Hot White Dwarfs
M. A. Barstow1 and K. Werner2
1Department of Physics and Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK
2Kepler Center for Astro and Particle Physics, University of Tübingen, Sand 1, 72076 Tübingen, Germany
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 estimating of mass and radius will be described, and the dependence of such determinations on theoretical calculations of the mass-radius relation discussed.
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.
SPECtroscopic Measurements of Effective temperature and surface gravity
1.1Balmer 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.
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 χ2 test. In addition, this allows formal determination of the statistical errors by examining the variation of χ2 with Teff and log g.
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.
1.2Lyman 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 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.
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.
ore 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.
UV and optical spectrum of the DA white dwarf plus A8-F2 main sequence star binary system BD+2701888 (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.
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.
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.
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.
1.3Temperature 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.
1.3.1DO white dwarfs
The first systematic non-LTE analysis of a large sample of DO stars was presented by Dreizler & Werner12. 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 4013. 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.
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).
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).
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.
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).
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.
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, 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.
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 on the AGB, dredge-up of carbon and oxygen into the intershell can achieve this agreement28. 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.