Pushing the frontiers of gravitational encounters and collisionless dynamics

Gravity plays the central role in structure formation and evolution in astronomical scales. Despite the apparently simple inverse square law for the gravitational force in the non-relativistic regime, the dynamics of self-gravitating many-body systems such as galaxies and dark matter (DM) halos is still not sufficiently well understood due to the long range nature of gravity. Relaxation/equilibration of galaxies and cold dark matter halos is typically not driven by two-body encounters but is a collective, collisionless process. Based on the interaction timescale, gravitational encounters can be broadly classified as impulsive (fast), resonant and adiabatic (slow). First, I am going to present a general non-perturbative formalism to accurately model the impulsive encounters between star-clusters, galaxies or DM halos. Next, I shall present a self-consistent, time-dependent, perturbative treatment of the secular evolution (dynamical friction) of massive perturbers in host galaxies or DM halos due to resonant interactions with field particles. This novel formalism resolves the long-standing problem of core-stalling observed in N-body simulations: the apparent cessation of dynamical friction driven in-fall of massive perturbers in spherical host systems with central cores. In our formalism, core-stalling naturally arises from a balance between a retarding torque (dynamical friction) outside and a hitherto unknown enhancing torque (dynamical buoyancy) inside the core-region. To this end, I shall also describe the precise nature of near-resonant field particle orbits responsible for dynamical friction and buoyancy. The dynamical phenomena of core-stalling and buoyancy imply that measuring the offsets of massive objects like globular clusters and black holes from the centers of DM dominated dwarf galaxies can potentially constrain their inner DM density profile and the DM particle nature. Finally, I shall present a comprehensive analysis of the response of disk galaxies to perturbations using linear perturbation theory. The oscillations of the disk response phase-mix away due to an intrinsic spread in the frequencies, giving rise to spiral-shaped features in the phase-space known as phase-space spirals akin to those observed by Gaia in the Milky Way disk. Impulsive (fast) and mildly adiabatic (slow) encounters excite different oscillation modes (bending vs breathing) and thus different looking phase-space spirals. I shall elucidate how these phase-space spirals can be used to constrain the dynamical history and detailed DM distribution of our Milky Way galaxy.