A NONLOCAL CONVECTION MODEL OF THE SOLAR CONVECTION ZONE

The models of the solar convection zone with various convective parameters c1 and c2 have been constructed based on Xiong's nonlocal convection theory (Xiong 1979, 1981). The departure form radiative equilibrium is taken into account by means of the generalized Eddington approximation (Xiong 1989a). The nonlocal convection model has a large temperature gradient in the surface superadiabatic convection zone and a rather shallow convectively instable zone in comparison with the local convection model with the same c1. The departures from radiative equilibrium are negligible except at the most upper layer of the convection zone, where the maximum relative departure \1 - aT4/E(r)\ is about 3%. A comparison of the model based on the Eddington approximation with the one based on the radiative diffusion approximation shows that they are very close.to each other. The theoretical rms turbulent velocity component and the rms relative temperature fluctuation at the photosphere are about 1.4 km s-1 and 0.04 respectively, and decrease exponentially with In P upwards. The e-folding length is about 1.4 square-root c1 c2 times the pressure scale height. Passing through the boundary of the convectively unstable zone the turbulent velocity-temperature correlation changes its sign. The turbulent kinetic energy is less than about 1.5% of the total energy flux, and has no significant direct influence on the structure of the convection zone. The turbulent pressure gradient can achieve few tenths in the upper layer of the convection zone and its influence on the structure of the convection zone cannot be neglected. A comparison of the theoretical eigenfrequencies of the adiabatic p-mode oscillations and the surface lithium depletion with the observed ones shows that the model with c1 = 0.75 and c2 = 0.25 seems to be optimal. The theoretical eigenfrequencies of the modes of degree l < 60 are systematically smaller than the observed ones and the overshooting seems slightly deeper in views of the surface lithium depletion. A reasonable explanation may be that there is an about 10(4) G magnetic field in the lower convection zone. The magnetic fields will brake extensive overshooting and block the convective heat transport, which will increase the temperature gradient in the lower convection zone.