On the structural and dynamical properties of a new class of galaxy models with a central BH

This thesis work focuses on the dynamical properties of two-component galaxy models characterized by a stellar density distribution described by a Jaffe profile, and a galaxy (stars plus dark matter) density distribution following a r^(-3) shape at large radii. The dark matter (hereafter, DM) density profile is defined by the difference between the galaxy and the stellar profiles. The orbital structure of the stellar component is described by the Osipkov-Merritt (OM) radial anisotropy, and that of the DM halo is assumed isotropic; a black hole (BH) is also added at the center of the galaxy. The thesis is organized as follows. In Chapter 2 the main structural properties of the models are presented, and the conditions required to have a nowhere negative and monothonically decreasing DM halo density profile are derived; a discussion is also given of how the DM component can be built in order to have the same asymptotical behaviour, in the outer regions and near the center, as the Navarro-Frenk-White (NFW) profile. In Chapter 3 an investigation of the phase-space properties of the models is carried out, both from the point of view of the necessary and sufficient conditions for consistency, and from the direct inspection of the distribution function; the minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. In Chapter 4 the analytical solution of the Jeans equations with OM anisotropy is presented, together with the projection of the velocity dispersion profile at small and large radii. Finally, in Chapter 5 the global quantities entering the Virial theorem are explicitly calculated; these can be used for energetic considerations that are briefly mentioned, and allow us to determine the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability as a function of the galaxy parameters. The main results are summarized in Chapter 6, and some technical details are given in the Appendices.