Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Stability Analysis of Differentially Rotating Polytropes -- New
  results for the m = 2 f-mode dynamical instability --   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.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg