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Dynamically formed black hole (BH) binaries (BBHs) are important sources ofgravitational waves (GWs). Globular clusters (GCs) provide a major environmentto produce such BBHs, but the total mass of the known GCs is small compared tothat in the Galaxy; thus, the fraction of BBHs formed in GCs is also small.However, this assumes that GCs contain a canonical initial mass function (IMF)similar to that of field stars. This might not be true because several studiessuggest that extreme dense and metal-poor environment can result in top-heavyIMFs, where GCs may originate. Although GCs with top-heavy IMFs were easilydisrupted or have become dark clusters, the contribution to the GW sources canbe significant. Using a high-performance and accurate $N$-body code,\textsc{petar}, we investigate the effect of varying IMFs by carrying out fourstar-by-star simulations of dense GCs with the initial mass of $5\times10^5M_\odot$ and the half-mass radius of $2$~pc. We find that the BBH merger ratedoes not monotonically correlate with the slope of IMFs. Due to a rapidexpansion, top-heavy IMFs lead to less efficient formation of merging BBHs. Theformation rate continuously decreases as the cluster expands because of thedynamical heating caused by BHs. However, in star clusters with a top-heavierIMF, the total number of BHs is larger, and therefore, the final contributionto merging BBHs can still be more than from clusters with the standard IMF, ifthe initial cluster mass and density is higher than those used in our model.

Impact of initial mass functions on the dynamical channel of gravitational wave sources