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THE ASTROPHYSICAL JOURNAL, 517 : 399 õ 415, 1999 May 20
( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

A COMPARATIVE STUDY OF THE MASS DISTRIBUTION OF EXTREME-ULTRAVIOLETõSELECTED WHITE DWARFS1 R. NAPIWOTZKI
Dr. Remeis-Sternwarte, Sternwartstrasse 7, 96049 Bamberg, Germany ; ai23=sternwarte.uni- erlangen.de

PAUL J. GREEN
Harvard-Smithsonian 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 ; saer=ast.vill.edu Received 1998 June 4 ; accepted 1998 December 28

ABSTRACT We present new determinations of eective 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 near-infrared survey for low-mass companions. Our analysis, based on hydrogen non-LTE model atmospheres, provides a map of LTE correction vectors, which allow a thorough comparison with previous LTE studies. We ïnd that previous studies underestimate 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 low-mass white dwarfs depends sensitively on their history. To compute white dwarf masses, we thus use theoretical mass-radius 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 M , in agreement with the results of previous analyses. However, we do _ not conïrm a trend of peak mass with temperature reported in two previous analyses. Analogous to other EUV-selected samples, we note a lack of low-mass 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 low-mass white dwarfs caused by interstellar absorption in EUV-selected samples. Subject headings : binaries : close õ stars : atmospheres õ stars : evolution õ ultraviolet : stars õ white dwarfs
1

. INTRODUCTION

UV observations of EUV-detected 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 wavelengths, these WDs are hidden because of their close proximity to much more luminous companions, which are main-sequence (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 oer 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 EUV-detected systems (e.g., six close, interacting 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 emission 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 Observatory 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 spectral type is early enough. RV variations (case [3]) require multiple observations at high spectral resolution, and detection strongly favors close and/or massive companions. All of the discoveries mentioned above have been strongly dominated by these selection eects, 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) estimate that "" at least twice as many close binary systems remain to be identiïed from EUV surveys, most of them with a low-mass 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 near-IR photometric survey for lowmass companions to hot WDs. By investigating only EUVdetected WDs, we obtain a very reasonably sized but complete sample of young WDs, next to which very latetype dwarf companions can be detected in the near-infrared by searching for a K excess over that expected from the WD. Many hot WDs (T [ 24,000 K ; Finley et al. 1993) have been detected in theeff recent EUV all-sky surveys. EUV 399


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detection of these hot WDs depends primarily on their temperature, distance, and the intervening Galactic interstellar medium (ISM). Our sample of EUV WDs (whose selection we deïne below) oers 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 T derivable eff from optical spectra for the WDs in our sample using non-LTE (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 established that the masses of WDs cluster in a narrow range around 0.6 M , remarkable given that WDs stem from _ progenitors with masses ranging from below 1 M up to _ B8 M . Precise knowledge of the WD mass distribution _ puts constraints on the theory of stellar evolution, especially the poorly understood mass-loss process during the ïnal stages of stellar evolution. With two recent exceptions (Beauchamp et al. 1996 and Dreizler & Werner 1996, who analyzed samples of helium-rich DB and DO WDs, respectively), the mass distribution has only been determined for hydrogen-rich 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 follow-up investigations in the early eighties, used photometric data of which the Stromgren and Greenstein multichannel colors were the most suitable. Both systems provide temperatureand gravity-sensitive 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 suers 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 high-quality 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, Saer, & 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 X-ray databases. Three soft X-ray sources corresponding to WDs were found having relatively low eective temperatures, B25,000 K, which were determined independently using complementary 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 eective observational low-temperature threshold for the detection of pure hydrogen DA WDs at soft X-ray 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 distribution of EUV-selected WDs. Due to the selection criterion, 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 EUVselected 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 eects (see the discussion in FKB97). More serious is a trend of the peak mass with temperature. V97 found that their mass distribution peaks at 0.598 M , while the BSL92 distribution peaks at _ 0.568 M , with masses computed using Woodîs (1995) _ relation with "" thick îî layers (M \ 10~4M , mass-radius H WD M \ 10~2M ). This discrepancy diminishes slightly if He "" very thin layer îî (M \ 10~4M , no hydrogen WD the WD layer) mass-radius relations He used (peak masses of 0.556 are and 0.532 M for the V97 and BSL92 samples, _ respectively). V97 interpreted this as evidence for a very thin hydrogen layer of the DA WDs. However, the eects are small, so this result depends strongly on the accuracy of the derived stellar parameters. FKB97 estimated the internal accuracy of dierent analysis methods from Monte Carlo simulations. The precision reachable by Balmer line ïtting is very compelling : *T /T \ 0.01 for T \ 60,000 K. However, for spectra eff eff eff with very high signal-to-noise ratios (S/N), errors introduced by details of the observation and reduction techniques (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 differences 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 oers the opportunity to determine the real accuracy of the spectral analysis of hot WDs, including many possible systematic eects. 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 EUV-selected 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 Ultraviolet 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 Catalogue (Pounds et al. 1993) yields 29 objects. We have removed from our uniform sample two wellknown stars with published sensitive optical spectrophotometry and IR photometry (Feige 24 and HZ 43). Two


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TABLE 1 ATMOSPHERIC PARAMETERS OF PROGRAM STARS RE J 0007]331 0134[160a 0237[122 0348[005 0427]740 0457[280 0512[004 0521[102 0841]032 0902[040 0907]505 0940]502 0957]852 1019[140 1029]450 1032]532 1033[114 1036]460e 1043]490e 1044]574 1100]713 1112]240 1122]434 1126]183e 1128[025 1148]183 1235]233b 1257]220b 1336]694 1431]370 1446]632 1629]780c 1638]350 1643]411b 1650]403b 1711]664d 1726]583b 1800]683 1820]580 1845]682 2116]735b 2207]252 2312]104 Other Names GD 2 GD 984, PHL 1043 PHL 1400 GD 50 MCT 0455[2812 T 46493 44866 32077 3950 48587 51199 31733 33186 38293 23218 32167 36034 51311 31524 35518 43587 24685 29361 41132 30338 41104 39824 26996 54334 30699 25758 46569 38926 29607 34404 37947 41043 35404 28815 38144 48989 53561 44723 44099 36120 50812 26964 53088 eff ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ log g 514 667 177 8464 1044 786 139 301 252 160 338 283 1348 102 247 506 252 251 1178 153 814 636 151 1983 380 299 523 142 87 115 254 338 142 81 211 757 542 424 264 189 354 174 968 7.83 7.77 8.45 9.07 7.93 7.72 7.40 8.60 7.75 7.84 8.11 7.69 8.37 7.92 7.70 7.95 7.85 8.02 7.94 7.81 7.84 7.78 8.31 7.76 8.24 7.91 7.83 7.78 8.34 7.91 7.79 7.92 7.98 8.22 7.97 8.89 8.23 7.80 7.78 8.23 7.72 8.27 7.85 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 0.05 0.05 0.04 0.06 0.08 0.05 0.03 0.06 0.03 0.02 0.07 0.04 0.10 0.02 0.04 0.05 0.03 0.05 0.13 0.03 0.09 0.07 0.02 0.13 0.08 0.04 0.05 0.02 0.02 0.02 0.04 0.04 0.02 0.02 0.03 0.06 0.04 0.04 0.03 0.03 0.03 0.03 0.07 M/M _ 0.602 0.572 0.890 1.215 0.646 0.570 0.458 0.980 0.544 0.544 0.695 0.519 0.866 0.606 0.520 0.644 0.553 0.648 0.635 0.550 0.593 0.563 0.803 0.594 0.767 0.587 0.602 0.560 0.824 0.608 0.562 0.627 0.642 0.753 0.643 1.141 0.795 0.585 0.574 0.770 0.569 0.779 0.624 Observation Date 1996 Jan 6 1996 Jan 5 1996 Jan 5 1996 Jan 4 1996 Jan 5 1996 Jan 4 1996 Jan 5 1996 Jan 5 1996 Jan 4 1996 Jan 4 1996 Jan 4 1997 Apr 9 1996 Jan 5 1997 Apr 9 1997 Apr 9 1996 Jan 4 1996 Jan 4 1996 Jan 4 1996 Jan 5 1996 Jan 4 1996 Jan 4 1996 Jan 5 1997 Apr 9 1996 Jan 4 1996 Jan 4 1996 Jan 4 1996 May 11õ12 1996 Jan 4, 1996 May 12 1996 May 10 1996 May 11 1996 May 11 1996 May 11 1996 May 10 1996 May 9 1996 May 9 1996 May 12, 1997 Apr 9 1996 May 9 1996 May 10 1996 May 9 1996 May 10 1996 Jan 5, 1996 May 9 1996 Jan 5 1996 Jan 4

401

PG 0904]511 PG 0937]506

PG 1026]454 G 162[66, LTT 3870 GD 123 PG 1041]580 PG 1057]719 Ton 61 PG 1120]439 PG 1123]189 PG 1125[026 PG 1145]188 PG 1232]238 GD 153 PG 1335]701 GD 336

PG 1636]351 PG 1642]414

PG 1725]586 KUV 18004]6836 KUV 18453]6819 KUV 21168]7338 GD 246

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 Close-by optical companion ; spectrum apparently not contaminated. e Red part of spectrum contaminated by cool companion ; Hb excluded from ït.

DAîs with broad-line 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, Bergeron, & Saer 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


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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 companion. RE J1440]750 turns out to be a magnetic DA (Dreizler et al. 1994). The uniform sample will be discussed in a follow-up 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 4õ 6, we obtained spectra at Steward

Observatoryîs Kitt Peak Station using the Bok 2.3 m reÿector equipped with the Boller & Chivens Cassegrain spectrograph and UV-ÿooded Loral 800 ] 1200 CCD. Most spectra were dispersed with a 600 line mm~1 ïrst-order grating used behind a 4A ] 4@ long slit. The instrumen.5 tation provided wavelength coverage jj3400õ5600 at a spectral resolution of D5 A FWHM. On the last night of the observing run, we employed a new 400 line mm~1 grating providing wavelength coverage jj3500õ 6790 at a spectral resolution of D7 A FWHM.


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FIG. 2.õSpectra of the MMT sample

We also obtained spectra at the Multiple Mirror Telescope (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 A, and the 2A slit width we used resulted in a spectral resolution of about 4 A FWHM. Several objects were kindly obtained for us using the identical 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 calculations of Filippenko (1982). The air masses were held below 1.5 in almost all cases. All spectra were extracted from the two-dimensional 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, ÿat-ïeld division by images obtained by exposing on dome or internal quartz lamps, centroiding and summation of the stellar traces on the two-dimensional images, sky subtraction, wavelength calibration using spectra of He/Ar arc lamps, and absolute


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FIG. 3.õLTE osets. The dierences 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 assumptions are those of static, plane-parallel 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 Stark-broadened hydrogen lines is taken into account consistently. As the hydrogen atmospheres of DA WDs are stable for T [ 15000 K, conveceff

tion is not included in our atmospheric models. Pressure dissolution of the higher levels is described by the Hummer & Mihalas (1988) occupation probability formalism following 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 Schoning & Butler (1989, private communication) and Lemke (1997). We followed the prescription of Bergeron (1993) and increased the critical ionizing 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 temperature range 17,000 K \ T \ 100,000 K (stepsize increasing with T from 2000 eff 10,000 K) and gravity to range 6.50 \ log geff 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 collisional rates between the atomic levels in the NLTE code.


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This forces the occupation numbers to be in LTE and guarantees consistency with the NLTE atmospheres. The synthetic LTE spectra were transformed into "" observed îî spectra by convolving them with a Gaussian of 5 A FWHM, rebinning them to 2 A, and adding Poisson noise corresponding to a continuum S/N of 100. These simulated spectra were analyzed with the NLTE grid following the procedure outlined in ° 5. One thousand simulations were run for every parameter set to eliminate the eect of random errors. The resulting osets 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 dierences 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 eects 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 temperature and lowest gravity seems to contradict this behavior. A look at the line proïles reveals that the NLTE deviations are larger for, say, the T \ 90,000 K, eff 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 dierence, but depend also on the way line proïles vary with temperature and gravity. The small corrections found for the high temperature/low gravity models are produced by the cancellation of these eects. We expect a reliable transformation 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 previous 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 T \ 30,000õ70,000 K in 10,000 K steps, and log g \eff for pure hydrogen models. Input physics are 8.0 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 temperature dierences were always below 1.5%, and the gravity dierences never exceeded 0.03 dex. Metals were ignored in our calculations, but they can modify the hydrogen line proïles by their eect 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 eect of metal line blanketing on the Balmer lines was relatively small, and the dierence between LTE and NLTE was found to be the most important eect. 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 eects of the order of the NLTE eects. 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.

lines with the NLTE model spectra described above. We use the least-square algorithm described in BSL92. The observed and theoretical Balmer line proïles are normalized to a linear continuum (both spectra are F ) in a consisj tent manner. Wavelength shifts are determined with a cross-correlation method and applied consistently to each complete spectrum. The synthetic spectra are convolved to the observational resolution with a Gaussian and interpolated to the actual parameters with bicubic splines and interpolated to the observed wavelength scale. The atmospheric parameters T and log g are then detereff mined by minimizing the s2 value by means of a LevenbergMarquardt 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 estimate 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 examples 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 observations 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 dierences found for RE J1650]403 and RE J2116]735 are signiïcantly 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 M-type mainsequence companion. The composite spectrum and the spectrum of the M star after subtracting the WD component are shown in Figure 5. The characteristic bands of TiO are easily recognizable. Catalan et al. (1995) determined 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 A) of the WD spectrum is not disturbed by the M dwarf. Thus we excluded Hb and the core of Hc from the ït and derived the parameters T \ 41,000 K and log eff g \ 7.92 from Hc to Hg. These parameters are in reason able agreement with the results of Catalan et al. (1995 ; T \ 41,800 K ; log g \ 8.0), who, however, included Hb, eff and Kidder (1991 ; T \ 42,500 K, log g \ 7.6), who ïtted eff Lya and the Balmer lines Hb and Hc.

SPECTRAL ANALYSIS AND RESULTS

Atmospheric parameters of our DA WDs are obtained by simultaneously ïtting line proïles of the observed Balmer


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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 uncontaminated. 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, a red excess is obvious. Subtraction of the 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 suggested by Bues & Aslan (1995) is almost certainly not present, since its ÿux would dominate in the blue. RE J1711]664.õSince a late-type star is separated from the WD by only 2A , we took care to get an uncontaminated .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 RE 1235]233 1257]220 1643]411 1650]403 1726]583 2116]735 T 46308 39349 28813 37798 52712 50131 eff ^ ^ ^ ^ ^ ^ log g 837 317 120 245 927 384 7.85 7.76 8.23 7.94 8.27 7.71 ^ ^ ^ ^ ^ ^ 0.08 0.04 0.02 0.04 0.06 0.03 T OBSERVATION 2 eff 46737 ^ 38820 ^ 28818 ^ 39126 ^ 54003 ^ 54604 ^ log g 670 159 111 413 669 906 7.82 7.78 8.21 8.01 8.20 7.76 ^ ^ ^ ^ ^ ^ 0.06 0.02 0.02 0.05 0.05 0.06

NOTE.õError estimates were taken from the s2 ïtting procedure.


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J1659]440 (PG 1658]441) is a well-known star, already analyzed by Schmidt et al. (1992). The discovery of the magnetic nature of RE J1440]750 (HS 1440]7518) was announced by Dreizler et al. (1994 ; note the naming confusion 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 pronounced Zeeman eect. Flux-calibrated spectra of the magnetic WDs are displayed in Figure 6. The PG 1658]441 analysis of Schmidt et al. (1992) resulted in T \ 30,500 K and log g \ 9.35. eff 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 B \ 2.3 MG). From the linear S Zeeman eect 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 aected by the magnetic 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 eects. 5.3. Internal, External, and Systematic Errors We have now presented the results of a homogeneous analysis of a sample of 46 hot, EUV-selected 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 T [ 70,000 K. This does eff not aect our sample, which has a maximum temperature closer to 54,000 K. Dierences (after correction to NLTE) in T and log g eff between studies for stars in common with M97, V97, and FKB97 are displayed in Figure 8 as a function of T . The 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 dierences between pairs of studies, e.g., our results (NGS) versus FKB97 (NGS-FKB97), V97-NGS, M97-NGS, FKB97M97, M97-V97, and so on. However, we chose another approach and performed an optimization that simultaneously took into account all values from all stars in common between any samples. In other words, the values given for the systematic dierences 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

FIG. 5.õFlux-calibrated 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


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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 T ^ 10%. Although this curve does not represent the best eff to the data plotted in Figure 8 ït alone, it is a fairly good representation of the dierences

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 non-Gaussian with many outliers, as evident in Figure 8, we decided to adopt an underlying Lorentzian (or Cauchy) distribution for the optimization. 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 conïdence 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 discussion below). If one ignores the hot end, the agreement between the FKB97 and our temperature scale is good ; dierences are below 1%, smaller than the maximum model dierences 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 dierences with M97 are present. These trends are most likely caused by dierent reduction and analysis techniques. Osets of the same order are found in our comparison with V97, where a dierent LTE model atmosphere code is used. Although basically the same input physics is included, this might at least partly explain those shifts in T and log g. 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 T \ 30,000 K, a hotter one with 30,000 eff K \ T \ 45,000 K, and the hottest considered group with eff \ T \ 70,000 K. NLTE eects are still negligi45,000 K eff ble in the range of eective temperatures of the two coolest groups. Mean shifts and the conïdence range of the mean (computed as described above) are provided for these


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TABLE 3 PARAMETERS OF THE MAGNETIC WHITE DWARFS RE 1440]750 1659]440a Other Names HS 1440]7518 PG 1658]441 eff 36154 ^ 275 30510 ^ 200 T log g 8.87 ^ 0.05 9.36 ^ 0.07 M/ M _ 1.128 1.311 S 7.7 2.3 B Observation Date 1996 May 10 1996 May 10

409

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 dierence between our results and M97 reach B0.1 dex for the coolest bin. However, we emphasize that all four analyses are based on state-of-theart 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 dierent combinations of the samples, we compute a mean scatter p for all possible combinations (weighted by the number diff of stars in common). For this purpose we correct for the systematic shifts calculated for each of the three T bins, eff whose temperature intervals are given in Table 6. The individual measurement errors p add quadratically, and if we ind

FIG. 8.õDierences in temperature (left-hand panel), and gravity (right-hand 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 dierences is plotted with solid lines, while the standard error of the mean dierence is indicated by the dotted lines. The T values used for the x-axis are NLTE from this paper, eff except for the bottom panel, which uses V97 (corrected to NLTE).


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TABLE 4 SYSTEMATIC TEMPERATURE DIFFERENCES Temperature (K) M97-NGS (*T /T ) eff eff [0.023 ^ 0.006 [0.013 ^ 0.003 0.036 ^ 0.006 [0.006 ^ 0.003 V97-NGS (*T /T ) eff eff 0.032 ^ 0.005 0.017 ^ 0.003 0.050 ^ 0.006 0.024 ^ 0.003 FKB97-NGS (*T /T ) eff eff 0.007 ^ 0.005 0.004 ^ 0.003 0.046 ^ 0.007 0.012 ^ 0.003

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T \ 30000 eff 30000 \ T \ 45000 eff 45000 \ T \ 70000 eff All with T \ 70000 eff NOTE.õFor each temperature range, each column gives the average dierence over the respective interval and the conïdence interval of the average dierence.

TABLE 5 SYSTEMATIC GRAVITY DIFFERENCES Temperature (K) T \ 30000 eff 30000 \ T \ 45000 eff 45000 \ T \ 70000 eff All with T \ 70000 eff NOTE.õFor details see M97-NGS (* log g) [0.112 [0.086 [0.066 [0.084 Table 4. ^ ^ ^ ^ 0.017 0.017 0.030 0.013 V97-NGS (* log g) [0.001 0.026 [0.067 [0.002 ^ ^ ^ ^ 0.016 0.016 0.026 0.012 FKB97-NGS (* log g) [0.064 [0.034 [0.062 [0.047 ^ ^ ^ ^ 0.018 0.016 0.027 0.012

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 (1/21@2)p . Not surprisingly, the smallest scatter is found diff îî group (T \ 30,000 K) with p(T ) \ 2.3% for the "" cool eff and p(log g) \ 0.07 dex.eff increases to p(T ) \ 3.3% and It eff 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 well-exposed 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 eects, such as details of the extraction or ÿuxing and normalization procedures, contribute more. Considering these systematic uncertainties, the 0.3 dex difference 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 mass-radius relations. The recent investigations of M97, V97, and FKB97 based their interpretation on the model sequences
TABLE 6 MEAN SCATTER p OF TEMPERATURE AND GRAVITY ind ETERMINATION D Temperature (K) T \ 30000 eff 30000 \ T \ 45000 eff 45000 \ T \ 70000 eff All with T \ 70000 eff

p(T ) eff 0.023 0.023 0.034 0.026

p(log g) 0.075 0.101 0.128 0.107

of Wood (1995). The applied models have H- and He-layer masses of 10~4M and 10~2M , respectively (thick WD WD layers), and a carbon core. These model sequences are based on a set of pre-WD models with end masses of 0.6, 0.8, and 0.95 M computed by Kawaler (see Wood 1994). Starting models_for other masses were constructed by homology transformations. The mass-radius relations we use are based on the evolu tionary calculations of Blocker (1995). These models are calculated ab initio from the main sequence. The resulting WDs show important dierences compared to Woodîs (1995) models. In contrast with the carbon core models widely used for mass determination, the degenerate core contains a mass-dependent 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 He-layer masses resulting from evolutionary calculations depend on the stellar mass (Blocker 1995 ; Blocker et al. 1997). While the canonical thick hydrogen layer mass of 10~4 M is met for a 0.6 M WD, it decreases from several _ 10~3 M_ for 0.3 M down to 10~6 M for 1.0 M . This _ a mass-radius relation, which is steeper _ _ _ results in 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 M , the _ limiting mass for central helium burning in low-mass 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 hydrogen-rich 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 Blocker (1995) and Driebe et al. (1998) cover the mass range 0.18õ 0.94 M . We supplement_


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ed this set with the 1.0, 1.1, and 1.2 M carbon core _ sequences of Wood (1995) with "" thin îî layers. Since the hydrogen envelope mass decreases with increasing WD mass in Blockerîs (1995) models, their highest mass models eectively correspond to thin layer models. Since high-mass WDs are already close to the zero-temperature conïguration, the remaining departures from consistent evolutionary 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 distribution is shown in Figure 10. We have also redetermined masses for the BSL92 sample with the Blocker/Driebe mass-radius relations and supplemented Figure 10 with the resulting distribution. Our mass distribution possesses the same basic features as found in the EUV-selected samples of M97, V97, and FKB97. The sharp peak centered at B0.59 M is in principal 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 high-mass 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 M . However, this value is strongly _ biased by the few very high-mass 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 principle, dependent on the adopted binning of the mass intervals. However, in some test calculations we found eects exceeding a few 0.001 M only if the bin width was larger _ than 0.05 M . The values given in this paper were derived _ by ïtting Gaussians to virtually unbinned mass distributions (formal bin width 0.001 M ). _ We were concerned by the possibility that the dierent fraction of low- and high-mass WDs found in dierent 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 low-mass peaks separately. We found no deviation higher than 0.003 M in any case and concluded that _ 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 M . We reanalysed the FKB97, M97, and V97 _ samples with our mass-radius relations. We applied the cor-

FIG. 9.õEective temperature and gravity of our WD sample compared with evolutionary tracks. Solid lines are Blocker (1995) ; dashed lines are Driebe et al. (1998) ; dotted lines are Wood (1995). The magnetic WDs are marked by open symbols.


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FIG. 10.õMass distribution of WDs (binned over 0.05 M ). The solid _ line histogram indicates the result for our sample. The dotted line is the BSL92 sample with masses redetermined from the Blocker/Driebe relations (normalized to the same sample size). The Gaussian curve represents the best ït to our mass distribution as described in the text.

because the fraction of low-mass WDs at higher T is much eff lower than it is for T \ 30,000 K. This viewpoint is supeff 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 (massdependent) 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 EUV-selected samples. We can explain in a similar fashion why high-mass WDs are found preferentially in the 30,000 K \ T \ 50,000 K eff 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 M track, the most massive _ stellar remnant calculated by Blocker (1995). This increases the detection probability of more massive WDs in EUVselected samples.
5.4.3. Interstellar Absorption

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 M (V97). These dierences reÿect the systematic dierences _ T and log g determinations in discussed above, and probablyeff dierent 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 M , but four _ WDs have masses in excess of 1.0 M . The frequency of _ and other EUVlow- and high-mass WDs found in our selected samples is qualitatively dierent 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 M . These numbers are reduced to 10 and 16, _ respectively, if we redetermine the masses with the mass radius relations of Blocker (1995) and Driebe et al. (1998). However, that is still a much higher fraction than we ïnd in our EUV-selected sample.
5.4.2. Cooling Rates and Detection Probability

Even if we restrict our comparisons to hot subsamples of WDs, the fraction of massive WDs is much higher in the EUV-selected 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 high-mass WDs discovered per sky area is similar for the whole-sky EUV surveys and the optical Palomar-Green (PG) survey (Green et al. 1986), which covered roughly 25% of the sky. In other words, a whole-sky version of the PG survey should have discovered all but one of the EUV-detected WDs with M [ 1.1 M . At a given temperature, WDs with lower _ masses are larger, consequently more luminous, and detectable to larger distances. For instance, at 30,000 K a WD of 0.5 M is detectable at distances D30% larger than a 0.7 _ M WD. At the maximum distance sampled by, e.g., the _ survey, the probability is very high that interstellar PG matter eectively absorbs all EUV radiation. Thus the dominant eect in EUV surveys is not a selection for massive WDs as suggested by V97, but a selection against low-mass WDs due to a sample volume strongly aected by interstellar absorption.
5.4.4. T emperature Dependence of the Derived Mass Peak

Why do optical- and EUV-selected samples contain different fractions of high- and low-mass WDs ? All helium WDs from the BSL92 sample have temperatures below 30,000 K ; the only helium WD candidate in our sample has T B 32,000 K. This implies that the detection probability eff of low-mass WDs in EUV-selected samples is much lower,

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 T \ 25,000 K, and therefore have a eff larger temperature baseline than pure EUV samples. Analogous to this ïnding, V97 found an 0.03 M oset between _ the peak of the mass distribution in their EUV-selected sample and the (cooler) WDs analyzed by BSL92. In both


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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 Blocker 1995 ; dashed lines). The tracks are labeled with the stellar masses.

cases this temperature dependence decreases if Woodîs (1995) models with very thin layers (M \ 10~4M , no WD hydrogen layer), instead of the canonicalHe thick layer models (M \ 10~2M , M \ 10~4M ), are used. However, He WD WD part of the trend notedHin V97 may be related to the systematic dierences between the analyses discussed in ° 5.3. Since V97 compared results from two dierent analyses, it is not possible to judge if the oset 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 atmospheres. 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 presented in ° 5.3. We showed that systematic dierences between the four investigated samples exist that vary with eective temperature. This might mimic a temperature dependence of the sample peak mass. A gravity oset of 0.1 dex transforms into mass osets of 0.050, 0.044, and 0.034 M for a 0.6 M WD with 25,000, 40,000, and 60,000 K, _ _ respectively. Even a relatively small systematic log g dierence of 0.05 dex (see Table 5) corresponds to a 0.02 M _

oset. The scatter p of individual gravity determinations reported in Table 6 corresponds to p(M) B 0.04 M , nearly _ independent of T . eff
5.4.5. Cooling T racks

Another part of the T dependence of the mass peak may eff be caused by the use of Woodîs (1995) cooling tracks by FKB97 and V97. These tracks are not completely selfconsistent 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 (Blocker & Schonberner 1990). We redetermined the masses of the BSL92 WDs with the Blocker/Driebe mass-radius relations and derived a peak mass of 0.559 M . That is 0.03 M lower than our peak mass, but having_ mind the range_of mass determination in derived for the EUV-selected samples, we cannot consider this a signiïcant dierence. FKB97 divided their sample into cool (T \ 35,000 K) and hot (35,000 K \ T \ eff 75,000 K) subsamples and derived a 0.029 M higher eff peak _ mass for the hot sample. Our reanalysis of the FKB97 LTE results with the Blocker/Driebe mass-radius relation yields


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virtually the same oset : 0.025 M . However, the dierence _ is brought down to 0.010 M (0.550 vs. 0.560 M ) if we _ can imagine that _ dierapply corrections to NLTE. One a ence of this order (if signiïcant at all) can easily be produced by our neglect of metallicity eects (see Lanz et al. 1996 ; Barstow et al. 1998). Therefore, given the combination of sample selection and systematic eects in analyses to date, our results do not conïrm the presence of intrinsic systematic mass dierences between hot and cool WDs.
6

. CONCLUSIONS

We have obtained temperatures, gravities, and masses for a sample of 46 EUV-selected DA WDs. These data complement a near-IR survey for low-mass 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 systematic errors and individual measurement scatter. Although all four analyses applied similar model atmospheres and ïtting techniques, we recognized systematic shifts up to 5% in temperature and 0.1 dex in gravity determinations. These systematic errors must be considered when the results are interpreted and compared to other studies. The individual measurement errors increase with temperature : p(T ) from 2.3% to 3.3% and p(log g) from 0.07 to 0.13 dex. eff is larger than the typical errors comThis puted with s2 ït procedures for a well-exposed spectrum, and it indicates that accuracy is limited by noise in combination with other eects 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 observer, 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 eects. Independent observations analyzed independently are necessary. Masses have been inferred from theoretical mass-radius relations based on the evolutionary calculations of Blocker

(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 M in agreement with _ the previous investigations of KSW79 and BSL92. We redetermined masses of the BSL92 WDs with the Blocker/Driebe mass-radius relation and derived a peak mass of 0.56 M . At ïrst glance this seems to conïrm the _ systematic oset reported by V97. However, this oset could be explained by systematic dierences of the model atmosphere analyses as well. Our reanalysis of the homogeneous FKB97 sample showed that the temperature dependence 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 M , which is a possible helium core WD, but four _ WDs with masses in excess of 1.0 M . This ratio of high_ and low-mass WDs is quite dierent from that found by BSL92. This can partly be understood as the result of variable evolutionary timescales of high- and low-mass WDs. We agree with FKB97 that another part can be explained by a selection against low-mass WDs in EUV-selected samples. The principal aim of our project is the search for and study of cool main-sequence 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 presenting 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. Blocker for providing 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 simultaneous 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 NAS8-39073 (ASC).

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