EDP Sciences
Free access
Issue A&A
Volume 505, Number 2, October II 2009
Page(s) 735 - 742
Section Stellar structure and evolution
DOI http://dx.doi.org/10.1051/0004-6361/20077713
Published online 28 July 2009

A&A 505, 735-742 (2009)
DOI: 10.1051/0004-6361/20077713

The solar-interior equation of state with the path-integral formalism

I. Domain of validity
A. Perez1, 2, K. Mussack3, 4, W. Däppen3, and D. Mao3

1  Laboratoire de Physique Théorique (UMR CNRS/ULP 7085), Université Louis Pasteur de Strasbourg, 67084 Strasbourg Cedex, France
    e-mail: perez@lpt1.u-strasbg.fr
2  Department of Applied Physics, Jerusalem College of Technology, 92221 Jerusalem, Israel
3  Department of Physics and Astronomy, USC, Los Angeles, CA 90089-1342, USA
    e-mail: [dappen;dmao]@usc.edu
4  Institute of Astronomy, University of Cambridge, Cambridge CB3 0HA, UK
    e-mail: mussack@ast.cam.ac.uk

Received 25 April 2007 / Accepted 19 July 2009

Aims. This is the first paper in a series that deals with solar-physics applications of the equation-of-state formalism based on the formulation of the so-called “Feynman-Kac (FK) representation”. Here, the FK equation of state is presented and adapted for solar applications. Its domain of validity is assessed. The practical application to the Sun will be dealt with in Paper II. Paper III will extend the current FK formalism to a higher order.
Methods. A recent rigorous quantum-statistical formalism for Coulomb systems is used to compute the thermodynamical quantities for solar modeling, taking into account the necessary requirements on smoothness and accuracy. The FK formalism being a virial expansion, it suffers from the well-known deficiency that it is limited to nearly full ionization. This point is elaborated in detail, and the quantitative criterion for the domain of validity of the FK equation of state is established.
Results. Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This includes the inner region of the Sun out to about .98 of the solar radius. Despite this limitation, in the parts of the Sun where it is applicable, the FK equation of state has the power to be more accurate than the equations of state currently used in solar modeling. The FK approach is especially suited to study physical effects such as Coulomb screening, bound states, the onset of recombination of fully ionized species, as well as diffraction and exchange effects.
Conclusions. Despite technical difficulties in its application, there are unique features in the FK approach that promise to turn it into the most exact of the available formalisms, provided FK is restricted to the deeper layers of the Sun where more than 90% of helium is ionized. The localizing power of helioseismology allows a test of the FK equation of state. Such a test will be beneficial both for better solar models and for tighter solar constraints of the equation of state.

Key words: equation of state -- stars: interiors -- Sun: interior -- Sun: helioseismology

© ESO 2009

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.

Editor-in-Chief: T. Forveille
Letters Editor-in-Chief: J. Alves
Managing Editor: N. Aghanim

ISSN: 0004-6361 ; e-ISSN: 1432-0746
Frequency: 12 volumes per year
Published by: EDP Sciences

Mirror sites: CDS | EDP Sciences
  RSS feeds
© The European Southern Observatory (ESO)