Revealing the Connection Between the Filamentary Hierarchy and Star Cluster Formation in a Simulated NGC 628 Galaxy

There is abundant observational evidence for the hierarchical, interconnected nature of filaments in the interstellar medium (ISM) extending from galactic down to sub-parsec scales. New JWST images of NGC 628 in particular, show clusters forming along the two spiral arms of this galaxy. In this paper we investigate filament and cluster properties in an NGC 628-like multi-scale high-resolution magnetohydrodynamic simulation. We use a filament finding tool to identify filaments and derive the probability density functions (PDFs) for the filament lengths and masses. Using a clustering algorithm we identify star clusters formed between 268 to 278 Myr and follow this population as the galaxy evolves for 60 Myr, calculating their mass PDFs, average radius growth rate, and average mass loss rate. We find a power-law index of alpha_m = -1.35 for the filament masses. Calculating the power-law index from our cluster mass PDF, we find a value of alpha_{c,m} = -1.35 when the clusters first form, exactly our filament mass power-law index. This shows that properties of young clusters arise from the gravitational fragmentation of their host filaments. We track the post-formation evolution of the clusters as they become unbound, increase in radius and decrease in mass yielding an ever steeper mass power-law index. After 60 Myr, the mass power-law index is alpha_{c,m} = -1.55, matching other simulations and observations.