SIRIUS project. III. Star-by-star simulations of star cluster formation using a direct <i> <b>N</b> </i>-body integrator with stellar feedback

One of the computational challenges cluster formation simulations is resolving individual stars and simulating massive clusters with masses more than $10^4 M_{\odot}$ without gravitational softening. Combining direct $N$-body code smoothed-particle hydrodynamics (SPH) code, we have developed a new \textsc{ASURA+BRIDGE}, in which can integrate stellar particles We add feedback model for \HII regions into this thermal momentum given within Str{\"o}mgren radius. perform $N$-body/SPH star formation. Without softening, portion are ejected from forming clusters. As result, works outside This enhances/suppresses initially sub-virial/super-virial clouds. find that formed denser currently observed open clusters, but mass--density relation consistent or even higher estimated as an initial density. also some multiple peaks their age distribution consequence hierarchical