Linear Stability Analysis of Differentially Rotating Polytropes: New Results for the m = 2 f-Mode Dynamical Instability

@article{Karino2003LinearSA,
  title={Linear Stability Analysis of Differentially Rotating Polytropes: New Results for the m = 2 f-Mode Dynamical Instability},
  author={Shigeyuki Karino and Yoshiharu Eriguchi},
  journal={The Astrophysical Journal},
  year={2003},
  volume={592},
  pages={1119-1123}
}
We have studied the f-mode oscillations of differentially rotating polytropes by making use of the linear stability analysis. We found that the critical values of T/|W| where the dynamical instability against the m = 2 f-mode oscillations sets in decrease down to T/|W| ~ 0.20 as the degree of differential rotation becomes higher. Here m is an azimuthal mode number and T and W are the rotational energy and gravitational potential energy, respectively. This tendency is almost independent of the… 

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