The impact of primordial binary on the dynamical evolution of intermediate massive star clusters

Abstract: Observations found that star clusters contain a large fraction of binaries. Tight binaries are an important heating source that influences the long-term dynamical evolution of star clusters. However, due to the limitation of $N$-body tool, previous theoretical modelling for globular clusters (GCs) by using direct $N$-body simulations have not investigated how a large fraction of primordial binaries affect their long-term evolution. In this work, by using the high-performance $N$-body code, PeTar, we carry out star-by-star models for intermediate massive GCs ($N=100000$) with the primordial binary fraction varying from 0 to 1. We find that when a stellar-mass black hole (BH) subsystem exists, the structural evolution of GCs (core and half-mass radii) only depends on the properties of massive primordial binaries, because they affect the number of BH binaries (BBHs), which dominate the binary heating process. Low-mass binaries including double white dwarf binaries (BWDs) have almost no influence on the dynamics. Meanwhile, only gravitational wave (GW) mergers from BBHs are strongly affected by dynamical interactions, while low-mass mergers from BWDs show no difference in the isolated environment (field) and in GCs. Low-mass binaries become important only after most BHs escape and the core collapse of light stars occurs. Our result suggests that for $N$-body modelling of GCs with a black hole subsystem dominating binary heating, it is not necessary to include low-mass binaries. These binaries can be studied separately by using standalone binary stellar evolution codes. This way can significantly reduce the computing cost.