SEISMOLOGY OF THE SOLAR ENVELOPE - THE BASE OF THE CONVECTIVE ZONE ASSEEN IN THE PHASE-SHIFT OF ACOUSTIC-WAVES

At the base of the convective zone, discontinuities in the derivatives of the sound speed produce a phase shift in acoustic waves. This phas e shift, alpha0(nu), is inferred by matching the measured solar p-mode s to a second-order asymptotic description, the contribution from the surface layers and the second helium ionization zone being subracted u sing modes with turning points well inside the convective zone. The re sulting phase shift varies quasi-periodically with frequency with a pe riod almost-equal-to 220 muHz, and has an amplitude almost-equal-to 8 (+/- 4) x 10(-4) at a frequency of 3000 muHz. The phase shift alpha0(n u) is also calculated using the same technique for two solar models, o ne with no convective penetration and one with penetration extending f or 1 per cent of the solar mass. We estimate the predicted phase shift for models of the convective zone, including possible convective pene tration modelled by extending the zone a distance epsilonH(p) below th e classical boundary; alpha(nu) has a quasi-periodic contribution with period almost-equal-to 1/(2tau(b)), where tau(b) = integral dr/c is t he acoustic depth of the base of the zone, and with amplitude A(nu) = [(g2/16pi3c2nu2)2 f2(epsilon) + (g/4pi2cnu)2 h2(epsilon)]1/2, where f( epsilon) and h(epsilon) are functions of epsilon which also depend on the variation of opacity with temperature and density. For nu = 3 000 muHz, and typical values at the base of the convective zone, A(nu) = 5 x 10(-4) for epsilon = 0, decreases slightly for small epsilon and th en increases to 1 x 10(-3) for - = 0.25, and to 1.7 x 10(-3) for epsil on = 0.5. The currently available data are consistent with an overshoo ting parameter 0 less-than-or-equal-to epsilon less-than-or-equal-to 0 .25.