Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978apj...221...51l&link_type=abstract
Astrophysical Journal, Part 1, vol. 221, Apr. 1, 1978, p. 51-61.
Astronomy and Astrophysics
Astrophysics
48
Astronomical Models, Galactic Rotation, Galactic Structure, Rotary Stability, Andromeda Galaxy, Angular Momentum, Mathematical Models, Milky Way Galaxy, Rotating Disks, Rotating Fluids
Scientific paper
A resonant instability of a fluid disk model of flat galaxies is discussed which may act to bring about a marginally stable state for which there is a unique self-similar solution with a flat rotation curve. The stability problem for small-scale perturbations of differentially rotating fluid disks is reconsidered using the analogy between a self-gravitating disk and a charged-particle ring. The linear initial-value problem for a low-'temperature' fluid disk is analyzed, focusing on perturbations that are large near the region of corotation resonance. It is shown that the function f(r), which is equal to the product of the surface mass density, the angular velocity of the differentially rotating disk material, and the inverse square of epicyclic frequency, has the role of the distribution function for angular momentum. It is shown that the instability, whose nature is related to that of the negative-mass instability of charged-particle rings, may occur if f(r) has a maximum or minimum as a function of r with (d/dr) times the angular velocity not equal to zero at the extremum of f. Values of the relevant parameters derived from observations of the Galaxy and M31 are employed to calculate f(r) for the two systems.
Hohlfeld R. G.
Lovelace Richard V. E.
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