4 Conclusions

By using updated versions of the OPAL and MHD EOS the seismic age of the Sun has been redetermined using SFSA with the latest GOLF/SOHO data. The important new ingredient in both equations of state is the inclusion of the special relativistic corrections. In both cases almost the same age has been obtained.

A crucial quantity in the determination of the seismic age is the proton-proton fusion rate. With the older versions of the equations of state, a rate about 4% higher as the value of Adelberger et al. (1998) appears to be favoured, in order to obtain a better agreement between seismic and meteoritic ages. However, with the updated versions of the OPAL and MHD EOS the seismic age obtained with Adelberger et al.'s (1998) value for $S_{\rm pp}(0)$ is $(4.57 \pm 0.11)$ Gyr, which is in excellent agreement with the meteoritic age of 4.57 Gyr (Bahcall et al. 1995).

Therefore, the presently favoured value for $S_{\rm pp}(0)$ is $4.00 \times 10^{-25}~{\rm MeV ~b}$. However, since the uncertainties, in particular, in the opacities are supposed to be of the order of a few percent, $S_{\rm pp}(0)$ can only be determined with a similar accuracy by comparing seismic and meteoritic ages.

A further source of uncertainty is the centrifugal and magnetic distortion, but these effects can be neglected for the Sun, as discussed by Dziembowski et al. (1999).

We expect to have asteroseismic data on solar-type stars with a precision of about $0.1~{\rm\mu Hz}$ from future space missions or high-precision ground-based multi-site spectrographic observations. We thus think that this effect must be included in the standard modelling of solar-like stars when discussing the evolutionary changes in the stellar core.

Acknowledgements

We thank H. M. Antia for many helpful discussions. The work of H. S. is supported by a Marie Curie Fellowship of the European Community programme "Human Potential'' under contract number HPMF-CT-2000-00951.