NUMERICAL-METHODS FOR AGB EVOLUTION

A set of numerical methods has been devised to deal with the special n eeds 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, alpha(MLT) ) as well). These models are intended to be used as the inner part of self-consistent stellar models with realistic atmospheres including du st-driven winds. Since thermally pulsing (TP-)AGB models are always ph ysically and numerically close to instability, the code was designed t o be both highly reliable and accurate. With the methods published her e we believe that we have overcome most of the notorious numerical dif ficulties of TP-AGB evolution. We computed 11 complete, straightforwar d evolutionary sequences with initial masses in the range 0.8 to 7.0 M . from the ZAMS up to and along the AGB through numerous pulses with b oth a high spatial and temporal resolution. We also present less accur ate, but fast techniques to transform given AGB models into others wit h (a) smaller total mass to mimic the evolution of a star with less in itial mass and / or (b) heavier cores to avoid the detailed computatio n of thermal pulses. The variation of the main global stellar paramete rs (such as luminosity maxima and interpulse period) both as a functio n of core mass within a single sequence and as a function of total mas s turns out to be very smooth and hence can be used to check the consi stency of such artificial models. Additionally, the initial core mass and the behaviour of the maximum helium luminosity in a pulse are func tions of the initial mass. They are used to obtain information about t he applicability of method (a).