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Stellar Inversion Techniques

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Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds

Part of the book series: Astrophysics and Space Science Proceedings ((ASSSP,volume 49))

Abstract

Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar models. In this lecture, we provide an introduction to this topic by explaining kernel-based inversion techniques. Specifically, we explain how various kernels are obtained from the pulsation equations, and describe inversion techniques such as the Regularised Least-Squares (RLS) and Optimally Localised Averages (OLA) methods.

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Notes

  1. 1.

    If one assumes that modes are proportional to exp(imφ), φ being the longitude, such a time dependence will lead to m > 0 modes being prograde, where m is the azimuthal order. If one uses, instead, a time dependence of the form exp(iωt), then m > 0 modes will be retrograde.

  2. 2.

    Throughout these lectures, the δ notation will be used to indicate a modification of the equilibrium stellar structure and associated pulsations rather than a Lagrangian perturbation.

  3. 3.

    See http://bison.ph.bham.ac.uk/spaceinn/inversionkit.

  4. 4.

    See http://bison.ph.bham.ac.uk/spaceinn/inversionpipeline.

  5. 5.

    See http://bison.ph.bham.ac.uk/spaceinn/nonlinearkit.

  6. 6.

    See http://sun.stanford.edu/~rmunk/SOLApack/index.html.

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Acknowledgements

I would like to thank the organisers of this Summer School for giving me the opportunity to give this lecture on inversions. Furthermore, I thank M.J. Thompson for introducing me to inversions, as well as S. Basu and G. Buldgen for many discussions on the topic.

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Authors and Affiliations

  1. LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC, Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Citée, 92195, Meudon, France

    Daniel R. Reese

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Correspondence to Daniel R. Reese .

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Editors and Affiliations

  1. School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom

    Tiago L. Campante

  2. Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, Porto, Portugal

    Nuno C. Santos

  3. Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, Porto, Portugal

    Mário J. P. F. G. Monteiro

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Reese, D.R. (2018). Stellar Inversion Techniques. In: Campante, T., Santos, N., Monteiro, M. (eds) Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds. Astrophysics and Space Science Proceedings, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-59315-9_4

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