Exact solutions for a generalized Mestel disc, and for truncated Toomre discs

Details Exact solutions for a generalized Mestel disc, and for truncated Toomre discs Exact solutions for a generalized Mestel disc, and for truncated Toomre discs

May 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984mnras.208....1h&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 208, May 1, 1984, p. 1-14.

Astronomy and Astrophysics

Astronomy

27

Angular Velocity, Density Distribution, Disk Galaxies, Galactic Rotation, Approximation, Density Wave Model

Scientific paper

Exact solutions for the surface density and rotational velocity of a type of infinitely flattened, self-gravitating, truncated disk are developed. The disk is a generalization of a Mestel-type disk and a finite version of a member of Toomre's family of infinite disks, with an index n = 0. It is shown that all truncated Toomre disks having an index of n greater than 0 can be generated by successive differentiations of the results for n = 0. For all finite Toomre disks, exact solutions beyond the truncation radii exhibit normally narrow regimes within which particle orbits can be made stable by a small modification of the surface density for each region. It is found that the nature of the truncation signature for finite Toomre disks is qualitatively similar to that of truncated exponential disks. The effect of adding spherical haloes to both generalized Mestel disks and finite Toomre disks of index n = 1 is examined, and the nature of spiral density waves that might persist in generalized Mestel disks is considered.

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