STELLAR TURBULENT CONVECTION - A SELF-CONSISTENT MODEL

We present a self-consistent model for stellar turbulent convection th at is similar in spirit to the CM model (Canuto & Mazzitelli 1991) sin ce it accounts for the full spectrum of the turbulent eddies rather th an only one eddy, as done in the mixing length theory (MLT). The model differs from the CM model in the treatment of the rate of energy inpu t n(s)(k) from the source that generates the turbulence. In the presen t model, n(s)(k) is controlled by both the source and the turbulence i t ultimately generates, thus ensuring a self-consistent modeling of th e turbulence. This improves the CM model in which n(s)(k) was taken to be equal to the growth rate of the linear unstable convective modes. However, since the formulation of a self-consistent treatment is far f rom simple, we were forced to use a representation of the nonlinear in teractions less complete than the one in the CM model. The ensuing equ ations were solved numerically for a wide range of convective efficien cies. The results are the convective flux, the mean square turbulent v elocity, the root mean squared turbulent pressure and the turbulent vi scosity. We implemented the model in the ATON stellar structure code a nd computed the evolution of a solar model. The results are generally similar to those of the CM model and thus quite different from the MLT . The present model requires a smaller overshoot into the upper radiat ive zone than does the CM model, in accord with recent empirical estim ates. Application to Population II stars and comparison with the very metal-poor globular cluster M68 yields an age in the range 11-12 Gyr. This is somewhat younger than the CM age, which in turn is younger tha n the corresponding MLT age, a result of possible cosmological interes t.