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