Feedback-Free Starbursts (FFB)

• Feedback-Free Starbursts are a mode of star formation in massive, high-redshift galaxies where the free-fall time is shorter than the delay in stellar feedback.
• They yield near-maximal star formation efficiency and produce observable signatures such as excess bright galaxies, compact morphologies, and high-velocity outflows.
• FFBs profoundly impact early galaxy evolution by driving rapid stellar mass buildup, influencing 21-cm signals, and seeding massive black holes in the early universe.

Feedback-Free Starbursts (FFB) are a distinct mode of intense star formation that arises in sufficiently massive, high-redshift galaxies when the dynamical timescale for star-forming gas to collapse and form stars is shorter than the onset timescale of energetic stellar feedback (winds, photoionization, supernovae). This regime enables near-maximal conversion of cold gas into stars in a short, quasi-explosive event, and underlies several recent efforts to interpret the early buildup of massive galaxies, quasar seeding, and the rapidly evolving 21-cm line at cosmic dawn.

1. Physical Definition and Critical Conditions

Feedback-Free Starbursts occur when the free-fall (collapse) time of dense, star-forming gas clouds is less than the characteristic delay before substantial mechanical or radiative feedback from newly formed massive stars can halt star formation. The critical physical requirements are:

• Density Criterion:

The cloud number density must satisfy

$n \gtrsim 3 \times 10^3\,\mathrm{cm}^{-3}$

such that the free-fall time

$$t_{\rm ff} = \sqrt{\frac{3 \pi}{32\, G \rho}} \lesssim 1\,\mathrm{Myr}$$

falls below the $\sim1$–3 Myr timescale for massive stars to evolve and produce winds and supernovae.

• Surface Density Criterion:

A gas surface density

$$\Sigma \gtrsim 2 \times 10^3\,M_\odot\,\mathrm{pc}^{-2}$$

is required to inhibit radiative feedback (e.g., radiation pressure on dust).

• Cooling Time:

The cooling time at $T \lesssim 100$ K must be shorter than $t_{\rm ff}$, fulfilled once metallicity exceeds a minimal threshold.

Under these joint conditions, star-forming clouds in the relevant halos undergo collapse and form stars before disruptive feedback mechanisms can intervene (Dekel et al., 2023, Li et al., 2023, Dekel et al., 13 Jun 2025).

The formation of FFBs is thus inherently regulated by a redshift-dependent halo mass threshold, parameterized as

$$M_{\rm FFB}(z) = 10^{10.8} \left(\frac{1+z}{10}\right)^{-6.2}\,M_\odot$$

Above this threshold, halos host the requisite gas densities and collapse times. The declining threshold with increasing $z$ means FFB conditions are reached more easily at earlier epochs (Libanore et al., 2023, Dekel et al., 13 Jun 2025).

2. Star Formation Efficiency, Dynamical Regulation, and Burst Timescales

The essence of the FFB phenomenon is the dramatic enhancement of the integrated and instantaneous star-formation efficiency (SFE):

• Integrated SFE:

$\epsilon = \frac{M_*}{f_b M_h}$

where $M_*$ is stellar mass, $M_h$ halo mass, $f_b$ the cosmic baryon fraction $(\approx 0.16)$. In the FFB regime, $\epsilon$ can reach $0.2$–$1$, compared to $\epsilon \lesssim 0.1$ in standard feedback-regulated scenarios.

• Instantaneous SFE:

$\epsilon' = \frac{\mathrm{SFR}}{f_b \dot{M}_h}$

In FFBs, $$\mathrm{SFR}_{\rm FFB} = \epsilon_{\max}\,\dot M_{\rm acc}$$, with $\epsilon_{\max}$ up to unity (optimistic) or $0.2$ (conservative).

Star formation proceeds in short, recurrent, and nearly feedback-free bursts lasting $\lesssim t_{\rm ff}$ in dense clumps (few Myr), stacked over a longer FFB episode of $100$–$200$ Myr as fresh cold gas is accreted via cosmological flows (Dekel et al., 2023, Li et al., 2023, Furlanetto et al., 2021).

A simplified analytic expression for the SFE transition is

$$\epsilon' (M,z) = \bigl[1-f_{\rm FFB}(M,z)\bigr]\,\epsilon_{\text{emp}}(M,z) + f_{\rm FFB}(M,z)\,\epsilon_\text{max}$$

with $f_{\rm FFB}$ a smooth step function centered at $M_{\rm FFB}(z)$.

3. Observable Signatures and Predictions

FFBs yield several pronounced observable effects:

• Enhanced number counts of bright galaxies at $z \gtrsim 9$:

The UV luminosity function (UVLF) and stellar mass function (GSMF) display order-of-magnitude excesses at the bright end relative to extrapolations of standard models. This excess grows rapidly at higher redshift, aligning with JWST’s reports of an unexpectedly high abundance of luminous $z > 10$ galaxies (Li et al., 2023, Dekel et al., 2023, Dekel et al., 13 Jun 2025).

• Bursty star formation histories (SFH):

The typical FFB galaxy exhibits $\sim 10$–Myr fluctuations in SFR, resulting in a log-normal scatter $\sim 0.3$ dex in instantaneous SFR and comparable scatter in UV luminosities. The rest-frame UV magnitude scatter can reach $\pm1$ mag for $M_h \sim 10^{10}\,M_\odot$ at $z \sim 7$ (Furlanetto et al., 2021).

• Compact morphology and high-velocity outflows:

FFB galaxies at threshold masses show effective half-light radii $R_e \sim 0.3\,{\rm kpc}\,(1+z)_{10}^{-\alpha}$ ($\alpha \sim 2$–3), high outflow velocities $\rm FWHM \sim 1{,}400$–$6{,}700$ km/s (for integrated SFE $\epsilon \sim 0.2$–$1$), and low gas fractions ($f_{\rm gas} \lesssim 0.1$) and metallicity ($Z \lesssim 0.1 Z_\odot$) (Li et al., 2023, Dekel et al., 2023).

• Low dust content and attenuation:

UV dust attenuation is modest: $A_{\rm UV} \sim 0.5$ mag at $z \sim 10$, decreasing with redshift.

• 21-cm global and fluctuating signals:

The increased SFRD from FFBs yields earlier and deeper absorption troughs in the global 21-cm signal, as well as boosted and shifted peaks in the 21-cm power spectrum. These features are expected to be detectable by next-generation arrays such as HERA, with FFB-induced signatures distinguishable even in the face of moderate foregrounds if Population II stars dominate the early star formation (Libanore et al., 2023).

FFB Observable	Predicted Value/Effect	Standard Scenario
SFE ($\epsilon$)	$0.2$–$1$ (FFB regime)	$\lesssim 0.1$
$R_e$	$\sim0.3$ kpc at $z \sim 10$	$\sim1$ kpc
$f_{\rm gas}$	$\lesssim 0.1$	$0.2$–$0.7$
Outflow FWHM	$1{,}400$–$6{,}700$ km/s	$\lesssim 500$ km/s
Metallicity	$Z \lesssim 0.1\,Z_\odot$	$\sim Z_\odot$ (by $z\sim2$)
UVLF bright-end (z>9)	Excess by $>10\times$	Standard LambdaCDM

The principal prediction is a redshift- and mass-dependent rise in SFE, rather than the nearly flat, low SFE in conventional abundance-matching and simulation frameworks. This produces accelerated cosmic star formation and reionization at earlier epochs.

4. Theoretical Modeling and Parameterization

Analytical and semi-analytical models implement the FFB scenario by:

• Integrating over the halo mass function:

Using the mass- and redshift-dependent SFE described above, predictions are generated for the evolution of the galaxy stellar mass function, UVLF, cosmic SFRD, and other global quantities.

• Star formation prescription:

The adopted formalism splits the SFR into a standard component and an FFB component, governed by smooth window functions that interpolate between the two regimes as a function of halo mass and redshift. For example,

$$\mathrm{SFR}_{\rm tot} = (1 - f_{\rm FFB}(z, M_h))\,\mathrm{SFR}_{\rm std} + f_{\rm FFB}(z, M_h)\,\mathrm{SFR}_{\rm FFB}$$

with $$\mathrm{SFR}_{\rm FFB} = \epsilon_{\max} \dot{M}_{\rm acc}$$.

• Treatment of Population III stars:

Pop III stars in minihalos introduce additional sources of ionizing photons at $z \gtrsim 20$ but can partially mask FFB signatures at the earliest times if their efficiency is high. However, provided Pop III SFE remains at or below $f_{*,{\rm III}}\sim10^{-2.5}$, FFB effects on 21-cm signals remain clearly distinguishable (Libanore et al., 2023).

• Constraints and Parameter Ranges:

The models generally adopt $\epsilon_{\rm max}=1$ (optimistic) or $0.2$ (conservative), window smoothing widths $\sim$0.15 dex, and relate observable quantities via scaling relations derived from dynamics and stellar evolution timescales.

5. Role in Black Hole Seeding and Early Quenching

The FFB regime provides natural sites for the formation and early growth of massive black holes (BHs):

• Intermediate-Mass Black Hole Seeds:

The dense, massive ($\sim10^4$–$10^7\,M_\odot$) star clusters formed in FFB episodes efficiently undergo core collapse, forming $10^3$–$10^4\,M_\odot$ BH seeds on timescales of a few $t_{\rm ff}$. The "gravo-gyro" instability and cluster rotation further accelerate core collapse. This process efficiently populates FFB disks with IMBHs, with seed-to-cluster mass ratios $\sim10^{-2}$ (Dekel et al., 27 Sep 2024).

• Mergers and Central Black Hole Assembly:

Post-disruption, IMBH seeds migrate inward via dynamical friction on $10^8$ yr timescales, assembling a $10^{6-8}\,M_\odot$ BH in the galactic nucleus by $z\sim4$–$7$. Monte Carlo modeling shows that most BHs are retained after mergers, even accounting for GW recoil kicks, especially if merger dynamics are in a cold, disk-like environment or if a "wet compaction" phase boosts the central escape velocity.

• Observed Elevated $M_{\rm BH}/M_*$:

Empirical analysis of JWST AGN at $z=4$–$7$ yields

$$\log\frac{M_{\rm BH}}{M_\odot}\approx -2.43 + 1.06 \log\frac{M_*}{M_\odot}$$

a factor $10$–$100$ above the local ratio, consistent with FFB-driven, merger-dominated SMBH growth (Dekel et al., 27 Sep 2024).

• Early Quenching and Bimodality:

The FFB phase, by depleting the dense gas reservoir and triggering massive bulge and black hole growth, initiates rapid postburst quenching. Secondary mechanisms—gas expulsion, morphological stabilization (compaction), suppression of cold-stream feeding by AGN- or compaction-driven CGM turbulence, and the onset of AGN feedback—conspire to terminate subsequent star formation, producing the compact quiescent systems that begin to populate the universe at $z\sim4$–$7$ (Dekel et al., 13 Jun 2025).

6. Observational Tests and Comparison to Non-FFB Starbursts

Key predictions that distinguish FFBs from non-FFB starbursts include:

• Order-of-magnitude bright-end excesses in the UVLF and GSMF at $z>9$,
• Very compact ($R_e\lesssim0.3$ kpc) morphologies in massive, young galaxies,
• High-velocity nebular and ISM line wings, FWHM up to several thousand km/s,
• Low gas fractions ($f_{\rm gas}<0.1$), subsolar metallicity, and modest dust attenuation,
• Bursty SFHs on $\sim$10 Myr timescales, measurable via H$\alpha$/UV SFR ratios,
• Elevated $M_{\rm BH}/M_*$ at $z=4$–$7$,
• Quiescent descendants at $z=4$–$7$ that are compact, faint in nebular emission, Balmer-absorption-dominated, sometimes with faint AGN signatures.

Next-generation surveys and instruments (e.g., JWST, ELTs, HERA) are poised to test these predictions systematically (Li et al., 2023, Libanore et al., 2023).

7. Relation to Lower-Redshift and AGN-Dominated Starburst Regimes

At cosmic noon ($z\sim2$), "pre-feedback" starbursts in the local universe lack the extreme densities, and generally exhibit SFEs and gas fractions ($f_{\rm gas}\sim0.4$) much higher than normal disks, but still below the essentially feedback-free conversion of FFBs. AGN in dusty starbursts at $z\sim2$ typically precede the onset of effective feedback, as traced by the similarity of gas fractions and SFRs between AGN-dominated and purely star-forming systems at the highest SFRs and AGN luminosities below the theoretical blow-out threshold ($L_{\rm bol}({\rm AGN}) \lesssim 10^{46}$ erg/s) (Rodighiero et al., 2019). This suggests that while "feedback-free" phases can occur at lower redshifts, the true FFB regime as defined above is generically associated with the unique dynamical and cooling conditions prevailing at cosmic dawn.

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Feedback-Free Starbursts constitute a physically and observationally distinct regime of galaxy formation, marked by a short-lived but highly efficient burst of star formation enabled by collapse times short compared to all available feedback mechanisms. This mode provides a coherent framework for interpreting early galaxy and quasar observations, explicable in $\Lambda$CDM without invoking exotic physics, and is subject to imminent observational validation across multiple wavebands and cosmic probes.