Dynamical models of dwarf spheroidal galaxies based on distribution functions depending on actions

In this thesis we have addressed the problem of the dynamical modeling of dwarf spheroidal galaxies (dSphs) through the use of distribution functions (DFs) that depend on the action integrals. dSphs are low luminosity, pressure supported, dwarf galaxies that are thought to be extremely dark-matter dominated. In the first part of this thesis, we have introduced a new family of Dfs showing that these DFs are optimal in modeling dSphs. With the aim to constrain their dark-matter distribution and intrinsic stellar velocity distribution, we have presented models of two dSphs: Fornax and Sculptor, comparing the models with state-of-the-art spectroscopic and photometric data sets of these galaxies. We argued that Fornax and Sculptor are dominated by massive dark-matter halos. The dark-matter halo of Fornax has a density distribution with a large core in its central parts, while we were not able to put constraints of the shape on the Sculptor dark-matter density distribution. In the second part of this thesis we have addressed the problem of extending action-based DFs to deal with flattening in a physical way. Since previous flattened models generated via action-based DFs show unphysical behaviors, we have motivated how and shy, in order to make physical and acceptable models, one has to limit the possible functional forms that a DF can assume. We have shown how the models behave when these restrictions are implemented and we have presented the very first flattened, axisymmetric DF-based models with general DFs depending of three independent integrals of motion. We conclude studying the integrability of a few classes of flattened potentials: the complexified Plummer model and flattened potentials generated through flattened DFs depending on actions. We have shown that, in the presented experiments, all the orbits integrated in the flattened DF-based potential remain regular and very few become trapped by resonance.