  The dynamical formation of stellar-mass black hole-black hole binaries has
long been a promising source of gravitational waves for the Laser
Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation,
gravitational focusing, and multibody dynamical interactions naturally increase
the interaction rate between the most massive black holes in dense stellar
systems, eventually leading them to merge. We find that dynamical interactions,
particularly three-body binary formation, enhance the merger rate of black hole
binaries with total mass M_tot roughly as ~M_tot^beta, with beta >~ 4. We find
that this relation holds mostly independently of the initial mass function, but
the exact value depends on the degree of mass segregation. The detection rate
of such massive black hole binaries is only further enhanced by LIGO's greater
sensitivity to massive black hole binaries with M_tot <~ 80 solar masses. We
find that for power-law BH mass functions dN/dM ~ M^-alpha with alpha <~ 2,
LIGO is most likely to detect black hole binaries with a mass twice that of the
maximum initial black hole mass and a mass ratio near one. Repeated mergers of
black holes inside the cluster result in about ~5% of mergers being observed
between two and three times the maximum initial black hole mass. Using these
relations, one may be able to invert the observed distribution to the initial
mass function with multiple detections of merging black hole binaries.
