Seismic tests of the Sun's interior structure, composition, and age, and implications for solar neutrinos

The structure of the deep interior of a variety of standard and nonstandard solar models constrained by the low-l p-mode oscillation data from GONG are presented. For standard models, we show that the effects of both helium and heavy-element diffusion must be included in order to find simultaneous agreement with both the p-mode spectrum and the observed value of (Z/T).. Related to this conclusion, we find that the average interior heavy-element abundance is greater than the observed surface abundance in models whose small spacings, which are derived from the p-mode oscillation spectra, best match the observations. The high-quality data from the Global Oscillation Network Group (GONG) now permit a precise determination of the seismic age of the Sun. The best agreement with the calculated oscillation spectra is achieved for 4.5 +/- 0.1 Gyr, an age closely consistent with the age of the Sun inferred from meteorites, i.e., 4.53 +/- 0.04 Gyr. This result lends strong support to the standard assumption of the theory of stellar evolution. With regard to the nonstandard solar models, we set limits on the extent to which the nonstandard assumptions can be applied to the model while still being consistent with the observed p-modes. The nonstandard assumptions investigated here are: forced mixing in the core, forced mixing in a shell surrounding the core, and near-zero heavy-element abundance in the core. These assumptions were selected because at one time or another they have all been proposed to reduce the neutrino flux of the solar model, thereby bringing the flux of the model more in line with the observed flux. All nonstandard models include helium and heavy element diffusion. We confirm, now using the latest solar model physics, that these nonstandard assumptions, when capable of reducing significantly the solar neutrino flux, perturb the interior structure too much to be consistent with p-mode observations. In addition, we set strict limits on the extent to which these nonstandard assumptions are tolerated by the current p-mode observations. For example, we show that the p-mode small spacings are incompatible with a low-Z core larger than 0.06 M. in the Sun. And we show that if the Sun's core is chemically mixed, the extent of the mixed core cannot exceed 0.02 M.. The seismic data are also incompatible with extensive rapid mixing of He-4 in the solar envelope. This, we believe, also argues against the possibility of slow mixing of He-3 occurring in a shell, as was recently proposed by Cumming and Haxton to lower the Be-7/B-8 neutrino flux ratio. But we note that the occurrence of some mixing of He-3 and other trace elements and isotopes in the region of the solar interior where the initial He-4 abundance is nearly uniform (which could not at this point be detected by seismology) might modify the calculated neutrino fluxes.