FEAST: Probing Hierarchical Star Formation with the Spatial Distributions of Young Star Clusters

We apply the angular two-point correlation function (TPCF) to the spatial distributions of young star clusters (YSCs) in four nearby star forming galaxies (NGC 628, NGC 4449, M51, and M83) in order to investigate their underlying hierarchical structuring. Using newly constructed catalogs of YSCs in the emerging phase (eYSCs), identified in the infrared with JWST, and optical YSCs detected in archival Hubble Space Telescope data, we compute the TPCFs for various cluster samples and age bins across the four galaxies, as part of the Feedback in Emerging extrAgalactic Star ClusTers (FEAST) program. We find clear evidence of hierarchical structuring, especially in eYSCs and YSCs with ages <10 Myr (referred to as oYSCs), which show similar TPCFs within each galaxy. NGC 628 exhibits a clear distinction between the TPCFs of eYSCs and oYSCs, implying a shorter randomization timescale. In contrast, clusters aged 10-300 Myr exhibit progressively more random spatial distributions, becoming effectively random after similar to 100 Myr, consistent with earlier studies. The two-dimensional fractal index D-2 values of the YSCs' underlying distributions are calculated from model fits to the TPCFs. Our values of D-2 derived from the youngest YSC populations align better with the expected value of D-2 similar to 1.3 for a universal star formation process compared to previous findings.