Hot White Dwarfs

M. A. Barstow1 and K. Werner2

1Department of Physics and Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK2Kepler Center for Astro and Particle Physics, University of Tübingen, Sand 1, 72076 Tübingen, Germany

INTRODUCTION

Theoretical and observational study of stellar behaviour has provided white dwarfs with their evolutionary context as one end point of the life-cycle of stars. In general terms, all stars with masses below about eight times that of the Sun will pass through one or more red giant phases before losing most of their original mass to form a planetary nebula. These earlier phases of evolution, dealing with the white dwarf progenitors have been discussed extensively by Herwig1. This paper discusses the phases of evolution immediately following, when the white dwarf first emerges from these as a hot, but more or less dead object. Quite when all nuclear burning ceases is still the subject of some debate, but it is certainly extinguished early in the lifetime of a white dwarf, unless the star is able to accrete material from a companion in sufficient quantities to restart the fusion process. Here we mostly only consider isolated objects, as binary systems containing white dwarf components are dealt with in detail by other articles in this volume.

In the absence of any internal source of energy, the temperature of a white dwarf, after its birth, is determined by how rapidly stored heat is radiated into space. Over time, white dwarfs will cool to invisibility, a process taking billions of years. Hence, white dwarfs are among the oldest objects in the galaxy. Since, the galaxy is younger than the cooling timescales; the lowest temperature (oldest) white dwarfs yield a lower limit to its age (Garcia-Berro & Oswalt2). Although modified by processes other than thermal radiation, such as neutrino cooling and phase changes in the internal structure, white dwarf cooling curves follow a quasi-exponential function. Hence, the temperature changes most rapidly when the star is young and hot. Consequently, we would also expect to see the most rapid evolution during this time. As a consequence, study of hot white dwarfs is of great importance in revealing the underlying physical processes.

So, just what is a “hot white dwarf”? In this chapter we will deal with white dwarfs from their formation at temperatures ~200,000K down to ~10,000K, encompassing the first ~1 billion years of evolution (depending on the stellar mass). In this temperature range the main observational signature of a white dwarf is largely determined by the principle photospheric component, either H or He (usually). At lower temperatures, below ~10,000K, even if present, the signatures of H and He become difficult and eventually impossible to detect. The physics of the atmospheres of these cooler objects is quite different, and understanding their compositions and physical structure is even more complex than for their hotter counterparts3.

The small radius and consequent low luminosity of white dwarfs has made them difficult to observe in detail. Hence, this original framework of their properties and astrophysical importance owed much more to theory than observation. Important physical characteristics such as temperature and surface gravity could, at first, only be based on broadband visual colours. During the past 25 years, there has been a revolution in astronomical observation techniques. The advent of electronic detectors and improvements in sensitivity of ground-based telescopes has been matched by the opening of ultraviolet, extreme ultraviolet and X-ray wave bands by satellite-borne observatories, which are of particular importance for study of hot white dwarfs.

A direct result of this has been a remarkable transformation in our observational knowledge concerning white dwarfs and major advances in our understanding of their physical characteristics and evolution. This review concentrates on some of the most important recent work contributing to studies of the white dwarf mass-radius relation and white dwarf composition from ultraviolet observations. Particular reference will be paid to measurements of temperature, surface gravity and composition, using spectroscopic data from a variety of wavelength ranges. The importance of Teff and log g, determined for an individual white dwarf, in

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estimating of mass and radius will be described, and the dependence of such determinations on theoretical calculations of the mass-radius relation discussed.

1 CLASSIFICATION OF HOT WHITE DWARFS

The basis for understanding the nature of most stars is analysis of their optical spectra and classification according to the characteristics revealed. A number of physical processes can alter the atmospheric composition of a white dwarf as it cools. As noted by Schatzman4, the strong gravitational field (log g ~ 8 at the surface) causes rapid downward diffusion of elements heavier than the principal H or He component. Hence, Schatzman predicted that white dwarf atmospheres should be extremely pure. Consequently, the spectra should be devoid of most elements, showing signatures of only hydrogen and, possibly, helium. White dwarfs are thus divided into two main groups according to whether or not their spectra are dominated by one or other of these elements. The hydrogen-rich stars are given the classification DA, while the helium-rich white dwarfs are designated DO if He II features are present (hotter than about 45000K) and DB if only He I lines are visible. Small numbers of hybrid stars exist, with both hydrogen and helium present. In these cases, two classification letters are used, with the first indicating the dominant species. For example, DAO white dwarfs are mostly hydrogen but exhibit weak He II features. There is also the important group of the PG1159 type [WC] central stars, exhibiting strong C IV and He II lines in the optical and which are believed to the progenitors of the DO white dwarfs.

The above classification scheme applies only to white dwarfs with temperatures above ~10000K, the hot white dwarfs with we are concerned in this chapter, when the H and He energy levels are sufficiently populated above the ground state to produce detectable features. However, at lower temperatures, although H and/or He may be present these elements are no longer directly detectable. Figure 1 summarises the current thoughts regarding the relationships between the hot white dwarf groups along with the principal mechanisms that provide evolutionary routes between them.

However, the gravitational force can be countered by that of radiation pressure which acts outward to support heavy elements in the atmosphere, a process termed “radiative levitation”. Another mechanism that can mix elements that have settled out in the stellar atmosphere is convection. If the convective zone reaches down to the base of the atmosphere then heavy elements can be dredged back up into the outer atmosphere. A further complication is that material can also be accreted from the interstellar medium (ISM).

The emergence from the Asymptotic Giant Branch (AGB) of two main white dwarfs channels, whose compositions are dominated by H or He, is beginning to be understood in relation to mass-loss processes and the number of times a star ascends the giant branch. However a demonstrable temperature gap in the He-rich cooling sequence, between the DO and DB groups, is problematic. Until recently, the temperature range from ~45,000K down to 30,000K was completely devoid of He-rich objects. However, a large increase, from the Sloan Digital Sky Survey, in the overall numbers of white dwarfs known has provided a few such stars in this temperature range. Nevertheless, the reason for the dearth of objects remains to be understood.

2 SPECTROSCOPIC MEASUREMENTS OF EFFECTIVE TEMPERATURE AND SURFACE GRAVITY

2.1 Balmer lines of DA white dwarfs

To solve the problems of white dwarf evolution it is necessary to measure a number of basic parameters for a significant fraction of the white dwarf population. To set a star in its evolutionary context we need to know its effective temperature and surface gravity. In early studies, these were estimated from broadband photometric observations, coupled with simple assumptions about the relation between temperature and spectral shape (e.g. the assumption of a blackbody). In modern astronomy we now have access to high signal-to-noise spectra and sophisticated stellar atmosphere models and associated synthetic spectra for comparison with the data.

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Figure 1. Schematic description of the production of H-rich and He-rich branches of white dwarf evolution

For the largest group of white dwarfs, the DA stars, there is a very powerful analysis technique based on the hydrogen Balmer absorption lines. The strength and shape of an individual line depends on the temperature and density structure of the atmosphere in which it is formed, which in turn are determined by the temperature and gravity of the star. Specifically, line strengths depend on the populations of atoms at the energy levels involved in a particular transition, which are temperature sensitive. An “indefiniteness” in the energy levels for individual atoms leads to line broadening. This arises from two sources. First, a perturbation of the radiative wave train through collisions with other particles in the gas causes pressure broadening, which depends mainly on gravity. Secondly, temperature dependent gas motions lead to Doppler broadening of the lines. Figure 2 shows a selection of optical spectra of hot DA white dwarfs ordered by decreasing temperature. By comparing the observed line profiles with predicted ones simultaneously for at least four lines it is possible to obtain a unique solution for Teff and log g for any DA white dwarf. This procedure, illustrated in Figure 3 for the hot DA white dwarf PG1342+444, allowed the first systematic spectroscopic study of a large sample of stars5. An important feature of this analysis technique is that it is completely objective. Rather than making a purely visual comparison and selection of the best-fit synthetic spectrum, the best match is determined by a goodness of fit statistic such as the χ 2 test. In addition, this allows formal determination of the statistical errors by examining the variation of χ 2 with Teff and log g.

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Figure 2. Sample of Balmer line spectra for a selection of hot DAs in order of decreasing temperature from the top.

The study of Bergeron et al.5 was based on the use of pure H model atmospheres computed under the

assumption of Local Thermodynamic Equilibrium (LTE), that the ion and level populations are entirely specified by the Saha and Boltzmann equations. Further work has involved the use of better non-LTE models, where the ion and level populations are determined by statistical equilibrium calculations, which take into account the radiation field besides the collisional interactions between particles. In addition, the assumed composition has an influence on the calculated Balmer line profiles. Barstow et al.6 assessed how this affects the temperature and gravity determinations, noting that the inclusion of significant quantities of metals lowers the inferred temperature, particularly for the hottest objects.

2.2 Lyman line studies of DA white dwarfs

In the samples studied using the Balmer line technique, the majority of the stars are isolated objects. If any are in binaries, they are either wide, resolved systems or the companions are late-type dwarfs, where the

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white dwarf can be spectroscopically isolated. However, when a white dwarf binary companion is spatially unresolved and of type K or earlier, the white dwarf visible signature is hidden in the glare of the more luminous object (e.g. Figure 4) and, therefore, the Balmer lines cannot be used for determination of Teff or log g. If the companion is not earlier than type A, the white dwarf spectrum dominates in the far-UV (see Figure 4) and the Lyman lines are accessible, allowing them to be used for determination of Teff and log g. A well-known illustration of this is the DA+K star binary V471 Tauri, which has been extensively studied and where the Lyman series spectrum obtained by the ORFEUS mission was used to obtain the first accurate measurements of Teff and log g7,8.

Figure 3. Example of the technique of comparing the Balmer lines from the spectrum (error bars) of the hot DA white dwarf PG1342+444, with the synthetic line profiles from stellar atmosphere calculations (solid curve).

While the Lyman α line is encompassed by the spectral coverage of IUE and HST data, a single line cannot provide an unambiguous measurement of Teff and log g. Access to the full Lyman series lines has been provided by the short duration missions of the Hopkins Ultraviolet Telescope (HUT) and Orbiting and Retrievable Far and Extreme Ultraviolet Spectrometers (ORFEUS). They provided observations of a number of white dwarfs at wavelengths down to the Lyman limit, yielding a first opportunity to compare Balmer and Lyman line measurements systematically. Barstow et al.9 carried out an evaluation of all the available archival data for these missions, including some early spectra from the Far Ultraviolet Spectroscopic Explorer (FUSE). Comparing the results with those from the standard Balmer line analysis, they found general overall good agreement between the two methods. However, significant differences were noted for a number of stars. These differences were not always consistent in that sometimes the Balmer temperature exceeded that derived from the Lyman lines and in other instances was lower, which would not be expected if the problems arose from the limitations of the stellar atmosphere calculations and the treatment of the Lyman and Balmer line broadening. The most likely conclusion was that systematic effects arising from the observations, the data reduction and the analysis were responsible for the discrepancies.

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More recently it has been possible to re-examine the issue of the Lyman line analysis with a greatly

expanded far-UV data set available from the FUSE mission. These spectra cover the complete Lyman line series from β to the series limit, excluding Lyman α, and cover a larger number of stars, particularly at values of Teff above 50,000K (a range that was sparsely sampled by Barstow et al.10). In addition, FUSE has observed some of the targets many times, for purposes of monitoring the instrument calibration, which provides a powerful tool for examining systematic effects in the instrument and analysis procedure. Figure 5 shows a sample of typical FUSE spectra, ordered by decreasing temperature from Teff~70,000K down to Teff~20,000K, and Figure 6 the results of the Lyman line analysis for GD659.

Figure 4. UV and optical spectrum of the DA white dwarf plus A8-F2 main sequence star binary system BD+27 01888 (error bars). A synthetic DA white dwarf model spectrum is shown for comparison (smooth curve).

With the availability of the FUSE data archive and observations from Guest Observer programmes, Barstow et al.11 examined the use of the Lyman series to determine the values of Teff and log g for a sample of 16 hot white dwarfs. Having a source of data produced by a single instrument and processed with a uniform pipeline, made it possible to eliminate some of the possible systematic differences between observations of the same or different stars associated with different instruments. However, it is clear from this study that systematic error in the overall observation, data reduction and analysis procedures dominate the measurement uncertainties. Using the scatter in values derived from multiple observations of some stars it was possible to determine more realistic errors in the measurements than obtained just from the statistical error values. The new results partially reproduce the earlier study of a more limited stellar sample, showing that Balmer and Lyman line determined temperatures are in good agreement up to ~50,000K. However, above this value there is an increasing systematic difference between the Lyman and Balmer line result, the former yielding the higher temperature (Figure 7). Furthermore, there are several outliers that do not follow the general trend. At the moment, there is no clear explanation of this effect but it is most likely associated with deficiencies in the detailed physics incorporated into the stellar model atmosphere calculations. Even so, the data do demonstrate that, for temperatures below 50,000K, the Lyman lines give reliable results. Furthermore, for the hotter stars, a useful empirical calibration of the relationship between the Lyman and Balmer measurements has been obtained, that can be applied to other FUSE observations.

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Figure 5. Sample FUSE spectra for all the DA white dwarfs in order of decreasing Teff (as measured with the Balmer lines) from the top of the figure.

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Figure 6. Lyman β-ε lines from a FUSE spectrum of the hot DA white dwarf GD659 (grey error bars), showing the comparison with the best-fit synthetic model spectrum (black curve). Data gaps arise from removal of the Lyman geocoronal emission and interstellar absorption. Other strong interstellar lines have also been removed for the analysis.

Figure 7. Scatter plot of the simple mean values of Teff measured using the ground-based Balmer and FUSE Lyman lines. The error bars are calculated from the variance of the values in multiple observations or are the statistical 1σ error for single observations. The solid line corresponds to equal Balmer and Lyman line temperatures.

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2.3 Temperature and gravity determination of hot hydrogen deficient white dwarfs

Reliable measurements of the high effective temperature and the surface gravity of DO white dwarfs and PG1159 stars are based on elaborated non-LTE model atmospheres. By definition, cool DO stars (Teff from ~40,000 K to ~80,000 K) display He I lines which together with He II lines can be used to fix the effective temperature. Detailed line profile fitting at the same time gives the surface gravity. Hot DO stars as well as PG1159 do not display He I lines, making the parameter determination significantly more difficult, because temperature and gravity derived from He II lines alone are uncertain to a large extent. This uncertainty can only be reduced when lines from another element, preferably from two ionization stages, are detectable. In particular the PG1159 stars display C IV and sometimes O V and O VI as well as Ne VII and Ne VIII lines in their optical spectra. Ultraviolet spectroscopy reveals many more species and greatly helps to confine the photospheric parameters.

2.3.1 DO white dwarfs

The first systematic non-LTE analysis of a large sample of DO stars was presented by Dreizler & Werner 12. The Sloan Digital Sky Survey (SDSS) has discovered a number of new DOs so that at present the total number of these stars with effective temperature and surface gravity measured amounts to 40 13. Temperatures cover a wide range, spanning from Teff=40,000 K to 200,000 K, and gravities range between log g=7 and 8.4. Figure 8 displays optical spectra of several DOs, demonstrating the relative strengths of the He I and He II lines as a function of Teff.

Figure 8. Normalised optical spectra (grey lines) of DO white dwarfs along with model atmosphere fits (black lines). The top two objects exhibit ultrahigh-ionisation features. Teff and log g of the models are given as labels on the right hand portion of the spectra. The spectra of the hottest stars are dominated by He II lines while increasing He I line strengths are observed with decreasing temperature. (From Hügelmeyer et al.13).

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Hydrogen is difficult to detect in DOs because the Balmer lines become rather weak with increasing

effective temperature and because of the dominant He II line blends. In only two objects trace hydrogen was definitely detected and its abundance determined (PG0038+199, H/He=0.2215; and HD149499B, H/He=0.212), although a closer inspection with higher spectral resolution and S/N might reveal that many more DOs are in fact DOA white dwarfs. Upper H abundance limits measured for most objects are of the order H/He=0.1 (number ratios). Some DOs display C IV lines in the optical spectrum, reminiscent of the same features seen in PG1159 stars, however, with much reduced strength. Consequently, the carbon abundance is much lower than in the PG1159 stars, namely of the order 0.1-1%. Carbon and other species present in even lower abundance can be seen in UV spectra (see below). A typical representative of a hot DO with 1% carbon is RE0503-289, which has remarkable UV and EUV spectral properties that will be discussed below.

KPD0005+5106, the hottest DO white dwarf, is a particularly interesting object. A Teff=120,000 K was derived from the He II lines15. A recent discovery, however, revealed that the temperature was severely underestimated, emphasizing the potential uncertainty of the Teff determination for hot DOs from He II lines alone. The identification of Ne VIII lines in the FUSE spectrum and in optical spectra (Figure 9) means that the temperature of KPD0005+5106 must be of the order 200,000 K16. It remains to be investigated whether this can explain the mysterious observed hard X-ray emission as of photospheric origin17. The optical Ne VIII lines appear in emission and were previously thought to stem from superionized (i.e., non-thermally excited) O VIII. This puts an end to speculations about how superionized lines could be produced in KPD0005+5106 (and some PG1159 stars, which show the same emission lines; see RX J2117+3412 in Figure 8).

Figure 9. Identification of Ne VIII lines in the hottest known DO white dwarf, KPD0005+5106. Overplotted are computed profiles from models with Teff and log g as depicted. Left panel: Several absorption lines of the n=5→6 transition are detected in the FUSE spectrum. Middle and right panels: Optical spectral regions with emissions lines from the Ne VIII n=5→8 and n=9→10 transitions.

This brings us to a still mysterious phenomenon that is observed in a large number of hot DOs, namely the occurrence of extremely high (super-) ionized absorption lines in the optical spectra (C V-VI, N VI-VII, O VII-VIII, and Ne IX-X18,19; see Figure 10). From the blue-shifted asymmetric line profiles it was concluded that they stem from an optically thick, extremely fast (~10,000 km/s) stellar wind. On the other hand, the He II lines are symmetric and, strangely enough, they are extraordinarily strong and cannot be fitted by any model atmosphere. This obviates a temperature and gravity determination. The lack of He I lines gives only a lower limit to Teff. Neither HST8, nor ORFEUS20, nor FUSE spectroscopy21 gave any conclusive hint as to the origin of these observed characteristics. It must be emphasized that almost every other hot DO exhibits this unexplained phenomenon and not just a few “rare freaks”. Interestingly, it has also been discovered in a hot DA and a PG1159 star, too22,13.

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Figure 10. Normalised optical spectrum of the prototype DO star displaying ultrahigh ionization lines of CNO. Overplotted is a DO model with Teff=70,000 K and log g=7.5. The observed He II lines are unusually strong and cannot be fitted by any model. (From Werner et al.19).

2.3.2 PG1159 stars

The optical spectra of PG1159 stars are characterized by weak and broad absorption lines of He II and C IV, sometimes with central emission reversals. The hottest objects also display O VI and Ne VII/NeVIII lines. Three spectral subclasses have been introduced that allow a coarse characterization of each star. According to the appearance of particular line features, the subtypes “A” (absorption lines, e.g., PG1424+535 in Figure 11), “E” (emission lines, e.g., PG1159-035), and “lgE” (low gravity with emission lines, e.g., RX J2117+3412) were defined by Werner23.

Quantitative spectral analyses became feasible with the first construction of line-blanketed non-LTE model atmospheres that accounted for peculiar chemical compositions24. At that time, only a handful of PG1159 stars had been identified. Today, 40 such stars are known. Most of them were found by systematic spectroscopic observations of the central stars of old, evolved planetary nebulae25, as well as follow-up spectroscopy of faint blue stars from various optical sky surveys (the Palomar-Green survey, Montreal-Cambridge-Tololo Survey, Hamburg-Schmidt and Hamburg/ESO Surveys, and SDSS) and soft X-ray sources detected in the ROSAT All-Sky Survey.

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Figure 11. Normalised blue spectra of representative PG1159 stars compared to a hot hydrogen-rich central star (top, NGC7293, Teff=120,000 K, log g=6.3). This sample illustrates the variety of possible spectral appearance. RX J2117+3412 is an extremely hot low-gravity object (Teff=170,000 K, log g=6) displaying Ne VIII lines. The prototype PG1159-035 (Teff=140,000 K, log g=7) represents a hot, high gravity PG1159 star with central emission reversals in the He II and C IV lines in the 4600-4700Å absorption trough region. PG1424+535 (Teff=110,000 K, log g=7) represents a cool high-gravity PG1159 star with a pure absorption-line spectrum. PG1144+005 exhibits N V emission lines. HS2324+3944 is a hybrid-PG1159 star, representing the subgroup of rare PG1159 stars with residual hydrogen detectable. H1504+65 is a unique PG1159 star (Teff=200,000 K, log g=8), being H and He-deficient; the He II 4686Å emission is lacking.

In Figure 12 we show the location of all analysed PG1159 stars in the Teff-log g diagram. They span a wide range in temperature and gravity, and they represent stars in their hottest phase of post-AGB evolution. Some of them (those with logg<~6.5) are still helium-shell burners (located before the “knee” in their evolutionary track), while the majority have already entered the WD cooling sequence.

From optical spectra the He/C ratio can be derived. In addition, the hottest objects (Teff>~120,000 K) exhibit oxygen lines (O VI and, sometimes, very weak O V), so the O abundance in cooler stars cannot be determined unless UV spectra are available. Similarly, only the hottest objects display optical neon lines, and only UV spectra allow access to the neon abundance in the case of cooler objects. The He, C, and O abundances show strong variations from star to star; however, a word of caution is also appropriate here. The quality of the abundance determination is also very different from star to star. For some objects, only relatively poor optical spectra were analyzed, while others were scrutinized with great care using high signal-to-noise ratio, high-resolution optical and UV/far-UV (FUV) data. Nevertheless, we think that the abundance scatter is real. The prototype PG1159-035 displays what could be called a mean abundance pattern: He/C/O = 0.33/0.50/0.17 (all abundances in this paper discussed in the context of PG1159 stars are given in mass fractions). For instance, an extreme case with low C and O abundances is HS 1517+7403, which has He/C/O = 0.85/0.13/0.02. Taking all analyses into account, the range of mass fractions for these elements is approximately He = 0.30–0.85, C = 0.13–0.60, and O = 0.02–0.20 (excluding the peculiar object H1504+65; see below). There is a strong preference for a helium abundance in the range 0.3–0.5,

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independent of the stellar mass. Only a minority of stars has a higher He abundance, namely in the range 0.6–0.8. There is a tendency for high O abundances only to be found in objects with high C abundances.

Figure 12. Hot H-deficient post-AGB stars in the g-Teff plane. We identify PG1159 stars, early and late-type [WC] central stars, as well as two transition-type objects. Evolutionary tracks are labeled with masses in M. (From Werner & Herwig30).

As in the case of DO stars, the hydrogen detection and abundance determination poses a special problem, because all Balmer lines are blended with He II lines. In medium-resolution (~1Å) optical spectra, hydrogen is only detectable if its abundance is higher than about 0.1. With high-resolution spectra, which are difficult to obtain because of the faintness of most objects, this limit can be pushed down to about 0.02. For PG1159 stars within a PN, the situation is even more difficult, because of the presence of nebular Balmer emission lines. Four objects clearly show photospheric Balmer lines, and they are called hybrid PG1159 stars. The deduced H abundance is quite high, H=0.1726. It is worthwhile to note for the discussion of their evolution that nitrogen is seen in the optical spectra of some of these stars, but quantitative analyses are still lacking. The hybrid star NGC 7094 shows Ne and F enhancements, as do many PG1159 stars (see below). Therefore, one can conclude that aside from the presence of H, the elemental abundance pattern of the hybrid PG1159 stars seems to resemble that of many other PG1159 stars. However, not all the hybrids have been analyzed appropriately yet, although good UV and optical spectra are available.

Some remarks on the possible analysis errors are necessary. As pointed out, the observational data are of rather diverse quality, but in general the following estimates hold. The temperature determination is accurate to 10–15%. The surface gravity is uncertain at the 0.5 dex level. Elemental abundances should be accurate within a factor of two. The main problem arises from uncertainties in line-broadening theory, which directly affects the gravity determination and the abundance analysis of He, C, and O.

Since the first quantitative abundance analyses it was speculated that the PG1159 stars exhibit intershell matter on their surface, however, the C and O abundances were much higher than predicted from stellar evolution models. It was further speculated that the H-deficiency is caused by a late He-shell flash, suffered by the star during post-AGB evolution, laying bare the intershell layers. The re-ignition of He-shell burning brings the star back onto the AGB, giving rise to the designation “born-again” AGB star27. If this scenario is true, then the intershell abundances in the models have to be brought into agreement with observations. By introducing a more effective overshoot prescription for the He-shell flash convection during thermal pulses

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on the AGB, dredge-up of carbon and oxygen into the intershell can achieve this agreement 28. Another strong support for the born-again scenario was the detection of neon lines in optical spectra of some PG1159 stars29. The abundance analysis revealed Ne=0.02, which is in good agreement with the Ne intershell abundance in the improved stellar models.

If we do accept the hypothesis that PG1159 stars display former intershell matter on their surface, then we can in turn use these stars as a tool to investigate intershell abundances of other elements. Therefore these stars offer the unique possibility to directly see the outcome of nuclear reactions and mixing processes in the intershell of AGB stars. Usually the intershell is kept hidden below a thick H-rich stellar mantle and the only chance to obtain information about intershell processes is the occurrence of the third dredge-up. This indirect view onto intershell abundances makes an interpretation of the nuclear and mixing processes very difficult, because the abundances of the dredged-up elements may have been changed by additional burning and mixing processes in the H-envelope (e.g., hot-bottom burning). In addition, stars with an initial mass below 1.5 M do not experience a third dredge-up at all.

The course of events after the final He-shell flash is qualitatively different depending on the moment when the flash starts. We speak about a very late thermal pulse (VLTP) when it occurs in a WD, i.e., the star had turned around the ``knee´´ in the HR diagram and H-shell burning has already stopped. The star expands and develops a H-envelope convection zone that eventually reaches deep enough that H-burning sets in (a so-called hydrogen-ingestion flash). Hence H is destroyed and whatever H abundance remains, it will probably be shed off from the star during the “born-again” AGB phase. A late thermal pulse (LTP) denotes the occurrence of the final flash in a post-AGB star that is still burning hydrogen, i.e., it is on the horizontal part of the post-AGB track, before the “knee”. In contrast to the VLTP case, the bottom of the developing H-envelope convection zone does not reach deep enough layers to burn H. The H-envelope (having a mass of about 10-4 M) is mixed with a few times 10 -3 M intershell material, leading to a dilution of H down to about H=0.02, which is below the spectroscopic detection limit. If the final flash occurs immediately before the star departs from the AGB, then we talk about an AFTP (AGB final thermal pulse). In contrast to an ordinary AGB thermal pulse the H-envelope mass is particularly small. Like in the LTP case, H is just diluted with intershell material and not burned. The remaining H abundance is relatively high, well above the detection limit (H>~0.1).

The central stars of planetary nebulae of spectral type [WC] are believed to be immediate progenitors of PG1159 stars, representing the evolutionary phase between the early post-AGB and PG1159 stages. This is based on spectral analyses of [WC] stars which yield very similar abundance results; see Werner & Herwig30 for a detailed comparison.

3 WHITE DWARF MASSES AND RADII

Two of the most important physical parameters that can be measured for any star are the mass and radius. They determine the surface gravity by the relation g=GM/R2. Hence, if log g is measured the mass can be calculated provided the stellar radius is known. One outcome of Chandrasekhar’s original work on the structure of white dwarfs was the relationship between mass and radius, arising from the physical properties of degenerate matter. Further theoretical work yielded the Hamada-Salpeter zero-temperature mass-radius relation31. However, white dwarfs do not have zero temperature, indeed many are very hot, as illustrated in section 2. Hence, the Hamada-Salpeter relation is only a limiting case and the effects of finite temperature need to be taken into account. Evolutionary calculations showing that the radius of a white dwarf of given mass decreases as the star cools have been carried out by Wood 32,33, Blöcker34 Blöcker et al.35 and others. The most recent Blöcker models are full evolutionary calculations from the AGB, while those of Wood have a semi-arbitrary starting point for the hottest models.

3.1 DA white dwarfs

Even the earliest measurements of surface gravity gave a strong hint that the distribution of log g values and, therefore, of mass was very narrow. This supposition was subsequently confirmed by the work of Bergeron et al.5 and other authors. Until recently, the largest sample, based mainly on EUV-selected objects comprised ~ 100 objects36. However, the Sloan Digital Sky Survey (SDSS) has yielded samples of several thousand white dwarfs, dramatically improving the statistics and allowing the white dwarf mass distribution

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to be studied in considerably more detail than in the past. There have been several papers based on the SDSS as the sample has built up over time. One of the most recent yields a peak mass of 0.578 M and an estimated FWHM of ~0.016 M for the distribution37. However, with the enhanced sample size and improved statistics, it is now possible to see some of the complexity of the mass distribution, with a secondary low mass peak at 0.381 M and a significant tail towards high masses. It is interesting that the EUV-selected sample yielded a larger fraction of high-mass white dwarfs than the earlier studies based entirely on optical surveys. This preferential detection of high mass objects in the hot DA sample probably arises from a drop in neutrino cooling which leads to a slow down of the evolution of the highest mass white dwarfs.

The narrowness of the observed mass distribution is a direct consequence of the evolution of single stars, with masses from 1M up to ~8M. While the details of the relationship between the initial mass of the progenitor star and the final white dwarf mass are not particularly well understood, it is clear that the small dispersion in the white dwarf masses is related to a similarly small range of stellar core masses and the fact that most of the outer stellar envelope is expelled through several phases of mass loss along the AGB. Importantly, any white dwarf with masses outside the approximate range 0.4-1.0M cannot arise from single star evolution and must have an origin in a binary, where mass exchange has taken place.

While, the basic model of the white dwarf mass-radius relation, which is used to derive masses from the spectroscopic data, is not in serious doubt, it is interesting to note that opportunities for direct observational tests of the work are rare. This is particularly true of the higher-level refinements that take into account the finite stellar temperature and details of the core/envelope structure, discussed above. Varying the assumed input parameters in these models can lead to quite subtle, but important differences in the model predictions. To test these requires independent measurements of white dwarf mass, which can be compared with the spectroscopic results. Such information can be obtained dynamically, if the white dwarf is part of a binary system, or from the gravitational redshift (Vgr [km s-1] = 0.636M/R), for which an accurate systemic radial velocity is required (often only possible in a binary). An additional important constraint is knowledge of the stellar distance. We have such data for only a very few white dwarfs. The four best examples (i.e. where we have the most complete and accurate information) are 40 Eri B, Procyon B, V471 Tauri B and Sirius B, where we can combine the assembled data with the Hipparcos parallax to test the mass radius relation (Figure 13). While there is good agreement between the observation and theory, there nevertheless remains a high degree of uncertainty in the mass determinations. As a result, for example, it is not possible to distinguish between different models, such as those with “thin” or “thick” H envelopes.

Clearly it would be very desirable to extend the sample of white dwarfs for which we have dynamical masses, gravitational redshifts and accurate parallaxes to more objects and, possibly, explore a wider range of masses and temperatures. A major result of the EUV sky surveys conducted by ROSAT and EUVE was the discovery of many unresolved binary systems containing white dwarfs and companion spectral types ranging from A to K38,38,40. Therefore, a large pool of potential sources exists, for which the required information may be forthcoming in the future. In most of these cases Lyman series observations will be essential to determine Teff and log g. Importantly, although most isolated white dwarfs were too faint for Hipparcos parallax measurements, the presence of the bright binary companion means that Hipparcos data is often available. Although these systems are not resolved in ground-base observations, the HST Wide Field Planetary Camera 2 has observed most of them in the UV, to measure their separations, or at least provide improved constraints. Images of 18 binary systems resolve 9 objects9. Figure 14 shows one of the most interesting examples, 56 Per, a known binary in which each component has been resolved into a pair, making it a quadruple star system. The white dwarf is a companion to 56 Per A and is labeled 56 Per Ab in the image. At a distance of 42pc, the measured 0.39 arcsec separation indicates a binary period of ~50 years for the Aa/Ab system. Therefore, the orbital motion of the two stars should be readily apparent with repeated exposures on timescales ~1-2 years, from which a dynamical white dwarf mass can ultimately be obtained. This is clearly demonstrated in Figure 9 which shows a zoomed view of the Aa/Ab pair from the main image and, on a similar, scale a second image obtained ~18 months after the first.

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Figure 13. Comparison of mass estimates for 40 Eri B, Procyon B, V471 Tau B and Sirius B with the evolutionary models of Wood33, displayed at various temperatures and with “thin” and “thick” H envelopes. The solid limiting curve represents the Hamada-Salpeter zero temperature relation for a carbon core (figure produced by Jay Holberg).

Figure 14. Wide Field Planetary Camera image of the binary 56 Per, where each component (A & B) is itself resolved into a pair (right). Successive images of the Aa/Ab pair taken ~18 months apart clearly show the orbital motion of the system.

3.2 The special case of Sirius B

As the nearest and brightest hot white dwarf, Sirius B is one of the best studied. Through its companionship with Sirius A it provides an important opportunity for astrometric mass determination. Indeed, this effort has been continuous since its discovery by Bessel in 1844. However, a disadvantage is that the close proximity of the A star has made detailed observation of the white dwarf difficult in the UV and visible wavebands. The advent of space-based observations has allowed short wavelength observations in the EUV and soft X-ray, where the emission from Sirius A is negligible, but the obtaining a spectroscopic mass estimate from the Balmer line series remains problematic. The first attempt was carried out by Greenstein et al.41 using photographic plate data. Unfortunately, this spectrum, and a similar one published by Kodaira 42, both suffer from a high level of scattered light contamination from Sirius A, amounting to ~1/4 to 1/3 of the total flux.

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Figure 15. HST Wide Field Planetary Camera 2 (WFPC2) image of the Sirius system showing the overexposed image of Sirius A, with its four diffraction spikes. The vertical bar is the “bleed” of Sirius A into adjacent pixels along the readout columns of the CCD, due to the overexposure. Sirius B lies just to the right of the bottom left diffraction spike. The grey box represents the dimensions of the 52x0.2" slit, which cuts across Sirius B and two of the diffraction spikes.

From space it is possible to take advantage of the superb spatial resolution of the Hubble Space Telescope to resolve the A and B components. Since the closest approach in 1993, the separation between the two stars has become increasingly favourable and Barstow et al.43 were able to obtain a spectrum of the complete Balmer line series for Sirius B using HST’s Space Telescope Imaging Spectrograph (STIS). Figure 15 shows a HST Wide Field Planetary Camera image of the Sirius system, with the location of Sirius B and the orientation of the slit used for the spectroscopic observation. The quality of the STIS spectra (see Figure 16) greatly exceed that of previous ground-based spectra, and were used to provide an important determination of the stellar temperature (Teff = 25,193K) and gravity (log g = 8.556). In addition a new, more accurate, gravitational red-shift of 80.42 ± 4.83 km s -1 was obtained for Sirius B. Combining these results with the photometric data and the Hipparcos parallax a new determination of the stellar mass was obtained for comparison with the theoretical mass-radius relation. However, there are some disparities between the results obtained independently from log g and the gravitational redshift which may arise from flux losses in the narrow 50x0.2″ slit. Combining the measurements of Teff and log g with the Wood33

evolutionary mass-radius relation a best estimate of 0.978 M was obtained for the white dwarf mass. Within the overall uncertainties, this is in agreement with a mass of 1.02 M obtained by matching the new gravitational red-shift to the theoretical M/R relation.

3.3 DO white dwarfs and PG1159 stars

One principal result of the earlier analyses of DO white dwarfs12 was that their mean mass (0.59±0.08 M), derived from temperature and gravity determination in comparison with theoretical evolutionary tracks, is virtually identical to the mean mass of DA white dwarfs. The newly discovered DOs from the SDSS have a mean mass that seemed to be significantly higher (0.68 M

13). Taken altogether, the mean mass of all analyzed DOs (0.65 M, 40 objects) would then be ~10% higher than the mean DA mass. This difference, however, is perhaps insignificant, because a reanalysis of the SDSS DOs yields different temperature and gravity values and, consequently, a lower mean mass (0.65 M instead of 0.68 M, Hügelmeyer priv. comm.). The reason is that the previous analysis was based on the spectra of SDSS Fourth Data Release (DR4), whereas the reanalysis is based on DR6 spectra with improved calibration. Dynamical mass determinations of DOs are not available. Interestingly, the mean mass of DB stars (0.67 M 45), the putative DO progeny, appears to be slightly larger than that of DA stars (0.638 M

46) and it is similar to the DO mean mass. DO white dwarfs are non-pulsating stars, so that asteroseismology methods cannot be applied for mass determination. Note that because of non-existing DO pulsators the so-called DOV variable stars are just an unfortunate designation for pulsating PG1159 stars.

The mean spectroscopic mass of PG1159 stars is 0.57 M. This result was derived from the spectroscopic temperature and gravity determinations of 37 PG1159 stars, accumulated over the last almost two decades,

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and comparison with modern evolutionary tracks for H-deficient post-AGB stars4. This value represents a significant shift towards a lower mean mass compared to a previously determined value (0.62 M ) that was derived from H-rich surface tracks17. Obviously, there is no strongly significant difference between the mean masses of DA, DO, DB, and PG1159 stars.

Figure 16. Flux calibrated and background subtracted spectra of Sirius B obtained, as described in the text, with the G430L (3000-5700Å) and G750M (6300-6900Å) gratings of the STIS instrument on HST.

At present no dynamical mass determination of any PG1159 star is possible. However, this might change in the near future, because recently the first discovery of a PG1159 star in a close binary system was announced48. Some PG1159 stars are multi-periodic non-radial pulsators, defining the group of GW Vir stars (also called misleadingly, as just mentioned, DOV stars). Stellar masses from asteroseismic modeling were derived for five objects and, considering possible error margins in both methods, the results are in good agreement with spectroscopic masses (see, e.g., Werner et al.49). The precise mass determination of a PG1159 star is particularly important, because the nucleosynthesis and mixing processes in the AGB progenitor star are strongly mass dependent. The interpretation of the element abundance pattern of a certain PG1159 star allows us to conclude on details of these processes, and this is particularly useful if the stellar mass is known.

4 ELEMENT ABUNDANCES FROM EUV AND UV SPECTROSCOPY

4.1 The Historical Picture

Determination of the photospheric He and heavy element content in DA white dwarfs provides important information on the prior evolutionary history of a white dwarf and the physical effects of mechanisms that may compete to alter the observed composition of the atmosphere. While H and He are readily detected in the visible region of the spectrum, it is much harder to detect other elements, unless the abundances are very high. For example, absorption lines from C IV can be seen in many He-rich white dwarf spectra, with an abundance (C/He) of ~10-2. However, in the DA stars, the C/H ratio is usually much lower and the carbon undetectable in the visible band. Indeed, He is also hard to detect in the DAs, requiring abundances in excess of a few times 10-3 in the visible band. Therefore, the most important and useful transitions (in particular for many resonance lines of elements heavier than H and He) lie in the far-ultraviolet (far-UV, 1000-2000Å), extreme ultraviolet (EUV, 100-1000Å) and soft X-ray (about 10-100Å)

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regions of the spectrum. Hence, access to these wavebands has been crucial for understanding the detailed atmospheric composition of white dwarfs. Unfortunately, absorption of the incident radiation by the Earth’s atmosphere prevents ground-based observations and the development of space observatories has largely determined what could be achieved.

The first far-UV and X-ray observatories, flown in the early 1970s, were largely insensitive to white dwarfs. Nevertheless, a handful of stars were detected stimulating future work. Subsequently, key contributions have been made by a succession of missions beginning with the International Ultraviolet Explorer (IUE), and continuing with Roentgen Satellit (ROSAT), the Extreme Ultraviolet Explorer (EUVE) and Hubble Space Telescope (HST).

Since the hottest white dwarfs radiate the majority of their energy in the soft X-ray and EUV regions of the spectrum, they are likely to provide a significant fraction of the ionising photons in the local interstellar medium (LISM). Hence, one original motivation for observing white dwarfs in the far-UV was to study their circumstellar environments and the LISM, by observing absorption lines projected onto their otherwise smooth hot blue continua. Such features were detected and usually associated with low ionisation stages of elements, usually of C I, C II, N I, N II, O I, O II, Si I, Si II and Si III, although sulphur has also been seen. Since these interstellar lines are weak and narrow, they are only visible at high resolution (R>20000). An example is a small section of the high-resolution spectrum of the DA white dwarf REJ0558-373, recorded with the Space Telescope Imaging Spectrograph (STIS) onboard HST (Figure 17), which shows the interstellar 1260.4Å line of Si II together with photospheric N V.

Interstellar absorption features typically arise from low ionisation species. However, high ionisation transitions were detected in some of the first IUE echelle spectra of DA white dwarfs50. Initially, it was suggested that these features were associated with circumstellar material, excited by the strong UV and EUV flux of the white dwarf. However, determination of the photospheric velocities of several stars, coupled with the EXOSAT EUV spectrum of Feige 2451, established that the observed features were photospheric in origin. Nevertheless, it was far from clear whether stars like Feige 24 or the similar G191-B2B were typical of the DA population or if stars with pure H atmospheres were more representative.

Ultimately, the larger statistical sample of the ROSAT WFC EUV sky survey provided the solution to that question. The emergent EUV continuum radiation from a white dwarf is very sensitive to the presence of absorbing heavy elements, which suppress the flux compared to the level that would be expected from a pure H atmosphere. In a sample of ~100 stars studied by ROSAT, it is clear that the EUV and soft X-ray luminosities of objects hotter than about 50,000K are much lower than expected, while white dwarfs below this temperature typically have luminosities consistent with pure H envelopes52,53. In most of the hottest white dwarfs, broadband soft X-ray and EUV photometry was able to rule out helium as the sole source of opacity, indicating that heavier elements play a significant role. This result is consistent with the view that radiation pressure can counteract the downward diffusion of heavy elements induced by gravity in the hottest white dwarfs54.

4.2 UV Spectroscopy

Broadband fluxes do not provide sufficient information to determine either the specific absorbing species or to estimate their abundances. Hence, the survey data must be complemented by more detailed spectroscopic observations in the EUV and far-UV, but, because of limits on the available observing time, for a smaller number of objects. Prior to the shutdown of the IUE satellite, high-resolution (R~20,000) echelle spectra were routinely obtained. These were very important for the initial exploitation of interesting white dwarfs newly discovered by the ROSAT survey (e.g. Holberg et al.55,56). However, the IUE spectra had a typical limiting signal-to-noise of ~3:1 and a limiting magnitude ~V=15 for practical exposure times. Subsequently, an effective technique was developed for coadding multiple exposures to improve signal to noise. This has been further enhanced, by reprocessing the original data, yielding a valuable archive of high dispersion white dwarf spectra (see Holberg et al.57). The overall quality of the archive is quite variable depending on the number of exposures taken of each star. Typically, those stars suspected of containing heavy elements have been observed more often, achieving a higher ultimate signal to noise than single observations of apparently pure H white dwarfs. An example of the result of combining several exposures is seen in Figure 18, which shows a region of the coadded IUE spectrum of G191-B2B (14 exposures). This is

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compared with a single optimally exposed spectrum of PG1234+482, showing a clear difference in signal-to-noise.

Figure 17. 1230Å to 1280Å region of the STIS spectrum of REJ0558-373, showing photospheric absorption lines of N V (1238.821/1242.804Å) and large numbers of Ni lines. The best-fit synthetic spectrum is shown offset for clarity. The strong line near 1260Å, present in the observation but not in the model, is interstellar Si II.

In parallel with the latter years of the operation of IUE, the Hubble Space Telescope has given further access to the far-UV waveband. However, with a considerably larger aperture than IUE, it is possible to observe fainter targets and achieve greater signal to noise. Initially, high dispersion (R~40,000-100,000) spectra were obtained by the Goddard High Resolution Spectrograph (GHRS) but, unlike the IUE echelle data could only cover a narrow (30-40Å) waveband in a single exposure. Hence, complete wavelength coverage similar to that obtained by IUE would have required a large number of individual exposures, yielding prohibitively long observations. The replacement of the GHRS by the Space Telescope Imaging Spectrograph (STIS) in 1997 provided an instrument with improved throughput and IUE-like wavelength coverage while retaining the high-resolution spectroscopic capabilities. In the E140M (medium echelle) mode, the resolving power is R~40,000 and far-UV coverage from ~1150-1750Å. The highest resolution E140H grating only gives a span of ~200Å at a time but can be tilted to build up full wavelength coverage in successive exposures. The capabilities of STIS are illustrated in the E140H exposure of G191-B2B in the region of the C IV resonance doublet, the equivalent IUE observation is also shown for comparison (Figure 19). It is interesting to see how the apparent single components seen by IUE have a clear asymmetric appearance indicating that each is a pair of blended lines, in this case circumstellar and photospheric contributions.

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Figure 18. Comparison of the signal-to-noise achieved from a co-added IUE spectrum (top, of G191-B2B) with a single exposure (bottom, of PG1234+482). The lower spectrum has been scaled to the flux of the upper one and then offset for clarity.

Between IUE and HST, good quality high-resolution spectra have been obtained for about 25 hot DA white dwarfs, spanning a temperature range from 110,000K down to 20,000K. Using the latest heavy element blanketed non-LTE stellar atmosphere calculations, Barstow et al.58 have addressed the heavy element abundance patterns. Completely objective measurements of abundance values and upper limits have been made using a χ2 fitting technique to determine the uncertainties in the abundance measurements, which can be related to the formal upper limits in those stars where particular elements are not detected. This work shows that the presence or absence of heavy elements in the hot DA white dwarfs largely reflects what would be expected if radiative levitation is the supporting mechanism, although the measured abundances do not match the predicted values very well, as reported by other authors in the past. Almost all stars hotter than ~50,000K contain heavy elements.

A few other strong temperature/evolutionary effects are seen in the UV abundance measurements. There is a decreasing Si abundance with temperature and a sharp decline in Fe and Ni abundance to zero, below ~50,000K. When detected, the Fe and Ni abundances maintain an approximately constant ratio, close to the cosmic value ~20. For the hottest white dwarfs observed by STIS, the strongest determinant of abundance appears to be gravity. Qualitatively, these results are in keeping with physical models of diffusion and radiative levitation, but the detailed abundance measurements do not match predicted values.

4.3 UV spectroscopy of DO white dwarfs

Heavy element abundances in DO white dwarfs are less well explored than in DAs and in PG1159 stars. Dreizler & Werner12 and Dreizler59 have summarized the state and presented new analyses. Lines of only a few species (CNO, Si, Fe) were discovered in selected DOs for which IUE and HST spectra were taken. Generally, the comparison of observed abundances with predictions from diffusion calculations was disappointing because of the significant deviations. A thorough investigation of this problem by Dreizler57

arrived at the surprising results that, in contrast to DA stars, the metal lines in DOs are better reproduced by chemically homogeneous model atmospheres than by self-consistently computed stratified models accounting for diffusion and radiative levitation. Since these studies a number of new spectroscopic observations of DOs were performed with FUSE.

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Figure 19. Comparison of the coadded IUE spectrum of G191-B2B with that obtained at higher spectral resolution by the STIS instrument on HST, in the region of the C IV 1548/1550Å doublet. The asymmetry of the line profiles in the STIS data reveals the presence of two absorbing components, not visible at the lower spectral resolution of IUE, where they are blended into a single gaussian.

A remarkable achievement was the discovery of trans-iron elements (Ge, As, Se, Zn, Te, I; Figure 20) in the cool DO white dwarfs HD149499B and (some of these species) in HZ21 60. Later on, most of these elements as well as Ga, Mo, and the noble gases Kr and Xe were detected in the hot DO RE0503-289 61

(Figure 21; see below for more details about his star). The observed number abundances are small, of the order log(X/He) = -6 to -8. The measured mass fractions, however, reveal overabundances ranging up to a factor of 1000 relative to the Sun. This could be the result of slow neutron capture nucleosynthesis, which would have occurred during the AGB phase of the stars´ evolution, although this interpretation is problematic. Diffusion and radiative levitation certainly influence the element abundances. This is underlined by the fact that a more than 100 times oversolar abundance was measured for argon in the hot DO PG1034+00162, although nucleosynthesis processes are not expected to affect argon. The solar argon abundance found in a PG1159 star, where we expect to see nuclear processed material, confirms this expectation.

RE0503-289 is a remarkable DO star. It is relatively hot and shows C IV lines in the optical spectrum (Teff=70,000 K, logg=7.5, C/He=0.005 by number). It has an extremely low ISM hydrogen column density along the line-of-sight so that EUV spectroscopy, with surprising results, was possible (see below). What is particularly interesting in our context is its UV spectrum observed with HST and FUSE. Barstow et al.63

have identified nickel lines (log Ni/He=-5) in the HST/GHRS spectrum, however, at the same time iron is not detectable at all (log Fe/He<-6). Hence, the Ni/Fe ratio is at least 10 times larger than observed in hot DA stars. This difference is not understood in terms of radiative levitation/diffusion processes alone. The FUV spectrum taken with FUSE shows numerous spectral lines which initially could not be identified64. A large fraction of them were later, also already mentioned above, identified as lines from trans-iron elements61.

We already described the remarkable optical spectrum of hottest DO white dwarf KPD0005+5106 (Sect. 2.3.1, Teff=200,000 K). Lines from highly ionized metals which were never seen before in a stellar photosphere are exhibited in the FUSE spectrum of the star, for example Ca X and Fe X 65,66 (Figures 22 and 23). The metal abundance pattern suggests that KPD0005+5106 might be a descendant of an RCrB star, hence, it could be the result of a binary white dwarf merger and therefore represent a different post-AGB evolutionary sequence towards the white dwarf stage66.

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4.4 UV spectroscopy of PG1159 stars

Abundance analyses of PG1159 stars are performed by detailed fits to spectral line profiles. Because of the high Teff all species are highly ionized and, hence, most metals are only accessible by UV spectroscopy. As mentioned above, optical spectra always exhibit lines from He II and C IV. Only the hottest PG1159 stars display additional lines of N, O, and Ne. For all other species we have utilized high-resolution UV spectra that were taken with HST and FUSE. FUSE allowed observations in the Lyman-UV range (~900-1200 Å) that is not accessible with HST. This turned out to be essential for most results reported here. For a more detailed discussion and references to these results see Werner & Herwig30.

A number of chemical elements could be identified for the very first time (F, P, S, Ar). In addition, very high ionisation stages of several elements, which were never seen before in stellar photospheric spectra, could be identified in the UV spectra for the very first time (e.g., Si V, Si VI, Ne VIII). To illustrate this, we display in Figures 24-31 details of FUSE and HST spectra of PG1159 stars. We discuss the spectroscopic results comparing with the PG1159 progenitors stars (the [WC] central stars) and stellar evolution model predictions.

Figure 20. Photospheric lines of trans-iron elements observed in FUSE, HST, and IUE spectra of HD149499B overplotted with computed line profiles. (From Chayer et al.60).

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Figure 21. Photospheric lines of krypton and xenon in the FUSE spectrum of the hot DO RE0503-289 overplotted with computed line profiles. (From Werner et al.61).

Figure 22. Two photospheric Ca X lines discovered in the hot DO KPD0005+5106 overplotted with computed line profiles. (From Werner et al.65).

Figure 23. Two photospheric Fe X lines discovered in the hot DO KPD0005+5106 overplotted with computed line profiles. (From Wassermann et al.66).

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Figure 24. Detail from FUSE spectra of two relatively cool PG1159 stars (see labels). Note the following features. The F VI 1139.5 Å line which is the first detection of fluorine at all in a hot post-AGB star; the P V resonance doublet at 1118.0 and 1128.0 Å, the first discovery of phosphorus in PG1159 stars; the N IV multiplet at 1132 Å. Also detected are lines from Si IV and S VI. The broader features stem from C IV and O VI. (From Reiff et al.67).

Hydrogen - Four PG1159 stars show residual H with an abundance of up to 0.35 (the so-called hybrid-PG1159 stars). These objects are the outcome of an AFTP. All other PG1159 stars have H<~ 0.1 and, hence, should be LTP or VLTP objects. H was also found in [WCL] stars (H=0.01-0.1).

Helium, carbon, oxygen - These are the main constituents of PG1159 stellar atmospheres. A large variety of relative He/C/O abundances is observed which might be explained by different numbers of thermal pulses during the AGB phase, except for the most He-rich stars. They might belong to a different post-AGB sequence involving the so-called O(He) stars (see Rauch et al.68). The He/C/O abundances in PG1159 stars are consistent with results found for [WC] stars.

Nitrogen - N is a key element that allows to decide whether the star is the product of a VLTP or a LTP. Models predict that N is diluted during an LTP so that in the end N=0.1%. This low N abundance is undetectable in the optical and only detectable in extremely good UV spectra. In contrast, a VLTP produces N (because of H-ingestion and burning) to an amount of 1% to maybe a few percent. N abundances of the order 1% are found in some PG1159 stars (e.g., PG1144+005 in Figure 11), while in others it is definitely much lower. This picture is similar to the [WC] stars.

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Figure 25. The high spectral resolution capability of STIS aboard HST allows to distinguish the photospheric NV resonance doublet from the weak blueshifted ISM components. This enabled the first reliable nitrogen abundance determination in the PG1159 prototype. (From Jahn et al.69).

Neon - Ne is made from 14N that was produced by CNO burning. In the He-burning region, α-captures transform 14N to 22Ne. Evolution models predict Ne=0.02 in the intershell. A small spread is expected as a consequence of different initial stellar masses. Ne=0.02 was first found from optical analyses of a few stars and, later, in a larger sample observed with FUSE (Werner et al.70,16; Figures 26 and 27). The neon abundance in [WC] stars is very similar (0.02-0.04).

Figure 26. First identification of the NeVII 973.3 Å line, shown here in the FUSE spectrum of the PG1159 star PG1520+525. This strong absorption feature is seen in the spectra of many hot post-AGB stars, but remained unidentified for some years .

Figure 27. Discovery of NeVIII lines in the FUSE spectrum of the PG1159-type central star of K1-16. This is the first detection of NeVIII in any photospheric spectrum. Lines from this ion are only exhibited by the very hottest post-AGB stars (T eff>~140,000 K).

Fluorine - F was discovered for the first time by Werner et al. (2005) in hot post-AGB stars; in PG1159 stars as well as hydrogen-normal central stars. A strong absorption line in FUSE spectra located at 1139.5 Å remained unidentified until we found that it stems from F VI (see Figure 24). The abundances derived for PG1159 stars show a large spread, ranging from solar to up to 250 times solar. This was surprising at the outset because 19F, the only stable F isotope, is very fragile and easily destroyed by H and He. A comparison with AGB star models of Lugaro et al.71, however, shows that such high F abundances in the intershell can indeed be accumulated by the reaction 14N(α,γ)18F(β+)18O(p,α)15N(α,γ)19F, the amount depends on the stellar mass. We find a good agreement between observation and theory. The results also suggest, however, that the F overabundances found in AGB stars can only be understood if the dredge-up in AGB stars is much more efficient than hitherto thought72.

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Silicon - Si is expected to remain almost unchanged, in agreement with PG1159 stars for which the Si abundance could be determined (Figure 22). The same holds for some [WC] stars, but in other cases overabundances were found (8-45 times solar).

Phosphorus - Systematic predictions from evolutionary model grids are not available; however, the few computed models show P overabundances in the range 4-25 times solar. This is at odds with spectroscopic measurements for two PG1159 stars (Figure 22) that reveal a solar P abundance.

Sulphur - Again, model predictions are uncertain at the moment. Current models show a slight (0.6 solar) underabundance. In strong contrast, a large spread of S abundances is found in PG1159 stars, ranging from solar down to 0.01 solar (Figure 28).

Argon - Ar was identified recently for the first time in hot post-AGB stars and white dwarfs 67. Among them is one PG1159 star for which a solar abundance has been determined (Figure 29). This is in agreement with AGB star models which predict that the Ar abundance remains almost unchanged.

Iron - From the non-detection of Fe VII lines it was previously concluded that PG1159 stars are possibly Fe-deficient75. Recently, however, lines from Fe VII, Fe VIII, or Fe X were discovered in a number of PG1159 stars (Figure 30). In all cases, a solar iron abundance was derived77,79.

Figure 28. FUSE enabled the first abundance determination of sulpur in PG1159 stars. Shown here is the S VI resonance doublet in the prototype of the PG1159 spectral class. (From Jahn et al69.).

Figure 29. Discovery of the Ar VII 1063.55 Å line in the FUSE spectrum of the PG1159 star PG1425+535. This is the first detection of Ar VII in a photospheric spectrum and the only detectable argon line in any wavelength region of hot post-AGB stars.

PG1159 stars do not exhibit wind features in their optical spectra. However, UV spectroscopy reveals that many of the low-gravity central stars display strong P Cygni profiles; e.g., the resonance lines from C IV

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and OVI, and subordinate lines from He II (1640 Å), O V (1371 Å), F VI (1139 Å, see Figure 31) and Ne VII (973 Å). Mass-loss rates in the range log (M-dot /[M]) = -8.3 to -6.9 were derived76,77,78, and it appears that they are in accordance with predictions from radiation driven–wind theory.

Figure 30. Fe VIII lines detected in the prototype PG1159-035 compared to model profiles. (From Werner et al.74).

Figure 31. Observed and computed P Cygni profiles of the F VI 1139.5 Å line in the FUSE spectra of the [WC]-PG1159 transition type object Abell 78 (top panel) and the hybrid PG1159 star NGC 7094 (bottom). Compare with the symmetric line shapes in higher-gravity PG1159 stars (Figure 26). (From Reiff et al.75).

In the year 1992 the extremely hot central star of Longmore 4 (Teff=170,000 K) showed a remarkable event during which its spectral type turned from PG1159 to [WCE] and back again to PG1159, most probably due to a transient but significant increase in the mass-loss rate79. Bond80,81 has been monitoring the spectrum of Longmore 4 since 2003 and he discovered that the phenomenon recurred twice in the year 2006 (Figure 32), and once again in 2008. The reason for these spectacular events is unknown. It might be connected to the fact that the star is a pulsator. This phenomenon has not been witnessed in any other PG1159 star.

4.5 EUV Spectroscopy

4.5.1 DA white dwarfs

A great deal of detailed information has been obtained from analysis of UV spectra of DA white dwarfs and this observing technique will continue to be of tremendous importance. However, as some UV results already indicate, where the detailed line profiles suggest that photospheric material is not homogeneously mixed, they do not necessarily tell the whole story concerning the structure and composition of the

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photosphere. The emergent EUV flux from a hot white dwarf star is highly sensitive to both the effective temperature and composition of the envelope. Hence, EUV observations were recognized to have important diagnostic potential even before any EUV astronomy missions were actually flown. Barstow and Holberg 82

have recently and extensively reviewed the development of EUV astronomy and some of the detailed results concerning white dwarfs. Therefore, this section discusses a subset of results that are particularly concerned with this review theme on the measurement of fundamental parameters of white dwarfs.

Figure 32. The mean of 29 normal spectra of Longmore 4 is shown at top. On 2006 Jan 16 (middle) and Nov 30 (bottom) the star was in its transient [WCE] stage, with strong C IV and He II emission. Spectra taken 53-56 days earlier, and 15-17 days later, showed the normal PG1159 spectrum. Tick marks on the y axis are spaced at 0.5 of the continuum level. (From Bond80).

Unlike the UV band, where high-resolution spectroscopy has been available for more than 20 years, the field of EUV astronomy has emerged more slowly, due to the greater difficulty of instrument development and practical observation in a region where the opacity of interstellar gas is at its greatest. Consequently, the spectrometers on board the Extreme Ultraviolet Explorer (EUVE) mission had relatively low effective area and modest spectral resolution (R~300) compared to UV instrumentation. Nevertheless, since hot white dwarf fluxes peak in the EUV, detailed observations could be made of a significant sample of white dwarfs. Those white dwarfs with pure H envelopes are the most luminous at the shorter EUV wavelengths, as illustrated in Figure 33, which shows an EUVE spectrum of the white dwarf HZ43. HZ43 was the first reported detection of an EUV source and has been studied frequently and, because of it pure H photosphere, often been used for calibration purposes. The flux corrected spectrum peaks near 200Å. The short wavelength decrease is determined entirely by the properties of the atmosphere but at long wavelengths, while some of the opacity is from the photosphere, the dominant effect is absorption by interstellar hydrogen and helium. Although interstellar opacity is not the topic of this review, a discussion of its characteristics in the EUV band is essential for understanding the photospheric results since photospheric He features could also be present at these same wavelengths in some stars. The interstellar features may interfere with or even completely mask any stellar component at the resolution of EUVE. The sharp step at 504Å is the He I ISM absorption edge. The important He II Lyman series lines also lie between the He II edge at 228Å and the He II Lyman α line at 304Å but the He II column density is too low for a significant detection of these interstellar lines in HZ43. However, when the total interstellar H I column density is higher (a few x 1018cm-2 compared to ~1018cm-2 for HZ43), and the He I & He II columns larger as a result, the He II edge can be readily detected, along with the He I autoionization edge at 206Å (Figure 34).

29

Figure 33. EUV spectrum of the pure H atmosphere white dwarf HZ43, recorded with the EUVE spectrometers and described in the text.

Figure 34. EUVE count spectrum of the DA white dwarf GD659 (error bars), showing the He I interstellar autoionization feature at 206Å and the interstellar He II Lyman edge at 228Å. The solid histogram that matches the data is the best fit model spectrum for a pure H atmosphere, while the histogram that does not match the observed flux is a model including N V at the abundance reported by Barstow et al.58 assuming that the mixture is homogeneous.

If the white dwarf atmosphere contains significant quantities of elements heavier than H or He, the EUV spectrum is cut off very sharply at short wavelengths. Figure 35 shows the spectrum of the white dwarf G191-B2B, which is the proto-type “heavy element-rich” object. In this object the peak flux is at a wavelength ~260Å, with hardly any flux detectable below 200Å, in contrast to those stars with pure H

30

envelopes. Initially, an understanding of the EUVE spectrum of G191-B2B and similar stars was quite elusive. First attempts to match the observation with synthetic spectra failed to reproduce either the flux level or even the general shape of the continuum (see Barstow et al.83 and Figure 35). This problem was perceived to be due to the inclusion of an insufficient number of Fe and Ni lines. Adding some 9 million predicted lines to the few thousand with measured wavelengths did provide a self-consistent model able to reproduce the EUV, UV and optical spectra (Lanz et al. 1996). However, good agreement between the observed EUVE spectrum and the model prediction could only be achieved by inclusion of a significant quantity of helium, either in the stellar photosphere or as an ionised interstellar/circumstellar component. Unfortunately, due to the limited resolution of EUVE (~0.5Å) in the region of the He II Lyman series, this inferred He contribution could not be directly detected.

Figure 35. EUVE spectrum of G191-B2B (thick solid line) compared with two non-LTE line-blanketed models for Teff=58000K, log g=7.5. The dashed model includes blanketing from 6,000 lines of Fe and Ni, while the thin solid line includes 300,000 lines.

The nature of the He opacity, if really present, is problematic. If all of it is interstellar, the implied He ionization fraction is much larger (by a factor ~2) than the 30-40% typical of the nearby ISM. Furthermore, the level of agreement between model and data at short wavelengths, below ~200Å, is poor, the predicted flux exceeding that observed by a factor ~10 (Figure 36). Empirically, Barstow et al. 85 showed that the overall flux distribution could be matched by assuming a different Fe abundance for models separately applied to the short (<190Å) and long (>190Å) ranges. Examination of the formation depths of the Fe lines at different wavelength hints at an explanation of the problem (Figure 37), showing that the formation depth has a strong wavelength dependence and indicating that abundance measurements made in the UV and EUV, and even in different parts of the EUV, are sampling quite different regions of the atmosphere. Therefore, the results imply that the Fe is not distributed homogeneously in the atmosphere, but has different abundances at different depths. A fairly simple model, dividing the atmosphere into two “slabs” with a lower Fe abundance in the outer region (Fe/H=10 -6 cf. 4x10-5) provides a good, but not completely unique, match to the data (Figure 38). Subsequently, important progress has been made in incorporating radiative levitation and diffusion self-consistently into the atmosphere calculations to give predictions of the depth dependent abundance profiles a firm physical basis86,88,88. Interestingly, the Fe profile determined from these calculations is similar to the simple slab model of Barstow et al. 85, but with a smoother transition region between the two main regions.

The need for a He opacity component, required to provide a good match to the homogeneous models, is reduced in the stratified models but not eliminated. Although, in principle EUV observations are more sensitive to the presence of He than any other waveband, there have been few real detections of the element in EUVE spectra. One example is the massive DA star GD50, where the He II Lyman line series is clearly visible (Figure 39). However, because of the high mass (1.2M ), it is likely that the star is a product of

31

binary evolution and other stars where He has been detected are in known binary systems. Therefore, the issue of whether or not photospheric He is present in the hottest DA white dwarfs is still needs to be resolved.

Figure 36. Comparison of the complete EUVE spectrum of G191-B2B (error bars) with a single model that give the optimum match to the >180Å wavelength range. Discontinuities near 170 and 320Å are regions where the EUVE spectrometer channels overlap, and arise from differing spectrometer effective area. The predicted short wavelength flux is a factor 5-10 greater than that observed.

Figure 37. Mass depth (total mass above the point of interest) of the line (upper, dashed curve) and continuum (lower curve) formation at monochromatic optical depth τυ=2/3 as a function of wavelength in the EUV and far UV.

Direct detection of He in those stars with significant heavy element opacity requires higher spectral resolution than was achieved with EUVE, to separate the He II Lyman lines from the much larger number from other elements. Recent developments in normal incidence optics have allowed the construction of a new generation of spectrographs combining high throughput with high spectral resolution. Thus far, the technique has only been applied on short duration sounding rocket flights, with exposure times far shorter than available with satellite missions. The spectrum of G191-B2B, obtained with the J-PEX mission, shows the promise of future instrumentation and partially solves the problem of the He inferred from the EUVE

32

analyses (Figure 40, Barstow et al.89). He is certainly directly detected and the best-fit model requires both interstellar and photospheric components. However, only the interstellar complex in the 228-230Å range is detected directly. The predicted strength of the photospheric He II line at 243Å is at a level similar to the signal-to-noise in that part of the spectrum and so a significant detection of photospheric He cannot be claimed at this stage. Further analysis of the spectrum, indicates that the interstellar He II has two components, one associated with the local ISM and a second that may be related to the circumstellar material detected in the far-UV90.

Figure 38. Comparison of the complete EUVE count spectrum of G191-B2B with the “slab” model of Fe depth dependent abundance described in the text.

Figure 39. EUVE spectrum of the massive DA white dwarf GD50, showing the presence of photospheric He II.

33

Figure 40. High-resolution EUV spectrum of G191-B2B, obtained with the J-PEX spectrometer, spanning the wavelength range 226-245 Å (error bars). The blue histogram is the best-fit theoretical model of the star and ISM.

More recently, a second high resolution EUV spectrum, of the white dwarf component in the pre-cataclysmic binary Feige 24, has been obtained in a re-flight of the J-PEX payload. If a WD has evolved as part of such a short period (4.23d) binary, then the mass-loss may have also been affected by a common envelope (CE) phase. Some evolutionary calculations predict that DA dwarfs are formed with comparatively massive H layers (~10-4M, e.g. Iben and Tutukov91), where He, having sunk out of the atmosphere, should be undetectable even in the EUV. One possible consequence of binary evolution is the expulsion of the CE, reducing the system angular momentum and leaving only a thin H-rich shell above the core compared to that expected in a single star92. However, the efficiency of CE ejection is poorly understood. Detection of He in the EUV might indicate that a large part of the H envelope has been expelled by some mechanism or that there is unexpected mixing. Comparative abundance measurements in EUV, FUV and optical bands can determine the H/He structure (stratified H upon He or homogeneous H+He) and distinguish between these situations.

Feige 24 is an important contrast to G191-B2B representing a close binary rather than an isolated object. The surprising result of the J-PEX observation is that there is no evidence for the existence of a thin H-layer or any photospheric HeR93. This is illustrated in Fig. 41a, which shows a section of the best fit model and observational data, where the H-layer mass has converged to the upper limit of the grid (10 -12.92M), a level at which no He is detectable. The sensitivity to the H-layer mass is illustrated in Figs. 41b and 41c, which show the effect of decreasing the H-layer mass in the model to 10-13.5 and 10-14 M. The strong constraints on the amount of He present are provided by the absence of detectable HeII lines, particularly at 237.3 Å and 243 Å, and the predicted suppression of the continuum flux below ~233 Å for thinner H-layers. Formally, the lower limit to the H-layer mass is 1.2x10-13 M, equivalent to a He abundance upper limit (90%) of 2.5x10-6. Hence, it is evident that the common envelope phase of evolution of the Feige 24 system has not led to erosion or expulsion of the WD’s H envelope and that, despite this more complex evolutionary path, the WD appears no different from G191-B2B.

Observations of isolated white dwarfs with Chandra and XMM-Newton are scarce. The Chandra LETG (Low Energy Transmission Grating) spectrum of HZ43 (50-170Å) together with EUV and UV spectra is perfectly matched by a pure hydrogen atmosphere, confirming previous results. The same holds for Sirius B94 and LB191995. More challenging is the LETG spectrum of GD246, a hot DA with significant trace metal abundances as derived from detailed studies with EUVE and (F)UV telescopes. Thanks to the superior spectral resolution of Chandra over EUVE, individual spectral lines from Fe could be identified in the soft X-ray spectrum of a DA star for the first time95,96. Figure 42 shows the Chandra spectrum which is

34

b)

a)

c)

dominated by a forest of Fe lines. XMM-Newton has observed two DAs, G191-B2B and GD153, for calibration purposes97 but no detailed results are available, yet. G191-B2B, as discussed above, contains trace metals and therefore is a less suitable calibration object than the pure-hydrogen WD GD153.

Figure 41.J-

PEX high resolution spectrum (black error bars) compared to a composite photospheric and interstellar model spectrum (blue histogram). a) Best fit model with H-layer mass of 10-12.92M; b) H-layer mass = 10-13.5M; c) H-layer mass = 10-14M.

35

Figure 42. Chandra LETG spectrum of the hot DA white dwarf GD246 (thin line) with fits by a chemically homogeneous model (top panel) and a stratified model (bottom). (From Adamczak et al.95).

4.5.2 DO white dwarfs and PG1159 stars

There are only two DO stars with low enough ISM column densities that are accessible for EUV observations, HD149499B99 and RE0503-289. The latter´s EUVE spectrum (Figure 43) represents a particular challenge. Model atmospheres including metal abundances as derived from UV spectroscopy predict an EUV flux that is significantly higher than observed. This problem is still unsolved. Decreasing the effective temperature of the model would help to explain the EUV flux level. This possibility, however, is excluded because such cooler models exhibit optical He I lines which are not observed. Another possibility is additional EUV opacity sources. In the FUSE spectrum, lines from many trans-iron elements were discovered recently64 (see above). The respective opacities were not yet included in the EUV analysis.

Figure 43. EUVE spectrum of the hot DO white dwarf RE0503-289 compared to models with Teff=70,000 K. To facilitate line identification, carbon or oxygen was added to the helium model (top and bottom panels, respectively). Labels and arrows indicate firm identifications of CIII/IV and OIII/IV lines. Most prominent are the lines of the He II resonance series, beginning with Lyα at 304Å. The models are normalized to the V magnitude. Values for HI and He I interstellar column densities were treated as free parameters and adjusted to fit the continuum in the 500-600Å region and the He I edge at 512Å, respectively. (From Werner et al.23)

36

PG1159 stars have high C and O abundances in addition to helium in their photospheres so that they are EUV emitters only if their effective temperature is very high (Teff>140,000 K). PG1520+525 is the only PG1159 star (except for H1504+65, see below) for which a reasonable EUVE spectrum could be obtained. Flux is detected in a very narrow region, 100-130Å, and it was used to estimate Teff=150,000 K. The star is a non-pulsator so that this result in combination with the temperature of the pulsating prototype PG1159-035 (Teff=140,000 K) constrains the location of the blue edge of the GW Vir instability strip in the Hertzsprung-Russell diagram100. This result was confirmed later by a Chandra LETG observation95,98

(Figure 44).

Figure 44. Chandra LETG spectrum of PG1520+525 (thin line) and simulated observations from two models with different effective temperature. The 140,000 K model overestimates the flux at λ>110Å. (From Werner et al.98)

The most bizarre PG1159 star is H1504+65. It was discovered as one of the brightest soft X-ray sources in the sky in the HEAO-1 survey101. Optical follow-up spectroscopy revealed a hot white dwarf closely related to the PG1159 class. It is (together with the DO KPD0005+5106) the hottest white dwarf known (Teff=200,000 K) and it has a unique photospheric composition. It is H- and He-free and mainly composed by C and O by equal parts. The EUVE spectrum shows flux in the 75-150Å range and it is dominated by strong and broad O VI and Ne VII absorption line102. Chandra has taken a spectacular LETG spectrum, arguably the richest X-ray absorption line spectrum recorded so far (Figure 45). Many lines from several ionisation stages of Ne and Mg can be seen and high abundances were derived: Ne=Mg=2% by mass. It is speculated that H1504+65 is a naked C-O white dwarf or even a WD with a O-Ne-Mg core resulting from carbon burning70. The recently discovered new class of “Hot DQ” white dwarfs, having carbon dominated atmospheres with Teff ~20,000 K103, could represent the progeny of H1504+65 and might hold the key for understanding the origin of H-He-deficient white dwarfs.

5 CONCLUSION

This paper has reviewed the range of techniques applied to measuring the parameters of the hot, hydrogen-and helium-rich white dwarf stars. The principle direct measurements are of effective temperature, surface gravity and photospheric composition. From these it is possible to infer more fundamental information such as the stellar mass and radius, which are essential for the calculation of cooling rates and the use of the white dwarf population to study the history and evolution of the galaxy. Spectroscopic data from a variety of wavelength ranges are required for this work and the important contributions from optical, ultraviolet and extreme ultraviolet studies have been outlined. While some important results have been obtained, a number of important questions remain to be answered. Continued access to high-resolution spectroscopy in the far-

37

UV and a new, similar capability in the EUV will be essential to provide final solutions for the outstanding problems.

Figure 45. Detail from the Chandra spectrum of H1504+65 (thin line). Overplotted is a model with parameters as given in the panel. (From Werner104)

Apart from a very few white dwarfs, where dynamically determined masses are available, we rely on the theoretical white dwarf mass-radius relation to determine these parameters from the values of Teff and log g. The issue of the accuracy of the theoretical mass-radius calculations is an important one and the discovery of a sample of white dwarfs in binary systems, from which we might ultimately extend the number of objects for which we have dynamical masses, indicates that we might finally be able to make a definitive test of this Nobel Prize-winning theory.

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