## Secular Dynamics of Binaries in Stellar Clusters

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The orbital evolution of two bound point masses (a 'binary') perturbed by external tidal forces represents one of the oldest problems in celestial mechanics. Most obviously, tidal perturbations may arise due to an external point mass bound to the binary, as in the Lidov-Kozai (LK) theory of hierarchical triples, but they can also stem from the gravitational field of an extended stellar system (e.g. galaxy or globular cluster) in which the binary resides. Due to the weakness of the external perturbation, the resulting orbital evolution is usually secular in nature, i.e. it occurs on timescales much longer than any characteristic orbital period. This thesis is concerned with the secular dynamical evolution of tidally perturbed binary systems.

If problems of this sort are centuries old, what motivation is there to further study them now? In fact, interest in the problem of tidally perturbed binaries has surged recently due to the discovery of various exotic astrophysical phenomena, not least the mergers of compact object (black hole and/or neutron star) binaries by the LIGO/Virgo collaboration. The question of how these binaries shrink rapidly enough to merge within a Hubble time is still an open one, but tidal perturbations may provide the answer. For instance, LK oscillations driven by a tertiary companion can naturally drive a binary orbit to become highly eccentric, boosting gravitational wave emission and substantially speeding up binary coalescence. Similar ideas (with different sources of dissipation at pericentre) have been previously considered for explaining the origin of other exotic objects, such as hot Jupiters, blue stragglers, and Type 1a supernovae. Thus, understanding the tidally-forced eccentricity evolution and possible mergers of binary systems has become a central focus of modern research in astrophysical dynamics.

In this thesis we consider the secular evolution of binaries driven by the tidal gravitational field of an arbitrary axisymmetric host system ('cluster') in which the binary moves. We formulate the most general possible theory of tide-driven secular evolution of two bound point masses, applicable to a wide variety of astrophysical systems. Our secular Hamiltonian theory (averaged over both the inner Keplerian orbit of the binary and its outer orbit within the cluster) reproduces classical results — such as LK evolution and the effect of the Galactic tide on Oort Cloud comets — in appropriate limits, but is more general. We then investigate the secular dynamics in detail, uncovering new dynamical characteristics that are far removed from the canonical LK behaviour. We also extend the secular theory by accounting for the important non-Newtonian effects of general relativistic (GR) perihelion precession and gravitational wave (GW) emission, and the non-secular effect of short-timescale fluctuations in the perturbing torque. These three effects, unavoidably important in many practical applications, add further levels of complexity and richness to the binary dynamics.

The central result of the theory is that the mean-field gravitational tidal potential of a star cluster is often sufficient to torque a binary so that it performs large-amplitude eccentricity oscillations. This result has significant consequences for the dynamical evolution of compact object binaries, many of which reside in stellar clusters. We show that it leads to mergers of compact object binaries which could not have merged if they were isolated, and calculate the resulting observable merger rate.

In summary, then, the purpose of this thesis is three-fold: to formulate a general unified theory of binary dynamical evolution; to propose a possible origin for LIGO/Virgo compact object merger events; and to uncover and explain a range of new, important and beautiful dynamical phenomena.