Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Dynamically Collapsing Gas Sphere   We discuss stability of dynamically collapsing gas spheres. We use a
similarity solution for a dynamically collapsing sphere as the unperturbed
state. In the similarity solution the gas pressure is approximated by a
polytrope of $ P = K \rho ^\gamma $. We examine three types of perturbations:
bar ($ \ell = 2$) mode, spin-up mode, and Ori-Piran mode. When $ \gamma < 1.097
$, it is unstable against bar-mode. It is unstable against spin-up mode for any
$ \gamma $. When $ \gamma < 0.961 $, the similarity solution is unstable
against Ori-Piran mode. The unstable mode grows in proportion to $ | t - t_0 |
^{-\sigma} $ while the central density increases in proportion to $ \rho_c
\propto (t - t_0) ^{-2} $ in the similarity solution. The growth rate, $ \sigma
$ is obtained numerically as a function of $ \gamma $ for bar mode and
Ori-Piran mode. The growth rate of the bar mode is larger for a smaller $
\gamma $. The spin-up mode has the growth rate of $ \sigma = 1/3 $ for any $
\gamma $.

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The categories of this paper are: stat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph