A new estimate of the mixing length and convective overshooting in massive stars

A new approach to estimating the length scale of turbulent motions in convection zones of stars is presented. It is based on a statistical model of turbulence specialized to the stellar interior. It is predicted that the length scale of turbulence is proportional to the turbulence Mach number and to the geometric mean of the pressure scale height and a length scale associated with variations in the strength of the buoyancy forces. This model is applied to a 15.57 solar mass star, and it predicts strong overshooting in a layer up to several solar masses thick outside the convective core. It produces significant increases in the core hydrogen-burning lifetime and in the luminosity after core hydrogen exhaustion, and it removes the conditions that produce semiconvection. 28 references.