Dynamical shear instability

The dynamical shear instability is an important mixing process in the advanced stages of the evolution of massive stars. We calculated different models of 15 M⊙ with an initial rotational velocity, υini = 300 km/s to investigate its efficiency. We found that the dynamical shear instability has a timescale shorter than Oxygen burning timescale and that it slightly enlarges the convective zones and smoothens the omega gradients throughout the evolution. However, its effect is too localized to slow down the core of the star. 1. Theory & computer model The stability criterion for dynamical shear instability is the Richardson criterion: Ri = N 2 (∂U/∂z) > 1 4 = Ric, where U is the horizontal velocity, z the vertical coordinate and N2 the Brunt-Väisälä frequency. Using this criterion, the timescale of the instability is the dynamical timescale and the instability is called dynamical shear instability (Endal & Sofia 1978). If heat losses are accounted for in Ri (Maeder 1997), the timescale is the thermal timescale and in that case the instability is called secular shear instability. The critical value, Ric = 1/4, is used by most authors as the limit for the occurrence of the dynamical shear. However, recent studies (Canuto 2002; Brüggen & Hillebrandt 2001) show that turbulence may occur as long as Ri < ∼ 1. Different formulae for the corresponding diffusion coefficient, D, are used at the present time (Zahn 1992; Maeder 1997; Heger et al 2000; Brüggen & Hillebrandt 2001). The following dynamical shear diffusion coefficient suggested by J.-P. Zahn is used in this study: