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Most stars are formed as star clusters in galaxies, which then disperse intogalactic disks. Upcoming exascale supercomputational facilities will enableperforming simulations of galaxies and their formation by resolving individualstars (star-by-star simulations). This will substantially advance ourunderstanding of star formation in galaxies, star cluster formation, andassembly histories of galaxies. In previous galaxy simulations, a simplestellar population approximation was used. It is, however, difficult to improvethe mass resolution with this approximation. Therefore, a model for formingindividual stars that can be used in simulations of galaxies must beestablished. In this first paper of a series of the SIRIUS (SImulationsResolving IndividUal Stars) project, we demonstrate a stochastic star formationmodel for star-by-star simulations. An assumed stellar initial mass function(IMF) is randomly assigned to newly formed stars. We introduce a maximum searchradius to assemble the mass from surrounding gas particles to form starparticles. In this study, we perform a series of N-body/smoothed particlehydrodynamics simulations of star cluster formations from turbulent molecularclouds and ultra-faint dwarf galaxies as test cases. The IMF can be correctlysampled if a maximum search radius that is larger than the value estimated fromthe threshold density for star formation is adopted. In small clouds, theformation of massive stars is highly stochastic because of the small number ofstars. We confirm that the star formation efficiency and threshold density donot strongly affect the results. We find that our model can naturally reproducethe relationship between the most massive stars and the total stellar mass ofstar clusters. Herein, we demonstrate that our models can be applied tosimulations varying from star clusters to galaxies for a wide range ofresolutions.

SIRIUS project. I. Star formation models for star-by-star simulations of star clusters and galaxy formation