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

The thermal convection occurring over many density scale heights in an A-type star outer envelope, encompassing both the hydrogen and helium convectively unstable zones, is examined by means of anelastic modal equations. The single-mode anelastic equations for such compressible convection display strong overshooting of the motions into adjacent radiative zones, which would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. In addition, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The two solutions that the nonlinear single-mode equations admit for the same horizontal wavelength are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is suggested that strong horizontal shear flows should be present just below the surface of the star, and that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows.