Resonant and Secular Evolution of Three Body Systems – With Applications on Planetary Systems and Gravitational Wave Sources.

This work focuses on the gravitational interactions of astrophysical systems. In particular, we focus on the triple system dynamics, including mildly hierarchical three body secular dynamics, as well as precession induced resonances of binaries under the perturbation of a third companion. We apply our theoretical investigations of these physical processes to wide-orbit planetary systems and black hole binaries embedded in AGN disks. More specifically, we consider the secular dynamics of a test particle in a mildly-hierarchical configuration. We find the limit within which the secular approximation is reliable, present resonances and chaotic regions using surface of sections, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer solar system. We focus on the distribution of extreme trans-neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet-9), and find that in addition to a low inclination Planet-9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations. Beyond mildly hierarchical triple dynamics, we also propose a novel pathway through which compact binaries could merge due to eccentricity excitation, including in a near coplanar configuration. Mechanisms have been proposed to enhance the merger rate of stellar mass black hole binaries, such as the Von Zeipel-Lidov-Kozai mechanism (vZLK). However, high inclinations are required in order to greatly excite the eccentricity and to reduce the merger time through vZLK. Specifically, a compact binary migrating in an AGN disk could be captured in a precession-induced resonance, when the apsidial and nodal precession rates of the binary are commensurable to the orbital period around the supermassive black hole. We find 8 such resonances upto quardupole order of the Hamiltonian.  We show that if a binary is captured in these resonances and is migrating towards the companion, it can experience large eccentricity and inclination variations. Eccentricity is excited when the binary sweeps through the resonance which happens only when it migrates on a timescale 10-100 times the libration timescale of the resonance. Libration timescale decreases as the mass of the disk increases. The eccentricity excitation of the binary can reduce the merger timescale by a factor up to $10^{3−5}$.