Effects of diffusion on the extent of overshoot below the solar convection zone

Abstract

Discontinuities in the derivatives of the sound speed at the base of the overshoot layer below the solar convection zone introduce a characteristic oscillatory component in the frequencies of solar p-modes as a function of the radial order n. The amplitude of this oscillatory part may be used to measure the extent of overshoot. However, sharp changes in the mean molecular weight due to gravitational settling of helium, as well as sharp changes in the opacity due to diffusion of metals, can also give rise to an oscillatory component in the frequencies of solar p-modes. Thus the estimate of overshoot will be affected by the diffusion of helium and metals. It is found that helium diffusion tends to increase the amplitude of the oscillatory component in the frequencies of p-modes, while metal diffusion tends to decrease this amplitude, but the net effect is to increase the amplitude. Apart from diffusion, the amplitude also depends on the depth of the convection zone, and to a lesser extent on the hydrogen and metal abundance in the solar envelope. In the absence of diffusion, or when the composition gradient near the base of the convection zone is smooth, the amplitude of the oscillatory component in a solar model with an overshoot of 0.05Hp is found to be consistent with that in the observed frequencies. Further, models with diffusion that have a sharp change in their composition profiles at the base of the solar convection zone do not seem to be favoured by observations.