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We use N-body simulations to study the dynamical evolution of Population III(Pop III) stellar systems and the resulting binary statistics. We design aphysically-motivated framework for the initial conditions of Pop III starclusters, based on small-scale hydrodynamic simulations and the scale-freenature of disk evolution during Pop III star formation. Our novel approachenables us to explore the dependence of binary statistics on initial conditionsand arrive at more robust predictions for the signals of Pop III X-ray binaries(XRBs) and binary black hole (BBH) mergers, compared to simple extrapolationsof Pop III protostar systems. We find that binary properties are highlysensitive to the initial cluster size and distribution of binary separation,while the effect of initial mass function is relatively minor. Our simulationspredict less close binaries, and thus, significantly lower efficiencies (by afactor of $\sim 10-10^{4}$) for the formation and accretion of Pop III XRBs,than found in previous studies, implying that the contribution of Pop III XRBsto the cosmic X-ray background is negligible and their feedback effects areunimportant. We estimate the efficiency of Pop III BBH mergers as $\sim10^{-5}-10^{-4}\ \rm M_{\odot}^{-1}$, for which 3-body hardening by surroundingstars in dense star clusters or close binary interactions is required tofacilitate in-spirals of BBHs. All simulation data, including catalogs of PopIII binaries and multiple systems, are publicly available.

Dynamical evolution of Population III stellar systems and the resulting binary statistics