Feedback in Emerging Extragalactic Star Clusters

• FEAST is a comprehensive paradigm defining how massive star feedback—through photoionization, radiative pressure, stellar winds, supernovae, and binary interactions—regulates cluster formation and the interstellar medium.
• Simulation frameworks combining hydrodynamics, radiative transfer, and N-body methods quantitatively capture star formation efficiency, emergence timescales, and the structural evolution of dense star clusters.
• Observations with JWST and multi-band spectroscopy reveal distinct emission line and SED signatures that calibrate feedback models and inform our understanding of galaxy-scale star formation regulation.

Feedback in Emerging extrAgalactic Star clusTers (FEAST) refers to the interconnected suite of physical processes by which young, massive stars—forming in clustered modes within dense giant molecular clouds—regulate their own formation and evolution, as well as the properties of their host environment, via the injection of radiation, mass, momentum, and energy into the surrounding interstellar medium (ISM). The FEAST paradigm incorporates the complex feedback landscape across multiple spatial and temporal scales using observations, numerical simulations, and analytical models, providing constraints on cluster emergence, survival, structural evolution, and the modulation of star formation efficiency in diverse extragalactic environments.

1. Physical Mechanisms of Feedback in Star-Forming Clusters

FEAST encompasses several key feedback processes originating from massive stars within clusters and their sequelae:

• Photoionization Feedback: Ultraviolet (UV; $h\nu \geq 13.6$ eV) photons ionize the surrounding neutral hydrogen, forming H II regions, heating gas to $T \sim 10^4$–$4 \times 10^4$ K, and producing overpressurized bubbles that expand dynamically. Analytical expressions for the size of H II regions,

$$r_{\mathrm{HII}} = \left(\frac{3 L_*}{4\pi n_e^2 \alpha_r}\right)^{1/3}$$

capture this early energy injection phase (Guillard et al., 2018, Fukushima et al., 2022).

• Radiative Pressure and FUV Feedback: Far–UV photons (6–13.6 eV) heat dust grains (photoelectric heating) and dissociate molecules, generating photodissociation regions (PDRs). The momentum imparted to gas by radiative pressure,

$$\Delta v = s\, (L_* h\nu)/(M_{\mathrm{HII}} c) \Delta t$$

disrupts dense structures, especially in lower-surface-density environments (Guillard et al., 2018, Fukushima et al., 2022).

• Stellar Winds: Kinetic energy and mass are injected continuously or episodically from OB and Wolf–Rayet stellar winds, contributing both mechanical and radiative input, and serving as the primary regulatory mechanism for cluster gas dispersion and termination of star formation (Dib et al., 2013, Calura et al., 4 Nov 2024).
• Supernovae (SNe): Delayed on Myr timescales (typically after $\sim$3–10 Myr), SNe inject substantial kinetic energy ($E_{\rm SN} \sim 10^{51}\,\mathrm{erg}$) and momentum per event, further disrupting and dispersing residual gas (Brown et al., 2022). The relative impact is modulated by existing bubbles cleared via earlier feedback mechanisms.
• Binary Interactions and Mass Transfer: Massive interacting binaries profoundly enhance the feedback output—both radiatively (by stripping hydrogen envelopes to expose hot helium cores) and mechanically (through non-conservative mass transfer and common envelope ejection). The resulting feedback increases local ionizing photon output by factors of up to $10^{3}$, expanding H II regions and driving more thermally dominated gas dynamics (Cournoyer-Cloutier et al., 3 Jul 2025).

2. Simulation Frameworks and Key Evolutionary Metrics

Modeling FEAST uses nested hydrodynamical (SPH, RAMSES-RT, Arepo, etc.), radiative transfer, and N-body approaches, with feedback modules implemented variously as source terms for heating, radiation/momentum injection, or direct removal of gas. Representative methodologies include:

• N-body continuation of hydrodynamical simulations: Evolving the stellar phase post-gas expulsion for $\sim$10 Myr, quantifying cluster structure (e.g., via the Q–parameter $Q = \bar{m}/\bar{s}$, where $Q < 0.8$ implies substructure) and measuring the dynamical evolution, bound fraction, and spatial expansion (Parker et al., 2013).
• Star Formation Efficiency (SFE) and Age Spread ($\Delta\tau_*$): Dual constraints are imposed by feedback termination (winds, ionization), encapsulated in the relationship between SFE and stellar age spread. Burst-like formation histories yield high SFE ($\sim$0.8–0.9) and short $\Delta\tau_* \lesssim 0.4$ Myr; more prolonged histories result in lower SFE ($\sim$0.1–0.3) and $\Delta\tau_* \sim 1$ Myr (Dib et al., 2013).
• Surface Density (Σ), Central Density ($\rho$), and Mass Functions: These metrics are monitored to evaluate the compaction, expansion, and possible segmentation or dissolution of emergent clusters. The bound fraction after gas expulsion is tightly correlated with the initial SFE and the dynamical state (e.g., sub-virial conditions, with $\alpha_{\rm vir,*} \sim 0.6$) (Li et al., 2019).
• Cluster Emergence Timescale: Observational color-color diagnostics (e.g., F300M–F335M and F115W–F187N in JWST imaging) reveal that transition from embedded (PAH-bright) to fully exposed, optically visible clusters typically occurs on timescales of $\sim$6 Myr, with shorter clearing times for massive clusters (Knutas et al., 13 May 2025).

3. Observational Diagnostics and Calibrations

FEAST leverages high spatial resolution, multi-band imaging, and spectroscopy, particularly with JWST (NIRCam/MIRI), to map and characterize young clusters and their feedback signatures:

• Emission Lines and Features: Pa$\alpha$, Br$\alpha$, and 3.3 $\mu$m PAH traces delineate the youngest, most embedded clusters—the emerging young star clusters (eYSCs). The correspondence of compact PAH and recombination-line emission substantiates cluster evolutionary classification (Gregg et al., 15 May 2024, Knutas et al., 13 May 2025).
• Star Formation Rate (SFR) Calibrations: On $\sim$40–120 pc scales, PAH and mid-IR ($21$/$24\,\mu$m) luminosity surface densities are tightly correlated (e.g., $$L_{3.3\,\mu m} \propto L_{\mathrm{Br}\,\alpha}^{0.75}$$, $$L_{21\,\mu m} \propto L_{\mathrm{Pa}\,\alpha}^{1.07}$$), though deviations from linearity occur due to PAH destruction, local heating, and IMF sampling stochasticity (Gregg et al., 15 May 2024, Calzetti et al., 3 Jun 2024). The hybrid SFR indicator

$$\Sigma(\mathrm{H}\alpha_{\rm corr}) = \Sigma(\mathrm{H}\alpha) + (0.095 \pm 0.007) \Sigma(24\,\mu{\rm m})$$

is recommended for compact H II regions, but the proportionality constant $b$ is found to be scale-dependent, increasing by up to factors of $3$–$5$ for small regions due to less contamination by dust heated from older populations.

• SED Fitting and NIR Excess: Combined HST+JWST SED analyses for eYSCs show a systematic $1.5$–$2.5\,\mu$m flux excess—particularly in low-mass and very young clusters—that is not captured by standard population models, suggesting contributions from young stellar objects (YSOs) and stochastic IMF effects, in addition to hot dust (Pedrini et al., 1 Sep 2025). Accurate SED-based age dating in this phase requires improved modeling components.
• Chemical and Dynamical Fingerprints: The presence of metallicity gradients (e.g., in tidal bridges of interacting dwarfs) and the mapping of spatially resolved bursts anchored to external interactions provide diagnostics of both intrinsic feedback mechanisms and environmental triggering (Bortolini et al., 1 Sep 2025, Correnti et al., 4 Jul 2025).

4. Diversity and Regulation of Star Cluster Properties Across Environments

The observed and simulated diversity of extragalactic clusters—ranging from open clusters to dense young massive clusters (YMCs) and globular cluster progenitors—emerges from interplay among feedback processes, cloud properties, and environmental context:

• Key Governing Parameters: The initial surface density $\Sigma_{\rm cl}$, cloud mass $M_{\rm cl}$, virial state, metallicity, and cloud geometry (turbulent vs. rotational support) are primary determinants of the efficiency and character of feedback. For $$\Sigma_{\rm cl}\lesssim 50\,M_\odot\,\mathrm{pc}^{-2}$$, FUV feedback alone can suppress star formation; at $\Sigma_{\rm cl}\sim 100$–$200\,M_\odot\,\mathrm{pc}^{-2}$, EUV-driven H II regions dominate and strongly lower SFE ($\epsilon \lesssim 0.3$) (Fukushima et al., 2022).
• Modes of Emergence and Survival: Clusters that form in dense environments with high SFE and centrally concentrated profiles can survive significant gas loss, while those forming at lower SFE often remain loosely bound or dissolve. The structural retention of substructure due to low initial densities and extended crossing times is a robust indicator of significant feedback during cluster formation (Parker et al., 2013).
• Role of Binaries and Cluster Dynamics: Massive interacting binaries enhance the ionizing and mechanical feedback, amplifying the thermal pressure within H II regions, expanding ionized volumes, and potentially accelerating the clearing of natal gas. Coupling with dynamical evolution in gas-rich environments introduces complex, non-secular evolution pathways (Cournoyer-Cloutier et al., 3 Jul 2025).
• Galaxy-scale Regulation and Environmental Effects: On >kpc scales, the global efficiency of clustered star formation is modulated by aggregate feedback, hierarchical clustering, and ambient galactic properties, including existing stellar mass and structural features (bars, spiral arms, nuclear regions). AGN feedback, where present, acts predominantly on massive galaxies’ gas reservoirs and may set second-order conditions for further cluster formation (Davies et al., 28 May 2025).

5. Evolutionary Pathways, Timescales, and Structural Diagnostics

The FEAST paradigm has enabled a unified evolutionary framework for star clusters:

• Embedded to Exposed Sequence: The transition from fully embedded (deeply PDR-dominated, PAH-bright) to partially emerged (ionic emission–dominated) to optically uncovered clusters defines a temporal sequence of $\sim$6 Myr in systems like M83, with possible acceleration for high-mass clusters and slower emergence for lower-mass ones (Knutas et al., 13 May 2025).
• Persistent Structural Imprints: Metrics such as the $Q$-parameter (substructure retention), mass segregation (quantified via minimum spanning tree ratios), and radial gradients in the mass function all encode the relative rates of dynamical mixing versus gas removal. Only clusters formed at low density and with strong early feedback maintain observable primordial structure over several Myr (Parker et al., 2013, Gavagnin et al., 2017).
• Discrepancies and Model Challenges: Systematic issues with SED fitting in the NIR for eYSCs (i.e., missing flux sources, stochastic IMF sampling) highlight persistent challenges and the need for incorporation of YSO emission and stochastic models (e.g., SLUG) (Pedrini et al., 1 Sep 2025).

6. Implications for Galaxy Evolution and Future Prospects

The feedback mechanisms encoded in FEAST have broad consequences for both cluster and galaxy evolution:

• Multi-Phase ISM Regulation: The combined radiative, mechanical, and chemical feedback from young clusters regulates the conversion rates of neutral and molecular gas, the thermal and pressure balance of the ISM, and the propagation of turbulence and metal enrichment on galactic scales. The true star formation efficiency in outer disks, for example, is now understood to be even lower than previously thought once diffuse HI is properly accounted for, emphasizing inefficient star formation under low-pressure feedback-dominated conditions (Wang et al., 22 Jul 2024).
• Calibration for Cosmological Models: Detailed observational results from FEAST provide essential benchmarks for star formation and feedback subgrid prescriptions in cosmological simulations, critical for recovering observed cluster mass functions, age spreads, and the emergence of globular clusters across cosmic time (Brown et al., 2022, Calura et al., 4 Nov 2024).
• High-Redshift and Extreme Environments: JWST’s ability to resolve emerging clusters during their embedded phase in a wide range of galactic environments, including interacting dwarfs and high-pressure starbursts, opens new opportunities to systematically calibrate the full lifecycle and feedback impact of clustered star formation across redshift (Bortolini et al., 1 Sep 2025, Correnti et al., 4 Jul 2025).
• Future Directions: Outstanding challenges include constructing SED models that incorporate YSO components and stochastic IMF effects, mapping cluster emergence and feedback as a function of environment and metallicity, and dissecting the co-evolution of clusters and their field populations in galaxies with varying merger histories and feedback regulation regimes.

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Feedback in Emerging extrAgalactic Star clusTers thus provides a rigorous, multi-faceted framework that integrates simulation, observation, and theory to understand the regulation of star formation, the structural evolution and survival of clusters, and the imprint of feedback physics on both small and galactic scales across the Universe.