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Astron. Astrophys. 321, 485-491 (1997)

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5. Conclusions

According to the results of Paper I it seemed possible that originally helium-rich atmospheres of post-AGB stars are transformed into metal-rich ones by diffusion. However, the present results show for [FORMULA], [FORMULA] that such a transformation takes about 800000 y. According to the post-AGB evolutionary tracks of Wood & Faulkner (1986) this exceeds the time-scales of stellar evolution by about a factor of 20. Whereas a significant oxygen enrichment up to a number fraction of 0.05, at maximum, is possible after 10000 y, the results for carbon are negative. In addition to the results shown in Fig. 2 we have done one calculation with an initial number ratio C/He of [FORMULA] instead of [FORMULA]. But even then only maximal carbon number fraction of 0.07 is reached after 50000 y in regions deep below the photosphere. Therefore, concerning the carbon enrichment in the stellar envelope, the "born-again AGB star" evolutionary scenario seems to be more promising, which results in a carbon mass fraction of more than [FORMULA] (Iben & Mc Donald, 1995).

For [FORMULA] and [FORMULA], after 1000 y the present results predict a thin outer layer with about [FORMULA] where carbon and neon are more abundant than helium. According to the evolutionary track of Wood and Faulkner (1986), a [FORMULA] post-AGB does not stay for more than 1000 y in this ultrahot region of the HRD, where the radiative forces acting on the heavy elements are extremely effective. After about 10000 y the star should have cooled down to [FORMULA], [FORMULA], which are the model parameters of the object H1504+65. As additional calculations have shown, for these values of [FORMULA] and [FORMULA] the thin metal-rich layer sinks back within less than 100 y. Therefore also for this case a pure diffusion scenario can be ruled out.

A comparison of the predictions of diffusion theory with observational results for cases with [FORMULA] and [FORMULA] and [FORMULA], respectively, leads to strong discrepancies in surface layer regions with masses [FORMULA]. This affects the carbon number fraction severily, which is predicted too low by three orders of magnitude. The results show that this contradiction cannot be solved by the assumption of long diffusion timescales. Near the photosphere the abundances relaxe to their values obtained from time-independent calculations within 1000 y. In deeper regions, where carbon and oxygen have hydrogen-like configuration, it seems that even large abundances can be levitated by radiative forces. However, diffusion takes place so slowly there that the diffusion theory has to be implemented into a stellar evolution code to obtain reliable predictions. Because other diffusion calculations with different physical assumptions (Chayer et al., 1995) also fail to predict the surface composition deduced from observations, it is necessary to investigate the effect of additional physical processes like convective mixing or mass loss. Whereas convective mixing tends to smear out composition gradients, the effect of mass loss seems to be not clear. It depends on the question which elements or ions are blown away preferably. In order to settle this question, a detailed investigation of the mechanism of momentum transfer via Coulomb collisions between the various ions would be required. According to Springmann & Pauldrach (1992) the usual assumption of regarding radiatively driven winds of hot stars as a simple one-component fluid is not always justified, especially in the case of thin winds with low mass loss rates and high final velocities.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998