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R-mode oscillations of general relarivistic and rapidly rotating stars by the Cowling approximation

Research Project

Project/Area Number 14540244
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 素粒子・核・宇宙線
Research InstitutionThe University of Tokyo

Principal Investigator

ERIGUCHI Yoshiharu  ERIGUCHI,Yoshiharu, 大学院・総合文化研究科, 教授 (80175231)

Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥2,900,000 (Direct Cost: ¥2,900,000)
Keywordsgeneral relativity / rapidly rotating star / nonradial oscillations / r-mode oscillations / gravitational wave emission / secular instability / 非動径振動 / 回転星 / カウリング近似 / r-モード / 線型安定性解析
Research Abstract

We have succeeded in developing anew formulation for solving r-mode oscillations of general relativistic and rapidly rotating stars in the framework of the Cowling approximation. By following this formulation we have developed a numerical code and obtained r-mode oscillations of several equilibrium sequences of rapidly rotating general relativistic polytropes. In order to check the numerical code works properly, we have computed r-mode oscillations of rotating stars in the Newtonian limit as well as those of slowly rotating general relativistic stars and compared our results with those obtained by different methods. they agree very well. We have computed r-mode oscillations of uniformly rotating polytropic sequences with the polytropic indices N=0.5 and 1.0 whose strengths of gravity are M/R=0.1 and 0.2. Here M and R are the gravitational mass and the radius of the spherical stars. Oscillation frequencies and eigenfunctions of m=2 r-modes are obtained for the equilibrium sequences from the spherical configurations to the critical configurations of mass shedding limits. The important results are as follows. First, the rations of the eigenfirequencies of the r-modes to the angular velocityies of the unperturbed rotating stars depend scarcely on the polytropic indices. This is the same as that in the Newtonian case. Second, contrary to this, the strength of where T and W are the rotational energy and the gravitational energy, respectively. The values of a and b are a=1.4 and b=1.9 for M/R=0.1 and a=1.5 and b=1.2~1.3 for M/R=0.2. Our present results for barotropic stars imply that there could exist r-mode oscillations for rapidly rotating general relativistic stars.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] Shin'ichirou Yoshida: "Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits"Astrophysical Journal Letters. 568,2. L41-L44 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeyuki karino: "Gravitationsl radiation reaction driven secular instability of f-mode oscillations in differentially rotating Newtonian stars"Astrophysical Journal. 575,1. 413-419 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaru Shibata: "Dynamical instability of differentially rotating stars"Monthly Notices of Royal Astronomical Society. 334,2. L27-L31 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeyuki Karino: "Linear stability analysis of differentially rotating polytropes---New results for the m=2 f-mode dynamical instability---"Astrophysical Journal. 592,1. 1119-1123 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaru Shibata: "Dynamical bar-mode instability of differentially rotating stars : Effects of compressibility and velocity profiles"Monthly Notices of Royal Astronomical Society. 343,1. 619-626 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] shin'ichi Yoshida: "Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits"Astrophysical Journal Letters. 568-2. L41-L44 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeyuki Karino: "Gravitational radiation reaction drive secular instability of f-mode oscillations in differentially rotating Newtonian stars"Astrophysical Journal. 575-1. 413-419 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaru Shibata: "Dynamical instability of differentially rotating stars"Monthly Notices of Royal Astronomical Society. 334-2. L27-L31 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] shigeyuki Karino: "Linear stability analysis of differentially rotating Polytropes=New results for the m=2 f-mode Dynamical instability"Astrophysical Journal. 592-1. 1119-1123 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaru Shibata: "Dynamical bar-mode instability of differentially Rotating stars: Effects of compressibility and Velocity profiles"Monthly Notices of Royal Astronomical Society. 343-1. 619-626 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeyuki Karino: "Linear stability analysis of differentially rotating polytropes --- New results for the m = 2 f-mode dynamical instability ---"Astrophysical Journal. 592,1. 1119-1123 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Masaru Shibata: "Dynamical bar-mode instability of differentially rotating stars : Effects of compressibility and velocity profiles"Monthly Notices of Royal Astronomical Society. 343,1. 619-626 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Yoshida: "Frequencies of f-modes in differentially rotating relativistic stars and secular stability limits"Astrophysical Journal. 568. L41-L44 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Shibata: "Dynamical instability of differentially rotating stars"Monthly Notices of Royal Astronomical Society. 334. L27-L31 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Karino: "Gravitational radiation reaction driven secular instability of f-modes oscillations in differentially rotating Newtonian stars"Astrophysical Journal. 578. 413-419 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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