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Helioseismology and Solar Abundances Physics Reports 457 (2008) 217–283 www.elsevier.com/locate/physrep Helioseismology and solar abundances Sarbani Basua,∗, H.M. Antiab a Department of Astronomy, Yale University, P.O. Box 208121, New Haven, CT 06520-8101, USA b Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India Accepted 13 December 2007 Available online 23 December 2007 editor: M.P. Kamionkowski Abstract Helioseismology has allowed us to study the structure of the Sun in unprecedented detail. One of the triumphs of the theory of stellar evolution was that helioseismic studies had shown that the structure of solar models is very similar to that of the Sun. However, this agreement has been spoiled by recent revisions of the solar heavy-element abundances. Heavy-element abundances determine the opacity of the stellar material and hence, are an important input to stellar model calculations. The models with the new, low abundances do not satisfy helioseismic constraints. We review here how heavy-element abundances affect solar models, how these models are tested with helioseismology, and the impact of the new abundances on standard solar models. We also discuss the attempts made to improve the agreement of the low-abundance models with the Sun and discuss how helioseismology is being used to determine the solar heavy-element abundances. A review of current literature shows that attempts to improve agreement between solar models with low heavy-element abundances and seismic inference have been unsuccessful so far. The low-metallicity models that have the least disagreement with seismic data require changing all input physics to stellar models beyond their acceptable ranges. Seismic determinations of the solar heavy-element abundances yield results that are consistent with the older, higher values of the solar abundance, and hence, no major changes to the inputs to solar models are required to make higher-metallicity solar models consistent with the helioseismic data. c 2007 Elsevier B.V. All rights reserved. PACS: 96.60.Jw; 96.60.Ly; 96.60.Fs Keywords: Solar interior; Helioseismology; Abundances Contents 1. Introduction.......................................................................................................................................................218 2. Making solar models ..........................................................................................................................................221 2.1. Equations of stellar structure and evolution ................................................................................................221 2.2. Input microphysics..................................................................................................................................224 2.2.1. The equation of state .................................................................................................................224 ∗ Corresponding author. E-mail address: [email protected] (S. Basu). 0370-1573/$ - see front matter c 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2007.12.002 218 S. Basu, H.M. Antia / Physics Reports 457 (2008) 217–283 2.2.2. Opacity....................................................................................................................................224 2.2.3. Nuclear reaction rates................................................................................................................224 2.3. Constructing standard solar models...........................................................................................................225 2.4. Sources of uncertainty in standard solar models..........................................................................................226 3. Helioseismology ................................................................................................................................................228 3.1. The basic equations.................................................................................................................................228 3.2. Determining the solar structure from seismic data.......................................................................................231 3.3. Determining the solar helium abundance ...................................................................................................235 3.4. Determining the depth of the solar convection zone.....................................................................................236 3.5. Testing equations of state.........................................................................................................................237 4. Helioseismic results............................................................................................................................................237 4.1. Results about solar structure.....................................................................................................................237 4.2. Seismic tests of input physics ...................................................................................................................239 5. Solar abundances ...............................................................................................................................................243 6. Consequences of the new abundances ...................................................................................................................248 6.1. The base of the convection zone ...............................................................................................................250 6.2. The convection-zone helium abundance.....................................................................................................252 6.3. The radiative interior ...............................................................................................................................253 6.4. The ionization zones ...............................................................................................................................254 6.5. Some consequences for stellar models.......................................................................................................255 7. Attempts to reconcile low-Z solar models with the Sun ..........................................................................................257 7.1. Increasing input opacities.........................................................................................................................257 7.2. Increasing diffusion.................................................................................................................................259 7.3. Increasing the abundance of neon and other elements..................................................................................260 7.4. Other processes ......................................................................................................................................262 8. Seismic estimates of solar abundances ..................................................................................................................263 8.1. Results that depend on the Z-dependence of opacity ...................................................................................264 8.2. Results from the core...............................................................................................................................265 8.3. Results that depend on the Z-dependence of the equation of state .................................................................267 9. Possible causes for the mismatch between seismic and spectroscopic abundances ......................................................272 10. Concluding thoughts...........................................................................................................................................275 Acknowledgments..............................................................................................................................................276 Appendix. Supplementary data..........................................................................................................................276 References ........................................................................................................................................................276 1. Introduction Arthur Eddington began his book “The Internal Constitution of the Stars” saying that “At first sight it would seem that the deep interior of the sun and stars is less accessible to scientific investigation than any other region of the universe. Our telescopes may probe farther and farther into the depths of space; but how can we ever obtain certain knowledge of that which is hidden behind substantial barriers? What appliance can pierce through the outer layers of a star and test the conditions within?” (Eddington, 1926). Eddington went on to say that perhaps we should not aspire to directly “probe” the interiors of the Sun and stars, but instead use our knowledge of basic physics to determine what the structure of a star should be. This is still the predominant approach in studying stars today. However, we now also have the “appliance” that can pierce through the outer layers of the Sun and give us detailed knowledge of what the internal structure of the Sun is. This “appliance” is helioseismology, the study of the interior of the Sun using solar oscillations. While solar neutrinos can probe the solar core, helioseismology provides us a much more detailed and nuanced picture of the entire
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