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.
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