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Study on the Stability of Rapidly Rotating Stars

Research Project

Project/Area Number 02640198
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Astronomy
Research InstitutionUniversity of Tokyo

Principal Investigator

ERIGUCHI Yoshiharu  Univ. of Tokyo, Coll. Arts & Sci., Asso. Professor, 教養学部, 助教授 (80175231)

Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1991: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1990: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsRotating Stars / Equilibrium Configurations / Secular Instability / Dynamical Instability / Bar Mode / タ-イナミカル不安定 / 非圧縮性流体 / 平衝形状 / マクロ-リン楕円体 / モ-ド解析 / 回転ポリトロ-プ / トロイド形状
Research Abstract

We have developed the numerical schemes which can be applied to study the stability of rapidly rotating stars with compressible and incompressible equation of states. Concerning the compressible models we have used rotating polytropes and made use of the Euler displacements to formulate the linearized equations which give the eigen value and eigen functions. We have analyzed rotating polytropes with polytropic indices N = 1.0, 1.5 and 3.0. Since the stability depends on the rotation laws, we have examined three types of rotation laws. The main results are as follows : The value of T/ IW I for the occurrence of the secular instability against the m=2 bar mode is not necessarily 0.14 which has been widely believed 'universal' irrespective of the rotation law and the compressibility. In particular for the constant specific angular momentum distribution models this value becomes rather small, which imp tics that they are apt to unstable against the gravitational radiation even for slowly rotating cases.
For the incompressible fluids since there appears no time derivative of the density, we need to formulate the stability analysis different from that for the compressible cases. The linearized equations obtained from the basic equations are not reduced to a linear eigen value problem but become a non-linear eigen value problem. Since we are concerned with the deformed configuration from the axisymmetric states, we can specify the, value of the Euler displacement of the surface on the equatorial plane. By doing so the problem can be reduced to solving ordinary non-linear different lat equations which can be handled by the Newton-Raplison iteration scheme. This developed scheme has been applied to the toroidal con figurations and we found that the principal mode of the shear instability is stabilized by the effect of the self -gravity.

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] Y.Eriguch: "Close encounter:tidally-induced non-radeal oscillation of a fluid star" Astronomy and Astrophysics. 229. 457-466 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Eriguch: "Disk evolution caused by gravitation al radiation reaction" Astronomy and Astrophysics. 231. 61-72 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Eriguch: "Equation of motion and a possibiligy of snapping of a free cosmic string loop" Progress of Theuretical physics. 86. 1227-1237 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Eriguch: "structure of rapidly rofating axisymmetvic stars" Astromomy and Astrophysics. 248. 435-447 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Eriguch: "The ring around SN 1987A and rotation of the progenitor" Astroghysical Journal. 392. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Eriguch: "Structure and ciculatim of selfgravitating toroids" A stronhysical Journal. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. ERIGUCHI: "Close encounter : tidally-induced non-radial oscillation of a fluid star" Astronomy & Astrophysics. 229. 475-466 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. ERIGUCHI: "Disk evolution caused by gravitational radiation reaction" Astronomy & Astrophysics. 231. 61-72 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. ERIGUCHI: "Equation of motion and a possibility of snapping of a free cosmic string loop" Progress of Theoretical Physics. 86. 1227-1237 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. ERIGUCHI: "Structure of rapidly rotating axisymmetric stars" Astronomy & Astrophysics. 248. 435-447 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. ERIGUCHI: "The ring around SN 1987A and rotation of the progenitor" Astrophysical Journal. 392. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. ERIGUCHI: "Structure and circulation of self-gravitating toroids" Astrophysical Journal. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Eriguchi: "Eguation of motion and a possibility of snapping of a free cosmic string loop" Progress of Theorefical physics. 86. 1227-1237 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Eriguchi: "Structure of rapidly rotating axisymmetric stars I." Astronomy and Astrophysics. 248. 435-447 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Eriguchi: "The ring around SN 1987 A and rotatim of the progemitor" Astrophysical. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] S.NiShida: "Geneval relativistic structure of starーtoroid system" Astrophysical Jaurnal. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Eriguchi: "Strccture and cirwlatim of selfーgravifating toroids" Astrophysical Journal. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Hashimoto: "Hot and seed seefーgravitating rotating toroids" Astronomy and Astrophysics. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Eriguchi: "Close encounter:tidallyーinduced nonーradial oscillation of a fluid star" Astronomy and Astrophysics. 229. 457-466 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Eriguchi: "Disk evolution caused by gravitational radiation reaction" Astronomy and Astrophysics. 231. 61-72 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Eriguchi: "Structure of rapidly rotationg axisymmetric stars I.Numerical method for stellar structure and meridimal circulation" Astronomy and Astrophysics. (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Eriguchi: "Structure of rapidly rotating axisymmetric stars II.Structure and circulatim of selfーgravitating toroids" Astronomy and Astrophysics. (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Eriguchi: "Stability analysis of rapidly rotating polytropes" Monthly Notices of Royal Astronomical Society.

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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