header graphic



[*] Scale-free dynamical models for galaxies: flattened densities in spherical potentials
de Bruijne J., van der Marel R.P., de Zeeuw P.T.
MNRAS, 282, 909-925, 1996
© 1996. The Royal Astronomical Society. All Rights Reserved.

[*] Citations to this paper in the ADS

This paper presents two families of phase-space distribution functions that generate scale-free spheroidal mass densities in scale-free spherical potentials. The assumption of a spherical potential has the advantage that all integrals of motion are known explicitly. The `case I' distribution functions are anisotropic generalizations of the flattened f(E,L_z) model, which they include as a special case. The `case II' distribution functions generate flattened constant-anisotropy models. Free parameters control the radial power-law slopes of the mass density and potential, the flattening of the mass distribution, and the velocity dispersion anisotropy. The models can describe the outer parts of galaxies and the density cusp structure near a central black hole, but also provide general insight into the dynamical properties of flattened systems. Because of their simplicity they provide a useful complementary approach to the construction of flattened self-consistent three-integral models for elliptical galaxies.

The dependence of the intrinsic and projected properties on the model parameters and the inclination is described. The case I models have a larger ratio of RMS tangential to radial motion in the equatorial plane than on the symmetry axis, the more so for smaller axial ratios. The case II models have a constant ratio of RMS tangential to radial motion throughout the system, as characterized by Binney's parameter beta. The maximum possible ratio v/sigma of the mean projected line-of-sight velocity and velocity dispersion on the projected major axis always decreases with increasing radial anisotropy. The observed ratio of the RMS projected line-of-sight velocities on the projected major and minor axes of elliptical galaxies is best fit by the case II models with beta > 0. These models also predict non-Gaussian velocity profile shapes consistent with existing observations.

The distribution functions are used to model the galaxies NGC 2434 (E1) and NGC 3706 (E4), for which stellar kinematical measurements out to two effective radii indicate the presence of dark halos (Carollo et al.). The velocity profile shapes of both galaxies can be well fit by radially anisotropic case II models with a spherical logarithmic potential. This contrasts with the f(E,L_z) models studied previously, which require flattened dark halos to fit the data.

Arrow Return to my bibliography.              Home Return to my home page.

Last modified December 8, 1998.
Roeland van der Marel, marel@stsci.edu.
Copyright Notice.