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By performing three-dimensional radiation hydrodynamics simulations, we studythe formation of young massive star clusters (YMCs, $M_{*}>10^4~M_{\odot}$) inclouds with the surface density ranging from $\Sigma_{\rm cl} = 80$ to$3200~M_{\odot}\;{\rm pc^{-2}}$. We find that photoionization feedbacksuppresses star formation significantly in clouds with low surface density.Once the initial surface density exceeds $\sim 100~M_{\odot}\;{\rm pc^{-2}}$for clouds with $M_{\rm cl}=10^{6}~M_{\odot}$ and $Z= Z_{\odot}$, most of thegas is converted into stars because the photoionization feedback is inefficientin deep gravitational potential. In this case, the star clusters are massiveand gravitationally bounded as YMCs. The transition surface density increasesas metallicity decreases, and it is $\sim 350~M_{\odot}\;{\rm pc^{-2}}$ for$Z=10^{-2}~Z_{\odot}$. We show that more than 10 percent of star-formationefficiency (SFE) is needed to keep a star cluster gravitationally bounded evenafter the disruption of a cloud. Also, we develop a semi-analytical modelreproducing the SFEs obtained in our simulations. We find that the SFEs are fitwith a power-law function with the dependency $\propto \Sigma_{\rm cl}^{1/2}$for low-surface density and rapidly increases at the transition surfacedensities. The conditions of the surface density and the metallicity matchrecent observations of giant molecular clouds forming YMCs in nearby galaxies.

Radiation hydrodynamics simulations of massive star cluster formation in giant molecular clouds