Feedback in Extragalactic Star Clusters (FEAST): Spectral Energy Distributions and the Physical Properties of Star Clusters in NGC 628 with CIGALE

With Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) observations of NGC~628 spanning 0.3–7.7,$\mu$m, we fit the spectral energy distributions (SEDs) of over 12,000 optically-selected star clusters, emerging young star clusters (eYSCs), and MIRI-selected sources with $\text{textsc}cigale$ to derive their ages, masses, extinctions, and dust properties. We find that near-infrared selected eYSC-I (compact Pa$\alpha$ and 3.3,$\mu$m PAH emission) and eYSC-II (compact Pa$\alpha$ and diffuse 3.3,$\mu$m PAH emssion) sources peak at $\sim$3–5~Myr, where $\sim 12\mathrm{\%}$ of the clusters have an $E(B-V)>2$, demonstrating the presence of dust-embedded populations as clusters emerge. Further, the distributions of the fractional polycyclic aromatic hydrocarbon (PAH) abundance ($q_{\mathrm{P}AH}$) and stellar-to-nebular attenuation ratio ($E(B-V{)}_{\star }\mathrm{/}E(B-V{)}_{\mathrm{n}\mathrm{e}\mathrm{b}}$) suggest an evolutionary sequence in which sources evolve from eYSC-I to eYSC-II as clusters clear their surrounding dust and gas. The photo-dissociation region (PDR) clearing timescale inferred from the ratio of eYSC-I to optically visible stellar clusters is $\sim$4~Myr. Additionally, we find that star clusters in the spiral arms of NGC 628 are preferentially more massive and more dust-reddened than those in inter-arm regions.~Finally, we find that $\sim$65% of eYSC-I, $\sim$27% of eYSC-II, and $\sim$40% of F335M-selected sources coincide with an F770W peak in our MIRI-selected catalog within 4 pixels, confirming that F770W-bright sources preferentially trace the youngest and dustiest regions. Overall, our results highlight the ability of JWST together with $\text{textsc}cigale$ model grids to identify and characterize eYSCs during their short-lived embedded phases, and provide constraints on the feedback mechanisms that govern the emergence of stellar clusters.