Black hole and neutron star mergers in galactic nuclei
  Nuclear star clusters surrounding supermassive black holes (SMBHs) in
galactic nuclei contain large numbers of stars, black holes (BHs) and neutron
stars (NSs), a fraction of which are likely to form binaries. These binaries
were suggested to form a triple system with the SMBH, which acts as a perturber
and may enhance BH and NS mergers via the Lidov-Kozai mechanism. We follow-up
previous studies, but for the first time perform an extensive statistical study
of BH-BH, NS-NS and BH-NS binary mergers by means of direct high-precision
regularized $N$-body simulations, including Post-Newtonian (PN) terms up to
order PN2.5. We consider different SMBH masses, slopes for the BH mass
function, binary semi-major axis and eccentricity distributions, and different
spatial distributions for the binaries. We find that the merger rates are a
decreasing function of the SMBH mass and are in the ranges $\sim 0.17$-$0.52 \
\mathrm{Gpc}^{-3}\ \mathrm{yr}^{-1}$, $\sim 0.06$-$0.10 \ \mathrm{Gpc}^{-3}\
\mathrm{yr}^{-1}$ and $\sim 0.04$-$0.16 \ \mathrm{Gpc}^{-3}\ \mathrm{yr}^{-1}$
for BH-BH, BH-NS and NS-NS binaries, respectively. However, the rate estimate
from this channel remains highly uncertain and depends on the specific
assumptions regarding the star-formation history in galactic nuclei and the
supply rate of compact objects. We find that $\sim 10\%$--$20\%$ of the mergers
enter the LIGO band with eccentricities $\gtrsim 0.1$. We also compare our
results to the secular approximation, and show that $N$-body simulations
generally predict a larger number of mergers. Finally, these events can also be
observable via their electromagnetic counterparts, thus making these compact
object mergers especially valuable for cosmological and astrophysical purposes.
