Helioseismic Estimation of Convective Overshoot in the Sun

By using the periodic signal present in the frequencies of oscillation due to the base of the solar convection zone, Monteiro, Christensen-Dalsgaard & Thompson (1994) gave an upper limit to the extent of a layer of convective overshooting in the Sun. Alternative studies (Roxburgh & Vorontsov, 1994) have suggested that it may not be possible to do so since the amplitude of the signal does not vary monotonically with the extent of the layer. In this work a new more complete set of models is used to compare the values of the amplitude obtained from the tting of the signal with the expected amplitudes. These are determined using the assumption that the rapid variation occurring at the base of the convection zone and creating the periodic signal can be described as discontinuities of the sound-speed derivatives. The amplitude of the signal due to the discontinuity of the third derivative of the sound speed is then proportional to the derivative of the radiative gradient, while the amplitude resulting from the discontinuity of the second derivative is proportional to the diierence between radiative and adiabatic gradients at the position where the transition occurs. The latter is non-zero only if overshoot is present. Asymptotic predictions of the amplitudes of the signal in the p-mode frequencies are in good agreement with the values found from tting models with substantial overshoot regions; as was also found by Monteiro et al. the observed solar frequencies place severe limits on the extent of overshoot of this nature.