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 they are still embedded in their surrounding gas, we need accurate integration of individual stellar orbits without gravitational softening in the systems including both gas and stars, as well as modeling of 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. The star clusters formed in our simulations include some dynamically formed binaries with minimum semi-major axes of a few au, and the binary fraction is higher for more massive stars.

中文翻译：

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天狼星项目。二、一种新的树直接混合代码，用于星团的平滑粒子流体动力学/N 体模拟

星团是通过在分子云内聚集恒星形成而形成的。为了了解星团在其早期阶段的动态演化，其中它们仍嵌入其周围的气体中，我们需要在包括气体和恒星在内的系统中准确整合单个恒星轨道而不会出现重力软化，以及建模具有真实质量函数的单个恒星。我们开发了一种新的树直接混合平滑粒子流体动力学/N 体代码 ASURA$+$BRIDGE，其中恒星使用直接 N 体方案或 PeTar（一种粒子-粒子粒子树方案代码）进行积分，没有引力软化。在 ASURA$+$BRIDGE 中，假设恒星的质量是从给定的初始质量函数中随机抽取的。有了这段代码，我们从没有引力软化的分子云开始进行星团形成模拟。我们发现，当我们不使用软化时，由于软化，星团中心的人造致密核心消失了。我们进一步证明了星团是通过较小的团块合并而成的。在我们的模拟中形成的星团包括一些动态形成的双星，它们的最小半长轴为几个 au，对于更大质量的恒星，双星比例更高。