  The dozens of compact object mergers detected by LIGO/Virgo raise a key
theoretical question: how do initially wide binaries shrink sufficiently
quickly that they are able to merge via gravitational wave (GW) radiation
within a Hubble time? One promising class of answers involves secular driving
of binary eccentricity by some external tidal perturbation. This perturbation
can arise due to the presence of a tertiary point mass, in which case the
system exhibits Lidov-Kozai (LK) dynamics, or it can stem from the tidal field
of the stellar cluster in which the binary orbits. While these secular
tide-driven mechanisms have been studied exhaustively in the case of no GW
emission, when GWs are included the dynamical behavior is still incompletely
understood. In this paper we consider compact object binaries driven to merger
via high eccentricity excitation by (doubly-averaged, test-particle quadrupole
level) cluster tides - which includes LK-driven mergers as a special case - and
include the effects of both general relativistic precession and GW emission. We
provide for the first time an analytical understanding of the different
evolutionary stages of the binary's semimajor axis, secular oscillation
timescale, and phase space structure all the way to merger. Our results will
inform future population synthesis calculations of compact object binary
mergers from hierarchical triples and stellar clusters.
