Energy transport, overshoot, and mixing in the atmospheres of M-type   main- and pre-main-sequence objects
  We constructed hydrodynamical model atmospheres for mid M-type main-, as well as pre-main-sequence (PMS) objects. Despite the complex chemistry encountered in these cool atmospheres a reasonably accurate representation of the radiative transfer is possible, even in the context of time-dependent and three-dimensional models. The models provide detailed information about the morphology of M-type granulation and statistical properties of the convective surface flows. In particular, we determined the efficiency of the convective energy transport, and the efficiency of mixing by convective overshoot. The convective transport efficiency was expressed in terms of an equivalent mixing-length parameter alpha in the formulation of mixing-length theory (MLT) given by Mihalas (1978). Alpha amounts to values around 2 for matching the entropy of the deep, adiabatically stratified regions of the convective envelope, and lies between 2.5 and 3.0 for matching the thermal structure of the deep photosphere. For current spectral analysis of PMS objects this implies that MLT models based on alpha=2.0 overestimate the effective temperature by 100 K and surface gravities by 0.25 dex. The average thermal structure of the formally convectively stable layers is little affected by convective overshoot and wave heating, i.e., stays close to radiative equilibrium conditions. Our models suggest that the rate of mixing by convective overshoot declines exponentially with geometrical distance to the Schwarzschild stability boundary. It increases at given effective temperature with decreasing gravitational acceleration. 
H.-G. Ludwig, F. Allard, P.H. Hauschildt