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Astron. Astrophys. 359, 1042-1058 (2000)

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1. Introduction

The model atmosphere analyses of hot white dwarfs with effective temperatures [FORMULA] revealed a variety of surface compositions. There are helium-, carbon- and oxygen-rich PG 1159 stars (Dreizler & Heber 1998), helium-rich DO's analyzed by Dreizler & Werner (1996) and Dreizler (1999), hydrogen-rich DAO's analyzed by Bergeron et al. (1994) and Napiwotzki (1999) with various abundances of helium and the DA's in which no helium can been detected, whereas traces of heavy elements may be present (e.g. Holberg et al. 1999; Koester et al. 1998). For a long time the question has been debated if these different compositions are preferably due to events which occur before the star evolves into a white dwarf (primordial scenario) or if the surface compositions are a consequence of processes, which occur on the cooling sequence (see the review of Fontaine & Wesemael 1997). Because of the lack of hydrogen-rich pre-white dwarfs, Fontaine & Wesemael (1987) suggested that most white dwarfs descend from helium-rich progenitors with some minor amounts of hydrogen mixed in their envelope. During the cooling hydrogen diffuses upwards. So the star evolves via the DAO stage with a stratified H/He atmosphere into a DA. After the detection of hydrogen-rich pre-white dwarfs and even "hybrid" objects with about similar abundances of hydrogen and helium (e.g. Napiwotzki & Schönberner 1991, 1995; Rauch et al. 1999) there is now clear observational evidence that pre-white dwarfs may have a variety of H/He ratios. In addition, from an analysis of helium line profiles Napiwotzki & Schönberner (1993) and Bergeron et al. (1994) ruled out the existence of stratified atmospheres for most of the DAO's.

From standard theory of stellar evolution, only the existence of hydrogen-rich white dwarfs is expected. The masses of the outer hydrogen layer and the helium-rich intershell region on top of the C/O interior may depend on the total stellar mass. For [FORMULA] a hydrogen layer mass of about [FORMULA] is predicted (Blöcker et al. 1997). As a possible explanation for the existence of H-deficient post-AGB stars the born-again AGB-star scenario originally developped by Iben et al. (1983) was proposed. A very late thermal pulse experienced by a white dwarf during its early cooling phase brings it back onto the AGB where mass loss may remove the H-rich envelope. After the inclusion of hydrodynamically based overshoot into the AGB model calculations, Herwig et al. (1999) have shown that due to the additional energy release from convective H-burning a convective instability reaches up to the surface. This produces a H-deficient and C-O-rich surface chemistry. The most recent results are summarized in Blöcker (2000).

There is clear observational evidence that not all properties of the white dwarfs surface chemistry can be explained by this scenario. Additional processes must exist, which operate when the star is already on the cooling sequence and change the surface composition. The existence of the DB-gap requires that all helium-rich white dwarfs evolve into hydrogen-rich ones until they have cooled down to [FORMULA]. The lower limit for PG 1159 stars is at [FORMULA] (Dreizler & Heber 1998). Therefore C und O must be removed from the surface regions. The most extensively investigated effects are gravitational settling possibly counteracted by radiative levitation (Chayer et al. 1995a,b and references therein). However, various phenomena cannot be explained with the assumption of an equilibrium between both effects. For example, the predicted helium abundances in DAO's are clearly too low (Vennes et al. 1988). In PG 1159 stars carbon and oxygen would sink in time scales of [FORMULA] only (Unglaub & Bues 1997). Therefore we investigated the influence of mass loss (Unglaub & Bues 1998; Paper I). The results have been quite promising. For a DAO with [FORMULA], [FORMULA] and a mass loss rate of the order [FORMULA] to [FORMULA], the surface abundance of helium decreases from [FORMULA] to [FORMULA] within a time scale of [FORMULA]. So in the presence of a weak wind the time scales of gravitational settling may be of the same order of magnitude as the cooling ages. In Unglaub & Bues (1999) we have shown that in PG 1159 stars winds with [FORMULA] (in the following we give the mass loss rates in [FORMULA] and omit the units) considerably retard or prevent the gravitational settling of the heavy elements.

In comparison to Paper I, the most important improvement of the present investigation is, that [FORMULA], [FORMULA] and the mass loss rate are allowed to vary during the calculations. So the cooling of the star can be taken into account quantitatively. This new aspect and the involved physics are summarized in Sect. 2. In Sect. 3 the numerical method is described in detail. As it is more stable than the one used in Paper I, the elements H, He, C, N and O can be simultaneously taken into account for all calculations.

In Sect. 4 we discuss the existence of winds and various estimates of the mass loss rates from a theoretical point of view. Winds have been detected in hydrogen-rich central stars of planetary nebulae (Kudritzki et al. 1997; Perinotto 1993) and in luminous PG 1159 stars (Koesterke et al. 1998; Koesterke & Werner 1998). The mass loss rates are of the order [FORMULA] to [FORMULA]. Thus we expect that in these phases of stellar evolution the effect of gravitational settling is still negligible. For hot white dwarfs there is some evidence for the existence of winds. Werner et al. (1995) and Dreizler et al. (1995a) detected absorption lines of highly ionized stages of several elements in some DO's and one DAO and suggest that they are formed in a rapidly accelerating wind (Werner et al. 1999). However, [FORMULA] and [FORMULA] of these objects are not yet known. Holberg et al. (1998a,b) report on the detection of detached, blue shifted features in the majority of hot DO's and in a few DA's. These features are possibly formed in circumstellar matter, which may be due to episodes of mass loss. From these observational results it seems that winds are more likely to exist in DO's rather than in DA's.

In Sects. 5, 6 and 7 we investigate the chemical evolution of white dwarfs on the cooling sequence starting from a given composition, which in the following will be denoted as initial composition. The computations start, when or just before the star enters the cooling sequence. Here the expected mass loss rates are large enough so that diffusion processes cannot yet have changed the surface composition significantly. In principle, the initial compositions may vary from star to star. In hydrogen-rich pre-white dwarfs, Méndez (1991) found evidence for a variety of carbon abundances. A detailed NLTE analysis of such objects is in progress, first results have been obtained for the case of iron. (Deetjen et al. 1999). Because of this poor knowledge of the initial composition, we assume solar ratios He/H and CNO/H. The results are presented in Sect. 5. We especially investigate the question, for which hot hydrogen-rich white dwarfs the presence of helium can be expected and when do DAO's transform into DA's. Close inspection of the element abundances in hydrogen-deficient post-AGB stars shows that each object has its individual He/C/N/O mixture (Werner 2000). In Sect. 6 we consider a typical case with an initial composition [FORMULA], [FORMULA] and [FORMULA] (number ratios) and discuss the evolutionary link between PG 1159 stars and DO's. In Sect. 7 for the case of PG 1159 with various admixtures of hydrogen, the transformation of helium-rich into hydrogen-rich white dwarfs is investigated. Finally, in Sect. 8 we summarize the most important results and discuss the existence of chemically stratified atmospheres and the origin of the DB-gap.

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© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000
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