  We investigate properties of black hole (BH) binaries formed in globular
clusters via dynamical processes, using direct N-body simulations. We pay
attention to effects of BH mass function on the total mass and mass ratio
distributions of BH binaries ejected from clusters. Firstly, we consider BH
populations with two different masses in order to learn basic differences from
models with single-mass BHs only. Secondly, we consider continuous BH mass
functions adapted from recent studies on massive star evolution in a low
metallicity environment, where globular clusters are formed. In this work, we
consider only binaries that are formed by three-body processes and ignore
stellar evolution and primordial binaries for simplicity. Our results imply
that most BH binary mergers take place after they get ejected from the cluster.
Also, mass ratios of dynamically formed binaries should be close to one or
likely to be less than 2:1. Since the binary formation efficiency is larger for
higher-mass BHs, it is likely that a BH mass function sampled by
gravitational-wave observations would be weighed toward higher masses than the
mass function of single BHs for a dynamically formed population. Applying
conservative assumptions regarding globular cluster populations such as small
BH mass fraction and no primordial binaries, the merger rate of BH binaries
originated from globular clusters is estimated to be at least 6.5 per yr per
Gpc^3. Actual rate can be up to more than several times of our conservative
estimate.
