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(gzipped) PostScript## On the axis ratio of the stellar velocity ellipsoid in disks of spiral galaxies
^{1} Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands (vdkruit@astro.rug.nl)^{2} Astronomy Department, University of Virginia, P.O. Box 3818, Charlottesville, VA 22903, USA (grijs@virginia.edu)
The spatial distribution of stars in a disk of a galaxy can be
described by a radial scale length and a vertical scale height. The
ratio of these two scale parameters contains information on the axis
ratio of the velocity ellipsoid, i.e. the ratio of the vertical to
radial stellar velocity dispersions of the stars, at least at some
fiducial distance from the center. The radial velocity dispersion
correlates well with the amplitude of the rotation curve and with the
disk integrated magnitude, as was found by Bottema (1993). These
relations can be understood as the result of the stellar disk being
(marginally) stable against local instabilities at all length scales.
This is expressed by Toomre's well-known criterion, which relates the
sheer in the rotation to a minimum value that the radial stellar
velocity dispersion should have for stability for a given surface
density. Via the Tully-Fisher (1977) relation, the velocity dispersion
then becomes related to the integrated magnitude and hence to the
scale length. The vertical velocity dispersion relates directly to the
scale height through hydrostatic equilibrium. It can be shown that the
ratio of the two length scales relates to the axis ratio of the
velocity ellipsoid only through the Toomre parameter We have applied this to the statistically complete sample of edge-on galaxies, for which de Grijs (1997) has performed surface photometry and has determined the length scales in the stellar light distribution.
Online publication: November 23, 1999 |