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Star cluster formation and cloud dispersal by radiative feedback: dependence on metallicity and compactness

We study star cluster formation in various environments with different metallicities and column densities by performing a suite of three-dimensional radiation hydrodynamics simulations. We find that the photoionization feedback from massive stars controls the star formation efficiency (SFE) in a star-forming cloud, and its impact sensitively depends on the gas metallicity $Z$ and initial cloud surface density $Σ$. At $Z=1~Z_{\odot}$, SFE increases as a power law from 0.03 at $Σ= 10~M_{\odot}{\rm pc^{-2}}$ to 0.3 at $Σ= 300~M_{\odot}{\rm pc^{-2}}$. In low-metallicity cases $10^{-2}- 10^{-1} Z_{\odot}$, star clusters form from atomic warm gases because the molecule formation time is not short enough with respect to the cooling or dynamical time. In addition, the whole cloud is disrupted more easily by expanding H{\sc ii} bubbles which have higher temperature owing to less efficient cooling. With smaller dust attenuation, the ionizing radiation feedback from nearby massive stars is stronger and terminate star formation in dense clumps. These effects result in inefficient star formation in low-metallicity environments: the SFE drops by a factor of $\sim 3$ at $Z=10^{-2}~Z_{\odot}$ compared to the results for $Z=1~Z_{\odot}$, regardless of $Σ$. Newborn star clusters are also gravitationally less bound. We further develop a new semi-analytical model that can reproduce the simulation results well, particularly the observed dependencies of the SFEs on the cloud surface densities and metallicities.