Gravity plays the central role in structure formation and evolution on astronomical scales. The long range nature of gravity complicates the modeling of the non-equilibrium dynamics of self-gravitating many-body systems such as galaxies and dark matter halos. In the standard ΛCDM paradigm of cosmology, galaxies and halos are constantly perturbed out of equilibrium through interactions and mergers, thus prevailing in a state of non-equilibrium or quasi-equilibrium at best. The discovery of a plethora of non-equilibrium features on galactic scales, e.g., those observed by Gaia in our own Milky Way galaxy, calls for a shift of gear from the standard equilibrium galactic dynamics to the less explored non-equilibrium dynamics.
I develop novel theories to describe the relaxation of collisionless self-gravitating systems like galaxies and halos. This equilibration process depends on the timescale of perturbation, i.e., whether it is impulsive/fast, adiabatic/slow or resonant. My general non-perturbative treatment of impulsive encounters between galaxies/halos accurately models penetrating encounters unlike the standard treatment which only works for distant encounters. I develop a linear perturbative formalism that provides a comprehensive understanding of how the response of a stellar disk to external perturbations (e.g., satellite impacts) phase-mixes away, giving rise to local phase-space spirals akin to those observed by Gaia in the Milky Way disk. I develop novel theories for the secular evolution (dynamical friction) of a perturber due to the near-resonant response of the host galaxy/halo. These theories explain the origin of secular phenomena observed in N-body simulations of cored galaxies but unexplained in the standard Chandrasekhar and LBK theories of dynamical friction, namely core-stalling and dynamical buoyancy. These processes have profound astrophysical implications, e.g. they can keep massive perturbers away from the central core regions of cored galaxies and thus potentially choke supermassive black hole mergers in such systems.
My dissertation offers novel contributions to the field of non-equilibrium galactic dynamics by shedding light into how quasi-equilibrium is re-established in perturbed galaxies and dark matter halos.