Two-component galaxy models: phase-space constraints

The properties of the analitycal phase--space distribution function of two-component spherical self-consistent galaxy models, where one density distribution follows the Hernquist profile, and the other a gamma=0 model, with different total masses and core radii (H0 models), presented in Ciotti (1998), are here summarized. A variable amount of radial Osipkov-Merritt orbital anisotropy is allowed in both components. The necessary and sufficient conditions that the model parameters must satisfy in order to correspond to a model where each one of the two distinct components has a positive DF (the so-called model consistency) are analytically derived, together with some results on the more general problem of the consistency of two-component gamma1+gamma2 models. The possibility to add in a consistent way a black hole at the center of radially anisotropic gamma models is also discussed. In particular, it is proved that a globally isotropic Hernquist component is consistent for any mass and core radius of the superimposed gamma=0 halo; on the contrary, only a maximum value of the core radius is allowed to the gamma=0 component when a Hernquist halo is added. The combined effect of halo concentration and orbital anisotropy is successively investigated