On the third dredgeup phenomenon in asymptotic giant branch stars
Abstract
The third dredgeup phenomenon in asymptotic giant branch (AGB) stars is analyzed through evolutionary model calculations of a \mass{3}, solar metallicity star. The Schwarzschild criterion is used to test the stability of a given layer against convection, and the calculations are performed either with or without extramixing below the convective envelope. Based on these calculations, several questions are addressed regarding the occurrence of the third dredgeup in AGB star models, the laws governing that phenomenon, and some of its implications on the structural and chemical evolution of those stars. The use of the Schwarzschild criterion without extramixing of any sort is shown to lead to unphysical afterpulse models which prevent the occurrence of third dredgeup. Model calculations of a \mass{3} star using no extramixing confirm the failure to obtain dredgeup in those conditions. That conclusion is found to be independent of the mixing length parameter, stellar mass, or numerical accuracy of the models. Model calculations performed on selected afterpulses of the \mass{3} star, but with extramixing (using a decreasing bubble velocity field in the radiative layers and a diffusion algorithm for the mixing of the chemical elements), lead to efficient dredgeups at a rate of \mass{10^{5}10^{4}}/yr. Test calculations using different extramixing extents and efficiencies reveal that the dredgeup predictions are rather insensitive to those extramixing parameters. This important conclusion is understood by analyzing the physics involved in the dredgeup process. It is shown that the dredgeup rate is determined by the thermal relaxation timescale of the envelope as Crich matter is added from the core into the envelope. The dredgeup predictions are, however, expected to depend on the convection prescription in the envelope. Linear relations both between the dredgeup rate and the core mass M_c and between the dredgeup efficiency lambda and M_c are predicted by the model calculations. Those linear relations are expected to still hold when the feedback of the dredgeups on the AGB evolution is taken into account. They predict the dredgeup efficiency to level off at unity during the AGB evolution, at which point the core mass remains constant from one pulse to the next. The core mass is concomitantly predicted to evolve towards an asymptotic value. The existence of such an asymptotic core mass naturally provides an upper limit to the mass of the white dwarf remnant, and helps to constrain the initialfinal mass of white dwarfs. Synthetic calculations taking into account the dredgeup laws obtained from the full AGB model calculations predict a continuous increase of the stellar luminosity L with time, contrary to the predicted behavior of M_c and lambda . This results from an adopted dependence of L on both M_c and the radius R_c of the Hdepleted core of the form L~ M_c(2/R_c) . As a result of this increase of L with time, the initialfinal mass relation can further be constrained if mass loss is taken into account. If, for example, a superwind is assumed to eject all the remaining envelope of the \mass{3} star at \lsun{L=15000}, then the mass of the white dwarf remnant is predicted to be \mass{0.66}, instead of \mass{0.73} predicted by models without dredgeup. Finally, the synthetic calculations predict the formation of a \mass{3} carbon star after about 20 pulses experiencing dredgeup. Taking into account the fact that the luminosity decreases by a factor of two during about 20% of the interpulse phases, such a \mass{3} carbon star could be observed at luminosities as low as \lsun{7500}.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 1999
 arXiv:
 arXiv:astroph/9903473
 Bibcode:
 1999A&A...344..617M
 Keywords:

 STARS: ABUNDANCES;
 STARS: CARBON;
 STARS: EVOLUTION;
 STARS: INTERIORS;
 STARS: AGB AND POSTAGB;
 STARS: WHITE DWARFS;
 Astrophysics
 EPrint:
 16 pages, 13 figures, accepted for publication in A&