Orbital anisotropy ansatz for the Jeans modeling of axisymmetric galaxies

The kinematics of galaxies is recovered for samples of ever-growing size and increasing quality thanks to the recent large integral-field spectroscopic surveys, and more sophisticated data analysis and modeling techniques. In this context, the Jeans equations (JEs) are one of the standard tools to extract physically relevant information from observations. However, they suffer from a closure problem, and in order to solve them a choice is the "b-ansatz", widely used in the Jeans modeling of regular rotators and stellar disks. In this thesis, we provide a general discussion on how this ansatz affects the solution of the JEs, being able to predict the qualitative features of the resulting kinematics for different choices of b. In this way, as a function of the structural properties of the model, we can constrain the values of b that assure the positivity of the average squared azimuthal velocity field, necessary for the model consistency, and of two otheer fields used for a decomposing the latter into its ordered and dispersion components. Then, by discussing some axisymmetric models, we apply this general procedure to some realistic case studies, understanding how the b-anisotropy is connected to the properties of the galaxy. We retrieve theoretically the empirical trend such that more flattened galaxies support a larger b, almost independently of the specific model. Finally, we conduct a first analysis of the b-anisotropy in massive, passive and axisymmetric early-type galaxies from the TNG50 simulation. We verify that they can be well modeled through the three-integral Jeans equations with the b-ansatz, where b is in general greater than unity. However, in this case the trend with the flattening is not apparent, as correlations with the galaxy properties. Overall, this work provides a general understanding of how the b-ansatz affects stellar kinematics, and strengthens the modeling techniques to interpret data.