Greatly enhanced merger rates of compact-object binaries in
  non-spherical nuclear star clusters
  The Milky Way and a significant fraction of galaxies are observed to host a
central Massive Black Hole (MBH) embedded in a non-spherical nuclear star
cluster. We study the secular orbital evolution of compact-object binaries in
these environments and characterize the excitation of extremely large
eccentricities that can lead to mergers by gravitational radiation. We find
that the eccentricity excitation occurs most efficiently when the nodal
precession timescale of the binary's orbit around the MBH due to the
non-spherical cluster becomes comparable (within a factor of ~10) to the
timescale on which the binary is torqued by the MBH due to the Lidov-Kozai (LK)
mechanism. We show that in this regime the perturbations due to the cluster
increase the fraction of systems that reach extreme eccentricities
($1-e\sim10^{-4}-10^{-6}$) by a factor of ~10-100 compared to the idealized
case of a spherical cluster, increasing the merger rates of compact objects by
a similar factor. We identify two main channels that lead to this extreme
eccentricity excitation: (i) chaotic diffusion of the eccentricities due to
resonance overlap; (ii) cluster-driven variations of the mutual inclinations
between the binary orbit and its center-of-mass orbit around the MBH, which can
intensify the LK oscillations. We estimate that our mechanism can produce black
hole-black hole and black hole-neutron star binary merger rates of up to
$\approx 15$ $\rm{Gpc}^{-3}yr^{-1}$ and $\approx 0.4$ $\rm{Gpc}^{-3}yr^{-1}$,
respectively. Thus, we propose the cluster-enhanced Lidov-Kozai mechanism as a
new channel for the merger of compact-object binaries, competing with scenarios
that invoke isolated binary evolution or dynamical formation in globular
clusters.
