DYNAMICAL FORMATION SIGNATURES OF BLACK HOLE BINARIES IN THE FIRST DETECTED MERGERS BY LIGO

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 proportional to M-tot beta, with beta greater than or similar to 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 less than or similar to 80 M-circle dot We find that for power-law BH mass functions dN/dM proportional to 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 similar to 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.