Astronomy and Astrophysics – Astrophysics
Scientific paper
2003-04-16
Astrophys.J. 592 (2003) 1119-1123
Astronomy and Astrophysics
Astrophysics
8 pages, 8 figures, accepted to ApJ
Scientific paper
10.1086/375768
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 $T/|W| \sim 0.20$ as the degree of differential rotation becomes higher. Here $m$ is an azimuthal mode number and $T$ and $W$ are the rotational energy and the gravitational potential energy, respectively. This tendency is almost independent of the compressibility of the polytropes. These are the {\it first exact results} of the linear stability analysis for the occurrence of the dynamical instability against the $m = 2$ $f$-modes.
Eriguchi Yoshiharu
Karino Shigeyuki
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