Binary systems are found everywhere in astrophysics. If a binary is completely isolated, the relative motion of the two bodies describes a Keplerian ellipse which repeats itself indefinitely. However, when a binary is perturbed, its elliptical orbital elements may change with time. In particular, a wide class of perturbations can drive large-amplitude secular oscillations in a binary’s eccentricity. As a result the binary may shrink or even merge, producing exotic phenomena like hot jupiters, blue stragglers and compact object mergers (i.e. LIGO/Virgo gravitational wave sources).
In my PhD have developed a mathematical theory for the evolution of binaries orbiting in arbitrary axisymmetric potentials, and applied the theory to black hole merger physics. One key result of my theory is that if a black hole binary orbits inside a star cluster, then the gravitational tidal force from a star cluster is often sufficient to periodically drive a binary’s eccentricity e to very high values (say e ≈ 0.99 or higher). This drastically reduces the closest-approach (‘periastron’) distance p = a(1 − e) of the black holes, where a is the semimajor axis. Repeated close passages of the black holes allow for significant dissipative bursts of gravitational radiation, shrinking the semimajor axis quickly. I have shown that this effect leads to mergers of black hole binaries which could not have merged if they were isolated.
In this talk I will (a) introduce the three-body problem as the archetypal example of a perturbed binary, (b) describe the general theory for secular evolution of binaries orbiting arbitrary axisymmetric potentials, and (c) discuss the application of the general theory to the problem of compact-object mergers (LIGO/Virgo gravitational wave sources) in stellar clusters.