SIRIUS project II: a new tree-direct hybrid code for smoothed particle
  hydrodynamics/N-body simulations of star clusters
  Star clusters form via clustering star formation inside molecular clouds. In
order to understand the dynamical evolution of star clusters in their early
phase, in which star clusters are still embedded in their surrounding gas, we
need an accurate integration of individual stellar orbits without gravitational
softening in the systems including both gas and stars, as well as modeling
individual stars with a realistic mass function. We develop a new tree-direct
hybrid smoothed particle hydrodynamics/N-body code, ASURA+BRIDGE, in which
stars are integrated using a direct N-body scheme or PeTar, a particle-particle
particle-tree scheme code, without gravitational softening. In ASURA+BRIDGE,
stars are assumed to have masses randomly drawn from a given initial mass
function. With this code, we perform star-cluster formation simulations
starting from molecular clouds without gravitational softening. We find that
artificial dense cores in star-cluster centers due to the softening disappear
when we do not use softening. We further demonstrate that star clusters are
built up via mergers of smaller clumps. Star clusters formed in our simulations
include some dynamically formed binaries with the minimum semi-major axes of a
few au, and the binary fraction is higher for more massive stars.
