Linear Stability Analysis of Differentially Rotating Polytropes: New Results for them = 2f‐Mode Dynamical Instability | Zendy

Shigeyuki Karino | Zendy; Yoshiharu Eriguchi | Zendy

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Linear Stability Analysis of Differentially Rotating Polytropes: New Results for them = 2f‐Mode Dynamical Instability

Author(s) -

Shigeyuki Karino,

Yoshiharu Eriguchi

Publication year - 2003

Publication title -

the astrophysical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.376

H-Index - 489

eISSN - 1538-4357

pISSN - 0004-637X

DOI - 10.1086/375768

Subject(s) - instability , physics , mode (computer interface) , stability (learning theory) , rotation (mathematics) , differential rotation , linear stability , classical mechanics , mechanics , mathematics , quantum mechanics , geometry , machine learning , computer science , operating system , magnetic field

We have studied the $f$-mode oscillations of differentially rotatingpolytropes by making use of the linear stability analysis. We found that thecritical values of $T/|W|$ where the dynamical instability against the $m = 2$$f$-mode oscillations sets in decrease down to $T/|W| \sim 0.20$ as the degreeof differential rotation becomes higher. Here $m$ is an azimuthal mode numberand $T$ and $W$ are the rotational energy and the gravitational potentialenergy, respectively. This tendency is almost independent of thecompressibility of the polytropes. These are the {\it first exact results} ofthe linear stability analysis for the occurrence of the dynamical instabilityagainst the $m = 2$ $f$-modes.Comment: 8 pages, 8 figures, accepted to Ap

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