Bursting Bubbles: Clustered Supernova Feedback in Local and High-redshift Galaxies

Abstract: We compare an analytic model for the evolution of supernova-driven superbubbles with observations of local and high-redshift galaxies, and the properties of intact HI shells in local star-forming galaxies. Our model correctly predicts the presence of superwinds in local star-forming galaxies (e.g., NGC 253) and the ubiquity of outflows near $z \sim 2$. We find that high-redshift galaxies may `capture' 20-50\% of their feedback momentum in the dense ISM (with the remainder escaping into the nearby CGM), whereas local galaxies may contain $\lesssim$10\% of their feedback momentum from the central starburst. Using azimuthally averaged galaxy properties, we predict that most superbubbles stall and fragment \emph{within} the ISM, and that this occurs at, or near, the gas scale height. We find a consistent interpretation in the observed HI bubble radii and velocities, and predict that most will fragment within the ISM, and that those able to break-out originate from short dynamical time regions (where the dynamical time is shorter than feedback timescales). Additionally, we demonstrate that models with constant star cluster formation efficiency per Toomre mass are inconsistent with the occurrence of outflows from high-$z$ starbursts and local circumnuclear regions.

• The paper introduces an analytic model that predicts superbubble evolution via clustered supernovae, delineating four outcome regimes based on gas fraction and dynamical time.
• It employs momentum injection methods and phase-space boundaries validated by observations of local NGC galaxies and high-redshift SMGs.
• The study quantifies feedback momentum deposition and turbulence driving scales, clarifying conditions necessary for galactic wind initiation.

Analytic Model of Clustered Supernova Feedback: Predictive Framework for Galactic Wind Dynamics

Model Construction and Superbubble Outcomes

The paper formulates an analytic model for the evolution of superbubbles generated via spatially and temporally clustered core-collapse SNe within galactic disks. The model leverages clustered star formation in marginally stable GMCs with efficiencies derived from local gas surface densities. Superbubble growth is modeled through momentum injection, tracking expansion until either stalling/fragmenting within the ISM or breaking out to drive galactic winds and fountains. Outcomes are partitioned via two fundamental local parameters: the gas fraction ($\tilde f_g$) and inverse dynamical time ($\Omega$). Four outcome regimes are delineated:

• Powered Break-out (PBO): Bubble reaches disk scale height prior to cessation of SNe.
• Coasting Break-out (CBO): Unpowered bubble reaches scale height post-SNe.
• Powered Stall (PS): Stalling occurs before SNe cease.
• Coasting Fragmentation (CF): Fragmentation post-SNe, with radius below scale height.

The phase-space boundaries (Figure 1) are derived from parametric constraints on $\tilde f_g$ and $\Omega$ and reproduce the evolution outcomes of superbubbles in stratified turbulent disks observed in simulations, including realistic ISM turbulence and feedback timescales.

Figure 1: Gas fraction--dynamical time phase space for superbubble outcomes, with observational and simulation data validating model case boundaries.

Empirical Validation: Local and High-Redshift Galaxies

Comparison to observations is systematically executed using spatially resolved data for molecular and atomic gas, stellar surface density, and rotation curves from local NGC galaxies and the Solar Circle. The analytic case boundaries are in agreement with empirical detection (or non-detection) of outflows, notably in NGC 253 and 4321. The model further incorporates high-$z$ SMGs using rotation curve and gas fraction data, demonstrating that nearly all $z\sim2$ galaxies are in the PBO regime. This predicts universality of SNe-driven outflows at cosmic noon, aligning with observed wind ubiquity.

Unexpectedly, the stalling and fragmentation boundary for local star-forming galaxies aligns closely with gas disk scale height, implying turbulence driving mechanisms at this scale. Superbubble fragmentation and momentum deposition are quantitatively reproduced in simulations, directly confirming the analytic predictions.

Turbulence Driving Scales and Feedback Momentum Deposition

A critical result is the prediction of the fragmentation radius ($R_b/H$) and effective feedback strength ($P/m_\star$) deposited locally (Figure 2). For local universe disks, fragmentation occurs very near scale height ($R_b/H \gtrsim 0.7$), reinforcing a scenario in which SN feedback is the dominant ISM turbulence driver at large scales. The model estimates momentum deposition efficiency, revealing that only $\sim$10% of feedback momentum from central starbursts is retained in the ISM for cases like NGC 253; by contrast, $z\sim2$ galaxies capture 20-50%, indicating a strong redshift dependence in feedback-regulated ISM evolution.

Figure 2: Fragmentation radius as fraction of disk scale height and momentum deposition efficiency as functions of gas fraction and dynamical time.

HI Bubble Observations and Remnant Interpretation

The model is further tested via observed HI bubble radii and expansion velocities across local star-forming galaxies (Figure 3). The analytic predictions organize bubbles in $v_b/\sigma$--$R_b/H$ space, separating those destined to fragment from those likely to break out. The majority of intact HI bubbles in local galaxies are shown to fragment within the ISM, except for those in central regions characterized by short dynamical times ($t_{\rm dyn} < 20$ Myr), consistent with nuclear origin of break-out events.

Figure 3: Observed properties of intact HI bubbles, demonstrating modeled fragmentation/break-out division within disk environments.

Implications for Star Cluster Formation Models

An alternative scenario assuming constant star cluster formation efficiency per Toomre mass is evaluated and empirically refuted (Figure 4). The model with constant efficiency fails to reproduce central outflows in high surface density regions, strongly contradicting observations of starburst-driven winds in both high-redshift SMGs and local circumnuclear disks. This result supports cluster formation scaling with gas surface density as necessary for physically realistic feedback models.

Figure 4: Case boundaries for constant cluster formation efficiency; observations favor the analytic model over the Toomre-mass scenario.

Conclusion

The analytic framework effectively encapsulates clustered SNe feedback mechanisms, predicting superbubble property evolution and outcome regimes as functions of gas fraction and dynamical time. It is validated against observations and simulations, accurately describing turbulence driving scales, momentum deposition, and conditions for galactic wind genesis—in both local and high-redshift galaxies. The model's exclusion of constant cluster formation efficiency is justified by empirical contradiction. The theoretical advance has direct implications for sub-grid feedback prescriptions in galaxy simulations and for interpreting resolved turbulent ISM structures. Future spatially resolved, multi-phase studies are anticipated to further constrain the parameterization of feedback and superbubble scaling relations under varying galactic conditions.