Numerical methods for AGB evolution

Astronomy and Astrophysics – Astrophysics

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Stars: Interiors, Stars: Evolution, Stars: Asymptotic Giant Branch, Methods: Numerical

Scientific paper

A set of numerical methods has been devised to deal with the special needs of a parameter study on hydrostatic Asymptotic Giant Branch (AGB) evolution at a high degree of accuracy. The aim is to provide a grid of initial models for AGB-sequences starting at different total masses M_*_ and core masses M_c_ as parameters (and later on (Y,Z,α_MLT_) as well). These models are intended to be used as the inner part of self-consistent stellar models with realistic atmospheres including dust-driven winds. Since thermally pulsing (TP-)AGB models are always physically and numerically close to instability, the code was designed to be both highly reliable and accurate. With the methods published here we believe that we have overcome most of the notorious numerical difficulties of TP-AGB evolution. We computed 11 complete, straightforward evolutionary sequences with initial masses in the range 0.8 to 7.0 Msun_ from the ZAMS up to and along the AGB through numerous pulses with both a high spatial and temporal resolution. We also present less accurate, but fast techniques to transform given AGB models into others with (a) smaller total mass to mimic the evolution of a star with less initial mass and/or (b) heavier cores to avoid the detailed computation of thermal pulses. The variation of the main global stellar parameters (such as luminosity maxima and interpulse period) both as a function of core mass within a single sequence and as a function of total mass turns out to be very smooth and hence can be used to check the consistency of such artificial models. Additionally, the initial core mass and the behaviour of the maximum helium luminosity in a pulse are functions of the initial mass. They are used to obtain information about the applicability of method (a).

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