Abstract
We use N-body simulations to study the dynamical evolution of Population III (Pop III) star clusters/groups 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 (compact object) remnant 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 10-10,000) 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. The efficiency of forming Pop III remnant mergers via the "classical".binary stellar evolution (BSE) channel is also reduced in the lack of close binaries. In light of this, we propose an alternative channel of forming Pop III mergers by dynamical hardening in nuclear star clusters, which is shown to be as efficient as the BSE channel. We conclude that gravitational N-body dynamics is an important context of Pop III remnant mergers for both initial formation of binaries and subsequent evolution in dense star clusters. Therefore, deeper understanding of the initial conditions of star clusters based on star formation theory is required to better model (high-z) star clusters and fully unleash the power of GW astronomy.
