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

We use N-body simulations to study the dynamical evolution of Population III (Pop III) stellar systems and the resulting binary statistics. We design a physically-motivated framework for the initial conditions of Pop III star clusters, based on small-scale hydrodynamic simulations and the scale-free nature of disk evolution during Pop III star formation. Our novel approach enables us to explore the dependence of binary statistics on initial conditions and arrive at more robust predictions for the signals of Pop III X-ray binaries (XRBs) and binary black hole (BBH) mergers, compared to simple extrapolations of Pop III protostar systems. We find that binary properties are highly sensitive to the initial cluster size and distribution of binary separation, while the effect of initial mass function is relatively minor. Our simulations predict less close binaries, and thus, significantly lower efficiencies (by a factor 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 XRBs to the cosmic X-ray background is negligible and their feedback effects are unimportant. We estimate the efficiency of Pop III BBH mergers as $\sim 10^{-5}-10^{-4}\ \rm M_{\odot}^{-1}$, for which 3-body hardening by surrounding stars in dense star clusters or close binary interactions is required to facilitate in-spirals of BBHs. All simulation data, including catalogs of Pop III binaries and multiple systems, are publicly available.