Balmer 1. INTRODUCTION

Transcription

1 THE ASTROPHYSICAL JOURNAL, 537:977È992, 2000 July 10 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. ADDING MORE MYSTERIES TO THE DA WHITE DWARF GD 394 JEAN DUPUIS,1 PIERRE CHAYER,2 STE PHANE VENNES,3 DAMIAN J. CHRISTIAN,4 AND JEFFREY W. KRUK2 Received 1999 December 3; accepted 2000 February 18 ABSTRACT We present spectroscopic and timing analyses of the hot DA white dwarf GD 394 showing abundance inhomogeneities across its surface. Lick Hamilton echelle, International Ultraviolet Explorer (IUE), HST GHRS, and Hopkins Ultraviolet Telescope (HUT) spectra show dominant Si III and Si IV features, while Extreme Ultraviolet Explorer (EUV E) spectra show evidence of a host of trace element opacities. We report the detection of Si III j4552 triplet with a measured radial velocity of 27 km s~1 in agreement with far ultraviolet (FUV) line velocities, but indicating a silicon abundance (Si/H \ 2 ] 10~5) a factor of 10 larger than measured in the FUV range [Si/H \ (2È7) ] 10~6]. E ective temperature measurements based on Lyman continuum (EUV E) and Lyman line series (HUT) are systematically cooler (*T D [4000 K) than measurements based on medium-dispersion Balmer line spectroscopy, an e ect attributed to yet unidentiðed opacities. A timing analysis of EUV E deep-survey and scanner time series, as well as spectrometer data, shows GD 394 to be variable in the extreme ultraviolet (EUV) with an amplitude of 25% and a period of ^ days. The EUV variability suggests abundance inhomogeneities in the atmosphere, and we explore di erent models to explain its origin. Subject headings: stars: abundances È stars: individual (GD 394) È stars: spots È ultraviolet: stars È white dwarfs 1. INTRODUCTION We examine the problem of the presence of heavy elements in the atmosphere of the hot white dwarf GD 394 (WD 2111]498). The detection of Si III and Si IV lines in a high-dispersion International Ultraviolet Explorer (IUE) spectrum of GD 394 (Bruhweiler & Kondo 1983), and EXOSAT soft X-ray observations (Jordan et al. 1987; Paerels & Heize 1989; Vennes 1992) already suggested that GD 394 did not possess a pure hydrogen atmosphere, a conclusion conðrmed with ROSAT WFC (Barstow et al. 1993) and Extreme Ultraviolet Explorer (EUV E) observations (Barstow et al. 1996; Wol et al. 1998). Having an e ective temperature of D39,000 K, the atmosphere of GD 394 is not expected to hold an appreciable abundance of helium (Vennes et al. 1988) or heavier elements (Chayer, Fontaine, & Wesemael 1995a; Chayer et al. 1995b); di usion calculations including the e ect of selective radiation pressure predict an abundance of heavy elements much too low to have an e ect on the extreme ultraviolet (EUV) continuum. GD 394 clearly challenges our understanding of the atmospheric composition of hot white dwarfs and deserves more attention. Vennes, Thejll, & Shipman (1991) Ðrst measured the silicon abundance in IUE spectra of GD 394 (log Si/ H \[5.8), but existing radial velocity measurements argued against a photospheric origin for the silicon lines (v \ 24 km s~1 versus v \ 94 km s~1 from Trimble & Greenstein Si 1972). They also Balmer determined an upper limit to the carbon abundance (log C/H ¹ [7.4). Shipman et al. (1995) observed GD 394 with the HST GHRS, measured radial velocities for the Si III and Si IV and determined a 1 Space Sciences Laboratory, University of California at Berkeley, Berkeley, CA 94720; jdupuis=ssl.berkeley.edu. 2 Bloomberg Center for Physics and Astronomy, The Johns Hopkins University, Baltimore, MD Department of Mathematics, Australian National University, Canberra, ACT 0200, Australia. 4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD silicon abundance of Si/H \ (3È4) ] 10~6 assuming a photospheric origin. Barstow et al. (1996) revisited GD 394Ïs radial velocity based on the Balmer line series (v \ 50 ^ 18 km s~1) and favored a photospheric Balmer origin for the Si III and Si IV absorption lines observed in IUE and HST GHRS spectra. Based on nonèlocal thermodynamic equilibrium (NLTE) models they also determined a silicon abundance of log Si/H \[5.6, close to the Vennes et al. results in local thermodynamic equilibrium (LTE). Barstow et al. (1996) also analyzed an EUV E spectrum of GD 394 and found that silicon alone does not account for the detected EUV opacity. Although they suggested that a mixture of C, N, O, and Si may provide the required opacity, their solution is clearly not unique. Moreover, many predicted spectral features could not be identi- Ðed. Other elements, such as iron, although undetected in the far ultraviolet (FUV), may provide required EUV opacities. Wol et al. (1998) modeled the overall EUV Ñux distribution of GD 394 including a more comprehensive mixture of heavy elements based on the abundance pattern observed in G191-B2B. Their Ðt indicate GD 394 has a lower metallicity than G191-B2B with an iron abundance of Fe/H \ 1.25 ] 10~6. Again, this result must be taken with some caution since many details of the EUV E spectrum are not reproduced by their model and as stated by the author, the relative abundances of metals in GD 394 are di erent. Previous analyses by Barstow et al. and Wol et al. provided useful constraints on the abundance pattern in the atmosphere of GD 394, but other EUV opacity sources remain to be identiðed. We present an analysis of EUV E ( 2.1), IUE, HST GHRS, and Hopkins Ultraviolet Telescope (HUT) spectra of GD 394 ( 2.2), as well as new Hamilton echelle spectroscopy obtained at Lick observatory ( 2.3). We also present a timing analysis of EUV light curves showing for the Ðrst time, evidence of variability in an apparently isolated hot DA white dwarf ( 3). The variability and the detection of the optical Si III triplet motivate a reanalysis of all available data ( 4). We explore di erent models to explain the varia-

2 978 DUPUIS ET AL. Vol. 537 bility and the heavy element abundance ( 5), and, Ðnally, we summarize ( 6). 2. OBSERVATIONS AND DATA REDUCTION We adopted a multiwavelength approach to the study of abundance anomalies in GD 394. We have assembled highresolution IUE and HST GHRS spectroscopy, mediumresolution HUT spectroscopy, and Hamilton echelle spectra (Lick Observatory), as well as EUV E spectroscopic and photometric data with unique timing information EUV Spectroscopy and Photometry: EUV E Table 1 lists observations obtained with the EUV E scanners, spectrometers, and deep-survey detector (DS) between 1992 October and 1996 November. The latest DS/ spectrometer observation (1995 October) used the spiral dithering mode ÏÏ to reduce Ðxed-pattern noise in the spectrum. We reduced the data using procedures in the EUV package within the IRAF environment and produced light curves for the spectrometers and DS data using timing routines found in the PROS XRAY.XTIMING package in IRAF. Finally, we corrected the light curves for deadtime and telemetry loss. We combined the 1995 October short-wavelength (SW, 70È190 A ), medium-wavelength (MW, 140È380 A ), and long-wavelength (LW, 280È760 A ) EUV E spectra expressed in photon Ñux units and binned the spectrum by 4 pixels (half of a resolution element) to improve the signal-to-noise ratio. Figure 1 shows the 1995 October light curve for the DS/ Lexan detector binned every 5760 s (\one EUV E orbit) as FIG. 1.ÈDS Lex/B (65È180 A ) and Spectrometer SW (70È190 A ) and MW (140È380 A ) EUV E light curves of GD 394 (1995 October). well as integrated count rate from the SW and MW spectrometer channels at a coarser time resolution. The photometry exhibits an obvious periodicity, unexpected for a presumably isolated DA at GD 394 temperature. The light curve will be discussed further in 3. Figure 2 shows the 1993 September light curves obtained with the SW and TABLE 1 EUV E OBSERVATIONS EXPOSURE TIME DS SW MW LW Scanners DATE AND TIME (GMT) (ks) (ks) (ks) (ks) (ks) OBSERVER NOTES 1992 Oct 27 15:20: Calibration Sep 13 20:52: D. Finley 1995 Oct 13 23:23: F. Bruhweiler Dithered 1995 Oct 19 15:49: F. Bruhweiler Dithered 1996 Nov 21 15:21: RAP TABLE 2 FUV OBSERVATIONS SV T SV T STL ISM Spectrum Date Exposure Time (km s~1) (km s~1) Instrument SWP May minutes 33.6 ^ ^ 4.9 IUE SWP Apr minutes 30.6 ^ 4.8 [1.2 ^ 4.9 IUE SWP Jan minutes 20.3 ^ 4.2 [7.3 ^ 6.2 IUE SWP Jan minutes 30.4 ^ 4.2 [8.9 ^ 4.0 IUE Z0YE0A08M Jun s 31.8 ^ 10.4 [6.0 ^ 10.4 HST GHRS Z0YE0A0AM Jun s 32.0 ^ 3.6 [9.3 ^ 3.8 HST GHRS Z0YE0A0CM Jun s 32.7 ^ HST GHRS gd a Mar 4 94 s Astro-2 HUT gd a Mar s Astro-2 HUT gd a Mar s Astro-2 HUT gd a Mar s Astro-2 HUT gd a Mar s Astro-2 HUT gd a Mar s Astro-2 HUT gd a Mar s Astro-2 HUT

3 No. 2, 2000 ADDING MORE MYSTERIES TO GD FIG. 2.ÈEUV E light curves of SW and MW spectrometers (1993 September) MW spectrometers, and Figure 3 shows the 1992 October and 1996 November light curves obtained with the scanners during in-orbit calibration and right-angle program (RAP) observations. A description of the performance of EUV E imaging telescopes is found in Sirk et al. (1997). All these observations suggest a periodic variation in the EUV emission of GD FUV Spectroscopy: IUE, HST GHRS, and HUT We obtained four images from the IUE Archives (Table 2) through the NASA Data Archives and Distribution Service (NDADS), and we extracted the individual spectral orders using the NEWSIPS data processing system. The observations were performed with the short-wavelength prime camera (SWP), which covers a wavelength range of 1150È1950 A with a resolution of j/*j \ 10,000 in the highdispersion mode. We measured average radial velocities of suspected photospheric and interstellar lines. We modiðed the velocity scale by applying a correction of ]8.3 km s~1 to the spectra, as suggested by Holberg, Barstow, & Sion (1998). To improve the signal-to-noise ratio, we co-added all available spectra in the following way: we brought back the photospheric line velocities to their laboratory values, resampled the spectra to make sure that each spectrum matches each other, and co-added all Ñux calibrated spectra weighted by their exposure time. We have to point out, however, that the SWP and SWP have Ñux levels a factor of 2.0 and 1.7 lower than the Ñux measured in the SWP and SWP spectra. Therefore, the resulting Ñux in the co-added spectrum is approximately 30% lower than the Ñux obtained with the HST observations. We retrieved three GD 394 spectraèz0ye0a08m (1196È1232 A ), Z0YE0A0AM (1290È1326 A ), and Z0YE0A0CM (1383È1419 A )Èfrom the HST Archives (Table 2). The observations were carried out with the Goddard High Resolution Spectrograph (GHRS) using the G160M grating and Large ScientiÐc Aperture (LSA) (Shipman et al. 1995; Heap et al. 1995). The grating was positioned to cover three wavelength ranges (1196È1232 A, 1290È1326 A, and 1383È1419 A ) with a nominal spectral resolution of j/*j B 18,000. Wavelength calibrations (WAVECALS with the Pt-Ne lamp) were obtained for the 1290È1326 A and 1383È1419 A spectra, but not for the 1196È1232 A spectrum, which, therefore, is a ected by larger radial velocity uncertainties. All observations were carried out before the installation of the Corrective Optics Space Telescope Axial Replacement instrument (COSTAR). Gilliland et al. (1992) demonstrated that the spherical aberration of the HST primary mirror had reduced the performance of the GHRS. They showed that, when using the LSA, the resolving power is decreased by a factor of 2. Given that GD 394 was observed with the LSA prior to COSTAR, the HST spectra must have a spectral resolution of about j/*j B 9000, which is comparable to IUE SWP high-dispersion spectra, and not 18,000 as stated by Shipman et al. (1995) and Barstow et al. (1996). Finally, we co-added spectra from the Ðve full-aperture HUT observations of GD 394 for a total observation time of 2808 s. The data were reduced and corrected for airglow as described in 3 of Kruk et al. (1999). The spectral resolution was D3 A at the Si IV doublet and varied from 1.8 to 4.5 A over the entire spectrum. The Ðve separate observations were obtained at intervals of 1.0, 1.7, 4.3, and 9.0 times the 1.15 day period seen in the EUV light curves. Ratios of the individual spectra show no signiðcant deviations from unity, but that may be a consequence of the sampling intervals rather than an indication that the FUV Ñux does not vary with time. Figure 4 shows the complete spectral energy distribution and a representative model. Complementary data are described in the caption Optical Spectroscopy: L ick Hamilton Echelle Table 3 lists high dispersion spectra of GD 394 obtained on 1996 September 6È7 at the Coude focus of the 3 m telescope at Lick observatory using the Hamilton echelle. The nominal resolving power is R \ 40,000 (7.5 km s~1). TABLE 3 LICK HAMILTON OBSERVATIONS Exposure Time v Start Date and Time (UT) (s) (km s~1) Notes 1996 Sep 06 09:12: ^ 1.9 Velocity based on Si III j Sep 06 10:15: ^ 2.3 Velocity based on Si III j Sep 07 07:14: ^ 1.4 Velocity based on Si III j Sep 07 08:07: Sky exposure 20A W30A N 27.6 ^ 1.3 Si III j4560 mean velocity 35.0 ^ 10.0 Ha mean velocity

4 980 DUPUIS ET AL. Vol. 537 FIG. 3.ÈLight curves of GD 394 from EUV E scanner observations (1992 October, 1996 November). Scanner A and B Lex/B cover passband 58È174 A, and Scanner A and B Al/Ti/C cover passband 156È234 A. We extracted and calibrated the spectra using standard NOAOÏs IRAF routines. We observed the radial velocity standards 10 Tau, HR 6349, and HR 7525 with a mean error of 0.4 km s~1. All extracted spectral orders (e.g., order 87 between 6533 and 6574 A, order 124 between 4547 and 4575 A ) were Ñat-Ðelded with quartz lamp exposures and wavelength-calibrated with Th-Ar lamp exposures. The Ha line core appears in absorption (v \ 35 ^ 10 km s~1) and is contaminated by nebular emission Ha (v \[20.5 ^ 1.0 km s~1) in the Galactic plane (l \ 91.37, neb b \ 1.13). The nebular emission appears to vary spatially, and deep imaging is required to resolve the structure of the emission region. We also report the detection of the Si III triplet, 3s4s(3S) [ 3s4p(3Po), j , , at a mean radial velocity of 27.6 ^ 1.3 km s~1, and without apparent variability. This is in agreement with the Balmer line radial velocity of 30.7 ^ 3kms~1 measured by Holberg et al. (1997). Accurate optical Si III and Ha radial velocity measurements set the photospheric velocity scale, in agreement with FUV Si IIIÈSi IV line velocities measured with IUE and HST. 3. ANALYSIS OF THE EUV LIGHT CURVES 3.1. Morphology and Periodogram The light curves shown in Figure 1 have sinusoidal shapes and appear to span a little more than Ðve cycles. There is a gap of about 1.3 days in the coverage which caused the loss of about one cycle. We computed a periodogram of the light curve using a program developed by Press et al. (1992) and based on LombÏs (1976) formulation of a periodogram for unevenly sampled data. Figure 5 shows the periodogram of the 1995 October light curve (Fig. 1) which displays a signiðcant peak at a frequency of 9.82 ] 10~6 Hz corresponding to a period of 1.18 ^ 0.05 days, in agreement with a period of ^ days determined by Ðtting a sinusoidal function to the light curve. The epoch of the Ðrst maximum observed in the light curve is T \ HJD 50, ^ This period is well separated from 0 the period of 0.98 day for passages through the South Atlantic Anomaly (SAA) during which dead-time and primbsching corrections are larger due to the high background rate (Gagne et al. 1999; Halpern & Marshall

5 No. 2, 2000 ADDING MORE MYSTERIES TO GD FIG. 4.ÈComplete spectral energy distribution including data from EUV E (80È400 A ), HUT (911È1950 A ), IUE (NEWSIPS LWP and SWP 41457; 1150È3250 A ), and AB magnitudes from Greenstein & Liebert (1990), along with a representative pure-hydrogen model. The IUE Ñux scale was adjusted by ]4%. 1996). There are no obvious instrumental e ects that can explain this period. For instance, the orbital period of EUV E (96 minutes) or the spiral dithering cycle (30 minutes) are both much shorter than the detected period. We also veriðed that the background light curve does not exhibit the same periodicity. We folded the SW and MW spectrometers light curves and obtained pulse shapes similar to the DS light curve. The detection of the periodicity in several instruments convinces us that the detected period is intrinsic to GD 394. GD 394 has been observed by EUV E at other epochs, and we conðrmed that it exhibits identical periodicity. Christian et al. (1999) showed light curves of GD 394 obtained during EUV E RAP observations which appear, at least in one case, similar to the DS light curve observed in 1995 October. We veriðed that measured periods are in agreement with the period of the 1995 October light curve. The amplitude of the light curves are also in agreement. It is important to note that the scanner light curve in the Al/C (200 A band) quadrant has properties similar to the Lexan (100 A band) quadrant light curve which shows there was little wavelength dependence of the EUV variability at this epoch. An earlier calibration observation on 1992 October (Fig. 3), which lasted less than 1.3 days, also suggests some variability, but the light curve is not as well deðned because the observation was shorter and the detector went into rate shutdown for a few EUV E orbits due to the high background. The dips in the light curve seem to be deeper than in the other light curves and may suggest that the amplitude was larger at this epoch. However, these data are uncertain because of the high background rate. During the other pointed observation with the EUV E DSS in 1993 September the light curve is unusable because the source was located on the DS dead spot. In summary, the available data suggest that the 1.15 day periodicity detected in the EUV E light curve of GD 394 persisted over at least 3 years L ight Curve Modeling We modeled the DS light curve folded on the 1.15 day period using a model based on the formalism developed by Budding (1977). The EUV variability is assumed to be produced by a circular spot on the photosphere of GD 394 as it moves relative to the line of sight and over the rotation period of the white dwarf. The spot may be dark if there is enough heavy element opacity to block EUV Ñux. The parameters of the model are the longitude (j) and latitude (b) of the spot center, the inclination of the rotation axis (i) relative to the line of sight, the angular extent of the spot (c), the Ðducial count rate from which the darkening is measured (U), and the ratio of the Ñux over the spot to the normal photosphere (k ). We neglect the e ect of limb- w darkening. The count rate (C) is given by C \ UM1 [ (1 [ k )p0n, (1) w 0 where p0 is the projected area of the spot in the plane perpendicular to the line of sight. The area is normalized to n and the radius of the star is assumed to be the unit of length. p0 has the following forms: 1. Annular case, d ¹ 1 [ k2 p0\k2z Partial case, d [ 1 [ k2 p0\ 1 [arccos s [ sj1 [ s2 0 n ] k2z (arccos l [ lj1 [ l2)]. 0 FIG. 5.ÈPeriodogram for the DS/Lex light curve of GD 394 (1995 October) 3. Totality case, c º n/2 and d ¹ 1 [ k2 p0\1. 0

6 982 DUPUIS ET AL. Vol. 537 Here k \ sin c is the semimajor axis of the spot, d is the apparent separation of spot center from the starïs center, z \ cos (j [ /) cos b sin i ] sin b cos i is the z-coordinate 0 of spot center, s \ (1 [ k2)/d, and l \ (d [ s)/kz. / corresponds to the phase of the light curve. More details 0 are found in Budding (1977). We Ðt the light curve using the Levenberg-Marquardt nonlinear least square minimization routine described in Press et al. (1992). The initial phase of the light curve is selected such that the spot longitude is equal to 180. As it is often the case with multiparameter Ðts, the best-ðt solution is highly dependent on the initial guess unless we Ðx some parameters. There is a family of solutions providing acceptable Ðts to the light curve over a large range of spot size (c), latitude (b), and darkness (k ). The approach we used is to Ðx the inclination of the axis w of rotation (i) and then perform Ðts for di erent values of spot latitude b. Table 4 summarizes our results. For an inclination of the rotation axis i \ 90, the latitude of the spot b cannot exceed As expected, the spot size and latitude are correlated. The light curve can be modeled equally well by a completely dark spot located at a latitude b \ 43.2 and angular size c \ (Fig. 6) and by a spot at the equator which is not completely dark in the EUV range but somewhat more extended angular size c \ Quite obviously, there are valid solutions for lower values of the inclination angle. However, we Ðnd the inclination angle cannot be lower than about 45. Although GD 394Ïs light curve is well explained by a circular dark spot model on the surface of FIG. 6.ÈExample of a light curve Ðt using circular dark spot model. The spot is assumed completely dark (i.e., k \ 0), and the data are folded on the 1.15 day period. The parameters of the solution are c \ , u \ 2.784, j \ 180, b \ , and i \ 90. the star, we cannot determine uniquely the parameters of the model with the information available. 4. ANALYSIS OF SPECTROSCOPIC DATA 4.1. Model Atmospheres A grid of LTE models was computed using the complete linearization method (Mihalas, Auer, & Heasley 1975) as applied to the analysis of white dwarf spectra by Vennes et al. (1997b). The models include the hydrogen-line blanketing e ect of the Ðrst four members of the Lyman and Balmer line series. Heavy element populations and EUV synthetic spectra were computed in LTE based on the above grid of models. A second, independent, grid of LTE and NLTE models was computed with the stellar atmosphere code TLUSTY version 195 (Hubeny & Lanz 1995), which uses the hybrid complete linearization/accelerated lambda iteration method (CL/ALI). All models include the dominant e ect of hydrogen line blanketing (Wesemael et al. 1980). For the NLTE calculations, we considered detailed hydrogen and silicon model atoms. Hydrogen.ÈThe hydrogen model atom was developed by Hubeny, Hummer, & Lanz (1994). It is represented by nine energy levels, and all transitions between the eight lowest levels are treated explicitly within the NLTE formalism. Levels from n \ 9ton \ 80 are merged together by taking into account the level dissolution computed within the framework of the occupation probability formalism of Hummer & Mihalas (1988). The merged line opacities near the Lyman (n \ 1 to merged level) and Balmer series limits (n \ 2 to merged level) are treated with adequate opacity distribution functions. The e ect of hydrogen line blanketing is included, with the Lyman and Balmer lines described by Stark]Doppler proðles, and all remaining lines described by Doppler proðles. Silicon.ÈWe used the silicon model atom developed by Becker & Butler (1990), who considered four ionization stages, Si II, SiIII, SiIV, and Si V, containing 12, 28, 18, and one energy levels, respectively. All radiatively permitted transitions are included in the computation, using the oscillator strengths listed in Becker & Butler (1990). The photoionization cross sections of Si II, Si III, and Si IV were computed by Mendoza et al. (1995), Butler, Mendoza, & Zeippen (1993), and Taylor (1999), respectively. All photoionization cross sections were extracted from TOPBASE (Cunto et al. 1993). The collisional excitation rates for the eight lowest LSstates of Si II and for the 12 lowest LSstates of Si III were computed with the the Eissner & Seaton (1974) formula, using the e ective collision strengths given by Dufton & Kingston (1989, 1991). For all other optically allowed and forbidden transitions we used the the Van TABLE 4 BEST-FIT PARAMETERS OF SPOT MODELING c u j b i (deg) k (counts s~1) (deg) (deg) (deg) s ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

7 No. 2, 2000 ADDING MORE MYSTERIES TO GD Regemorter (1962) and Eissner & Seaton (1974) formulae, respectively. All collisional ionization rates are given by the Seaton (1962) formula Global Properties of GD 394 Table 5 summarizes new and published e ective temperature and surface gravity measurements. Measurement techniques involve hydrogen line proðle Ðtting (e.g., Balmer line series, Lya) and optical, FUV, and EUV continuum Ñux measurements. H I Balmer L ine Series.ÈThe measurements are based on hydrogen line-blanketed models in LTE. Several analyses based solely on the Balmer line series (Bergeron, Sa er, & Liebert 1992; Marsh et al. 1997; Vennes et al. 1997b; Finley, Koester, & Basri 1997) provide consistent results which average T \ 39,440 ^ 350 K and log g \ 7.90 ^ Individual analyses agree within a few standard deviations with these mean values. KidderÏs (1991) analysis of the Balmer line series and Lya proðle measured with IUE is possibly dominated by optical data and is consistent with these analyses, but the results of McMahan (1989) appear inconsistent (*T D ]4000 K) with the Ðve previously cited analyses. EUV /FUV /Lya.ÈThe measurements are also based on hydrogen line-blanketed models in LTE. E ective temperature measurements based on EUV/FUV data are systematically lower than measurements based on the H I Balmer series by *T D [3000 K. Holberg, Wesemael, & Basile (1986) analyzed the IUE Lya proðle and the FUV to optical Ñux ratio and measured T \ 36,125 ^ 940 K; Finley, Basri, & Bowyer (1990) also Ðtted the FUV continuum to optical Ñux ratio and obtained T \ 36,910 `1630 ~1410 K (assuming log g \ 8); Ðnally, Vennes (1992) compared EXOSAT Low-Energy telescope EUV Ñux measurements with Lya proðle and concluded that (1) GD 394Ïs e ective temperature is T \ 37,000 ^ 1500 K, and (2) its atmo- sphere is contaminated by trace elements. H I L yman L ine Series.ÈFigure 7 shows an analysis of the Lyman line series measured with HUT. The e ective temperature obtained from the Lyman line series (T \ 35,044 K) is lower than the temperature from the Balmer line series by *T D [4400 K but is close to other FUV measurements. The Ðt is restricted to the range 930È1790 A using models normalized at the V magnitude. Surface TABLE 5 EFFECTIVE TEMPERATURE AND SURFACE GRAVITY MEASUREMENTS T log g (K) (c.g.s.) Spectral Range Reference ^ ^ 0.25 Lya ^ ^ 0.07 Balmer ` FUV 3 ~ ^ ^ 0.31 Lya/Balmer ^ ^ 0.25 EUV/Lya/FUV ^ ^ 0.04 Balmer ` `0.08 Lya/Balmer 7 ~500 ~ ^ ^ 0.10 Balmer ^ ^ 0.04 Balmer ^ ^ Balmer ^ ^ 0.02 FUV Lyman 11 REFERENCES.È(1) Holberg et al. 1986; (2) McMahan 1989; (3) Finley et al. 1990; (4) Kidder 1991; (5) Vennes 1992; (6) Bergeron et al. 1992; (7) Barstow et al. 1996; (8) Marsh et al. 1997; (9) Vennes et al. 1997b; (10) Finley et al. 1997; (11) this work. FIG. 7.È(Top) Astro-2 HUT spectrum with pure-hydrogen LTE models normalized to V \ The best Ðt is for T \ 35,044 ^ 25 K and log g \ 7.86 ^ 0.02, which is D4000 K cooler than the optical temperature. (Bottom) ConÐdence contours (1, 2, and 3 p) in the e ective temperature and surface gravity plane. gravity measurements are consistently found close to log g \ 7.9. Ha L ine Core.ÈA new high-dispersion observation of the Ha line core also constrains the e ective temperature. Figure 8 shows the Ha line core modeled using the NLTE model atmosphere code TLUSTY (version 195; Hubeny & Lanz 1995) including traces of He, C, N, O, Si with an abundance log X/H \[6.0, but excluding traces of Fe. Pure hydrogen NLTE models were virtually identical to the models with traces of He, C, N, O, and Si. The line core is characteristic of considerably lower temperatures (T \ 34,000 K) than the corresponding analysis of the Balmer line series (39,800 K; Vennes et al. 1997b) evidence for a weak Balmer line problem (Napiwotzki 1992). Werner (1996) suggested that the proper inclusion of opacities from metals up to the iron-group may resolve the problem. In summary, the optical photosphere appears warmer than the FUV photosphere by D4000 K relative to a pure hydrogen atmospheric structure. Moreover, NLTE modeling of the Ha line core shows evidence of the Balmer line problem usually attributed to the e ect of opacities from metals. We conclude that the atmosphere of GD 394 must contain elements heavier than silicon in relatively large abundance Silicon Abundance We computed a grid of LTE models and grid of NLTE models with e ective temperatures ranging from T \ 35,000 to 39,000 K (log g \ 8.0), and a chemical composition of log Si/H \[4.4, [4.8, [5.2, [5.6, [6.0, and [6.4. The models were computed with the stellar atmo-

8 984 DUPUIS ET AL. Vol. 537 FIG. 8.ÈLick Hamilton echelle spectrum of the Ha line core of the hot DA GD 394. Note the detection of nebular emission at v \[20.5 km s~1 possibly associated to di use emission in the Galactic plane. Taking into account the nebular component, with the intensity adjusted by ]60%, the resulting stellar radial velocity is v \ 35 ^ 10 km s~1. FIG. 9.ÈGHRS spectra of GD 394 showing the silicon lines detected in the three selected ranges (1196È1232 A, 1290È1326 A, and 1383È1419 A ). Each single line or multiplet were Ðtted individually for a model with T \ 39,000 K and log g \ 8.0. The resulting abundances are given above each feature. O I j A and Si II j A are interstellar lines. sphere code TLUSTY Version 195. Only hydrogen and silicon are explicitly considered in the calculations. Next, we utilized the above models to calculate a grid of synthetic spectra using the spectral synthesis code SYNSPEC version 42. The synthetic spectra cover the FUV and optical wavelength ranges which include the observed silicon and aluminum features. Looking carefully at Figure 4b of Barstow et al. (1996), we observed that the Si III j1298 sextuplet line cores are too deep and do not match the GHRS spectrum. We believe that this discrepancy is related to the fact that Barstow et al. used incorrect spectral resolution, uncorrected for the spherical aberration of the HST primary mirror. As mentioned in 2.2, i.e., knowing that GD 394 was observed with the GHRS and the LSA prior to the installation of COSTAR, we reanalyzed the GHRS spectra taking into account the degradation of the resolution by about a factor of 2. Figure 9 illustrates all silicon lines observed with the GHRS, and NLTE model Ðts with Ðxed parameters T \ 39,000 K and log g \ 8.0. We Ðtted each line or multiplet individually using a chi-square minimization method with the abundance treated as the free parameter. The continuum was adjusted to the observed spectrum by independently Ðtting a solid angle in each selected spectral band. The resulting abundances are indicated above each line or multiplet in Figure 9. Figure 10 shows the Si III triplet , , and A, in the high-resolution optical spectrum of GD 394. This observation is the Ðrst detection of the optical Si III triplet in a white dwarf. The radial velocity of the Si III lines is in excellent agreement with silicon line velocities measured in the FUV range, indicating that the Si III triplet originates in the photosphere. Also, it is unlikely that these lines would form in the interstellar medium (ISM) because of the relatively high energy of the lower level (E \ 153,377 l cm~1). The measured equivalent width is 40.6 ma at j , 23.4 ma at j , and 14.9 ma at j , for a total of 78.9 ma. Our best Ðt of the optical Si III triplet is illustrated in Figure 10 for a NLTE model at T \ 39,000 K, log g \ 8.0, and an abundance of log Si/H \[4.66. The co-added HUT spectrum of GD 394 clearly shows the Si IV doublet at A and A (see Fig. 7). Figure 11 shows the Si IV resonance doublet along with a NLTE model Ðt at T \ 39,000 K and log g \ 8.0. We FIG. 10.ÈHamilton echelle spectrum of GD 394 showing the presence of the Si III triplet j ( A, A, and A ) along with our best model at T \ 39,000 K, log g \ 8.0, and log Si/H \[4.66.

9 No. 2, 2000 ADDING MORE MYSTERIES TO GD FIG. 11.ÈSi IV resonance doublet j and j A detected in the HUT spectrum of GD 394 during the Astro-2 space shuttle mission. We measured an abundance of log Si/H \[5.72 for a NLTE model with T \ 39,000 K and log g \ 8.0. measured a silicon abundance of log Si/H \[5.72. Many other faint silicon lines can be seen in the FUV range. Although the Si III j1206 lines and the Si III sextuplet j1298 are not detected because of signiðcant geocoronal emission at wavelengths corresponding to Lya and O I j1304, photospheric features such as the Si III triplet j996.09, the Si III sextuplets j1111.6, j1143.1, and j1159.2, and the Si IV triplet j are observed in the HUT spectrum of GD 394 (see Fig. 7). Interstellar features such as the Si II j and j lines, and the N I triplet j are also observed in the Lya wing. Table 6 summarizes our results and shows a comparison between the LTE and NLTE abundances for two e ective temperatures (T \ 35,000 and 39,000 K). The entries under p ÏÏ are the uncertainties associated to each measurement, including measurement errors of the order of 0.1 dex, and errors on the oscillator strengths of the order 0.05 to 0.25 dex. To overcome difficulties in assessing uncertainties on oscillator strengths, we used the error limits compiled by Wiese, Smith, & Glennon (1966). As demonstrated in Table 6, both LTE and NLTE models provide similar abundances. The NLTE models predict a silicon abundance higher than LTE models by D0.05 dex, if we exclude the Si III j4560 triplet, which appears more sensitive to NLTE e ects. Some disagreements exist between abundances derived from each line or multiplet for both LTE and NLTE models. Table 6 reveals that the scatter of abundance measurements is mostly due to three measurements: Si III j1206, j1312, and Si III triplet j4560. We put aside the j1206 line, as we suspect the presence of a blend with its interstellar counterpart; Table 2 shows that the di erence in radial velocities between the photospheric and interstellar lines is small enough that both j1206 photospheric and interstellar lines may be blended. We excluded the j1312 line because it should be much weaker than the j1417 line, but instead the lines have similar equivalent widths; the lines share the same lower energy level, but the oscillator strength of j1312 is a factor of 5 smaller than that of j1417. The anomaly could be, for instance, the result of an unidentiðed blend or Ðx pattern noise. As the Si III triplet j4560 did not show any apparent anomalies, we decided to keep it along with the j1298, j1417, and j1398 lines in our study of the silicon abundance in GD 394. Table 6 shows that abundance discrepancies still persist. It also suggests a correlation with the e ective temperature. For each line or multiplet, the silicon abundance increases with a corresponding increase of the e ective temperature. For instance, the abundance derived from the Si III j1298 multiplet rises from log Si/H \[6.12 to [5.64 when the e ective temperature rises from 35,000 to 39,000 K. If we take into account the Si III j1298 and j1417, and Si IV j1398 lines, a consistent abundance is obtained for T \ 39,000 K which supports a higher e ective temperature for GD 394. Interestingly, Barstow et al. (1996) obtained a similar result by Ðtting simultaneously the Si III j1206 and j1298, and Si IV j1398 lines present in GHRS spectra. But, when we added the j4560 triplet in our determination of the silicon abundance, we did not Ðnd any satisfactory solution for the range of e ective temperatures taken under consideration. The di erence between the silicon abundance derived by taking into account either the FUV or optical lines may indicate that unknown processes are operating in the atmosphere of GD 394. Because the optical spectra were obtained at a more recent epoch than the FUV spectra, we do not exclude the possibility of an increase in the abundance over that interval. The EUV light curve also suggests that, if the EUV luminosity variation is due to the rotation of a inhomogeneous photosphere, the silicon abundance may well vary TABLE 6 SILICON ABUNDANCE ANALYSIS (log Si/H) T \ 35,000 K T \ 39,000 K ION LTE NLTE pa LTE NLTE pa INSTRUMENT Si III j [5.81 [ [5.35 [ GHRS Si III j [6.15 [ [5.69 [ GHRS Si III j [5.38 [ [5.00 [ GHRS Si IV j [5.65 [ [5.60 [ GHRS Si IV j [5.82 [ [5.76 [ HUT Si III j [5.62 [ [6.01 [ GHRS Si III j [5.12 [ [4.89 [ Lick a p indicates the uncertainties associated with each abundance.

10 986 DUPUIS ET AL. Vol. 537 with time. To verify this hypothesis, we compare in Table 7 the silicon abundance collected over a period of 14 years using HST, IUE, and HUT, and Hamilton echelle at Lick observatory. The abundance measured in the co-added HUT spectrum should correspond to a mean silicon abundance, since this spectrum is the co-addition of spectra taken during the period of 1995 March 6 to 16 (see Kruk et al. 1999). We found no signiðcant abundance variations within the FUV observation series, but one does exist between FUV and optical observations. A plausible explanation for the abundance variation is that the optical observations were obtained with a dark spot over the photosphere of the white dwarf in plain view, which corresponds to the EUV minimum where the abundance is expected to be the highest. The variations may also be attributed to unresolvable deðciencies in the silicon model atom used in NLTE calculations. A model with an inhomogeneous abundance distribution over the surface of a rotating white dwarf remains plausible. Examining the phased EUV light curve (Fig. 6), we may assume that the Ðrst Lick spectrum, taken on September 6 at 09:12:13, is near phase 0.6. The second Lick spectrum, 1 hr later, should be at phase D0.63 with no abundance variations expected. Then, the third Lick spectrum, taken 21 hr later, should be at phase 0.4 where the EUV E/DS count rate has the same value as the count rate of phase 0.6. It could imply that the optical observations were taken near the EUV minimum and that the FUV observations correspond to the maximum EUV brightness. To investigate this case further we must obtain phase-resolved optical and FUV spectroscopy over the 1.15 day period Aluminum Abundance We measured the abundance of aluminum using Al III j and j spectral lines in the co-added IUE high-dispersion spectrum. Holberg et al. (1998) reported the presence of this doublet in their IUE co-added spectrum of GD 394. Using LTE models, we determined an abundance of log Al/H \[6.2. Figure 12 shows the observed Al III doublet along with our best Ðt (see top of the Ðgure) for a model with T \ 39,000 K and log g \ 8.0. It also shows the four individual IUE high-dispersion spectra of GD 394. Individual spectra do not clearly display the aluminum doublet, because of poor signal-to-noise ratio, but the coadded spectrum may well indicate the presence of aluminum in the atmosphere of GD 394. FIG. 12.ÈIUE high-dispersion spectra of GD 394 showing the wavelength range containing the aluminum doublet Al III and A. The vertical dotted lines indicate the position of each component. The spectrum at the top of the Ðgure was obtained by co-adding the four IUE high-dispersion spectra. Our best Ðt (thick line) is superposed upon of the co-added spectrum and gives an abundance of log Al/ H \[6.2 for a model at T \ 39,000 K and log g \ 8.0. The detection of a substantial amount of aluminum in the photosphere of GD 394 was unexpected, given that the radiative levitation theory, for instance, predicts negligible amount of aluminum in the photosphere of a star with physical parameters similar to GD 394. In the conditions prevailing in the photosphere of this star, aluminum is mainly in its inert gas conðguration (Al IV). In this ionization stage, atoms absorb, via bound-bound transitions, photons with energy in the soft X-ray range where the available Ñux is very small. Consequently, the total transfer of momentum to the atoms is reduced and the radiative support is dramatically decreased (see, e.g., Chayer et al. 1995a, 1995b). Therefore, the gravitational settling must compete with a mechanism able to supply some aluminum to the photosphere of GD 394. In the next section we explore the e ect of accretion onto the surface of GD 394 as TABLE 7 SERIES OF SILICON ABUNDANCE MEASUREMENTSa log Si/H SPECTRUM INSTRUMENT DATE Si III j1298 Si IV j1398 Si III j4560 SWP IUE 1982 May 5 [5.90 ^ 0.10 [5.81 ^ SWP IUE 1984 Apr 15 [5.70 ^ 0.15 [5.79 ^ Z0YE0A0AM... GHRS 1992 Jun 18 [5.64 ^ Z0YE0A0CM... GHRS 1992 Jun [5.63 ^ SWP IUE 1994 Jan 3 [5.70 ^ 0.15 [5.61 ^ SWP IUE 1994 Jan 4 [5.59 ^ 0.14 [5.51 ^ Co-added... HUT 1995 Mar 6È16... [5.72 ^ Hamilton... Lick 1996 Sep [4.71 ^ 0.09 Hamilton... Lick 1996 Sep [4.59 ^ 0.09 Hamilton... Lick 1996 Sep [4.61 ^ 0.09 a Based on a NLTE model at T \ 39,000 K, and log g \ 8.

11 No. 2, 2000 ADDING MORE MYSTERIES TO GD a plausible mechanism to account for the observed aluminum abundance Accretion Model The di erence between the silicon abundance measured in FUV observations and the abundance measured in optical observations could indicate that the silicon abundance varies as a function of depth in the atmosphere of GD 394. Until now, we have only considered stellar model atmospheres with a vertically homogeneous abundance of silicon. But the abundance of heavy elements may vary by many orders of magnitude in the atmospheres of hot white dwarfs (see, e.g., Vauclair, Vauclair, & Greenstein 1979, Chayer et al. 1995a, 1995b, and Dreizler & Wol 1999). Mechanisms such as ordinary di usion, radiative levitation, mass loss, or accretion may compete against gravitational settling and cause a wide variation of abundance as a function of depth. To estimate the silicon distribution in the atmosphere of GD 394, we must determine which mechanism explains the observed silicon abundance pattern. Chayer et al. (1995a, 1995b) have shown that radiative levitation can support only a small fraction of silicon in the photospheres of stars like GD 394. They computed detailed radiative equilibrium abundances at the Rosseland optical depth, q \ 2. We can argue, however, that computations Ross 3 of radiative equilibrium abundance proðles such as those carried out by Dreizler & Wol (1999) could explain the observed silicon in GD 394. But, by examining the silicon ionization fractions through the atmosphere of GD 394, we noted that the radiative support should be important only in a small portion of the atmosphere. Figure 13 shows NLTE silicon ionization fractions as a function of depth in a model with T \ 39,000 K and log g \ 8.0. The Ðgure shows that silicon is mainly in its inert gas conðguration (Si V) at the top and bottom of the atmosphere, so that the radiative support must be negligible in those regions. FIG. 13.ÈNLTE silicon ionization fractions as a function of depth in a model with T \ 39,000 K and log g \ 8.0. The vertical dotted line at the top of the Ðgure indicates the location of the Rosseland optical depth, q \ 2. Ross 3 Silicon equilibrium abundance should be maintained by radiative levitation in a small portion of the atmosphere where [3.5 \ log m \ [1.5. Even in that region, though, radiative support should be small and we do not expect that detailed radiative calculations performed through the atmosphere of GD 394 could account for the observed silicon. Consequently, since radiative levitation in the atmosphere of GD 394 can support only a fraction of the observed silicon abundance, another mechanism has to be invoked to explain the presence of this element. Accretion could supply aluminum and silicon to the photosphere of GD 394 and account for the observed abundances. Even if we do not know the source of aluminum and silicon yet, computing an estimate of the accretion rate can constrain the origin of the accreted material. We Ðrst estimated the accretion rate necessary to maintain the observed silicon abundance in the photosphere of GD 394. In this model, the silicon distribution is determined by a quasiequilibrium situation between the accretion (material falling onto the surface of the white dwarf) and the di usion (material sinking to the bottom of the atmosphere). To compute the silicon distribution we assumed a steady and spherically symmetric accretion onto the white dwarf surface. The distribution of silicon in a steady state situation that expresses the conservation of the silicon Ñux at each point in the atmosphere is given by the relation 4nr2oX (Si)w \ M0 Si Si, (2) where r is the radius, o is the density, X (Si) is the silicon mass fraction, w is the di usion velocity, and M0 is the Si Si accretion rate of silicon given in units of grams per second. The di usion velocity of silicon with respect to hydrogen, neglecting the concentration gradient, the radiative acceleration and the thermal di usion, is w Si \ D HSi m p g kt AZ ] 1 Si B [ A, (3) 2 Si where D is the di usion coicient, m is the proton mass, HSi p g is the local gravity, T is the temperature, Z is the average Si charge of silicon, and A is the silicon atomic weight. We Si used the physical parameters given by a NLTE model atmosphere (T \ 39,000 K and log g \ 8.0) to evaluate the di usion velocity and, consequently, the silicon distribution throughout the atmosphere. We evaluated the di usion coicient using spline formulae provided by Paquette et al. (1986). We used the Chandrasekhar mass-radius relationship to estimate the radius of GD 394 by assuming that log g \ 8.0. The radius is then ] 108 cm. We assumed that the silicon is accreted in solar proportions, X (Si) \ 9.97 ] 10~4. Figure 14 shows the computed silicon _ distribution for three di erent accretion rates, and indicates that the silicon abundance decreases by at least a factor of 30 from the surface to the bottom of the atmosphere. Moreover, Figure 14 points out that each accretion rate yields a unique silicon abundance proðle. Using silicon distributions corresponding to di erent accretion rates, we Ðrst computed NLTE model atmospheres to take into consideration the silicon abundance variation as a function of depth. Then, we computed a small grid of synthetic spectra. In our chi-square Ðtting analysis, we treated the accretion rate as the free parameter instead of the abundance. Based on our silicon abundance analysis ( 4.3), we put in Table 8 the accretion rates corresponding

12 988 DUPUIS ET AL. Vol. 537 FIG. 14.ÈSilicon abundance distribution as a function of atmospheric mass loading m (g cm~2) at T \ 39,000 K and log g \ 8.0 in the presence of continuous accretion. Accretion rates are 1 ] 10~15 ( full line), 3.2 ] 10~16 (dotted line), and 1 ] 10~16 M yr~1 (dashed line). Silicon is assumed to accrete in solar proportions. _ to the observation of the Si III j1298, Si IV j1398, Si III j1417, and Si III j4560 features. The uncertainties include measurement and oscillator strength errors. The accretion rate based on the Si III j4560 triplet is about a factor of 6 higher than the mean accretion rate estimated from the FUV lines. This result demonstrates that even if we take into account inhomogeneous silicon distributions in the atmosphere, di erences between FUV and optical observations are not resolved. This may indicate, though, that GD 394 experienced a higher accretion episode during the optical observations taken at the Lick observatory in But again, as stated earlier, phase-resolved optical and FUV spectroscopy, as well as a review of our silicon atom model could shed light on the unresolved discrepancies. A very interesting result came out of the computation of the silicon accretion rate. By measuring the silicon abundance from the silicon distribution at q \ 2, we noted that the abundance was almost the same as Ross the one 3 given by a model with vertically homogeneous abundance. This is illustrated in Table 8, where we compare the silicon abundance obtained from the silicon distribution at q \ 2, to the abundance obtained from a vertically homogeneous Ross 3 model. Even though the abundance varies as a function of depth in the model with accretion, its value at q \ 2 is comparable to the one given by the vertically homogeneous Ross 3 model. The only exception is for the Si III j4560 feature, where a di erence of 0.23 dex is observed between the abundances given by the inhomogeneous and homogeneous models. Based on this Ðnding, we assumed that the determination of the accretion rate needed to account for the aluminum observation can be estimated, to a very good approximation, at q \ 2. Consequently, we computed the alu- minum accretion Ross rate 3 required to maintain the observed abundance at this optical depth. By substituting the silicon parameters for the aluminum ones in equations (2) and (3), and by evaluating them at q \ 2, we obtained an alumin- um accretion rate of M0 Ross 3 yr~1 in a acc \ 5.01 ] 10~16 M model with T \ 39,000 K and log g \ 8.0. _ 4.6. EUV E Spectrum We analyzed the spectrum using pure-hydrogen model structure in LTE and synthetic spectra with various chemical compositions in the trace-element approximation. We computed synthetic spectra with pure-h, H ] He, CNO ] Si, and Fe ] Si compositions. The following ionic species are included in the models: C III, C IV, N III, N IV, N V, OIII, OIV, OV, SiIII, SiIV, SiV, FeIV, FeV, FeVI, and Fe VII. The atomic data for the line transitions are from the KURUCZ CD-ROM No. 1, which contains the compilation of Kurucz & Bell (1996) and KuruczÏs (1992) semiempirical calculations of iron-group transitions. Photoionization cross sections were obtained from TOPBASE (Cunto et al. 1993) and based on calculations by Peach, Saraph, & Seaton (1988) for C III and N V, by Tully, Seaton, & Berrington (1990) for C IV, NIV, OV, by Fernley et al. (1999) for N III and O IV, by Luo & Pradhan (1989) for O III, by Butler, Mendoza, & Zeippen (1993) for Si III, by Taylor (1999) for Si IV, by Scott (1999) for Si V, by Nahar & Pradhan (1994) for Fe V, by Butler, Mendoza, & Zeippen (1999) for Fe VI, and by Sawey & Berrington (1992) for Fe VII. Best-Ðt parameters are obtained using the Levenberg- Marquardt algorithm: the model parameters are the e ective temperature, the abundance of helium or heavier TABLE 8 ACCRETION RATE AND SILICON ABUNDANCE ANALYSES INHOMOGENEOUSa,b M0 log Si/H HOMOGENEOUSb,c acc ION (M yr~1) (q \ 2/3) log Si/H _ ross Si III j1298 (1.10 ^ 0.31) ] 10~16 [5.73 ^ 0.11 [5.64 ^ 0.12 Si IV j1398 (1.38 ^ 0.20) ] 10~16 [5.63 ^ 0.05 [5.63 ^ 0.06 Si III j1417 (1.26 ^ 0.78) ] 10~16 [5.67 ^ 0.20 [5.58 ^ 0.20 Si III j4560 (7.76 ^ 2.00) ] 10~16 [4.89 ^ 0.10 [4.66 ^ 0.09 a Stellar model atmosphere where the silicon abundance is computed within the framework of the steady state accretion model. b T \ 39,000 K and log g \ 8.0. c Stellar model atmosphere where the silicon abundance is vertically homogeneous.