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

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8. Summary and conclusions

In the [FORMULA]-[FORMULA] diagram the white dwarfs evolve from a region where winds exist into a region where no winds exist. Therefore somewhere on the cooling sequence mass loss must terminate, this is the wind limit. When the white dwarfs approach the wind limit and the mass loss rate decreases below about [FORMULA] we expect the onset of gravitational settling. The heavy elements (and helium in hydrogen-rich white dwarfs) begin to sink slowly. During the ongoing cooling the surface gravity increases. This and the decreasing abundances of heavy elements (and helium) favour the diminution of the mass loss rates. Then the elements sink rapidly and, for example, DAO's transform into DA's or PG 1159 stars into DO's. In Fig. 20 the most important results are summarized. The dashed line near [FORMULA] represents the wind limit for hydrogen-rich white dwarfs. These DAO's, which had approximately solar composition before they entered the cooling sequence, should transform into DA's near this line. This is in good agreement with the observational results. With one exception, in all objects above this line helium has been detected, whereas below more and more DA's appear. If the mass loss rates obtained from the two estimates used in our calculations are of the correct order of magnitude, the majority of the DAO's cannot be descendants of hydrogen-poor PG 1159 stars. For initial ratios [FORMULA] and 0.01 hydrogen floats up near the upper and lower dotted line, respectively. Dreizler & Werner (1996) report on an increasing ratio of hydrogen- to helium-rich white dwarfs with decreasing [FORMULA]. This result is expected, if their progenitors have a continuous distribution of H/He ratios with a variety of metal abundances.

For PG 1159 stars with initial H/He ratios below 0.01, according to our results the wind limit is between about [FORMULA] and 8.0 (solid line in Fig. 20). Near this line PG 1159 stars with an initial composition [FORMULA], [FORMULA] and [FORMULA] (number ratios) should be transformed into DO's. In agreement with this prediction, no PG 1159 star exists below this line. From the results in Sect. 6 we have seen that during the cooling the CNO elements first sink very slowly and then we expect a sharp transition into a DO. Because the initial compositions and thus the mass loss rates of the various objects may differ, an overlap of the regions populated by PG 1159 and DO's must be expected. Therefore the existence of PG 1159 stars and DO's with similar stellar parameters near a line with [FORMULA] is consistent with the existence of an evolutionary link. This implies that the majority of the DO's may belong to an evolutionary sequence which leads from the helium- and carbon-rich central stars of planetary nebulae (spectral type [WC]) via the PG 1159 phase into the DO white dwarfs. It is not clear, however, if this is true for all ones. Rauch et al. (1998) analyzed several helium -rich pre-white dwarfs (O(He) stars) in the range [FORMULA], [FORMULA], which do not show the strong lines of carbon typical for PG 1159 stars. This may be an indication for the existence of a distinct sequence, which never passes through the PG 1159 phase.

In Sect. 7 we have shown that PG 1159 stars with initial number ratios [FORMULA] directly evolve into DAO's, whereas the DO phase is left out. During the floating up of hydrogen some mass loss may still be present, so that the stellar atmosphere is in good approximation chemically homogeneous. According to Paper I weak winds with [FORMULA] prevent the development of an equilibrium between gravitational settling and concentration gradients. Stratified H/He atmospheres as calculated by Jordan & Koester (1986) or Vennes & Fontaine (1992) can exist only in the absence of any significant mass loss. PG 1159 stars which have initial ratios [FORMULA] transform into DO's. Due to the decreasing metal abundances we expect the termination of mass loss. In the absence of mass loss, however, hydrogen should float up rapidly. In Paper I it has been shown, that a DO with an initial ratio [FORMULA] may evolve into a DA within a time scale of [FORMULA] to [FORMULA]. In cooling DO's, at [FORMULA] helium recombination leads to the formation of an outer convection zone (Tassoul et al. 1990) with a mass of less than [FORMULA]. If, in the presence of a wind, the mass within this zone is lost rapidly, the influence of convection is negligible. When the mass loss rate approaches zero, convection may somewhat prolong the time scales, in which the surface composition changes. However, as diffusion acts in regions below, this thin convection zone probably cannot prevent the floating up of hydrogen. So we expect that finally all helium-rich white dwarfs evolve into DA's, if any traces of hydrogen are present. From these arguments it is plausible that in the [FORMULA]-[FORMULA] diagram below the wind limit a region exist where all white dwarfs are DA's. This scenario could be a possible explanation for the existence of the DB-gap, if mass loss terminates for all white dwarfs before they have reached the blue end near [FORMULA]. It fits into this picture that the only DAO of the sample of Bergeron et al. (1994), which shows evidence for stratification (PG 1305-017) is with [FORMULA] indeed one of the coolest ones. The existence of a stratified atmosphere is a clear indication for the absence of mass loss.

For a detailed comparison of the theoretical predictions with the abundances of individual objects a precise knowledge of the mass loss rates would be required. Diffusion calculations which assume an equilibrium between gravitational settling and radiative levitation are appropriate only in the absence of mass loss or if at least [FORMULA]. This has been shown in Paper I for mixtures of hydrogen and helium and by Chayer et al. (1997) for the case of silicon in DA's. An example is G 191-B2B with [FORMULA], [FORMULA] (Wolff et al. 1998). Dreizler & Wolff (1999) analyzed the ultraviolet and extreme-utraviolet spectra using self-consistent diffusion models. The results can reproduce the flux distribution and the ultraviolet lines at least of iron. The abundance distribution in the atmosphere is stratified, a result which has also been suggested by Barstow et al. (1999). So for DA's equilibrium diffusion calculations seem to be promising. This is consistent with our results, which predict the absence of mass loss in DA's with [FORMULA], especially if the abundances of the heavy elements are clearly below the solar one. For DO's the diffusion calculations of Dreizler (1999) cannot explain the observed spectra, they can best be fitted with chemically homogeneous models. From the calculations presented in this paper and from previous calculations with fixed [FORMULA] and [FORMULA] we obtain the following results. For DO's with mass loss rates in the range [FORMULA] the surface composition is more or less affected by gravitational settling. However, the CNO elements should still be present. Therefore the hotter DO's analyzed by Dreizler (1999) should have mass loss rates within this range, if they are descendants of PG 1159 stars and thus the composition is a consequence of gravitational settling. Abundances of the CNO elements of [FORMULA] and lower as found in the two cooler DO's HZ 21 and HD 149499 B with [FORMULA] and [FORMULA] are expected only for [FORMULA]. Therefore for these two DO's [FORMULA] is an upper limit for the mass loss rate. These result support the hypothesis that for DO's near the blue end of the DB-gap the mass loss rate approaches to zero, which favours the floating up of hydrogen. In addition, the results indicate that in DO's winds more probably exist rather than in DA's. However, the driving mechanism still has to be investigated in detail.

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© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000
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