Numerical construction of precise distribution functions for self-gravitating disks of given surface density profile

This thesis presents an algorithm to numerically produce distribution function (DF) models which represent exact collisionless equilibria for a thin and truncated self-gravitating disk with a fixed-in-advance surface density profile ΣD(ρ). Firstly a Shu-type DF is modified in such a way that the self-consistency condition leads to an integral equation for an unknown function S(ρ) whose specification completes the determination of the DF. Then a discretized form of the integral equation is solved to obtain numerically S(ρ). Families of different DFs yielding the same initial density profile ΣD(ρ) can be produced by choosing different input radial velocity dispersion profiles σρ(ρ). The algorithm leads to DFs which, while constrained in principle only to exactly reproduce the imposed surface density profile ΣD(ρ), in practice reproduce also to a good accuracy the imposed velocity dispersion profiles σρ(ρ), hence allowing to have control on the kinematic properties (e.g. the Q-profile) of the disk. Several properties of the obtained DFs are discussed and compared to the predictions of epicyclic and post-epicyclic theory for a disc with Schwarzchild’s DF. N-Body realizations of the algorithm are produced in an example of a galactic-type disc embedded in a live halo. The constancy in time and stability properties of the N-body system whose initial conditions are obtained through the computed DFs are tested via N-body simulations.