Dynamical modelling of early-type galaxies: analytical multi-component systems, and application to spherical gas accretion

Dynamical models, even when simplified, are of great importance, because they can be used, for example, to understand the dynamics of more complicated (i.e., realistic) models, as well as to obtain first indications about sensible choices of parameters to be subsequently refined with more time-consuming numerical methods. In this Thesis we present the construction of galaxy models simple enough to provide some insight into the main structural and dynamical properties of real galaxies. The work focuses on axisymmetric Jeans modelling for galaxies, assumed to be stationary collisionless stellar systems. In particular, we consider ellipsoidal galaxies characterized by weakly flattened shape: this allows for the application of a technique, known as homoeoidal expansion, representing the theoretical framework underlying the entire modelling procedure. We apply this technique to two families of two-component galaxy models, solving the two-integral Jeans equations also in presence of a central black hole. The expansion method is then reviewed, analyzing and applying its two different interpretations to the case of simple one-component models: here the effectiveness of the homoeoidal approximation is examined using both analytical and numerical techniques; this method is finally adopted for the phenomenological interpretation of a real globular cluster. A part of the Thesis is devoted to the study of the polytropic accretion of gas onto the black hole at the centre of spherical galaxies, modelled as the spherical limit of one of the two families of axisymmetric models previously discussed. In order to study the motion of gas flows we generalize the classical Bondi problem by taking into account the effects of the gravitational field of the host galaxy, and the radiation pressure due to electron scattering. We also elucidate some important thermodynamical properties of accretion, determining the underlying cooling/heating function leading to the phenomenological value of the polytropic index.