Black hole mergers from quadruples
  With the hundreds of merging binary black hole (BH) signals expected to be
detected by LIGO/Virgo, LISA and other instruments in the next few years, the
modeling of astrophysical channels that lead to the formation of compact-object
binaries has become of fundamental importance. In this paper, we carry out a
systematic statistical study of quadruple BHs consisting of two binaries in
orbit around their center of mass, by means of high-precision direct $N$-body
simulations including Post-Newtonian (PN) terms up to 2.5PN order. We found
that most merging systems have high initial inclinations and the distributions
peak at $\sim 90^\circ$ as for triples, but with a more prominent broad
distribution tail. We show that BHs merging through this channel have a
significant eccentricity in the LIGO band, typically much larger than BHs
merging in isolated binaries and in binaries ejected from star clusters, but
comparable to that of merging binaries formed via the GW capture scenario in
clusters, mergers in hierarchical triples, or BH binaries orbiting
intermediate-mass black holes in star clusters. We show that the merger
fraction can be up to $\sim 3$--$4\times$ higher for quadruples than for
triples. Thus even if the number of quadruples is $20\%$--$25\%$ of the number
of triples, the quadruple scenario can represent an important contribution to
the events observed by LIGO/VIRGO.
