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Astron. Astrophys. 334, 703-712 (1998)

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5. Conclusion

The new solar evolution code described in this paper has been shown to produce results broadly consistent with previous calculations, as well as having well-controlled truncation errors both in space and time. The effects of using interpolating tables for the opacity and equation of state have been quantified, with the conclusion that at present the interpolation of the OPAL opacity tables sets the limit on errors in the calibrated hydrogen abundance and mixing-length parameters.

The effect of including helium diffusion and settling in the evolution calculation is very similar to that found by previous authors. There is a significant increase in the predicted neutrino flux for the chlorine experiments ([FORMULA]), and a somewhat smaller increase ([FORMULA]) for the gallium experiments. When heavy-element diffusion is also included, the corresponding increases relative to the non-diffusive models are [FORMULA] and [FORMULA], both similar to the values found by Turck-Chièze & Brun (1997). The actual value of the predicted count rate for the chlorine experiment, 7.86 SNU, is somewhat smaller than that reported by most other authors, but larger than the 7.2 SNU reported by Turck-Chièze & Brun. These differences point to the need for further investigation.

The inclusion of the variation of the overall heavy-element mass fraction in the calculation of the equation of state has been shown to have an almost negligible effect on the sound speed on the computed model, rendering the effect of the variation of individual heavy-element abundances in the equation of state calculation undetectable at the current precision of structure inversions. This is, however, not the case in the calculation of the opacity, and opacity data taking into account detailed changes in composition are necessary.

A comparison is provided here between models constructed using the OPAL and MHD-E equations of state. The agreement is not as good as that reported in previous comparisons between OPAL and MHD, principally due to inclusion of the relativistic correction to the electron pressure in the newly-calculated MHD-E equation of state. The significant effect that this correction has on the sound speed of calibrated models should perhaps prompt efforts to include it consistently in future equation of state calculations.

A simple model of the sub convection-zone mixing associated with the solar tachocline has been shown to improve the agreement in sound speed with the sun just below the base of the convection zone. Further study is required to understand fully the sound speed enhancement found in this region of the sun.

In spite of improvements in solar evolution calculations, it is as well to point out that there are still considerable unknowns in many of the physical assumptions (Gough & Toomre 1991). The high accuracy of the calculation presented here facilitates detailed comparison with models by other authors, but belies some of the inherent uncertainties. Perhaps most serious is the assumption of uniform chemical composition at zero age, which is contingent on the sun having passed through a fully-convective Hayashi phase of evolution. Calculations by Larson (1969) have suggested that this may not have occurred. Another significant failing of the standard solar model is its neglect of large-scale macroscopic motions (aside from convection). It is known that such motions must occur in any rotating star, which could have important repercussions for its evolution by redistributing both material and angular momentum. Mass loss and accretion are known to be important processes in stellar evolution but are again entirely neglected in the standard solar model prescription. The modular nature of MoSEC should permit refinements of the physical assumptions to be easily incorporated, allowing the code to keep pace with our improving understanding of solar evolution.

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© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998

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