The Star Clusters As Links between galaxy Evolution and Star formation (SCALES) project I: Numerical method

Stellar clusters are critical constituents within galaxies: they are the result of highest-density star formation, and through their spatially and temporally correlated feedback they regulate their host galaxy evolution. We present a novel numerical method to model star clusters as individual units of star formation using sink particles. In our method, star clusters grow via gas accretion and via merging with less massive clusters. We describe the implementation in the radiation hydrodynamics code GIZMO and run a large grid of marginally bound, turbulent clouds of $10^7~{\rm M}_{\odot}$ to explore the effect of modeling ingredients on the evolution of the clouds and the star clusters. We find both gas accretion and mergers to be critical processes to form star clusters of masses up to $\sim10^5$-$10^6~{\rm M}_{\odot}$, while ionising radiation is the main feedback mechanism regulating the growth of star clusters. The majority of our star clusters assemble their mass in $0.3$-$2.6~{\rm Myr}$, and the most massive ones take $\sim10~{\rm Myr}$. By removing high density gas by accretion, our sink-based cluster formation prescription allows the newly-formed star clusters to inject their stellar feedback in less dense environments. This makes feedback more efficient at ionising and disrupting the cloud than if we were to use a standard star formation approach, indicating that our numerical method is the missing critical step to model the interplay between star clusters and their host galaxies.