The effect of photospheric heavy elements on the hot DA white dwarf temperature scale

Mon. Not. R. Astron. Soc. 299, 520 534 (1998) The effect of photospheric heavy elements on the hot DA white dwarf temperature scale M. A. Barstow, 1 I. Hubeny 2 and J. B. Holberg 3 1 Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH 2 Laboratory for Astronomy and Solar Physics, NASA/GSFC, Greenbelt, Maryland, MD 20711, USA 3 Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA Accepted 1998 May 6. Received 1998 April 24; in original form 1998 February 20 ABSTRACT Using the latest non-local thermodynamic equilibrium (non-lte) synthetic spectra and stellar model calculations, we have evaluated the potential effect of the presence of heavy elements in the photospheres of hot H-rich DA white dwarfs. In particular, we have examined their influence on the effective temperature and surface gravity perceived from analysis of the Balmer line profiles. It is apparent that both the inclusion of non-lte effects in the models and significant quantities of heavy elements act independently to lower the value of T eff determined from a particular spectrum. Hence, the true effective temperatures of the heavy element-rich DA white dwarfs, currently estimated to be above 55 000 K, are apparently lower than previously reported from pure-h LTE analyses, by some 4000 7000 K. We do not see any similar influence on measurements of log g. This work concentrates on a group of relatively bright well-studied objects, for which heavy element abundances are known. As a consequence of this, establishment of correct temperatures for all other hot white dwarfs will require a programme of far-uv spectroscopy in order to obtain the essential compositional information. Since only stars with effective temperatures lying notionally in the range from 55 000 to 70 000 K (52 000 62 000 K when the non-lte effects and heavy elements are taken into account) have been considered here, important questions remain regarding the magnitude of any similar effects in even hotter white dwarfs and pre-white dwarfs. The resulting implications for the plausibility of the evolutionary link between the main hot DA population and their proposed precursors, the H-rich central stars of planetary nebulae, need to be investigated. Key words: stars: abundances stars: atmospheres white dwarfs ultraviolet: stars X-rays: stars. 1 INTRODUCTION In order to study the evolution of white dwarfs and the relationship of these stars to their progenitors, the central stars of the planetary nebulae (CSPN), we need to know accurately several physical parameters for each star. For example, a measurement of effective temperature (T eff ) establishes how far along its evolutionary sequence the star has progressed. A determination of the surface gravity, when combined with a theoretical mass radius relation such as that of Wood (1992, 1995), yields an estimate of the stellar mass and, as a result, gives some indication of the evolutionary history of the object, whether it is a product of single star evolution from the asymptotic giant branch (AGB) or perhaps arises from the Extended Horizontal Branch (EHB) or through interaction in a binary. A long-standing question has been the origin of two distinct groups of white dwarfs, having either hydrogen-rich or helium-rich atmospheres. Mapping the abundances of trace heavy elements as a function of T eff and log g in the otherwise pure H or pure He envelopes is crucial to understanding the origin of these two distinct compositional paths and, perhaps, to solving the problem of the 45 000 to 30 000 K gap in the He-rich track between the hot DO and cooler DB white dwarfs. Intriguingly, while the very hottest H-rich DA white dwarfs outnumber the He-rich DOs by a factor 7 (Fleming, Liebert & Green 1986), the relative number of H- and He-rich CSPN is only about 3:1. Very few true white dwarfs have effective temperatures above 70 000 K and, therefore, establishing a direct evolutionary link between H-rich CSPN and white dwarfs has been difficult. An earlier proposal that DAs might form from DOs through the buildup of thin H layers by gravitational settling of He (e.g. Liebert, Fontaine & Wesemael 1987) has been undermined on two fronts. First, photospheric He has not been directly detected in the extreme ultraviolet (EUV) spectra of any of the hottest DA white dwarfs (Barstow, Holberg & Koester 1995; Barstow et al. 1997a), although 1998 RAS

The hot DA white dwarf temperature scale 521 indirect evidence still holds out the possibility that it might be present (Lanz et al. 1996; Barstow et al. 1997c), apart from its existence in peculiar objects such as the DAO+dM binary REJ0720¹318 (Burleigh, Barstow & Dobbie 1997) and the massive object GD50 (Vennes Bowyer & Dupuis 1996a). Secondly, a detailed survey of DAO white dwarfs, H-rich objects which have He features in their visible spectra, indicates that these cannot be the transitional objects between DO and DA compositions that they were thought to be (Bergeron et al. 1994). The discovery of several very hot DA white dwarfs with temperatures well in excess of 70 000 K has appeared to provide the direct link to the H-rich CSPN. REJ1738+665 (90 000 K; Barstow et al. 1994b), EGB1 (100 000 K; Napiwotzki & Schönberner 1993) and WDHS1 (100 000 to 160 000 K; Liebert, Bergeron & Tweedy 1994). All these stars have comparatively high surface gravities (log g in the range 7.5 to 8.0), indicating that they are true white dwarfs rather than lower gravity CSPN. However, hotter H-rich central stars such as NGC7293 and LSV+4621, with temperatures around 100 000 K, all contain some He. Bergeron et al. (1994) have observed that the quantity of He assumed to be present in any individual star will affect the temperature determined from the Balmer line profiles. At an effective temperature of 60 000 K, an He/H abundance of 10 ¹4, which is spectroscopically undetectable in the visible or UV bands, would lower the measured temperature by approximately 10 per cent. Barstow et al. (1994b) note that if 2 10 ¹4 of He (the visible limit) were present in REJ1738+665, the true temperature of the star would be 70 000 rather than 90 000 K. Hence, whether or not these super hot DA stars can really bridge the gap between the H-rich CSPN and the beginning of the main DA cooling sequence must depend on their He content. It is remarkable that, despite the large range of progenitor masses (up to 8 M ) from which white dwarfs evolve, the distribution of their masses is extremely narrow. Although this property of the white dwarf sample has been known for some time (e.g. Weidemann & Koester 1984), only relatively recently have large-scale spectroscopic surveys provided an accurate and reliable determination of the narrow peak in the white dwarf mass distribution. The key to this is the measurement of T eff and log g from the Balmer line profiles in the optical spectrum. This procedure, pioneered by Holberg et al. (1985) and Kidder (1991), involves comparing the calculations of theoretical model atmospheres with an observed spectrum. Bergeron, Saffer & Liebert (1992, hereafter BSL) later used it to carry out a systematic survey of the H-rich DA white dwarf population. Combining these results with the white dwarf evolutionary models of Wood (1992), they were able to study the stellar mass distribution in detail, obtaining a mean of 0:56 M. The initial Wood (1992) models did not take into account the possible effect of a significant hydrogen envelope, effectively assuming that the H- layer mass was negligible. While there is some strong circumstantial evidence that this might be so (see Fontaine & Wesemael 1997 for a review), theoretical studies predict that the residual H mass should be 10 ¹4 M (e.g. Iben & Tutukov 1984). Subsequently, Wood (1995) established that, for DA white dwarfs, the evolutionary calculations are significantly affected by the assumed H layer mass, and applying these later models (with M H ¼ 10 ¹4 M ) to the BSL sample raises the mean mass of the white dwarfs to 0:590 M. The BSL sample was constructed from a somewhat heterogeneous group of optically selected stars, lying in the temperature range 13 000 to 40 000 K, but actually including very few objects with temperatures in excess of 25 000 K. Yet it is these hotter stars that are the most important test of the evolutionary models, having the greatest departure from the zero temperature Hamada & Salpeter (1961) mass radius relation. The Palomar Green (PG) survey includes a large number of white dwarfs, with effective temperatures extending up to 80 000 K or so. Preliminary results including 200 PG white dwarfs obtain a slightly higher mean mass (0:609 M, Wood 1995 models) than for the BSL sample. Finley (1995) and Finley, Koester & Basri (1997) report an even higher mean (0:63 M, Wood 1995 models). However, this sample contains a significant fraction of EUV-selected objects as well as those discovered by optical means. Marsh et al. (1997a) and Vennes et al. (1997) have studied the mass distribution of completely EUVselected samples of white dwarfs. These show a significant highmass tail, biasing the mean towards higher values (0:644 M for Marsh et al. 1997a; Vennes et al. 1997 do not report a mean value). Finley et al. (1997), however, attribute the apparent excess of massive DA white dwarfs in the EUV sample to a deficit of stars with more typical masses, since the lower mass stars are selected against in EUV surveys by interstellar absorption. The reliability of all these studies of the DA population depends on the assumption that the Balmer line profile technique is a reliable estimator of T eff in all cases. Yet Bergeron et al. (1994) have already warned that spectroscopically undetectable traces of He may undermine the DA temperature scale at temperatures above 50 000 K. Furthermore, if temperatures are incorrectly determined, might not the surface gravities, from which the masses are obtained, also be in error? The absence of spectroscopic evidence for the presence of photospheric He in most hot DA stars (Barstow et al. 1995, 1997a) could be used to argue against this being a real problem. However, photometric and spectroscopic data do exist which demonstrate that sources of opacity, in addition to hydrogen, are ubiquitous in the hottest DA stars. The ROSAT all-sky EUV and X-ray survey showed that all DAs with T eff above 55 000 K exhibited substantial flux deficits compared to the predictions of pure H atmospheres (Marsh et al. 1997b). Neither homogeneous nor stratified H+He atmospheres could explain the observations, implying that heavier elements must be responsible for the observed EUVopacity. This is consistent with the expectation that radiation pressure should be able to support heavy elements in the stellar photosphere, particularly Fe, acting against the downward force of gravity (e.g. Chayer, Fontaine & Wesemael 1995a; Chayer et al. 1995b), and is supported by the direct detection of C, N, O, Si, S, P, Fe and Ni ions in the far-uv spectra of hot DAs such as G191¹B2B (Vennes et al. 1992; Sion et al. 1992; Holberg et al. 1994; Werner & Dreizler 1994; Vidal-Madjar et al. 1994; Vennes et al. 1996b), Feige 24 (Vennes et al. 1992), REJ2214¹492 (Holberg et al. 1993, 1994) and REJ0623¹377 (Holberg et al. 1993). Subsequent EUV spectroscopy has revealed the strong decrease in flux towards shorter wavelengths, expected from the blanketing effects of these elements, in particular Fe and Ni. However, reconciling the detailed shape and flux level of these spectra has proved to be rather difficult (e.g. Barstow et al. 1996). Recent improvements in the model atmosphere calculations, increasing dramatically the number of Fe and Ni lines taken into account, now give a self-consistent model for optical, UVand EUV spectra of G191¹B2B (Lanz et al. 1996). Such results can be extended to other similar objects (Barstow et al. 1997c). Dreizler & Werner (1993) first posed the question as to whether or not the presence of significant quantities of heavy elements would affect the shape of the Balmer line profiles. They concluded that, with non-lte models, the line blanketing from Fe group elements would only have a very small effect. These early models may not have incorporated sufficient line blanketing but we can now have confidence that the current generation of non-lte model

522 M. A. Barstow, I. Hubeny and J. B. Holberg calculations provide a good representation of the true structure of these very hot white dwarfs. Lanz et al. (1996) compared the value of T eff estimated using local thermodynamic equilibrium (LTE), weakly blanketed non-lte and fully blanketed non-lte models, concluding that a significant effect was present but was attributable mainly to differences between LTE and non-lte rather than to the effect of line blanketing. For example, the effective temperature obtained with a H+He+O model was some 4500 K lower than the 60 500 K obtained with an LTE model, while adding Fe further reduced the temperature by only a few hundred degrees. Calculating fully blanketed non-lte models, including some 10 million transitions of Fe and Ni, is a highly CPU-intensive operation, taking a few days for one computation, representing a single temperature, gravity and composition point in parameter space. Consequently, Lanz et al. (1996) restricted the grid of models used for their analysis of the Balmer lines to a fixed value of log g (7.5) and only a few temperature points. In extending the G191¹B2B study to other hot DAs with different temperature and gravity, we have enlarged this grid substantially. In particular, it now spans a representative range of log g (from 7.0 to 8.0) and T eff from 52 000 to 68 000 K. Repeating the Balmer line analysis of Lanz et al. (1996) for G191¹B2B and other stars reveals that their original conclusion was an oversimplification. We demonstrate here that the presence of substantial line blanketing from Fe, Ni and other heavy elements does significantly alter the Balmer line profiles at a given effective temperature. Hence, the hot DA temperature scale established by studies using only pure H photospheric models cannot be viewed as reliable and needs to be revised. Furthermore, any values of T eff and log g inferred from the optical spectra must take into account the composition of the photosphere and, in some cases, this will require additional observations in the far-uvor EUV to provide that information before an object can be reliably placed in its evolutionary context. 2 OBSERVATIONS Above approximately 55 000 K, there exists a set of well-observed hot DA white dwarfs which have been extensively studied in the optical, far-uv, EUV and X-ray wavebands. We have selected nine of these stars (see Tables 2 and 3, below) to study the effects of heavy element abundances and non-lte model atmospheres on the temperatures and gravities derived from Balmer line profiles. Approximately half these objects had already been catalogued prior to the ROSAT and EUVE all-sky surveys, but the remainder were discovered as EUV and soft X-ray sources (e.g. Holberg et al. 1993; Barstow et al. 1994a,b). Detailed interpretation of the survey data and subsequent far-uvobservations required that the effective temperature and surface gravities of all these objects be known, hence optical spectra already exist for the Balmer line profile measurements (e.g. Marsh et al. 1997a; Vennes et al. 1997). In addition, a handful of far-uv spectra have been obtained in the region spanning the H Lyman line series, providing an important alternative and complementary means of determining T eff and log g for a few objects. No new observations were obtained for this work. 2.1 Optical spectroscopy To fully exploit the short wavelength photometric data obtained from the white dwarf sample in the ROSAT X-ray and EUV sky surveys, a programme of spectroscopic observations was undertaken in both Northern and Southern hemispheres. This was mainly focused on obtaining data for the newly discovered group of white Figure 1. Optical spectra of the nine hot DA white dwarfs included in this study in RA order from the top Feige 24, REJ0457, G191, REJ0623, PG1123, PG1234, REJ2214, GD246, REJ2334.

The hot DA white dwarf temperature scale 523 dwarfs, but observations were also made of those previously catalogued stars for which suitable spectra did not exist, together with a number of well-studied DAs for reference purposes. The optical spectra used here are all taken from this work. Southern hemisphere observations were made in 1993 October and 1994 March using the 1.9-m Radcliffe reflector of the South African Astronomical Observatory (SAAO), while stars in the Northern hemisphere were observed with the Steward Observatory 2.3-m telescope on Kitt Peak. Full details of these observations have already been published by Marsh et al. (1997a). The main difference between the Southern and Northern hemisphere data is their spectral resolution, 3Å (FWHM) and 8Å (FWHM) respectively. The optical Balmer line spectra used here are illustrated in Fig. 1. 2.2 Far-ultraviolet spectroscopy High-resolution EUVand far-uv spectra of two stars in our sample, G191¹B2B and REJ0457¹281 (¼MCT0455¹2812), were obtained with the ORFEUS mission during the 1993 September flight of the space shuttle Discovery. An important paper reporting the discovery of sulphur and phosphorus in their photospheres has already been published along with effective temperature and surface gravity determinations using Lyman line profiles (Lyb to Lye; Vennes et al. 1996b). These spectra are now available in the public domain and can be included in our new analysis. A detailed description of the Berkeley spectrometer is given by Hurwitz & Bowyer (1991), while the observation procedures and instrument calibration are found in Hurwitz & Bowyer (1995). The spectral resolution achieved during this first ORFEUS flight was l=dl 3000, corresponding to a velocity 100 km s ¹1, with an intrinsic uncertainty of 100 km s ¹1 in the wavelength scale arising from the unknown position of each target within the telescope aperture. Observations of G191¹B2B and REJ0457¹281 were obtained during 1993 September, with exposure times of 8225 and 8698 s, respectively. Full details are included in the analysis of Vennes et al. (1996b) and the spectra are displayed in Fig. 2. The raw spectra suffer from contamination by a scattered light component, which is a combination of flux from the second spectral order and direct scatter from the grating (Hurwitz, private communication). When added to the stellar spectrum, the apparent level of the continuum flux will be higher than the true one. In measurements of T eff and log g, the line profiles, whether Balmer or Lyman, are measured from the continuum. Hence, the scattered light component must be accounted for in any analysis to avoid obtaining erroneously high temperatures from apparently weaker lines. Shortward of the Lyman limit, the stellar spectrum makes no contribution to the net flux, as a result of absorption by interstellar neutral hydrogen. Hence, the value of the scattered light component was estimated from the observed flux in the 850 900 Å range. In our own analysis of the archival data of G191¹B2B and REJ0457¹281, the estimated level of the scattered light component is 3.5 and 2.0 photon cm ¹2 s ¹1 Å ¹1 respectively, corresponding to about 4 per cent of the far-uv flux of each star. 2.3 The hot DA sample We have selected the group of stars included in this study on the grounds of their nominal effective temperature, as determined from Balmer line spectroscopy using pure-h LTE models for the analysis. We refer to the work of Marsh et al. (1997a) which places all Figure 2. ORFEUS spectra of G191¹B2B (bottom) and REJ0457¹281 (top). these stars above 55 000 K and in the group of objects which contain significant quantities of heavy elements in their photospheres (Barstow et al. 1993; Marsh et al. 1997b; Wolff, Jordan & Koester 1996). The quality of information on the detailed photospheric abundances found in each object is highly variable, depending on the visual magnitude of the object and the level of photospheric opacity. For example, lines of Fe and Ni are readily detected in the International Ultraviolet Explorer (IUE) echelle spectrum of REJ2214¹492 (Holberg et al. 1993, 1994; Werner & Dreizler 1994). However, it is one of the visually brightest hot white dwarfs (V ¼ 11:7) and appears to have the most extreme Fe abundance 3 10 ¹5. In contrast, Vennes, Thejll & Shipman (1991) reported only possible, but not firm, detections of C IV and Si IV in a single IUE exposure of GD246 (V ¼ 13:09) with no indication of any other elements. Even so, the EUV photometry and spectroscopy show significant absorption (Barstow et al. 1993; Marsh et al. 1997b; Vennes et al. 1993) and a more recent analysis of coadded spectra does show that N V, SiIV and C IV are really present (Holberg, private communication). It is useful to summarize briefly what we know about the properties of each of the stars in this sample. For convenience we divide them according to their apparent photospheric composition from estimates of the level of absorption in the EUV (e.g. see Marsh et al. 1997b). Koester et al. (1997) and Wolff et al. (1998) have attempted to define a metallicity for the hot DAs, using the EUV spectra and scaling abundances uniformly to the values (relative to hydrogen) determined for G191¹B2B. Their results provide a useful indicator, but in some cases it is clear that the abundances cannot be reduced to a single parameter and scaled, as we will discuss below. Fig. 3 shows the ratio of the observed fluxes compared to the predictions of a pure-h model atmosphere for the ROSAT PSPC band for all the stars in our hot DA sample, as a function of the nominal stellar temperature, extracted from Marsh et al. (1997b). The effects of interstellar absorption are minimized in the soft X-ray range, while the suppression of the photospheric flux by heavy elements is at its greatest.

524 M. A. Barstow, I. Hubeny and J. B. Holberg approximation, G191¹B2B probably represents the composition of all four objects. 2.3.2 Intermediate opacity objects Initial study of the DA white dwarf REJ0457¹281, first reported as a result of its discovery in the ROSAT WFC survey, indicated that it might be considered as a spectroscopic twin to G191¹B2B. However, the photometric EUV fluxes of REJ0457¹281 and REJ2334¹471 indicate that they do not have as large a heavy element content as the above group of stars (see Marsh et al. 1997b). The IUE observations reveal some heavy elements (C, N, and Si) but do not detect Fe or Ni. However, this might be a result of the comparatively poor signal-to-noise ratio of the data. Some direct evidence has been gleaned from a preliminary anaysis of the EUV spectrum of REJ0457¹281 (Barstow et al. 1997c), which requires a Fe abundance 3 10 ¹6 to reproduce the EUV flux, a level consistent with the upper limit to the Fe abundance imposed by the UV data. Both the Fe and C abundances in REJ0457¹281 are lower than in G191¹B2B. In particular the carbon content is only about 1/20 of the G191¹B2B value. Yet the abundances of the other elements (N, O and Si) are rather similar, showing that a metallicity determined by scaling from a particular star should be treated cautiously. Figure 3. Ratio of ROSAT PSPC normalized emergent fluxes for the sample of hot DAwhite dwarfs to those predicted for a pure-h atmosphere with zero interstellar absorption, as a function of temperature for each individual star. Error bars are only applied to T eff, from Balmer line fits to pure-h models. The values for Feige 24, REJ0623 and REJ2214 are upper limits. Hence, these data provide the best indication of the relative photospheric abundances. 2.3.3 Low opacity objects No positive detections of heavy elements in the IUE spectra of PG1234+481 and PG1123+189 have been reported, yet it is clear from analyses of the EUV spectra that additional sources of opacity other than H and He must be present in their atmospheres (Jordan, Koester & Finley 1997; Barstow et al. 1997a). While heavy elements have recently been detected in a coadded IUE spectrum of GD246 (Holberg, private communication), its EUV spectrum is very similar to those of PG1123+189 and PG1234+481 (Vennes et al. 1993; Barstow et al. 1997a; Jordan et al. 1997). 2.3.1 Extreme EUV opacity objects The four hot DA white dwarfs falling within this group Feige 24, G191¹B2B, REJ0623¹371 and REJ2214¹492 have all been studied in considerable detail using the IUE echelle spectrometer. Transitions from many heavy elements, including C, N, O, Si and Fe, are readily identified in single exposures (Vennes et al. 1992; Holberg et al. 1993) and Ni has also been seen in the coadded spectra of G191¹B2B, REJ2214¹492, REJ0623¹371 and Feige 24 (Holberg et al. 1994; Werner & Dreizler 1994). Spectroscopically, these objects are nearly identical, except that REJ0623 and REJ2214 seem to be hotter (63 000 and 69 000 K respectively) than Feige 24 and G191¹B2B (both 60 000 K) and have larger Fe abundances. Nominally, the estimated Fe abundances in REJ0623 and REJ2214 are 3 10 ¹5 (Holberg et al. 1993) compared to 0:5 ¹ 1 10 ¹5 for Feige 24 and G191¹B2B (Vennes et al. 1992). However, caution must be exercised in such comparisons, since the Vennes et al. (1992) results were based on LTE calculations and those of Holberg et al. (1993) on non-lte models. Furthermore, in the light of the Lanz et al. (1996) analysis of G191¹B2B, as neither earlier study was based on adequate treatment of the heavy element line blanketing, the quoted abundances cannot be treated as definitive. Lanz et al. (1996) obtain an Fe abundance of 10 ¹5 for G191¹B2B but revise the effective temperature downwards, compared to the pure-h LTE analysis, to 56 000 K. To a first-order 3 NON-LTE MODEL ATMOSPHERE CALCULATIONS The heavy-element-rich models used here are based on the work reported by Lanz et al. (1996), but are extended over a range of T eff and log g to cover the parameter space occupied by the hottest DA white dwarfs. A total of 26 ions of H, He, C, N, O, Si, Fe and Ni are included in calculations utilising the programme tlusty (Hubeny 1988; Hubeny & Lanz 1992, 1995). Hydrogen is treated essentially exactly: the first eight levels are treated separately, while the upper levels are merged into the average non-lte level accounting for level dissolution as described by Hubeny, Hummer & Lanz (1994). All radiative transitions are treated explicitly; Lyman and Balmer lines with Stark profiles, while the lines of the other H series use Doppler profiles. The lines from the n ¼ 1 and n ¼ 2 levels to the merged upper level are treated by means of an opacity distribution function (ODF), as described by Hubeny et al. (1994). The radiative data for the light elements have been extracted from TOPBASE, the data base of the Opacity Project (Cunto et al. 1993), or from extended models of carbon atoms, kindly communicated by K. Werner. Typically, the lowest 12 45 levels are included. All allowed radiative transitions are included with Doppler line profiles. A test adopting Stark profiles for the light elements (excluding H) makes little difference to the atmospheric structure. We noted above that the important H Balmer and Lyman lines are

The hot DA white dwarf temperature scale 525 treated with Stark profiles, since their broad wings have a significant effect on the photospheric opacity and, consequently, influence the model structure. However, the observed effect is mainly an increase in the predicted continuum flux when changing from Doppler to Stark profiles. In calculating synthetic spectra, the latest linebroadening tables of Schöning & Butler (private communication), extending their original work (Schöning & Butler 1989) to higher densities, provide the detailed profiles used for analysing the data. Although small changes are seen between the detailed line shapes for the Doppler and Stark models, tests show that in practice negligible differences are obtained for values of T eff and log g. For iron and nickel, all the levels predicted by Kurucz (1988) are included in the models, totalling over 70 000 individual energy levels grouped into 235 non-lte superlevels. The effect of over 9.4 million iron and nickel lines are accounted for. This is an improvement on previous models containing some 11 000 lines (Lanz & Hubeny 1995) and is responsible for the ability of Lanz et al. (1996) to explain the EUV spectrum of G191¹B2B. Each transition between superlevels is represented by one or several opacity distribution functions (see Hubeny & Lanz 1995), with the line data to generate these taken from Kurucz (1988). To construct the ODFs, the lines included are computed with Voigt profiles. We use an early version of iron photoionization cross-sections calculated by Pradhan & Nahar (private communication) in the framework of the Iron Project, while approximate hydrogenic cross-sections are used for nickel photoionization. Collisional rates are calculated with the general formula of Seaton (1962) and Van Regemorter (1962). In calculating a grid of high metallicity models for the analysis of the very hot DA white dwarfs, we initially fixed the abundances of the heavy elements at the values determined from the earlier homogeneous analysis of G191¹B2B (Table 1). The temperature and gravity range, spanned 52 000 to 68 000 K (grid points at 52 000, 53 000, 54 000, 56 000, 63 000, 68 000 K) and 7.0 to 8.0 (0.5 dex steps), respectively. These limits were determined empirically by repeated analysis of stars in the sample, adding new models in both high and low temperature directions until all the values of T eff and log g measured were within the grid boundaries. In studying the potential effect of photospheric heavy elements on the DA temperature scale, it is important that all other possible influences are examined carefully. For example, since all earlier work has been carried out with LTE models, the introduction of non-lte calculations may, at least in part, be responsible for any differences in the values of T eff and log g determined. Such an effect needs to be ruled out or (at least) quantified. Another important contribution may be from the 10 ¹5 of helium incorporated into the model composition. Bergeron et al. (1994) have demonstrated that, in LTE, addition of He at this level has a significant effect on temperature determinations and a similar result may occur when Table 1. Heavy element abundances (relative to hydrogen) adopted for the model calculations. Element H+He Abundance (N elem /H) metal-rich low metallicity (H+O) Helium 1:0 10 ¹5 0 1:0 10 ¹5 Carbon 0 0 2:0 10 ¹6 Nitrogen 0 0 1:6 10 ¹7 Oxygen 0 9:6 10 ¹7 9:6 10 ¹7 Silicon 0 0 3:0 10 ¹7 Iron 0 0 1:0 10 ¹5 Nickel 0 0 1:0 10 ¹6 non-lte models are used. To separately assess the several possibilities, we have calculated a series of models free of all the opacity sources. These include pure-h LTE, pure-h non-lte, H+He non- LTE and models including only a trace of oxygen, which formed the basis of a low metallicity non-lte grid used to determine T eff and log g in our earlier studies of G191¹B2B and REJ0457¹281 (Lanz et al. 1996; Barstow et al. 1997c). The H+He models have a homogeneous structure with an He/H abundance of 10 ¹5, which matches that included in the full heavy element grid. Table 1 summarizes the abundances included in the models use for this work. The heavy elements are also homogeneously mixed. For reference to our earlier work on the effective temperatures and surface gravities of these stars (see Holberg et al. 1993; Marsh et al. 1997a), we also make use of the homogeneous LTE H+He models utilized in those studies and computed by D. Koester in 1992 (Koester 1991). 4 DETERMINATION OF TEMPERATURE AND GRAVITY Balmer line spectra exist for all the stars in this hot DA white dwarf sample, and the technique for determining T eff and log g, by comparing the line profiles with the predictions of synthetic spectra, is well established (see Holberg, Wesemael & Basile 1986; Bergeron, Saffer & Liebert 1992, and many subsequent authors). In addition, two Lyman line spectra are also available (for G191¹B2B and REJ0457¹281) which can either be used as completely independent data sets, or be included in a combined analysis with the Balmer lines. We have described our Balmer line analysis technique in several earlier papers (e.g. Barstow et al. 1994b), but, as the results presented in this paper rely heavily on it, we repeat the details here. The same technique can also be applied to analysis of the Lyman lines, as we have already demonstrated for V471 Tau (Barstow et al. 1997b). The analysis is performed using the program xspec (Shafer et al. 1991), which adopts a x 2 minimization technique in order to determine the model spectrum which gives the best agreement with the data. All the lines included are fit simultaneously and an independent normalization constant was applied to each, ensuring that the result was independent of the local slope of the continuum and reducing the effect of any systematic errors in the flux calibration of the spectrum. As xspec interpolates the synthetic spectra linearly between points, we have considered the effect of the size of the T eff and log g steps, particularly as the T eff points do not constitute a regular, constant spacing in these models (see section 3). Examination of the best-fitting values of T eff and log g using pure H models identical to those included in our analysis, but having a regular 5000 K spacing, yields results differing by only a few hundred degrees K, within the formal statistical errors of the analysis. The optical data available to us come from two sources. The SAAO RPCS, used to record the southern hemisphere spectra (REJ0457¹281, REJ0623¹371, REJ2214¹492 and REJ2334¹ 471), is a photon-counting instrument. Consequently, the data errors can be determined simply from the Poisson statistics associated with the source and background counts in each spectral bin. In contrast, the northern spectra were recorded with a CCD. Here it is difficult to determine errors on individual points and we take the following approach. First, an initial fit to the data is performed without any errors included. From the scatter on the residuals between the best-fitting models, we estimate the average errors on the data points, which are included in a subsequent fit. In

526 M. A. Barstow, I. Hubeny and J. B. Holberg addition, for both data groups, we correct for any systematic deviation in the spectral slope between model and data, arising from second-order errors in the flux calibration. The ORFEUS detectors are also photon-counting, hence the data errors are dealt with in the same manner as on the SAAO RPCS. However, as these spectra are already flux calibrated, it is not necessary to apply any corrections to account for any systematic errors of the kind that arise when dealing with atmospheric extinction in optical data. Nevertheless, we must remember that the ORFEUS instrument calibration may contain systematic errors of which we are not aware. To make sensible estimates of the uncertainty in the fitted parameters, the value of the reduced x 2 should be less than 2. Errors on T eff and log g were determined by allowing the model parameters to vary until the dx 2 reached the value corresponding to the 1j level for 2 degrees of freedom (see Section 2.3). It should be noted that these only include statistical uncertainties and do not take into account any possible systematic effects related to the model spectra. 4.1 Balmer line analyses with non-lte and LTE models Tables 2 and 3 summarize the results of the Balmer line analyses for Table 2. Values of T eff and log g for all stars in the hot DA sample, determined from analysis of the Balmer lines using Koester LTE pure H, tlusty pure-h LTE and tlusty pure-h non-lte models. Star Koester pure-h LTE tlusty pure-h LTE tlusty pure-h non-lte T eff 1j(K) T eff 1j(K) T eff 1j(K) log g 1j log g 1j log g 1j Feige 24 62000ðþ1500= ¹ 1860Þ 68000 ðþ0 = ¹ 1790Þ 64000ðþ2000= ¹ 1250Þ 7:46ðþ0:11= ¹ 0:10Þ 7:35ðþ0:10= ¹ 0:12Þ 7:35ð0:12= ¹ 0:13Þ REJ0457¹281 57450ðþ2460= ¹ 1150Þ 62680ðþ2500= ¹ 1840Þ 58270ðþ1670= ¹ 1890Þ 7:92ðþ0:12= ¹ 0:10Þ 7:82ðþ0:12= ¹ 0:09Þ 7:78ðþ0:11= ¹ 0:08Þ G191¹B2B 58200ðþ1190= ¹ 1070Þ 63180ðþ1460= ¹ 1110Þ 59160ðþ1270= ¹ 1070Þ 7:58ðþ0:07= ¹ 0:08Þ 7:44ðþ0:06= ¹ 0:08Þ 7:36ðþ0:08= ¹ 0:07Þ REJ0623¹371 63190ðþ2270= ¹ 2080Þ 68000 ðþ0 = ¹ 1360Þ 66880ðþ1120 = ¹ 2580Þ 7:29ðþ0:11= ¹ 0:13Þ 7:12ðþ0:13= ¹ 0:11Þ 7:00 ðþ0:11= ¹ 0:00 Þ PG1123+189 57400ðþ1300= ¹ 1150Þ 62770ðþ1260= ¹ 1230Þ 58450ðþ1120= ¹ 1050Þ 7:71ðþ0:08= ¹ 0:07Þ 7:56ðþ0:06= ¹ 0:10Þ 7:53ðþ0:03= ¹ 0:10Þ PG1234+482 57860ðþ1110= ¹ 1200Þ 61990ðþ1270= ¹ 1170Þ 58930ðþ970= ¹ 1220Þ 7:58ðþ0:07= ¹ 0:07Þ 7:42ðþ0:07= ¹ 0:07Þ 7:41ðþ0:07= ¹ 0:07Þ REJ2214¹492 69500ðþ2520= ¹ 2540Þ 68000 ðþ0 = ¹ 420Þ 68000 ðþ0 = ¹ 1060Þ 7:44ðþ0:20= ¹ 0:13Þ 7:40ðþ0:18= ¹ 0:14Þ 7:28ðþ0:11= ¹ 0:12Þ GD246 58200ðþ1160= ¹ 1120Þ 64420ðþ1150= ¹ 1700Þ 59280ðþ980= ¹ 1340Þ 7:94ðþ0:08= ¹ 0:07Þ 7:75ðþ0:07= ¹ 0:06Þ 7:73ðþ0:07= ¹ 0:06Þ REJ2334¹471 60250ðþ1660= ¹ 2160Þ 66020ðþ1880 = ¹ 2070Þ 60900ðþ2400= ¹ 1340Þ 7:70ðþ0:10= ¹ 0:11Þ 7:57ðþ0:10= ¹ 0:10Þ 7:54ðþ0:10= ¹ 0:14Þ * Value or error bar at the limit of the model grid Table 3. Values of T eff and log g for all stars in the hot DA sample, determined from analysis of the Balmer lines using tlusty non-lte H+He, weakly blanketed non-lte and fully blanketed heavy element-rich non-lte models. Star tlusty H+He non-lte tlusty low metallicity non-lte tlusty high metallicity non-lte T eff 1j(K) T eff 1j(K) T eff 1j(K) log g 1j log g 1j log g 1j Feige 24 64310ðþ1710= ¹ 1440Þ 64140ðþ1690= ¹ 1620Þ 56370ðþ1530= ¹ 760Þ 7:34ð0:12= ¹ 0:12Þ 7:35ðþ0:12= ¹ 0:13Þ 7:36ð0:11= ¹ 0:12Þ REJ0457¹281 58750ðþ1700= ¹ 1590Þ 57850ðþ2150= ¹ 1400Þ 53640ðþ630= ¹ 690Þ 7:79ðþ0:09= ¹ 0:10Þ 7:80ðþ0:10= ¹ 0:09Þ 7:80ðþ0:10= ¹ 0:11Þ G191¹B2B 59190ðþ1410= ¹ 820Þ 59060ðþ1130= ¹ 1090Þ 53840ðþ400= ¹ 160Þ 7:36ðþ0:07= ¹ 0:07Þ 7:36ðþ0:08= ¹ 0:07Þ 7:38ðþ0:07= ¹ 0:08Þ REJ0623¹371 66740ðþ1260 = ¹ 2370Þ 66570ðþ1430 = ¹ 2400Þ 59740ðþ1690= ¹ 1700Þ 7:00 ðþ0:11= ¹ 0:00 Þ 7:01ðþ0:11= ¹ 0:01 Þ 7:00 ðþ0:11= ¹ 0:00 Þ PG1123+189 58800ðþ1010= ¹ 1070Þ 58210ðþ1280= ¹ 980Þ 52740ðþ150= ¹ 180Þ 7:52ðþ0:07= ¹ 0:10Þ 7:53ðþ0:07= ¹ 0:09Þ 7:52ðþ0:07= ¹ 0:10Þ PG1234+482 59030ðþ1090= ¹ 1020Þ 58640ðþ1040= ¹ 1100Þ 53860ðþ200= ¹ 170Þ 7:41ðþ0:07= ¹ 0:07Þ 7:42ðþ0:07= ¹ 0:07Þ 7:42ðþ0:08= ¹ 0:07Þ REJ2214¹492 68000 ðþ0 = ¹ 1030Þ 68000 ðþ0 = ¹ 1020Þ 62050ðþ2290= ¹ 2150Þ 7:28ðþ0:11= ¹ 0:13Þ 7:28ðþ0:12= ¹ 0:10Þ 7:23ðþ0:12= ¹ 0:11Þ GD246 59300ðþ1350= ¹ 830Þ 59070ðþ940= ¹ 1330Þ 53740ðþ220= ¹ 310Þ 7:73ðþ0:06= ¹ 0:07Þ 7:74ðþ0:06= ¹ 0:07Þ 7:74ðþ0:06= ¹ 0:06Þ REJ2334¹471 60930ðþ2490= ¹ 1200Þ 61160ðþ1840= ¹ 1860Þ 54630ðþ860= ¹ 760Þ 7:57ðþ0:09= ¹ 0:14Þ 7:54ðþ0:10= ¹ 0:13Þ 7:58ðþ0:10= ¹ 0:10Þ * Value or error bar at the limit of the model grid

The hot DA white dwarf temperature scale 527 Figure 4. Values of T eff determined from Balmer line analyses using high metallicity non-lte models versus the results from the pure-h LTE studies. The solid line is the locus of equal temperature points. all the stars in the sample for each of the model types Koester pure-h LTE, TLUSTY pure-h LTE, TLUSTY pure-h non-lte, TLUSTY H+He non-lte, low metallicity non-lte and high metallicity non- LTE with all heavy elements included. Two general features are immediately apparent when comparing the models calculated using the tlusty code. First, the effective temperature obtained with the heavy-element-rich non-lte models is systematically lower than for the pure-h LTE models, the standard grid normally used for Balmer line analyses. This is illustrated in Fig. 4. The data points lie well below the line corresponding to equal temperature values, indicating temperature differences of 8000 10 000 K between pure-h LTE and heavy element non-lte analyses, corresponding to a change of 15 per cent in the perceived temperature. Interestingly, the uncertainties in T eff appear to increase with increasing T eff. This is a combination of two effects. First, in the tlusty non- LTE metal-rich models, the predicted Balmer line profiles vary more rapidly over a smaller temperature interval at the low temperature end of the grid than at the higher temperatures. Secondly, the hotter stars have poorer signal-to-noise ratio spectra than the cooler objects, exaggerating the above effect. Although significant temperature differences are seen in Fig. 4 there is little, if any, apparent effect on the gravity, as can be seen in Fig. 5, in which the data points lie along the locus of equal gravity. It is clear that the model calculations which include all the significant heavy element opacity sources and detailed treatment of the line-blanketing yield a lower effective temperature than the conventionally adopted pure-h LTE models in a Balmer line analysis. However, the underlying reason for this effect is less Figure 5. Values of log g determined from Balmer line analyses using high metallicity non-lte models versus the results from the pure-h LTE studies. The solid line is the locus of equal gravity points. obvious. It is necessary to consider whether it arises simply from dropping the assumption of LTE to calculate a fully non-lte model, or from the inclusion of a modest He abundance, at a level known to have a significant effect in LTE models (Bergeron et al. 1994), rather than the heavy elements. Examination of the pure-h non-lte temperature measurements does show a difference in comparison with the LTE results which is an approximately constant 4000 K across the temperature range (Fig. 6). However, including a modest abundance of helium (He/H ¼ 10 ¹5 ) in the model appears to make no difference to the values of T eff inferred from the Balmer line analysis (Fig. 7), in contrast to the effect seen in LTE models which yields a temperature shift of 4000 K at 60 000 K (see Bergeron et al. 1994). Similarly, the inclusion of a low abundance of oxygen does not alter the derived temperature significantly (Fig. 8). In summary, the inclusion of significant quantities of heavy elements does affect the determination of effective temperature for a given star. In comparison with pure-h LTE models, almost half the difference is attributable to computation of the models in non-lte, while the rest can be accounted for by the heavy elements themselves. Since neither He nor O have any effect on their own, the effect is most probably a result of the presence of Fe and Ni in the calculations, which are known to have the greatest influence on the model structure (e.g. Hubeny & Lanz 1995; Barstow et al. 1996). We note here that the inclusion of heavy elements in LTE models may also affect the effective temperature determination in a manner similar to that in the non-lte models. Since we have not computed a heavy-element-rich LTE grid, we are not able to quantify this, but it is interesting to note that Vennes et al.

528 M. A. Barstow, I. Hubeny and J. B. Holberg Figure 6. Values of T eff determined from Balmer line analyses using pure-h non-lte models versus the results from the pure-h LTE studies. The solid line is the locus of equal temperature points. Figure 7. Values of T eff determined from Balmer line analyses using H+He non-lte models versus the results from the pure-h non-lte studies. The solid line is the locus of equal temperature points. (1996b) report a lowering of T eff, determined from the Lyman lines, when heavy elements are included in their LTE models. It may be that LTE/non-LTE differences are smaller when heavy elements are included. We have not considered this issue because of the existing evidence that non-lte calculations are needed to produce models which are self-consistent across all wavebands (see Lanz et al. 1996 and references therein). The most important comparison to make is between the pure-h LTE results, as the existing standard for determining the DA temperature scale, and the heavy-elementrich non-lte analyses. 4.2 Lyman line studies with high metallicity non-lte models The Lyman line data available for G191¹B2B and REJ0457¹281 provide an important comparison with the results of T eff and log g determinations from the Balmer lines and a potential test of the reliability of this work. Any particular model can only be claimed to be a good representation of a white dwarf atmosphere if consistent results are achieved across all wavebands. Accordingly, the values obtained using the Lyman lines should match, within error, the Balmer line results. Table 4 lists the results of the T eff and log g determinations performed using the high metallicity non-lte models. The values obtained from the Balmer lines, using the same models, already listed in Tables 2 and 3, are also included here for ease of comparison. The x 2 and x 2 red are given as an indication of the relative quality of the match between model and data. There are clear differences between the results obtained for G191¹B2B and REJ0457¹281. While the Lyman and Balmer line temperatures of G191¹B2B are similar, within a 3j confidence interval, there is a large difference between the REJ0457¹281 determinations of T eff, well outside the uncertainties in the analysis. A similar discrepancy was reported in Vennes et al. (1996b) LTE analysis of the ORFEUS data, both with and without the inclusion of heavy elements. For a pure-h model they found a Lyman line effective temperature 9000 K higher than the Balmer result (60 700 K). When heavy elements were added the Lyman line temperature was 5000 K below the Balmer measurement. Differences in surface gravity are also obtained for REJ0457¹281, but not G191¹B2B. It is helpful to evaluate the possible significance of the differences in REJ0457¹281 by comparing the quality of the fit in each case, using the F test. The F test calculates the significance of differences in the values of x 2 determined from separate fits as a means of deciding whether or not one fit might be better than another. The F parameter is simply the ratio of the two values of x 2 red and, its significance, depending on the number of degrees of freedom (the ratio of x 2 =x 2 red), can be determined from standard mathematical tables. For example, comparing the Lyman only and Balmer only fits, which have 693 and 385 degrees of freedom, respectively, the value of F is 1.018. This corresponds to a confidence level of 63 per cent, which is lower than the 1j (68 per cent) or 90 per cent confidence levels conventionally invoked to indicate that the results are significantly different. This indicates that neither the Lyman nor Balmer fits are significantly better than the other. Hence, neither result should be given greater weighting.

The hot DA white dwarf temperature scale 529 4.3 Joint Balmer and Lyman line analyses with high metallicity non-lte models In principle, a more accurate determination of T eff and log g could be achieved by modelling the Balmer and Lyman lines simultaneously. Comparison of these results with those from the individual line series might also shed light on the significance of the differences noted above for REJ0457¹281. The procedure is straightforward, dealing with all eight lines (Lb,Lg,Ld,Le,Hb,Hg,Hd,He) in the manner already described for four, and the results are included in Table 4. Since the separate Balmer and Lyman results are very close, it is no surprise that the combined analysis for Figure 8. Values of T eff determined from Balmer line analyses using H+O non-lte models versus the results from the pure-h non-lte studies. The solid line is the locus of equal temperature points. G191¹B2B should yield a consistent result. The value of T eff obtained for REJ0457¹281 lies in between the Balmer and Lyman line determinations, as might be expected. However, it is surprising that the combined study gives a lower surface gravity than does either treatment of the individual line series. Application of the F test, to compare the joint fits with those for each of the separate line series, provides no indication that one is significantly better than another. 5 DISCUSSION 5.1 The effect of heavy elements on the synthetic spectra When determined from Balmer and/or Lyman lines, T eff and log g depend in a complex way on their width, shape and strength. Unique values of each cannot be determined from a single line and observations of several lines are needed to resolve the ambiguity. It is certainly difficult, if not impossible, to identify the detailed behaviour of the profiles empirically from the observations of real stars, apart from their broadening with high gravity and weakening at high temperature. The result of this is the reliance on carrying out any analysis with the aid of synthetic spectra. The analyses described above clearly demonstrate that the temperature and gravity obtained for any individual star is sensitive to several possible systematic effects within the models, the use of non-lte calculations and inclusion of heavy elements in particular. It is important, and interesting, to establish just what features of the synthetic spectra determine the outcome of these studies and what effect the progression from LTE models, through non-lte, H+He non-lte to those with heavy elements has on the Balmer line profiles. Fig. 9 compares synthetic spectra calculated for pure-h LTE, pure-h non-lte, H+He non-lte and metal-rich non-lte models at a single temperature and gravity (54 000 K and log g ¼ 7:5) and with a bin size of 1Å, oversampling the resolution of the optical data by a factor of 3 8. At first glance, the differences between spectra are clearly rather subtle, since only two can be clearly distinguished. In fact, the lower curve in Fig. 9 is the overlapping combination of the pure-h LTE, pure-h non-lte and H+He non-lte models, and only very close inspection reveals that three individual synthetic spectra are present. The upper curve is the metal-rich spectrum which has an Eddington flux approximately 10 12 per cent greater than the others. Indeed, this model is nearly identical to a 60 000 K spectrum without heavy elements (pure-h non-lte in this example) which is superimposed on the metal-rich curve in Fig. 9. This flux enhancement over those models without metals is a result of the attenuation of the EUV flux at short wavelengths, which must then Table 4. Values of T eff and log g for REJ0457¹281 and G191¹B2B determined from analysis of the Lyman lines, Balmer lines together with the Lyman and Balmer lines jointly. All these results use the fully blanketed heavy-element-rich non-lte models described in the text. Star Parameter Lyman only Balmer only Lyman+Balmer REJ0457¹281 x 2 1136.2 612.5 1807.6 x 2 red 1.64 1.59 1.67 T eff 1j(K) 61150ðþ470= ¹ 650Þ 53640ðþ630= ¹ 690Þ 58670ðþ430= ¹ 210Þ log g 1j 7:53ðþ0:07= ¹ 0:04Þ 7:80ðþ0:10= ¹ 0:11Þ 7:45ðþ0:01= ¹ 0:02Þ G191¹B2B x 2 1078.6 263.8 1353.4 x 2 red 1.51 0.98 1.37 T eff 1j(K) 52920ðþ350= ¹ 350Þ 53840ðþ400= ¹ 160Þ 53720ðþ150= ¹ 160Þ log g 1j 7:36ðþ0:03= ¹ 0:03Þ 7:38ðþ0:07= ¹ 0:08Þ 7:39ðþ0:03= ¹ 0:02Þ