Stellar evolution with a variable mixing - length

By simulating the convection in the upper layers of seven diierent stars and matching these simulations to 1D mixing-length models using the same input physics, we have been able to infer the behaviour of the T-relation and the mixing-length parameter, , as the stellar parameters change. We have then used this knowledge in stellar evolution calculations, in order to investigate the consequences of changing and the T-relation as the stars evolve. 1. The convection simulations Using the convection code of Stein & Nordlund (1989), we have performed radiation coupled hydrodynamical simulations of convection in a small box at the surface of seven stars, ranging from the sub giants Boo and Procyon and down to the 0.9 M dwarf, Cen B. About 20% of the simulation domain is above hT i = T ee , and the simulations cover between 11 and 13 pressure scale heights or 10{11 decades in optical depth. Horizontally they each contain 5{7 granules. At optical depths below = 300, the simulation treats radiative transfer in detail using the Feautrier technique, in three dimensions and with monochro-matic opacities. For larger the diiusion approximation is used. For the atomic physics we use an updated version (Trampedach 1997) of the continuous opacities of Gustafsson et al. (1975) the opacity distribution functions of Kurucz (1992), and the so-called MHD equation of state (EOS) (Hummer & Mihalas 1988; DD appen et al. 1988).