Feedback in Extragalactic Star Clusters (FEAST)

• FEAST is a comprehensive framework that integrates high-resolution observations and simulations to examine how stellar feedback influences the formation and evolution of extragalactic star clusters.
• The study leverages JWST imaging and advanced N-body/hydrodynamic simulations to quantify metrics such as star formation efficiency and cluster compactness in feedback-regulated environments.
• Results reveal that radiative, mechanical, and chemical feedback critically dictate cluster survival and structural evolution, with implications for galaxy-wide star formation regulation.

Feedback in Emerging Extragalactic Star Clusters (FEAST) encompasses the theoretical, observational, and numerical paper of how various stellar feedback mechanisms regulate the formation, evolution, and observable properties of young star clusters beyond the Milky Way. FEAST leverages high-resolution multiwavelength observations (notably with JWST), advanced N-body and hydrodynamical simulations, and integrative population analyses to address the imprint of radiative, mechanical, and chemical feedback on star cluster emergence, survivability, and galactic context.

1. Feedback Processes in Star Cluster Formation

Stellar feedback in extragalactic star clusters primarily arises from photoionization by massive stars, stellar winds, and, at later stages, supernovae. In the early formation phase, feedback is dominated by photoionizing radiation from OB stars ($m \gtrsim 20~M_\odot$). The feedback operates via several interlinked mechanisms:

• Photoionization: Ionizing photons heat and ionize surrounding gas, creating H II regions, driving mass loss, and preemptively reducing available star-forming material (Parker et al., 2013, Gavagnin et al., 2017, Sirressi et al., 15 Feb 2024).
• Stellar Winds: Mechanical energy and momentum injected by winds from massive stars create cavities, compress surrounding material, and may ultimately expel remaining natal gas if the cumulative kinetic energy rivals the gravitational binding energy (Dib et al., 2013, Wall et al., 2020, Calura et al., 4 Nov 2024).
• Radiative Pressure: Especially near massive clusters, intense UV fields accelerate ambient gas, sometimes exceeding the quenching efficiency of SN feedback in dense environments (Guillard et al., 2018, Fukushima et al., 2022).
• Supernovae: At later stages, SNe inject both energy and momentum but may be subdominant for gas removal if most dense gas is already dispersed by earlier feedback (Guillard et al., 2018, Li et al., 2017, Brown et al., 2022).

The dynamic interplay of these processes determines the star formation efficiency (SFE), age spread of stars, initial mass function shape, and the ultimate fate (bound/unbound) of emerging clusters. For momentum and energy accounting, the ratio of feedback energy or force to cloud gravitational binding energy sets the regime and efficiency of disruption—one widely used analytic criterion is $E_\mathrm{feedback}/|E_\mathrm{grav}| \approx 1$, marking when feedback expels gas and halts star formation (Dib et al., 2013, Li et al., 2019, Fukushima et al., 2022).

2. Simulation Methodologies and Structural Evolution

FEAST research utilizes high-resolution simulations informed by both hydrodynamics (SPH, AMR, moving-mesh) and collisional N-body dynamics (Parker et al., 2013, Li et al., 2017, Calura et al., 4 Nov 2024). Approaches include:

• Initial Conditions: Simulations start from turbulent, often bound ($\alpha_\mathrm{vir} \lesssim 1$) clouds with realistic density profiles (e.g., $r^{-2}$). Properties such as total mass ($10^3$–$10^5~M_\odot$), size, and virial ratio are systematically varied (Parker et al., 2013, Li et al., 2017, Calura et al., 4 Nov 2024).
• Feedback Implementation: Radiative transfer modules track photon-matter coupling (photoionization), while mechanical feedback is implemented through wind and SN injection regions. Efficiency factors (e.g., wind coupling parameter $\kappa$ or SN momentum boost $f_\mathrm{boost}$) modulate net feedback impact (Dib et al., 2013, Li et al., 2017, Brown et al., 2022).
• Structural Metrics: Analysis proceeds using structural diagnostics:
  • The $\mathcal{Q}$-parameter, $\mathcal{Q} = \bar{m}/\bar{s}$, quantifies substructure versus central concentration; $\mathcal{Q} < 0.8$ implies substructured morphology (Parker et al., 2013).
  • Half-mass radius ($r_{1/2}$) and central/surface densities track cluster expansion and densification (Parker et al., 2013, Gavagnin et al., 2017).
  • Relaxation time, $t_\mathrm{relax} = (N/8\ln N) t_\mathrm{cross}$, predicts the timescale for erasure of substructure (Parker et al., 2013, Li et al., 2017).

Clusters formed with strong photoionization feedback tend to have lower initial densities, longer $t_\mathrm{relax}$, and retain substructure for longer. In contrast, high-density, feedback-free clusters undergo rapid dynamical mixing and erasure of initial structure (Parker et al., 2013, Gavagnin et al., 2017).

3. Constraints on Star Formation Efficiency and Stellar Age Spread

Dual constraints on SFE and the age spread of stars in clusters directly result from feedback-regulated gas removal (Dib et al., 2013, Li et al., 2019, Li et al., 2017, Fukushima et al., 2022). Important findings and scalings include:

• SFE: Defined as SFE $= M_\mathrm{cluster}/M_\mathrm{cloud}$. Constant core formation efficiency (CFE) models yield typically $0.025 \leq$ SFE $\leq 0.25$, while accelerated (burst-like) CFE models produce SFE up to $0.8$–$0.9$ (Dib et al., 2013). The integrated SFE scales with cloud surface density ($\Sigma$) and inversely with feedback strength, with analytic forms such as $\epsilon_* \approx 1 - 1/\Gamma$ in the high $\Sigma$ limit, where $$\Gamma \sim \Sigma_\mathrm{sh}/\Sigma_\mathrm{crit}$$ gives the ratio of shell to critical surface densities (Li et al., 2019, Fukushima et al., 2022).
• Stellar Age Spreads: Accelerated models, often associated with dynamically triggered bursts (e.g., cloud collisions), yield very short age spreads, $\Delta \tau_* \lesssim 0.4$ Myr, replicating starburst clusters (NGC 3603 YC, Westerlund 1). Uniform SFR models yield broader age spreads (up to several $10^5$–$7 \times 10^5$ yr), typical of the Orion Nebula Cluster (Dib et al., 2013).

The SFE–age spread relation and its metallicity dependence (weaker winds at lower metallicity yield higher SFE and larger $\Delta \tau_*$) offer key diagnostics, with the SFE–$\Delta \tau_*$ diagram serving as a “benchmark” for cluster formation scenario discrimination and model validation (Dib et al., 2013).

4. Feedback Impact on Cluster Dynamics and Survival

Simulations consistently find that feedback regulates internal cluster structure and the survivability of clusters post-gas expulsion (Parker et al., 2013, Li et al., 2017, Li et al., 2019). Key points are:

• Sub-virial and Centrally Concentrated Initial States: Clusters form sub-virial (e.g., $\alpha_\mathrm{vir} \sim 0.48$–$0.6$), and their stars are centrally concentrated ($\rho_* \propto r^{-2.8}$ vs. gas $\propto r^{-1.9}$ at SFR peak). This configuration increases the bound fraction after gas removal, as slow stellar velocities and a deep central potential well resist disruption (Li et al., 2019).
• Bound Fraction: The fraction of stellar mass that remains gravitationally bound ($f_\mathrm{bound}$) increases monotonically with integrated SFE; clusters with SFE $<0.5$ still retain high bound fractions due to sub-virial velocities and steep profiles. This is captured quantitatively by Maxwellian-based integrals linking $f_\mathrm{bound}$ to $\epsilon_\mathrm{int}$ and $\alpha_*$ (Li et al., 2019).
• Mass Segregation and Multiple Systems: Feedback enhances primordial mass segregation by preferentially removing lower-mass stars, while higher binary fractions for massive stars and a reduction in runaways are observed in clusters with feedback (Gavagnin et al., 2017, Wall et al., 2020).
• Cluster Expansion and Dissolution: Feedback-driven clusters are less prone to rapid dissolution; high-density, no-feedback clusters experience accelerated evaporation and expansion due to dynamical heating and frequent close encounters (Gavagnin et al., 2017).

5. Observational Diagnostics and FEAST Survey Insights

The FEAST project employs high-resolution JWST/NIRCam and MIRI mapping to directly observe embedded young star clusters (“eYSCs”) in external galaxies, allowing the assessment of feedback signatures and cluster emergence timelines (Gregg et al., 15 May 2024, Pedrini et al., 3 Jun 2024, Knutas et al., 13 May 2025). Core diagnostic strategies include:

• Identification of eYSC Stages: Emerging clusters are categorized as “eYSCI” (compact Pa$\alpha$ and 3.3 μm PAH emission) or “eYSCII” (Pa$\alpha$ only), forming a sequence from fully embedded, through natal cloud clearing, to optically exposed YSCs. The timescale from eYSCI to optically visible YSC is $\sim 6$ Myr, with the compact PAH phase lasting $\sim 4.4$ Myr (Knutas et al., 13 May 2025).
• PAH and Mid-IR Indicators: Calibration of SFR via 3.3 μm PAH and 21–24 μm MIR emission reveals tight, but generally sublinear, relations with hydrogen recombination lines. The 3.3 μm to 7.7 μm PAH ratio remains constant as a function of age and morphology, consistent with simultaneous destruction of both neutral and ionized PAH carriers during feedback—but the absolute emission in both bands decreases as young clusters disrupt their natal material (Gregg et al., 15 May 2024, Pedrini et al., 3 Jun 2024).
• SED Analysis and Modeling Shortcomings: The observed SEDs of eYSCs display a NIR (1.5–2.5 μm) flux excess unaccounted for by conventional stellar population models, particularly in low-mass and very young clusters. Stochastic IMF sampling effects (as shown by slug simulations) and likely contributions from pre-main-sequence stars or young stellar objects (YSOs) are required to reconcile SED modeling with observed cluster properties (Pedrini et al., 1 Sep 2025).
• Environmental and Mass Dependence: Larger, more massive clusters emerge from their embedded phase faster (∼5 Myr vs. ∼7 Myr for $10^3~M_\odot$ clusters), with feedback efficacy tied to both cluster mass, ISM column density, and galactic location (e.g., starburst vs. bar regions) (Knutas et al., 13 May 2025).

6. Implications for Galaxy Evolution and Future Directions

FEAST work demonstrates that feedback in extragalactic star clusters imposes fundamental limits on star formation and cluster structure, with consequences for galactic scaling relations and the fate of molecular gas reservoirs (Adamo et al., 2020, Fukushima et al., 2022, Pedrini et al., 1 Sep 2025):

• Regulation of Star Formation History: Feedback constrains the integrated SFE, limits cluster mass growth, and determines the fraction of stars born in bound clusters. The feedback-regulated star cluster population shapes the host galaxy’s stellar mass assembly and chemical enrichment.
• Interpretation of Observed Cluster Populations: Empirical tools such as the SFE–$\Delta \tau_*$ diagram, the boundedness parameter $\Pi = \mathrm{age}/t_\mathrm{cross}$, and direct MIR calibrations allow discrimination between formation modes (e.g., burst vs. uniform), connect observed high-redshift progenitors to local massive clusters, and impose constraints on subgrid prescriptions in cosmological simulations (Dib et al., 2013, Calzetti et al., 3 Jun 2024, Calura et al., 4 Nov 2024).
• Future Research Directions: Suggested avenues include modeling higher-mass and higher-resolution clusters, combining multiple feedback channels (stellar winds, radiation pressure, SNe), refining SED templates for embedded clusters including YSO contributions, and expanding JWST coverage to statistically sample various environments (Parker et al., 2013, Knutas et al., 13 May 2025, Pedrini et al., 1 Sep 2025).

7. Limitations and Requirements for Robust Inference

Feedback signatures in emerging extragalactic star clusters are degenerate with respect to several initial conditions and environmental properties. Inferring the strength or mode of feedback from structural metrics (e.g., $\mathcal{Q}$, cluster compactness) at a given epoch requires knowledge of both the initial density and virial state of the system (Parker et al., 2013). Contamination by stochastic IMF sampling, uncertainties in dust and PAH modeling, and environmental variations (e.g., metallicity, turbulent pressure) must be carefully disentangled, necessitating both comprehensive modeling and high spatial resolution multiwavelength observations (Pedrini et al., 1 Sep 2025, Pedrini et al., 3 Jun 2024).

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In summary, FEAST research has synthesized simulations and cutting-edge JWST observations to reveal that stellar feedback is central to the evolutionary trajectories, structural properties, and census of emerging extragalactic star clusters. The interplay of feedback physics with ISM conditions and dynamical processes uniquely shapes the star cluster population, establishing FEAST as a bridge from stellar physics to galaxy assembly.