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Far and extreme UV radiation feedback in molecular clouds and its influence on the mass and size of star clusters

We study the formation of star clusters in molecular clouds by performing three-dimensional radiation hydrodynamics simulations with far ultraviolet (FUV; $6 ~{\rm eV} \leqq h ν\leqq 13.6 ~{\rm eV}$) and extreme ultraviolet (EUV; $hν\geqq 13.6~{\rm eV}$) radiative feedback. We find that the FUV feedback significantly suppresses the star formation in diffuse clouds with the initial surface densities of $Σ_{\rm cl} \lesssim \rm 50~M_{\odot} \; pc^{-2}$. In the cases of clouds with $Σ_{\rm cl} \sim \rm 100-200~M_{\odot} \; pc^{-2}$, the EUV feedback plays a main role and decrease the star formation efficiencies less than $0.3$. We show that thermal pressure from PDRs or H{\sc ii} regions disrupts the clouds and makes the size of the star clusters larger. Consequently, the clouds with the mass $M_{\rm cl} \lesssim 10^{5}~\rm M_{\odot}$ and the surface density $Σ_{\rm cl} \lesssim 200~\rm M_{\odot}\; pc^{-2}$ remain the star clusters with the stellar densities of $\sim 100~\rm M_{\odot}\; pc^{-3}$ that nicely match the observed open clusters in the Milky Way. If the molecular clouds are massive ($M_{\rm cl} \gtrsim 10^{5}~\rm M_{\odot}$) and compact ($Σ\gtrsim 400~\rm M_{\odot}\; pc^{-2}$), the radiative feedback is not effective and they form massive dense cluster with the stellar densities of $\sim 10^{4}~\rm M_{\odot}\; pc^{-3}$ like observed globular clusters or young massive star clusters. Thus, we suggest that the radiative feedback and the initial conditions of molecular clouds are key factors inducing the variety of the observed star clusters.