deKool &
Ritterîs (1993) results, Vennes & Thorstensen (1994) esti­
mate that ```` at least twice as many close binary systems
remain to be identiïed from EUV surveys, most of them
with a low­mass secondary. îî The resulting sample of
binaries known to date, therefore, must diverge strongly
from the intrinsic distribution, in overall normalization, as
well as in mass and spectral type of the main sequence
companions.
The current study, conceived as a complement to optical
studies, began as a near­IR photometric survey for low­
mass companions to hot WDs. By investigating only EUV­
detected WDs, we obtain a very reasonably sized but
complete sample of young WDs, next to which very late­
type dwarf companions can be detected in the near­infrared
by searching for a K excess over that expected from the
WD. Many hot WDs K ; Finley et al. 1993)
(T eff [ 24,000
have been detected in the recent EUV all­sky surveys. EUV
399

400 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
detection of these hot WDs depends primarily on their tem­
perature, distance, and the intervening Galactic interstellar
medium (ISM). Our sample of EUV WDs (whose selection
we deïne below) o+ers excellent ÿux contrast in the IR
relative to optical ; cool companions will almost always be
brighter in the K band than the hot WDs.
To know what K magnitude to expect for the WDs, we
beneït from constraints on log g, radius, and derivable
T eff
from optical spectra for the WDs in our sample using
non­LTE (NLTE) model atmosphere ïts (Napiwotzki et al.
1993 ; Napiwotzki 1997). The resulting predictions for K
magnitudes allow a direct search for any IR excess from a
cool companion. In some cases, IR colors will also provide
a preliminary spectral type. Results from the IR survey will
be presented in an upcoming paper.
An additional motivation is the study of the WD mass
distribution. Since the pioneering work of Koester, Schulz,
& Weidemann (1979, hereafter KSW79), it is well estab­
lished that the masses of WDs cluster in a narrow range
around 0.6 remarkable given that WDs stem from
M _ ,
progenitors with masses ranging from below 1 up to
M _
B8 Precise knowledge of the WD mass distribution
M _ .
puts constraints on the theory of stellar evolution, especially
the poorly understood mass­loss process during the ïnal
stages of stellar evolution. With two recent exceptions
(Beauchamp et al. 1996 and Dreizler & Werner 1996, who
analyzed samples of helium­rich DB and DO WDs,
respectively), the mass distribution has only been deter­
mined for hydrogen­rich DA WDs. However, this is not a
severe limitation because this spectral class comprises about
80% of all known WDs.
The analysis of KSW79, along with other follow­up
investigations in the early eighties, used photometric data of
which the and Greenstein multichannel colors
Stro
# mgren
were the most suitable. Both systems provide temperature­
and gravity­sensitive indices. Alternatively, KSW79 and
others used trigonometric parallax measurements to
directly calculate the stellar radius ; however, the latter
method is practical only for a small sample and su+ers from
considerable measurement uncertainty. Unfortunately, the
photometric indices have their highest sensitivity near
10,000 K. At this temperature, DA WDs have a convective
atmosphere, and the results depend critically on the
adopted parameters of mixing length theory.
The situation improved at the beginning of the nineties
when the development of modern, highly efficient detectors
made it possible to obtain high­quality spectra of large
numbers of WDs and determine the stellar parameters from
a ït to the detailed proïles of the Balmer lines. This method
yields sufficient accuracy for WDs hot enough to have a
radiative envelope. The ïrst comprehensive sample of WDs
analyzed by this method was presented by Bergeron, Sa+er,
& Liebert (1992, hereafter BSL92). As attributed to higher
precision of spectroscopic methods, this investigation
yielded a WD mass distribution even narrower than found
by KSW79 and other previous studies.
At the same time, Kidder (1991) analyzed a sample of hot
DA WDs discovered through positional coincidences of
cataloged hot DA WDs in existing soft X­ray databases.
Three soft X­ray sources corresponding to WDs were found
having relatively low e+ective temperatures, B25,000 K,
which were determined independently using complemen­
tary optical and UV spectroscopy. Kidder et al. (1992)
analyzed an expanded sample to derive photospheric He
abundances for the hotter objects and to establish an e+ec­
tive observational low­temperature threshold for the detec­
tion of pure hydrogen DAWDs at soft X­ray wavelengths.
In 1997 three groups (Marsh et al. 1997, hereafter M97 ;
Vennes et al. 1997, hereafter V97 ; Finley, Koester, & Basri
1997, hereafter FKB97) published results on the mass dis­
tribution of EUV­selected WDs. Due to the selection cri­
terion, these samples contain the hottest WDs (T
eff [
25,000 K), as cooler WDs do not emit signiïcant EUV
radiation. The derived mass distributions in the EUV­
selected samples are similar to that of BSL92 but show
some interesting deviations in detail. The frequency of very
high mass WDs is much larger, and that of very low mass
WDs much smaller, than in BSL92. These ïndings can at
least partly be explained by selection e+ects (see the dis­
cussion in FKB97). More serious is a trend of the peak mass
with temperature. V97 found that their mass distribution
peaks at 0.598 while the BSL92 distribution peaks at
M _ ,
0.568 with masses computed using Woodîs (1995)
M _ ,
mass­radius relation with ```` thick îî layers (M H \ 10~4M WD ,
This discrepancy diminishes slightly if
M He \ 10~2M WD ).
the ```` very thin layer îî no hydrogen
(M He \ 10~4M WD ,
layer) mass­radius relations are used (peak masses of 0.556
and 0.532 for the V97 and BSL92 samples,
M _
respectively). V97 interpreted this as evidence for a very thin
hydrogen layer of the DA WDs. However, the e+ects are
small, so this result depends strongly on the accuracy of the
derived stellar parameters.
FKB97 estimated the internal accuracy of di+erent
analysis methods from Monte Carlo simulations. The preci­
sion reachable by Balmer line ïtting is very compelling :
for K. However, for spectra
*T eff /T
eff \ 0.01 T eff \ 60,000
with very high signal­to­noise ratios (S/N), errors intro­
duced by details of the observation and reduction tech­
niques (e.g., extraction, ÿat ïelding, ÿux, and wavelength
calibration) might be more important but are very difficult
to determine. Additionally, one must take into account dif­
ferences in the model atmosphere calculations and ïtting
procedure. Together with the results presented in this paper,
we now have four samples of hot WDs analyzed in a similar
way and with signiïcant overlap. This o+ers the
opportunity to determine the real accuracy of the spectral
analysis of hot WDs, including many possible systematic
e+ects.
We present the selection criteria of our sample in ° 2 and
the observations and data reduction procedures in ° 3.
Details on our model atmospheres are given in ° 4. The
results and a detailed comparison with the previous
analyses of EUV­selected WDs are presented in ° 5. We
ïnish with a discussion of our results and an outlook.
2. SAMPLE SELECTION CRITERIA
We chose to limit our uniform sample to DAîs, for which
models provide the best temperature and mass constraints.
We start with 73 known DA WDs in the Extreme Ultraviol­
et Explorer (EUV E) bright source list (Malina et al. 1994).
Excluding sources at low galactic latitudes ( o b o \ 15) and
southerly declinations (d \[20) yields a list of 28 DAîs. A
similar procedure for nonoverlapping DAîs listed in the
ROSAT Wide Field Camera survey Bright Source Cata­
logue (Pounds et al. 1993) yields 29 objects.
We have removed from our uniform sample two well­
known stars with published sensitive optical spectropho­
tometry and IR photometry (Feige 24 and HZ 43). Two

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 401
TABLE 1
ATMOSPHERIC PARAMETERS OF PROGRAM STARS
RE J Other Names T eff log g M/M _ Observation Date
0007]331 GD 2 46493 ^ 514 7.83 ^ 0.05 0.602 1996 Jan 6
0134[160a GD 984, PHL 1043 44866 ^ 667 7.77 ^ 0.05 0.572 1996 Jan 5
0237[122 PHL 1400 32077 ^ 177 8.45 ^ 0.04 0.890 1996 Jan 5
0348[005 GD 50 3950 ^ 8464 9.07 ^ 0.06 1.215 1996 Jan 4
0427]740 48587 ^ 1044 7.93 ^ 0.08 0.646 1996 Jan 5
0457[280 MCT 0455[2812 51199 ^ 786 7.72 ^ 0.05 0.570 1996 Jan 4
0512[004 31733 ^ 139 7.40 ^ 0.03 0.458 1996 Jan 5
0521[102 33186 ^ 301 8.60 ^ 0.06 0.980 1996 Jan 5
0841]032 38293 ^ 252 7.75 ^ 0.03 0.544 1996 Jan 4
0902[040 23218 ^ 160 7.84 ^ 0.02 0.544 1996 Jan 4
0907]505 PG 0904]511 32167 ^ 338 8.11 ^ 0.07 0.695 1996 Jan 4
0940]502 PG 0937]506 36034 ^ 283 7.69 ^ 0.04 0.519 1997 Apr 9
0957]852 51311 ^ 1348 8.37 ^ 0.10 0.866 1996 Jan 5
1019[140 31524 ^ 102 7.92 ^ 0.02 0.606 1997 Apr 9
1029]450 PG 1026]454 35518 ^ 247 7.70 ^ 0.04 0.520 1997 Apr 9
1032]532 43587 ^ 506 7.95 ^ 0.05 0.644 1996 Jan 4
1033[114 G 162[66, LTT 3870 24685 ^ 252 7.85 ^ 0.03 0.553 1996 Jan 4
1036]460e GD 123 29361 ^ 251 8.02 ^ 0.05 0.648 1996 Jan 4
1043]490e 41132 ^ 1178 7.94 ^ 0.13 0.635 1996 Jan 5
1044]574 PG 1041]580 30338 ^ 153 7.81 ^ 0.03 0.550 1996 Jan 4
1100]713 PG 1057]719 41104 ^ 814 7.84 ^ 0.09 0.593 1996 Jan 4
1112]240 Ton 61 39824 ^ 636 7.78 ^ 0.07 0.563 1996 Jan 5
1122]434 PG 1120]439 26996 ^ 151 8.31 ^ 0.02 0.803 1997 Apr 9
1126]183e PG 1123]189 54334 ^ 1983 7.76 ^ 0.13 0.594 1996 Jan 4
1128[025 PG 1125[026 30699 ^ 380 8.24 ^ 0.08 0.767 1996 Jan 4
1148]183 PG 1145]188 25758 ^ 299 7.91 ^ 0.04 0.587 1996 Jan 4
1235]233b PG 1232]238 46569 ^ 523 7.83 ^ 0.05 0.602 1996 May 11õ12
1257]220b GD 153 38926 ^ 142 7.78 ^ 0.02 0.560 1996 Jan 4, 1996 May 12
1336]694 PG 1335]701 29607 ^ 87 8.34 ^ 0.02 0.824 1996 May 10
1431]370 GD 336 34404 ^ 115 7.91 ^ 0.02 0.608 1996 May 11
1446]632 37947 ^ 254 7.79 ^ 0.04 0.562 1996 May 11
1629]780c 41043 ^ 338 7.92 ^ 0.04 0.627 1996 May 11
1638]350 PG 1636]351 35404 ^ 142 7.98 ^ 0.02 0.642 1996 May 10
1643]411b PG 1642]414 28815 ^ 81 8.22 ^ 0.02 0.753 1996 May 9
1650]403b 38144 ^ 211 7.97 ^ 0.03 0.643 1996 May 9
1711]664d 48989 ^ 757 8.89 ^ 0.06 1.141 1996 May 12, 1997 Apr 9
1726]583b PG 1725]586 53561 ^ 542 8.23 ^ 0.04 0.795 1996 May 9
1800]683 KUV 18004]6836 44723 ^ 424 7.80 ^ 0.04 0.585 1996 May 10
1820]580 44099 ^ 264 7.78 ^ 0.03 0.574 1996 May 9
1845]682 KUV 18453]6819 36120 ^ 189 8.23 ^ 0.03 0.770 1996 May 10
2116]735b KUV 21168]7338 50812 ^ 354 7.72 ^ 0.03 0.569 1996 Jan 5, 1996 May 9
2207]252 26964 ^ 174 8.27 ^ 0.03 0.779 1996 Jan 5
2312]104 GD 246 53088 ^ 968 7.85 ^ 0.07 0.624 1996 Jan 4
NOTE.õError estimates were taken from the s2 procedure.
a Spectrum slightly contaminated by cool companion ; the cores of Hb and Hc are excluded from the ït.
b Weighted mean of individual observations.
c Red part of spectrum contaminated by cool companion ; Hb and the core of Hc excluded from ït.
d Close­by optical companion ; spectrum apparently not contaminated.
e Red part of spectrum contaminated by cool companion ; Hb excluded from ït.
DAîs with broad­line proïles due to magnetic splitting were
also excluded (PG 1658]441 and PG 0136]251). Eight
known binaries are also excluded from the uniform sample :
V471 Tau (Vennes, Christian, & Thorstensen 1998), PG
0824]289 (Heber et al. 1993), HD 74389B (Liebert, Ber­
geron, & Sa+er 1990), RE J1016[052 (V97), PG 1033]464
(GD 123 ; Green, Schmidt, & Liebert 1986), RE J1426]500
(V97), RE J1629]780 (Catalan et al. 1995), and IK Peg
(Wonnacott, Kellett, & Stickland 1993), leaving 47 objects.
In this paper, a handful of objects that fell outside the
uniform sample deïnitions just outlined were included for
observation. These include the known binaries PG
1033]464 and RE J1629]780, and the magnetic WD PG
1658]441, as well as MCT 0455[2812, which was outside
the sample declination limits.
Due to observing constraints (a combination of weather,
poor seeing, and faint objects, or celestial placement of
objects), no spectra were obtained for sample objects RE
J0443[034, RE J0916[194, or PG 1040]451. PG
1234]482 was originally classiïed as an sdB star and thus
excluded ; it has since been reclassiïed as a DA (Jordan,
Heber, & Weidemann 1991). The ïnal sample we analyze
here thus includes 46 DA WD stars for which we present
new model NLTE ïts to optical spectra.
We note that since the sample selection was performed,
several relevant discoveries pertaining to sample objects

402 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
FIG. 1.õSpectra of the WDs observed at Steward Observatory
have been made. RE J0134[160 (GD 984) has central
Balmer emission components produced by a dMe compan­
ion. RE J1440]750 turns out to be a magnetic DA
(Dreizler et al. 1994). The uniform sample will be discussed
in a follow­up paper treating the IR photometry and binary
fraction.
3. OBSERVATIONS
Dates are listed for all observations in Table 1. On the
nights of 1996 January 4õ6, we obtained spectra at Steward
Observatoryîs Kitt Peak Station using the Bok 2.3 m reÿec­
tor equipped with the Boller & Chivens Cassegrain spectro­
graph and UV­ÿooded Loral 800 ] 1200 CCD. Most
spectra were dispersed with a 600 line mm~1 ïrst­order
grating used behind a long slit. The instrumen­
4A. 5 ] 4@
tation provided wavelength coverage jj3400õ5600 at a
spectral resolution of D5 FWHM. On the last night of
A#
the observing run, we employed a new 400 line mm~1
grating providing wavelength coverage jj3500õ6790 at a
spectral resolution of D7 FWHM.
A#

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 403
FIG. 2.õSpectra of the MMT sample
We also obtained spectra at the Multiple Mirror Tele­
scope (MMT) on Mt. Hopkins 1996 May 9õ11 using the
300 line mm~1 grating in ïrst order on the Loral 3 k ] 1 k
CCD of the blue channel spectrograph. This yields coverage
from about 3350 to 8800 and the 2A slit width we used
A# ,
resulted in a spectral resolution of about 4 FWHM.
A#
Several objects were kindly obtained for us using the identi­
cal instrumental conïguration at the MMT by P. Berlind
on 1997 April 8.
Exposures at both telescopes ranged from 1 to 30 minutes
for program stars, and for all observations the long slit was
rotated to the parallactic angle according to the calcu­
lations of Filippenko (1982). The air masses were held below
1.5 in almost all cases. All spectra were extracted from the
two­dimensional images and reduced to linear wavelength
and intensity scales using standard reduction packages in
the Image Reduction and Analysis Facility (IRAF). These
operations included bias subtraction, ÿat­ïeld division by
images obtained by exposing on dome or internal quartz
lamps, centroiding and summation of the stellar traces on
the two­dimensional images, sky subtraction, wavelength
calibration using spectra of He/Ar arc lamps, and absolute

404 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
FIG. 3.õLTE o+sets. The di+erences are magniïed 3 times. The vectors give the correction that must be applied to transform LTE results to the NLTE
scale.
ÿux calibration using the ÿux standards of Massey et al.
(1988). Details of these reduction procedures are given by
BSL92.
We present in Figures 1 and 2 our collection of WD
spectra. The spectra obtained at the Steward Observatory
2.3 m telescope are found in Figure 1, and the MMT spectra
are in Figure 2. Some stars observed repeatedly appear in
both ïgures. The S/N of our spectra ranges from 35 to 200,
with an average of 90. Ninety percent of our spectra have an
S/N of at least 45.
4. MODEL ATMOSPHERES
We calculate hydrogen model atmospheres with the
NLTE code developed by Werner (1986). Basic assump­
tions are those of static, plane­parallel atmospheres in
hydrostatic and radiative equilibrium. In contrast to the
atmospheres commonly used to analyze DA WDs, we relax
the assumption of LTE and solve the detailed statistical
equilibrium instead. As described in Werner (1986), the
accelerated lambda iteration (ALI) method is used to solve
the set of nonlinear equations. The impact of NLTE on WD
atmospheres is discussed in detail in Napiwotzki (1997).
H I levels and lines are included in NLTE up to n \ 16.
Line blanketing by the Stark­broadened hydrogen lines is
taken into account consistently. As the hydrogen atmo­
spheres of DA WDs are stable for K, convec­
T eff [ 15000
tion is not included in our atmospheric models. Pressure
dissolution of the higher levels is described by the Hummer
& Mihalas (1988) occupation probability formalism follow­
ing the NLTE implementation by Hubeny, Hummer, &
Lanz (1994). The synthetic spectra are computed with the
extended VCS broadening tables (Vidal, Cooper, & Smith
1970) provided by & Butler (1989, private
Scho
# ning
communication) and Lemke (1997). We followed the pre­
scription of Bergeron (1993) and increased the critical ion­
izing ïeld adopted to calculate the occupation probability
by a factor of 2. The motivation is not a ÿaw in the Hummer
& Mihalas (1988) formalism, but a compensation for the
inadequacy of the standard Stark broadening theory when
line wings overlap. Our NLTE model grid covers the tem­
perature range 17,000 K (stepsize
K\T
eff \ 100,000
increasing with from 2000 to 10,000 K) and gravity
T eff
range 6.50 \ log g \ 9.75 (stepsize 0.25).
Although deviations from LTE are small for most DA
WDs, they become signiïcant for the hottest stars in our
sample (see, e.g., Napiwotzki 1997). Since we intend to
compare our results with three other samples analyzed by
means of LTE atmospheres, we have produced a map with
LTE correction vectors. For this purpose we calculated a
set of LTE model atmospheres using the technique
described in Napiwotzki (1997) of drastically enhancing col­
lisional rates between the atomic levels in the NLTE code.

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 405
This forces the occupation numbers to be in LTE and guar­
antees consistency with the NLTE atmospheres.
The synthetic LTE spectra were transformed into
```` observed îî spectra by convolving them with a Gaussian of
5 FWHM, rebinning them to 2 and adding Poisson
A# A# ,
noise corresponding to a continuum S/N of 100. These
simulated spectra were analyzed with the NLTE grid fol­
lowing the procedure outlined in ° 5. One thousand simula­
tions were run for every parameter set to eliminate the e+ect
of random errors. The resulting o+sets are displayed in
Figure 3. The orientation of the vectors corresponds to the
correction, which must be applied to transform LTE results
to the NLTE scale.
As expected from the results of Napiwotzki (1997), the
di+erences are negligible for DA WDs cooler than B40,000
K, but can be signiïcant for hotter stars. The LTE vectors
show the trend that NLTE e+ects increase with increasing
temperature and decreasing gravity (see, e.g., Figs. 3 and 4
in Napiwotzki 1997 for the case of DA WDs). The small
corrections found for the models with the highest tem­
perature and lowest gravity seems to contradict this behav­
ior. A look at the line proïles reveals that the NLTE
deviations are larger for, say, the K,
T eff \ 90,000
log g \ 7.0 model than the 70,000 K, 8.0 model. However,
the correction vectors are not a simple function of NLTE
deviations measured, e.g., as equivalent width di+erence,
but depend also on the way line proïles vary with tem­
perature and gravity. The small corrections found for the
high temperature/low gravity models are produced by the
cancellation of these e+ects. We expect a reliable transform­
ation between the LTE and NLTE temperature scales only
if the deviations are not too large. A conservative upper
limit is B70,000 K. A thorough comparison with the pre­
vious LTE analyses is presented in ° 5.3.
We checked our models by a comparison of our LTE
spectra with some DA model spectra kindly provided by D.
Koester (1998, private communication). Model parameters
were K in 10,000 K steps, and
T eff \ 30,000õ70,000
log g \ 8.0 for pure hydrogen models. Input physics are
very similar. In particular, both model calculations adopt
twice the critical ionizing ïeld for the calculation of line
proïles. We treated D. Koesterîs model spectra the same
way we treated the LTE spectra above and ïtted them with
our LTE grid. The result was quite satisfactory : the tem­
perature di+erences were always below 1.5%, and the
gravity di+erences never exceeded 0.03 dex.
Metals were ignored in our calculations, but they can
modify the hydrogen line proïles by their e+ect on the
atmospheric structure. Lanz et al. (1996) analyzed the
Balmer lines of the hot DA G191 B2B with pure hydrogen
LTE and NLTE atmospheres and an NLTE model with full
metal line blanketing. They concluded that the e+ect of
metal line blanketing on the Balmer lines was relatively
small, and the di+erence between LTE and NLTE was
found to be the most important e+ect. A recent study by
Barstow, Hubeny, & Holberg (1998), which investigated
several hot WDs in the temperature range around 60,000 K,
derived larger metal line blanketing e+ects of the order of
the NLTE e+ects. Since the LTE analyses of M97, V97, and
FKB97 are based on pure hydrogen models, our results
should be consistent with theirs in any case.
5. SPECTRAL ANALYSIS AND RESULTS
Atmospheric parameters of our DAWDs are obtained by
simultaneously ïtting line proïles of the observed Balmer
lines with the NLTE model spectra described above. We use
the least­square algorithm described in BSL92. The
observed and theoretical Balmer line proïles are normal­
ized to a linear continuum (both spectra are in a consis­
F j )
tent manner. Wavelength shifts are determined with a
cross­correlation method and applied consistently to each
complete spectrum. The synthetic spectra are convolved to
the observational resolution with a Gaussian and inter­
polated to the actual parameters with bicubic splines and
interpolated to the observed wavelength scale.
The atmospheric parameters and log g are then deter­
T eff
mined by minimizing the s2 value by means of a Levenberg­
Marquardt steepest descent algorithm (Press et al. 1986).
Several tests revealed that our interpolation routine is
rather robust concerning spacing of our model grid and
yields reliable results even at the edge of the model grid.
Finally, an estimate of the internal errors can be derived
from the covariance matrix. In contrast to BSL92, we esti­
mate the noise of the spectra (p) used for the s2 ït from the
neighboring continuum of each line. The S/N is adopted to
be constant throughout the line.
The results are given in Table 1, with illustrative exam­
ples shown in Figure 4. We adopt, for the moment, the
usual practice and indicate in Table 1 the internal errors
estimated from the quality of the s2 ït. However, one
should keep in mind that these errors can only serve as
lower limits. We will show below (° 5.3) that these formal
errors derived from the s2 ït signiïcantly underestimate the
real errors.
External errors can be estimated from multiple obser­
vations and analysis of the same star. We obtained repeat
observations for a subsample of six stars, for which results
are given in Table 2. The gravity values of all six stars agree
within the estimated internal errors. The same is also true
for four temperature comparisons. However, the di+erences
found for RE J1650]403 and RE J2116]735 are signiï­
cantly larger. This is in line with the external errors we
estimate from a comparison with the studies of M97, V97,
and FKB97 (see ° 5.3).
5.1. Binaries
Five stars in our sample, RE J0134[160, RE
J1036]460, RE J1043]490, RE J1126]183, and RE
J1629]780, show clear signs of binarity in the red part of
their spectra. Two more stars, RE J1711]664 and RE
J2207]502, are members of visual binaries.
RE J1629]780.õThe red part of the spectrum of RE
J1629]780 is heavily contaminated by an M­type main­
sequence companion. The composite spectrum and the
spectrum of the M star after subtracting the WD com­
ponent are shown in Figure 5. The characteristic bands of
TiO are easily recognizable. et al. (1995) deter­
Catala
# n
mined a spectral type of dM4. The Ha and Hb lines are seen
in emission, which indicates a chromospherically active Me
star. Sion et al. (1995) detected a ÿarelike increase of the
Balmer line emission.
The comparison in Figure 5 demonstrates that the blue
part (j \ 4400 of the WD spectrum is not disturbed by
A# )
the M dwarf. Thus we excluded Hb and the core of Hc from
the ït and derived the parameters K and log
T eff \ 41,000
g \ 7.92 from Hc to Hg. These parameters are in reason­
able agreement with the results of et al. (1995 ;
Catala
# n
K ; log g \ 8.0), who, however, included Hb,
T eff \ 41,800
and Kidder (1991 ; K, log g \ 7.6), who ïtted
T eff \ 42,500
Lya and the Balmer lines Hb and Hc.

406 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
FIG. 4.õBalmer line ïts for a representative set of WDs
RE J1036]460, RE J1043]490, RE J1126]183.õ
Three more WDs of our observed sample are known
binaries (RE J1036]460 and RE J1126]183, Green,
Schmidt, & Liebert 1986 ; RE J1043]490, Schwartz et al.
1995) and show red excesses in our spectra : since the Hb
lines of the WDs are contaminated, they were excluded
from the ït. Hc and higher Balmer lines are virtually uncon­
taminated. A discussion of these stars and newly discovered
binaries will be given in a forthcoming paper.
RE J0134[160 (GD 984).õAlthough our spectrum ends
at only 5600 a red excess is obvious. Subtraction of the
A# ,
theoretical WD ÿux leaves an M star spectrum. The M
dwarf contribution is much smaller than in RE J1629]780,
and we excluded only the cores of Hb and Hc, ïlled in by
the Balmer line emission, from the ït. Bues & Aslan (1995)
suspected a hot third component in RE J0134[160.
However, outside of the Hb and Hc cores, the Balmer lines
are well reproduced by our best ït without any indication of
a third component. Indeed, a subdwarf component as sug­
gested by Bues & Aslan (1995) is almost certainly not
present, since its ÿux would dominate in the blue.
RE J1711]664.õSince a late­type star is separated from
the WD by only we took care to get an uncontaminated
2A.5,
WD spectrum. We obtained a spectrum under good seeing
conditions. No excess is present up to the red limit at
8500 A# .
RE J2207]252.õThis WD has a red companion 8A. 5
away. Schwartz et al. (1995) estimated spectral type K4 V
and distance 65 pc from its colors. With the parameters
from Table 1, a WD distance of 62 pc results. Thus it is
TABLE 2
RESULTS OF REPEATED OBSERVATIONS
OBSERVATION 1 OBSERVATION 2
RE T eff log g T eff log g
1235]233 46308 ^ 837 7.85 ^ 0.08 46737 ^ 670 7.82 ^ 0.06
1257]220 39349 ^ 317 7.76 ^ 0.04 38820 ^ 159 7.78 ^ 0.02
1643]411 28813 ^ 120 8.23 ^ 0.02 28818 ^ 111 8.21 ^ 0.02
1650]403 37798 ^ 245 7.94 ^ 0.04 39126 ^ 413 8.01 ^ 0.05
1726]583 52712 ^ 927 8.27 ^ 0.06 54003 ^ 669 8.20 ^ 0.05
2116]735 50131 ^ 384 7.71 ^ 0.03 54604 ^ 906 7.76 ^ 0.06
NOTE.õError estimates were taken from the s2 ïtting procedure.

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 407
FIG. 5.õFlux­calibrated spectrum of the DA plus M pairs RE
J0134[160, RE 1036]460, RE J1043]490, RE J1126]183, and RE
J1629]780. From top to bottom we show the composite spectrum, the
best ït of the WD, and the resulting spectrum of the M star. The spectrum
of the M star companions of RE J0134[160 and RE J1126]183 are
multiplied by 3.
likely that both stars form a physical pair. The angular
separation corresponds to B500 AU.
5.2. Magnetic W Ds
Two WDs of our sample show Zeeman splitting of
the Balmer line cores, indicative of a magnetic ïeld. RE
J1659]440 (PG 1658]441) is a well­known star, already
analyzed by Schmidt et al. (1992). The discovery of the mag­
netic nature of RE J1440]750 (HS 1440]7518) was
announced by Dreizler et al. (1994 ; note the naming confu­
sion corrected in Dreizler, Werner, & Heber 1995õHS
1412]6115 should have been HS 1440]7518). Although
RE J1440]750 was analyzed by V97, they did not remark
on its magnetic nature. This is likely due to the lack of
coverage of the Ha line, which displays the most pro­
nounced Zeeman e+ect.
Flux­calibrated spectra of the magnetic WDs are dis­
played in Figure 6. The PG 1658]441 analysis of Schmidt
et al. (1992) resulted in K and log g \ 9.35.
T eff \ 30,500
The magnetic splitting was best reproduced by a 3.5 MG
dipole inclined 60¡ to the line of sight (producing a mean
surface ïeld strength MG). From the linear
B S \ 2.3
Zeeman e+ect we estimated a mean magnetic strength of 8
MG for RE J1440]750, consistent with the estimate given
in Dreizler et al. (1994).
The temperature and gravity of RE J1440]750 were
derived from a ït of the higher Balmer lines Hc to Hg
displayed in Figure 7, which are less a+ected by the mag­
netic splitting. Results are given in Table 3 supplemented by
the Schmidt et al. (1992) ït of PG 1658]441. Our own ït
gave similar results, albeit with lower accuracy. Our ïts of
RE J1440]750 can only provide a rough estimate of the
stellar parameters. Accurate results can only be expected
from a detailed treatment of the magnetic e+ects.
5.3. Internal, External, and Systematic Errors
We have now presented the results of a homogeneous
analysis of a sample of 46 hot, EUV­selected WDs based on
Balmer line ïtting. Three other large samples analyzed with
the same method were recently published by M97, V97, and
FKB97. Since considerable overlap exists between all four
samples, this allows a direct check for systematic errors and
the individual scatter on a star by star basis for WDs hotter
than 25,000 K.
Since in contrast to previous works our analysis is based
on NLTE model atmospheres, we applied the correction
vectors given in Figure 3 to correct for the LTE assumption.
Since for the hottest WDs these corrections become large
while the accuracy of temperature and gravity estimates
decreases for both LTE and NLTE analyses, one should
exclude comparison of stars with K. This does
T eff [ 70,000
not a+ect our sample, which has a maximum temperature
closer to 54,000 K.
Di+erences (after correction to NLTE) in and log g
T eff
between studies for stars in common with M97, V97, and
FKB97 are displayed in Figure 8 as a function of The
T eff .
magnetic WDs and the binaries, which show signiïcant
contamination of the WD spectrum by the companion, are
excluded. One can now focus on systematic di+erences
between pairs of studies, e.g., our results (NGS) versus
FKB97 (NGS­FKB97), V97­NGS, M97­NGS, FKB97­
M97, M97­V97, and so on. However, we chose another
approach and performed an optimization that simulta­
neously took into account all values from all stars in
common between any samples. In other words, the values
given for the systematic di+erences between our study and
the M97, V97, and FKB97 samples form a system for direct
transformation between, say, FKB97 and the three other
samples. The running averages computed this way are
plotted in Figure 8 as a solid line. The actual value was

408 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
FIG. 6.õSpectra of the magnetic WDs PG 1658]441 and RE J1440]750. The position of the p components of the Balmer lines are indicated.
computed in 1000 K steps for all WDs in the respective
temperature intervals Although this curve does
T eff ^ 10%.
not represent the best ït to the data plotted in Figure 8
alone, it is a fairly good representation of the di+erences
FIG. 7.õBest ït of the magnetic WD RE J1440]750. As indicated by
the dashed line, Hb was not used for the parameter determination.
computed directly between our measurements and those of
M97, V97, and FKB97.
Since the distribution is highly non­Gaussian with many
outliers, as evident in Figure 8, we decided to adopt an
underlying Lorentzian (or Cauchy) distribution for the opti­
mization. The tails of the Cauchy distribution are much
larger than that of the corresponding Gaussian, yielding a
much lower weight for deviant points (see discussion in
Press et al. 1986). The dotted lines represent the 1 p con­
ïdence interval of the mean, computed conservatively from
the rms deviations.
First, we notice a considerable scatter larger than
expected from the internal error estimates (see the dis­
cussion below). If one ignores the hot end, the agreement
between the FKB97 and our temperature scale is good ;
di+erences are below 1%, smaller than the maximum model
di+erences to the Koester models (see ° 4), which were used
by FKB97. The same atmospheres are used in M97, and it is
therefore surprising that signiïcant di+erences with M97
are present. These trends are most likely caused by di+erent
reduction and analysis techniques. O+sets of the same order
are found in our comparison with V97, where a di+erent
LTE model atmosphere code is used. Although basically the
same input physics is included, this might at least partly
explain those shifts in and log g.
T eff
Our results are quantiïed in Tables 4 and 5. We divided
the WDs into three groups according to their temperature :
a cool group with K, a hotter one with 30,000
T eff \ 30,000
K, and the hottest considered group with
K\T eff \ 45,000
45,000 K. NLTE e+ects are still negligi­
K\ T eff \ 70,000
ble in the range of e+ective temperatures of the two coolest
groups. Mean shifts and the conïdence range of the mean
(computed as described above) are provided for these

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 409
TABLE 3
PARAMETERS OF THE MAGNETIC WHITE DWARFS
RE Other Names T eff log g M/M _ B S Observation Date
1440]750 HS 1440]7518 36154 ^ 275 8.87 ^ 0.05 1.128 7.7 1996 May 10
1659]440a PG 1658]441 30510 ^ 200 9.36 ^ 0.07 1.311 2.3 1996 May 10
a Parameters from Schmidt et al. 1992.
groups and the complete sample (except stars with T eff [
70,000 K). The shifts discussed above and shown in Figure 8
are statistically signiïcant and reach values of B5% in T eff
in the hottest bin. In log g the di+erence between our results
and M97 reach B0.1 dex for the coolest bin. However, we
emphasize that all four analyses are based on state­of­the­
art model atmospheres and s2 ïtting techniques. Since there
are no strong arguments to favor or discard one analysis, it
seems these are the systematic shifts characteristic of
modern analyses of hot WDs.
If we take the systematic shifts into account, we can use
the samples to derive estimates of the observational scatter,
which can be compared with the internal error estimates.
Since we have approximately the same scatter for di+erent
combinations of the samples, we compute a mean scatter
for all possible combinations (weighted by the number
p diff
of stars in common). For this purpose we correct for the
systematic shifts calculated for each of the three bins,
T eff
whose temperature intervals are given in Table 6. The indi­
vidual measurement errors add quadratically, and if we
p ind
FIG. 8.õDi+erences in temperature (left­hand panel), and gravity (right­hand panel) between the M97, V97, FKB97 samples, and our own on a star by star
basis. The same comparison is carried out for the LTE studies of M97 and V97 in the bottom panel. The smoothed average of the di+erences is plotted with
solid lines, while the standard error of the mean di+erence is indicated by the dotted lines. The values used for the x­axis are NLTE from this paper,
T eff
except for the bottom panel, which uses V97 (corrected to NLTE).

410 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
TABLE 4
SYSTEMATIC TEMPERATURE DIFFERENCES
Temperature M97­NGS V97­NGS FKB97­NGS
(K) (*T eff /T eff ) (*T eff /T eff ) (*T eff /T eff )
T eff \ 30000 [0.023 ^ 0.006 0.032 ^ 0.005 0.007 ^ 0.005
30000 \ T eff \ 45000 [0.013 ^ 0.003 0.017 ^ 0.003 0.004 ^ 0.003
45000 \T eff \ 70000 0.036 ^ 0.006 0.050 ^ 0.006 0.046 ^ 0.007
All with T eff \ 70000 [0.006 ^ 0.003 0.024 ^ 0.003 0.012 ^ 0.003
NOTE.õFor each temperature range, each column gives the average di+erence
over the respective interval and the conïdence interval of the average di+erence.
TABLE 5
SYSTEMATIC GRAVITY DIFFERENCES
Temperature M97­NGS V97­NGS FKB97­NGS
(K) (* log g) (* log g) (* log g)
T eff \ 30000 [0.112 ^ 0.017 [0.001 ^ 0.016 [0.064 ^ 0.018
30000 \ T eff \ 45000 [0.086 ^ 0.017 0.026 ^ 0.016 [0.034 ^ 0.016
45000 \ T eff \ 70000 [0.066 ^ 0.030 [0.067 ^ 0.026 [0.062 ^ 0.027
All with T eff \ 70000 [0.084 ^ 0.013 [0.002 ^ 0.012 [0.047 ^ 0.012
NOTE.õFor details see Table 4.
assume that the inherent scatter is the same for all analyses
(and we found no reason to discard this assumption), the
individual measurement errors can be estimated as p ind \
Not surprisingly, the smallest scatter is found
(1/21@2)p
diff .
for the ```` cool îî group K) with
(T
eff \ 30,000 p(T eff ) \ 2.3%
and p(log g) \ 0.07 dex. It increases to and
p(T eff ) \ 3.3%
p(log g) \ 0.13 dex for the hottest bin. This trend is
expected from the statistical analysis presented in Fig. 1 of
FKB97. However, the values are larger by a factor of 3 or
more than the internal parameter errors for a well­exposed
spectrum (see, e.g., Table 1). Therefore, we conclude that the
accuracy is not limited by the noise for good spectra, and we
suggest that other e+ects, such as details of the extraction or
ÿuxing and normalization procedures, contribute more.
Considering these systematic uncertainties, the 0.3 dex dif­
ference between the gravity determinations of FKB97 and
Napiwotzki et al. (1993) for HZ 43A is only a 1.5 p deviation
and therefore not as serious as considered by FKB97.
5.4. Mass Distribution
5.4.1. Derivation and Sample Comparisons
Once the temperature and gravity of the WDs are known,
the mass can be determined from theoretical mass­radius
relations. The recent investigations of M97, V97, and
FKB97 based their interpretation on the model sequences
TABLE 6
MEAN SCATTER OF TEMPERATURE AND
p ind
GRAVITY DETERMINATION
Temperature
(K) p(T eff ) p(log g)
T eff \ 30000 0.023 0.075
30000 \ T eff \ 45000 0.023 0.101
45000 \ T eff \ 70000 0.034 0.128
All with T eff \ 70000 0.026 0.107
of Wood (1995). The applied models have H­ and He­layer
masses of and respectively (thick
10~4M WD 10~2M WD ,
layers), and a carbon core. These model sequences are based
on a set of pre­WD models with end masses of 0.6, 0.8, and
0.95 computed by Kawaler (see Wood 1994). Starting
M _
models for other masses were constructed by homology
transformations.
The mass­radius relations we use are based on the evolu­
tionary calculations of (1995). These models are
Blo
# cker
calculated ab initio from the main sequence. The resulting
WDs show important di+erences compared to Woodîs
(1995) models. In contrast with the carbon core models
widely used for mass determination, the degenerate core
contains a mass­dependent mixture of carbon and oxygen
(and trace elements). However, note that Wood (1995) also
presented some WD sequences with C/O cores. The H­ and
He­layer masses resulting from evolutionary calculations
depend on the stellar mass 1995 ; et al.
(Blo
# cker Blo
# cker
1997). While the canonical thick hydrogen layer mass of
10~4 is met for a 0.6 WD, it decreases from several
M _ M _
10~3 for 0.3 down to 10~6 for 1.0 This
M _ M _ M _ M _ .
results in a mass­radius relation, which is steeper than a
relation based on a constant layer mass. Consequently, the
derived mass distribution will be narrower if evolutionary
layer masses are used.
The lower mass limit for a C/O core WD is 0.46 the
M _ ,
limiting mass for central helium burning in low­mass stars
(Sweigart, Greggio, & Renzini 1990). Thus WDs with a
lower mass possess a helium core. At the current age of the
universe He WDs have not been produced by single star
evolution, but are the result of binary evolution where the
hydrogen­rich envelope was stripped away along the (ïrst)
red giant branch (Kippenhahn, Kohl, & Weigert 1967 ; Iben
& Tutukov 1986). We use the recent evolutionary models of
He WDs calculated by Driebe et al. (1998) based on this
scenario.
The combined tracks of (1995) and Driebe et al.
Blo
# cker
(1998) cover the mass range 0.18õ0.94 We supplement­
M _ .

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 411
ed this set with the 1.0, 1.1, and 1.2 carbon core
M _
sequences of Wood (1995) with ```` thin îî layers. Since the
hydrogen envelope mass decreases with increasing WD
mass in (1995) models, their highest mass models
Blo
# ckerîs
e+ectively correspond to thin layer models. Since high­mass
WDs are already close to the zero­temperature conïgu­
ration, the remaining departures from consistent evolution­
ary calculations can be ignored for practical purposes.
The position of the analyzed WDs in the temperature/
gravity plane is shown in Figure 9 along with the tracks
used for the mass determination. The individual WD
masses are given in Table 1, and the resulting mass distribu­
tion is shown in Figure 10. We have also redetermined
masses for the BSL92 sample with the Blo
# cker/Driebe
mass­radius relations and supplemented Figure 10 with the
resulting distribution.
Our mass distribution possesses the same basic features
as found in the EUV­selected samples of M97, V97, and
FKB97. The sharp peak centered at B0.59 is in prin­
M _
cipal agreement with the earlier investigations of KSW79,
Weidemann & Koester (1984), and BSL92, with a sharp
fallo+ toward lower masses and a less steep decline toward
higher masses with a tail of high­mass WDs. Considering
the relatively large observational scatter we found in ° 5.3,
the underlying distribution may be extremely sharp. The
mean mass is 0.67 However, this value is strongly
M _ .
biased by the few very high­mass WDs.
We decided to follow the recipe of FKB97 and ïtted the
mass peak with a Gaussian. Although a Gaussian is not a
good representation of the WD mass distribution, it gives a
robust estimate of the peak mass. The ït result is, in prin­
ciple, dependent on the adopted binning of the mass inter­
vals. However, in some test calculations we found e+ects
exceeding a few 0.001 only if the bin width was larger
M _
than 0.05 The values given in this paper were derived
M _ .
by ïtting Gaussians to virtually unbinned mass distribu­
tions (formal bin width 0.001 M _ ).
We were concerned by the possibility that the di+erent
fraction of low­ and high­mass WDs found in di+erent
samples (see discussion below) may skew the Gaussian ït of
the main peak to higher or lower masses. We tested this by
ïtting the BSL92, FKB97, and our mass distributions with
multicomponent Gaussians, which ïtted the secondary
high­ and low­mass peaks separately. We found no devi­
ation higher than 0.003 in any case and concluded that
M _
the single Gaussian ït of the main peak yields a rather
stable estimate.
With this method, we derived a peak mass of our sample
of 0.589 We reanalysed the FKB97, M97, and V97
M _ .
samples with our mass­radius relations. We applied the cor­
FIG. 9.õE+ective temperature and gravity of our WD sample compared with evolutionary tracks. Solid lines are (1995) dashed lines are Driebe
Blo
# cker
et al. (1998) ; dotted lines are Wood (1995). The magnetic WDs are marked by open symbols.

412 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
FIG. 10.õMass distribution of WDs (binned over 0.05 The solid
M _ ).
line histogram indicates the result for our sample. The dotted line is the
BSL92 sample with masses redetermined from the rela­
Blo
# cker/Driebe
tions (normalized to the same sample size). The Gaussian curve represents
the best ït to our mass distribution as described in the text.
rections to NLTE and excluded the WDs with temperatures
in excess of 70,000 K. The peak masses are 0.555 (FKB97),
0.535 (M97), and 0.582 (V97). These di+erences reÿect
M _
the systematic di+erences in and log g determinations
T eff
discussed above, and probably di+erent selection criteria in
the case of FKB97.
The probable He core WD RE J0512[004 is the only
object in our sample with a mass below 0.5 but four
M _ ,
WDs have masses in excess of 1.0 The frequency of
M _ .
low­ and high­mass WDs found in our and other EUV­
selected samples is qualitatively di+erent from that found in
optically selected samples such as BSL92. BSL92 detected
in their sample of 129 WDs 16 objects with masses below
the limiting mass for C/O core WDs and a total of 28 WDs
with M\ 0.5 These numbers are reduced to 10 and 16,
M _ .
respectively, if we redetermine the masses with the mass­
radius relations of (1995) and Driebe et al. (1998).
Blo
# cker
However, that is still a much higher fraction than we ïnd in
our EUV­selected sample.
5.4.2. Cooling Rates and Detection Probability
Why do optical­ and EUV­selected samples contain dif­
ferent fractions of high­ and low­mass WDs? All helium
WDs from the BSL92 sample have temperatures below
30,000 K ; the only helium WD candidate in our sample has
K. This implies that the detection probability
T eff B 32,000
of low­mass WDs in EUV­selected samples is much lower,
because the fraction of low­mass WDs at higher is much
T eff
lower than it is for K. This viewpoint is sup­
T eff \ 30,000
ported by the helium WD sequences calculated by Driebe et
al. (1998). We have plotted the variation of temperatures
with time for WDs with helium and C/O cores in Figure 11.
The detection probability in a given evolutionary stage goes
as the inverse of the rate of temperature decrease at that
stage. New He WDs cool down rapidly to a certain (mass­
dependent) temperature, whereafter the cooling rate drops
drastically and the star remains on a temperature plateau
for a long time. This behavior is most pronounced for the
lowest masses. Hydrogen shell burning plays an important
role for this plateau phase. Although the energy production
by hydrogen burning drops down dramatically after the
star enters the WD sequence, it still produces a signiïcant
fraction of the total luminosity, enough to bring the cooling
to a standstill. We can conclude from Figure 11 that it is
extremely unlikely to detect a helium WD during its ïrst
rapid cooling phase ; it is easier to ïnd them during their
plateau phase or afterward. This means there is a strong
bias toward detecting helium WDs in samples of relatively
```` cool îî DA stars (like BSL92) instead of the overall much
hotter EUV­selected samples.
We can explain in a similar fashion why high­mass WDs
are found preferentially in the 30,000 K
K\T eff \ 50,000
range. Due to the drop in neutrino cooling, the evolutionary
speeds of massive WDs are relatively low in this range, as
demonstrated by the 0.940 track, the most massive
M _
stellar remnant calculated by (1995). This increases
Blo
# cker
the detection probability of more massive WDs in EUV­
selected samples.
5.4.3. Interstellar Absorption
Even if we restrict our comparisons to hot subsamples of
WDs, the fraction of massive WDs is much higher in the
EUV­selected samples than it is in optically selected ones.
An extensive discussion of this problem is carried out by
FKB97. FKB97 argue that the number of high­mass WDs
discovered per sky area is similar for the whole­sky EUV
surveys and the optical Palomar­Green (PG) survey (Green
et al. 1986), which covered roughly 25% of the sky. In other
words, a whole­sky version of the PG survey should have
discovered all but one of the EUV­detected WDs with
M[ 1.1 At a given temperature, WDs with lower
M _ .
masses are larger, consequently more luminous, and detect­
able to larger distances. For instance, at 30,000 K a WD of
0.5 is detectable at distances D30% larger than a 0.7
M _
WD. At the maximum distance sampled by, e.g., the
M _
PG survey, the probability is very high that interstellar
matter e+ectively absorbs all EUV radiation. Thus the dom­
inant e+ect in EUV surveys is not a selection for massive
WDs as suggested by V97, but a selection against low­mass
WDs due to a sample volume strongly a+ected by inter­
stellar absorption.
5.4.4. Temperature Dependence of the Derived Mass Peak
FKB97 noted a moderate apparent trend of the WD peak
mass with temperature. Since their sample also included
optically selected WDs, they analyzed a considerably higher
fraction of stars with K, and therefore have a
T eff \ 25,000
larger temperature baseline than pure EUV samples. Analo­
gous to this ïnding, V97 found an 0.03 o+set between
M _
the peak of the mass distribution in their EUV­selected
sample and the (cooler) WDs analyzed by BSL92. In both

No. 1, 1999 DISTRIBUTION OF EUV­SELECTED WHITE DWARFS 413
FIG. 11.õTime evolution of stellar surface temperature for helium core WDs (tracks from Driebe et al. 1998 ; solid lines) and C/O WDs (tracks from
1995 ; dashed lines). The tracks are labeled with the stellar masses.
Blo
# cker
cases this temperature dependence decreases if Woodîs
(1995) models with very thin layers no
(M He \ 10~4M WD ,
hydrogen layer), instead of the canonical thick layer models
are used. However,
(M He \ 10~2M WD , M H \ 10~4M WD ),
part of the trend noted in V97 may be related to the system­
atic di+erences between the analyses discussed in ° 5.3. Since
V97 compared results from two di+erent analyses, it is not
possible to judge if the o+set is real or just an artifact. The
case of FKB97 is stronger, because they based their case on
a homogeneously analyzed sample. FKB97 warned that the
temperature dependence of the mass distribution peak may
be caused by inadequacies remaining in the model atmo­
spheres. A more detailed discussion is given in the next
section.
Some evidence that part of the temperature trend stems
from the analyses comes from our intercomparisons pre­
sented in ° 5.3. We showed that systematic di+erences
between the four investigated samples exist that vary with
e+ective temperature. This might mimic a temperature
dependence of the sample peak mass. A gravity o+set of 0.1
dex transforms into mass o+sets of 0.050, 0.044, and 0.034
for a 0.6 WD with 25,000, 40,000, and 60,000 K,
M _
M _
respectively. Even a relatively small systematic log g di+er­
ence of 0.05 dex (see Table 5) corresponds to a 0.02 M _
o+set. The scatter p of individual gravity determinations
reported in Table 6 corresponds to p(M) B 0.04 nearly
M _ ,
independent of T eff .
5.4.5. Cooling Tracks
Another part of the dependence of the mass peak may
T eff
be caused by the use of Woodîs (1995) cooling tracks by
FKB97 and V97. These tracks are not completely self­
consistent since not all model sequences were not calculated
ab initio from the main sequence. This is not important for
cooler WDs, but it may cause deviations from ab initio
tracks, especially for the hottest WDs where structure
depends sensitively on the evolutionary history &
(Blo
# cker
1990).
Scho
# nberner
We redetermined the masses of the BSL92 WDs with the
mass­radius relations and derived a peak
Blo
# cker/Driebe
mass of 0.559 That is 0.03 lower than our peak
M _ . M _
mass, but having in mind the range of mass determination
derived for the EUV­selected samples, we cannot consider
this a signiïcant di+erence. FKB97 divided their sample
into cool K) and hot (35,000
(T eff \ 35,000 K\T eff \
75,000 K) subsamples and derived a 0.029 higher peak
M _
mass for the hot sample. Our reanalysis of the FKB97 LTE
results with the mass­radius relation yields
Blo
# cker/Driebe

414 NAPIWOTZKI, GREEN, & SAFFER Vol. 517
virtually the same o+set : 0.025 However, the di+erence
M _ .
is brought down to 0.010 (0.550 vs. 0.560 if we
M _ M _ )
apply corrections to NLTE. One can imagine that a di+er­
ence of this order (if signiïcant at all) can easily be produced
by our neglect of metallicity e+ects (see Lanz et al. 1996 ;
Barstow et al. 1998).
Therefore, given the combination of sample selection and
systematic e+ects in analyses to date, our results do not
conïrm the presence of intrinsic systematic mass di+erences
between hot and cool WDs.
6. CONCLUSIONS
We have obtained temperatures, gravities, and masses for
a sample of 46 EUV­selected DA WDs. These data com­
plement a near­IR survey for low­mass companions. The
stellar parameters were determined by ïtting the hydrogen
Balmer line proïles with NLTE model spectra. A map of
LTE correction vectors was constructed, which allows the
transformation of LTE results to the NLTE scale. These
shifts become important for temperatures above 50,000 K
(see also Napiwotzki 1997).
Three recent analyses of DA WDs have a considerable
overlap with our sample and allow a direct check for sys­
tematic errors and individual measurement scatter.
Although all four analyses applied similar model atmo­
spheres and ïtting techniques, we recognized systematic
shifts up to 5% in temperature and 0.1 dex in gravity deter­
minations. These systematic errors must be considered
when the results are interpreted and compared to other
studies. The individual measurement errors increase with
temperature : from 2.3% to 3.3% and p(log g) from
p(T eff )
0.07 to 0.13 dex. This is larger than the typical errors com­
puted with s2 ït procedures for a well­exposed spectrum,
and it indicates that accuracy is limited by noise in com­
bination with other e+ects such as details of the extraction,
ÿuxing, or normalization procedures. It is unclear if these p
values indicate lower limits or scale (at least partially) with
the S/N of the spectra. It will be a challenge to resolve this
question. Repeated observations performed by one obser­
ver, at one telescope, reduced the same way, and analyzed
with one method as performed by BSL92, FKB97, and us
(Table 2) do not reveal all e+ects. Independent observations
analyzed independently are necessary.
Masses have been inferred from theoretical mass­radius
relations based on the evolutionary calculations of Blo
# cker
(1995) for C/O WDs and Driebe et al. (1998) for He WDs.
An important feature of these calculations are the hydrogen
and helium layer masses, which depend on stellar mass. We
ïnd a sharp peak centered at B0.59 in agreement with
M _
the previous investigations of KSW79 and BSL92. We
redetermined masses of the BSL92 WDs with the
mass­radius relation and derived a peak
Blo
# cker/Driebe
mass of 0.56 At ïrst glance this seems to conïrm the
M _ .
systematic o+set reported by V97. However, this o+set
could be explained by systematic di+erences of the model
atmosphere analyses as well. Our reanalysis of the homoge­
neous FKB97 sample showed that the temperature depen­
dence of the mass peak nearly vanishes when corrected for
their LTE assumption. We conclude that the observational
data presented here and in similar studies are well explained
by canonical stellar evolution theory, i.e., WDs with thick
envelopes.
We ïnd only one object (RE J0512[004) with a mass
below 0.5 which is a possible helium core WD, but four
M _ ,
WDs with masses in excess of 1.0 This ratio of high­
M _ .
and low­mass WDs is quite di+erent from that found by
BSL92. This can partly be understood as the result of vari­
able evolutionary timescales of high­ and low­mass WDs.
We agree with FKB97 that another part can be explained
by a selection against low­mass WDs in EUV­selected
samples.
The principal aim of our project is the search for and
study of cool main­sequence companions of our WD
sample. Five WDs already show red contamination in our
optical spectra. A comprehensive discussion of these and
other binaries will be given in a forthcoming paper present­
ing IR photometry for the WD sample. In this article we
provided the basic WD data necessary to interpret our
binary sample.
We thank T. Driebe, F. Herwig, and T. for pro­
Blo
# cker
viding us with their tracks and computing the WD masses,
and D. Koester, who made some model spectra available
for our model comparison. We are grateful to Steward
Observatory for an unexpected generous award of six
nights of unclaimed 2.3 m time, which made possible simul­
taneous optical and IR observations of our sample of stars.
We thank Perry Berlind for obtaining several WD spectra.
P. J. G. acknowledges support through NASA contract
NAS8­39073 (ASC).
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