- [*] Scale-free dynamical models for galaxies: flattened densities in
- 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.
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
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.
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