A novel formulation by Lagrangian variational principle for rotational equilibria: Towards multidimensional stellar evolutions

Nobutoshi Yasutake, Kotaro Fujisawa, Shoichi Yamada

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This Letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of O(10<sup>-4</sup>) in the virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.

    Original languageEnglish
    Pages (from-to)L56-L60
    JournalMonthly Notices of the Royal Astronomical Society: Letters
    Volume446
    Issue number1
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    stellar evolution
    variational principles
    formulations
    equation of state
    angular momentum
    nuclear physics
    mesh
    equations of state
    energy
    stars
    configurations
    calculation
    distribution
    comparison
    method
    test

    Keywords

    • Stars: evolution
    • Stars: protostars
    • Stars: rotation

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science

    Cite this

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    T1 - A novel formulation by Lagrangian variational principle for rotational equilibria

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    AU - Yasutake, Nobutoshi

    AU - Fujisawa, Kotaro

    AU - Yamada, Shoichi

    PY - 2014

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    N2 - We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This Letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of O(10-4) in the virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.

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