Astronomy and Astrophysics – Astrophysics
Scientific paper
Oct 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...185..160h&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 185, no. 1-2, Oct. 1987, p. 160-164.
Astronomy and Astrophysics
Astrophysics
16
Accretion Disks, Astronomical Models, Dynamic Stability, Rotating Cylinders, Astrophysics, Corotation, Perturbation Theory, Resonance, Runge-Kutta Method
Scientific paper
Dynamical instabilities are investigated for a cylinder whose angular velocity Ω is proportional to r-1.5 where r is the radial distance. The eigenfunctions and the growth rates of the instability are computed. The cylinder is found to be unstable against non-axisymmetric perturbations. The rotation law adopted here is that of a Keplerian disk, i.e., a geometrically thin disk rotating around a compact object. The results imply that such disks are unstable for all ratios of the outer to the inner radius in excess of some small value. For the cylinder considered here, the critical value was 1.4. The amplitude of the tangential displacement of the eigenfunctions is large at the corotation point where the mean velocity is equal to the pattern velocity of the perturbation. Thus, it is concluded that this instability is due to the corotation resonance.
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