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How accurately do we know the parameters of hot DA
white dwarfs?
R. Napiwotzki
Dr. Remeis­Sternwarte, Sternwartstr. 7, 96049 Bamberg, Germany
Paul J. Green
Harvard­Smithsonian Center for Astrophysics, 60 Garden St.,
Cambridge, MA 02138, USA
Rex A. Saffer
Dept. of Astronomy & Astrophysics, Villanova University, 800
Lancaster Ave., Villanova, PA 19085, USA
Abstract. We present new determinations of effective temperature,
surface gravity, and masses for a sample of hot DA white dwarfs selected
from the EUVE and ROSAT Wide Field Camera bright source lists in the
course of a near­IR survey for low mass companions. Our analysis, based
on hydrogen NLTE model atmospheres, provides a map of LTE correction
vectors, which allow a thorough comparison with previous LTE studies.
We find previous analyses underestimate both the systematic errors and
the observational scatter in the determination of white dwarf parame­
ters via fits to model atmospheres. We find a peak mass of our white
dwarf sample of 0:59M fi , in basic agreement with the results of previous
investigations. However, we do not confirm a trend of peak mass with
temperature reported in two previous analyses.
1. Introduction
Precise knowledge of the white dwarf mass distribution puts constraints on the
theory of stellar evolution, especially the poorly understood mass loss processes
during the final stages of stellar evolution. About twenty years ago Koester,
Schulz & Weidemann (1979; KSW) established that the masses of white dwarfs
cluster in a narrow range around 0:6M fi . The analysis of KSW, along with other
follow­up investigations in the early eighties, used photometric data. Higher
precision became achievable at the beginning of the nineties, when it became
possible to obtain high­quality spectra of large numbers of white dwarfs and
determine the stellar parameters from a fit to the detailed profiles of the Balmer
lines. The first comprehensive sample of white dwarfs analyzed by this method
was presented by Bergeron, Saffer & Liebert (1992; hereafter BSL).
In 1997 three groups (Marsh et al. 1997, M97; Vennes et al. 1997, V97;
Finley, Koester & Basri 1997, FKB) published results on the mass distribution
of Extreme Ultraviolet (EUV) selected white dwarfs. Due to the selection crite­
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rion, these samples contain the hottest white dwarfs (T eff ? 25000K), as cooler
white dwarfs do not emit significant EUV radiation. The derived mass distrib­
utions in the EUV­selected samples are similar to that of BSL. V97 and FKB
found a trend of the peak mass with temperature. The V97 mass distribution
peaks at 0:598M fi , while the BSL distribution of cooler white dwarfs peaks at
0:568M fi , with masses computed using Wood's (1995) mass­radius relation with
``thick'' layers (MH = 10 \Gamma4 MWD , M He = 10 \Gamma2 MWD ). This discrepancy dimin­
ishes slightly, if the ``very thin layer'' (M He = 10 \Gamma4 MWD , no hydrogen layer)
mass­radius relations are used. V97 interpreted this as evidence for a very thin
hydrogen layer of the DA white dwarfs. However, the effects are small so this
result depends strongly on the accuracy of the derived stellar parameters. The
obvious question one has to ask is, whether the achievable accuracy of spectral
analysis is good enough to draw such conclusions. We will use the results of our
recent NLTE analysis of EUV selected white dwarfs (Napiwotzki, Green, Saffer
1998; NGS) to focus on this topic.
2. Observational and methological error sources
FKB estimated the internal accuracy of different analysis methods from Monte
Carlo simulations. The precision reachable by Balmer line fitting is very com­
pelling: \DeltaT eff =T eff ! 0:01 for T eff ! 60000K. However, for spectra with very high
signal­to­noise ratios (S/N), errors introduced by details of the observation and
reduction techniques (e.g., extraction, flat fielding, flux and wavelength calibra­
tion) might be more important, but are very difficult to determine. Additionally,
one has to take into account differences in the model atmosphere calculations
and fitting procedure.
Systematic errors may be introduced by simplifications used in the model
atmospheres calculations. The analyses of FKB, F97, and V97 applied pure hy­
drogen models computed in local thermal equilibrium (LTE). We relax the LTE
assumption and solve the detailed statistical equilibrium instead. Atmospheres
are computed with the NLTE code developed by Werner (1986). Although de­
viations from LTE are small for most DA white dwarfs they become significant
for the hottest stars in our sample (cf. Napiwotzki 1997). Since we intend to
compare our results with LTE results, we have produced a map with LTE cor­
rection vectors. For this purpose we calculated a set of LTE model atmospheres
using the technique described in Napiwotzki (1997). The resulting offsets are
displayed in Fig. 1. We checked our models by a comparison of our LTE spectra
with some DA model spectra kindly provided by D. Koester. The result was
quite satisfactory: the temperature differences were always below 1.5% and the
gravity differences never exceeded 0.03 dex.
Metals were ignored in our calculations, but they can modify the hydrogen
line profiles by their effect on the atmospheric structure. Lanz et al. (1996)
found these effects to be small in their analysis of the hot DA G 191 B2B. A
recent study by Barstow et al. (1998) derived larger metal line blanketing effects
of the order of the NLTE effects. Since the LTE analyses of M97, V97, and FKB
are based on pure hydrogen models, our results should be consistent with theirs
in any case.
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Figure 1. LTE offsets. The differences are magnified three times.
The vectors give the correction, which must be applied to transform
LTE results to the NLTE scale.
Once the temperature and gravity of the white dwarfs are known, the mass
can be determined from theoretical mass­radius relations. The choice of the
model sequences influences the derived masses. Since a detailed discussion is
given in the article of Driebe et al. (1999, in these proceedings) we will only
mention some important topics here.
The mass­radius relation depends on the thickness of the hydrogen and
helium layer masses. Usually a constant mass fraction (either ``thick'' or ``thin'')
is adopted. However, Bl¨ocker et al. (1997) have shown that the envelope masses
of evolutionary models depend on the stellar mass. The chemical mixture of the
degenerate core is a function of mass, too. White dwarf with masses higher than
0:46M fi have a carbon­oxygen core, but lower mass white dwarfs possess a helium
core. Furthermore the structure, and therefore the mass­radius relation, of hot
white dwarfs depends on the evolutionary history. Therefore it is important to
use model sequences, which follow the evolution self­consistently from the main
sequence through the red giant stages to the white dwarf cooling sequence.
We use the recent evolutionary models of C/O and He white dwarfs calcu­
lated by Bl¨ocker et al. (1995) and Driebe et al. (1998), respectively. We sup­
plement this set with the 1.0, 1.1, and 1:2M fi carbon core sequences of Wood
(1995) with ``thin'' layers.
3. Sample and analysis
The current study, conceived as a complement to optical studies, began as a near­
IR photometric survey for low mass companions to hot white dwarfs (WDs). By
investigating only EUV­detected WDs, we obtain a very reasonably­sized but
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Figure 2. Balmer line fits for a representative set of white dwarfs.
complete sample of 45 young WDs. Results from the IR survey will be presented
in an upcoming paper.
Spectra were obtained at Steward Observatory's Kitt Peak Station using the
2.3­m reflector equipped with the Boller & Chivens Cassegrain spectrograph and
with the MMT on Mt Hopkins equipped with the Blue Channel spectrograph.
The minimum spectral coverage was from about 3500 to 5600 š A with spectral
resolution ranging from 4 š A to 8 š A. Exposures at both telescopes ranged from
one to thirty minutes for program stars yielding an average signal­to­noise ratio
for the sample of 90.
Atmospheric parameters of our DA white dwarfs are obtained by simulta­
neously fitting line profiles of the observed Balmer lines with the NLTE model
spectra described above. We use the least­square algorithm described in BSL
and NGS. Illustrative examples are shown in Fig. 2. Detailed results are available
in NGS. The position of the analyzed white dwarfs in the temperature/gravity
plane is shown in Fig. 3 along with the tracks used for the mass determination.
4. Results and conclusions
We have now combined our results of a homogeneous analysis of a sample of
45 hot, EUV selected white dwarfs with the three other large samples analyzed
with similar methods (M97, V97, and FKB). 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 white dwarfs hotter than 25000K.
Since in contrast to previous works our analysis is based on NLTE model at­
mospheres, we applied the LTE correction vectors given in Fig. 1 to correct for
the LTE assumption.
4

Figure 3. Effective temperature and gravity of our white dwarf sam­
ple compared with evolutionary tracks. Solid lines: Bl¨ocker (1995);
dashed lines Driebe et al. (1998); dotted lines: Wood (1995). Two
magnetic white dwarfs are marked by open symbols.
First, we noticed considerable scatter, which is larger than expected from
the internal error estimates. The smallest scatter is found for the ``cool'' group
(T eff ! 30000K) with oe(T eff ) = 2:3% and oe(log g) = 0:07 dex. It increases to
oe(T eff ) = 3:3% and oe(log g) = 0:13dex for the hottest bin. This trend is in ac­
cordance with our expectations, because the Balmer lines become shallower and
less temperature and gravity sensitive with increasing temperature. However,
the values are larger by a factor of three or more than the internal parameter
errors for a well exposed spectrum. Therefore, we conclude that the accuracy is
not limited by the noise for good spectra, and we suggest that other effects, such
as details of the extraction or fluxing and normalization procedures, contribute
more.
We noticed statistically significant systematic offsets, which are tempera­
ture dependent and reach values up to ú5% in T eff and ú0.1 dex in log g. If
one ignores the hot end, the agreement between the FKB and our tempera­
ture scale is good. Differences are below 1%, smaller than the maximum model
differences to the Koester models (cf. Sect. 4), which were used by FKB. The
same atmospheres are used in M97, and it is therefore surprising that significant
differences with M97 are present. These trends are most likely caused by differ­
ent reduction and analysis techniques. Offsets of the same order are found in
our comparison with V97. In this case a different LTE model atmosphere code
is used. This might explain at least partly the shifts in T eff and log g in this
case. However, we emphasize that all four analyses are based on state­of­the­art
model atmospheres and ü 2 fitting techniques. Thus it seems that these are the
systematic shifts characteristic of modern analyses of hot white dwarfs.
5

We computed individual white dwarf masses from the Bl¨ocker/Driebe mass­
radius relations described in Sect. 2. We decided to follow the recipe of FKB
and fitted the mass peak with a Gaussian. With this method we derived a peak
mass of our sample of 0:589M fi . We reanalysed the FKB, M97, and V97 samples
with our mass­radius relations. We applied the LTE corrections and excluded
the white dwarfs with temperatures in excess of 70000K. The peak masses are
0:555M fi (FKB), 0:535M fi (M97), and 0.582 (V97). These differences reflect the
systematic differences of T eff and log g determination discussed above.
We also redetermined the masses of the ``cool'' BSL white dwarfs and derived
a peak mass of 0:559M fi . That's 0:03M fi lower than our peak mass. However,
this deviation may stem from systematic differences like those found for the
four investigated samples. Even a relatively small systematic log g difference
of 0.05 dex corresponds to a 0:02M fi offset. Even a temperature dependence of
the sample peak mass might be mimicked by systemtatic errors varying with
temperature. The scatter oe of individual gravity determinations corresponds to
oe(M) ú 0:04M fi nearly independent of T eff .
FKB divided their sample into a cool (T eff ! 35000K) and a hot (35000K
! T eff !75000K) subsample and derived a 0:029M fi higher peak mass for the
hot sample. The difference is brought down to 0:010M fi if we apply our LTE
corrections and reanalyse the sample with the Bl¨ocker/Driebe mass­radius re­
lations. One can imagine that a difference of this order (if significant at all)
can easily be produced by our neglect of metallicity effects (cf. Lanz et al. 1996,
Barstow et al. 1998). Therefore, given the combination of sample selection and
systematic effects in analyses to date, our results do not confirm the presence of
intrinsic, systematic mass differences between hot and ``cool'' white dwarfs.
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