Stellar convection theory. III - Dynamical coupling of the two convection zones in A-type stars by penetrative motions

Anelastic modal equations are used to examine thermal convection occurring over many density scale heights in the entire outer envelope of an A-type star, encompassing both the hydrogen and helium convectively unstable zones. Single-mode anelastic solutions for such compressible convection display strong overshooting of the motions into adjacent radiative zones. Such mixing would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. Indeed, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The nonlinear single-mode equations admit two solutions for the same horizontal wavelength, and these are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. The upward directed flows experience large pressure effects when they penetrate into regions where the vertical scale height has become small compared to their horizontal scale. The fluctuating pressure can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone, even though the mean stratification is still superadiabatic. The pressure and buoyancy work there serves to decelerate the vertical motions and deflect them laterally, leading to strongmore » horizontal shearing motions. Thus the shallow but highly unstable hydrogen ionization zone may serve to prevent convection with a horizontal scale comparable to supergranulation from getting through into the atmosphere with any significant portion of its original momentum. This suggests that strong horizontal shear flows should be present just below the surface of the star, and similarly that strong horizontal shear flows should be present just below the surface of the star, and similarly that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows.« less