Scale-free dynamical models for galaxies: flattened densities in spherical potentials

This paper presents two families of phase-space distribution functions (DFs)that generate scale-free spheroidal mass densities in scale-free sphericalpotentials. The `case I' DFs are anisotropic generalizations of the flattenedf(E,L_z) model, which they include as a special case. The `case II' DFsgenerate flattened constant-anisotropy models, in which the constant ratio ofrms tangential to radial motion is characterized by Binney's parameter beta.The models can describe the outer parts of galaxies and the density cuspstructure near a central black hole, but also provide general insight into thedynamical properties of flattened systems. The dependence of the intrinsic and projected properties on the modelparameters and the inclination is described. The observed ratio of the rmsprojected line-of-sight velocities on the projected major and minor axes ofelliptical galaxies is best fit by the case II models with beta > 0. Thesemodels also predict non-Gaussian velocity profile shapes consistent withexisting observations. The distribution functions are used to model the galaxies NGC 2434 (E1) andNGC 3706 (E4), for which stellar kinematical measurements out to two effectiveradii indicate the presence of dark halos (Carollo et al.). The velocityprofile shapes of both galaxies can be well fit by radially anisotropic case IImodels 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.Comment: LaTeX file, uses standard macros mn.sty, epsf.sty. 17 pages including 7 figure