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The Incidence of Large Ionized Bubbles at Redshift 13

Using JWST-calibrated galaxy luminosity functions, this paper demonstrates that galaxy-driven ionized bubbles with radii of at least 2.5 cMpc are statistically plausible at redshift 13, suggesting that the large ionized environment observed around the Witstok source is consistent with standard population models, though the specific source may still require additional factors like bursty star formation or non-stellar ionization.

Original authors: Peter Ziwei Hu, Massimo Stiavelli, Colin Norman

Published 2026-06-17

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CC BY 4.0

Original authors: Peter Ziwei Hu, Massimo Stiavelli, Colin Norman

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Lighting Up the Cosmic Fog

Imagine the early universe (about 13 billion years ago) as a giant, thick room filled with dense, invisible fog. This "fog" is made of neutral hydrogen gas. In this era, light from stars couldn't travel far because the fog absorbed it.

However, the first galaxies started forming. These galaxies were like powerful lighthouses. As they shone, they didn't just emit light; they emitted a special kind of energy (ionizing photons) that acted like a laser cutter, burning holes through the fog and creating clear, transparent bubbles around themselves.

This paper asks a simple question: How big are these bubbles, and how often do they get big enough to let light escape?

Specifically, the authors are looking at a time called Redshift 13 (very early in the universe's history). They want to know if it's common for galaxies to create bubbles large enough to explain a specific, mysterious galaxy recently discovered by the James Webb Space Telescope (JWST), known as the "Witstok" source. This source is special because it's glowing brightly in a way that suggests it's sitting inside a huge, clear bubble, even though the rest of the universe is still foggy.

The Experiment: A Digital Sandbox

To answer this, the authors built a computer simulation. Think of this as a giant, 3D digital sandbox.

The Cast of Characters: They populated this sandbox with thousands of virtual galaxies. They didn't just guess how many there were; they used real data from JWST (the "UV Luminosity Function") to decide how many bright and dim galaxies exist.
The Rules of the Game:
- Each galaxy acts as a lightbulb.
- The "brightness" of the bubble depends on two things: how many photons the galaxy produces and how many of those photons actually escape the galaxy to hit the fog (the "escape fraction").
- The bubble grows until the fog tries to "heal" itself (recombination) and fill the hole back in.
The Conservative Approach: The authors made a specific, cautious choice. They treated every bubble as a separate, non-touching sphere. They did not let the bubbles merge together to form giant, connected islands of clear air.
- Analogy: Imagine dropping many soap bubbles into a room. If you let them touch, they merge into one giant, complex shape. The authors decided to count them as if they were all floating separately, never touching. This makes their estimate of "large clear areas" a minimum (a conservative baseline). If real bubbles merge, the clear areas would be even bigger.

The Main Findings

1. Big Bubbles Are Not Rare

The simulation showed that in a universe with the galaxy population we see today, bubbles with a radius of 2.5 "comoving megaparsecs" (a huge cosmic distance) are actually quite common.

The Statistic: They found that for every square of sky the size of a postage stamp (a specific unit called an arcminute), there is roughly a 1.3% chance of finding such a large bubble in a slice of time.
The Takeaway: You don't need a miracle to find a galaxy like the "Witstok" source. The standard population of early galaxies is capable of producing these large, clear environments naturally.

2. The "Witstok" Source Might Be a Special Case

Even though big bubbles are common, the specific galaxy the authors are studying (Witstok) might still be unique.

The Analogy: Imagine a forest where it's common for trees to grow 50 feet tall. You find one tree that is 50 feet tall. That's normal. But if that specific tree is glowing with a strange, extra-bright light that no other tree has, it might still be special.
The Paper's Claim: The environment (the big bubble) is normal. But the galaxy inside it might need to be extra efficient at shooting out ionizing light, or it might have had a recent "burst" of star formation that has since faded, leaving a large bubble but a dimmer-looking galaxy today.

3. What Controls the Bubble Size?

The authors tested what makes the bubbles bigger or smaller:

Bright Galaxies Matter Most: The size of the bubble depends heavily on the brightest galaxies in the mix. If you change the model to say there are fewer super-bright galaxies, the big bubbles disappear.
Efficiency Matters: How well the galaxy lets light escape is crucial.
Time Matters: Bubbles need time to grow. Older galaxies have bigger bubbles.

The "Conservative" Warning

The authors are very careful to say their numbers are a floor, not a ceiling.

Because they didn't let bubbles merge in their simulation, the real universe likely has even more large clear areas than they calculated.
Because they didn't account for galaxies clustering together (huddling in groups), the real clear areas might be even larger.
Conclusion: If their "conservative" model says big bubbles are common, then in reality, they are almost certainly very common.

Summary in One Sentence

Using a cautious computer model based on real JWST data, the authors found that it is quite normal for early galaxies to carve out massive clear bubbles in the cosmic fog, meaning the mysterious "Witstok" galaxy likely sits in a typical environment, even if the galaxy itself has some unique, high-efficiency traits.

Technical Summary: The Incidence of Large Ionized Bubbles at Redshift 13

Problem Statement
Ionized bubbles surrounding early galaxies serve as the spatial units of cosmic reionization, linking galaxy populations to the escape of ionizing photons, the topology of the intergalactic medium (IGM), Ly $\alpha$ visibility, and 21 cm structure. With the James Webb Space Telescope (JWST) now constraining the abundance of luminous galaxies at $z \gtrsim 10$ and detecting rare Ly $\alpha$ emitters deep within the neutral era, a critical question arises: how frequently do galaxy populations produce large ionized environments? Specifically, the detection of a Ly $\alpha$ emitter at $z \approx 13$ by Witstok et al. (2025) necessitates a sufficiently large ionized region to allow the line to redshift out of resonance before encountering the predominantly neutral IGM. This paper investigates whether baseline galaxy-driven models, calibrated to JWST UV luminosity functions (UVLFs), predict a non-negligible abundance of such "Witstok-sized" regions ( $R \ge 2.5$ cMpc) at $z \approx 13$ .

Methodology
The authors employ a simulation framework tracking the growth of ionized regions in a comoving cubic volume from $z=25$ to $z=5$ . The model operates under a conservative, non-overlapping-sphere limit, treating each source's H II region as an independent sphere without uniting overlaps. The framework consists of three components:

Galaxy Population Synthesis: Galaxies are seeded according to the double power-law (DPL) UVLF from Donnan et al. (2024). Sources are retained across redshift steps, with new sources sampled from the incremental abundance and assigned random positions (no clustering).
Bubble Growth and Recombination: The ionized volume $V$ evolves according to the balance between ionizing photon injection and recombinations:
$\frac{dV}{dt} = \frac{\dot{N}_{\text{ion}}}{\bar{n}_{\text{H},0}} - \alpha_B C \bar{n}_{\text{H},0}(1+z)^3 V$
where $\dot{N}_{\text{ion}} = f_{\text{esc}} \xi_{\text{ion}} L_{\text{UV}}$ . The model incorporates a duty cycle ( $f_{\text{duty}}$ ) to account for intermittent activity and an effective clumping factor ( $C$ ) to absorb unresolved sinks.
Incidence Quantification: The primary metric is the sky surface density $\Sigma_{\ge 2.5}$ , representing the number of bubbles with comoving radius $R \ge 2.5$ cMpc per square arcminute per unit redshift interval ( $\Delta z = 1$ ).

Key Contributions and Results

Fiducial Incidence: For the fiducial model (Donnan et al. 2024 UVLF, $f_{\text{esc}}=0.2$ , $\log \xi_{\text{ion}}=25.5$ , $f_{\text{duty}}=1$ , $C=3$ ), the authors find $\Sigma_{\ge 2.5} \simeq 1.33 \times 10^{-2}$ arcmin $^{-2}$ per $\Delta z = 1$ at $z \approx 13$ . This corresponds to approximately 0.5 Witstok-sized regions in a JADES-class field ( $\sim 40$ arcmin $^2$ ) and 5 in a COSMOS-Web-scale field ( $\sim 0.5$ deg $^2$ ).
Population vs. Source Distinction: The results indicate that regions of the required size are plausible within the broader galaxy population. However, this is a population-level statement; the specific Witstok source may still require unusual effective ionizing efficiency, a recent fading/bursty history, or non-stellar contributions (e.g., AGN) to explain its large bubble relative to its observed UV luminosity.
Parameter Sensitivity: The high-radius tail of the bubble size distribution is most sensitive to the bright end of the UVLF and the product $f_{\text{esc}}\xi_{\text{ion}}$ $f_{esc} ξ_{ion}$ .
- Replacing the Donnan DPL UVLF with a Schechter-like form (Bouwens et al. 2021) reduces the incidence of large bubbles by two orders of magnitude.
- Variations in $f_{\text{esc}}$ or $\xi_{\text{ion}}$ shift the distribution horizontally ( $R \propto (f_{\text{esc}}\xi_{\text{ion}})^{1/3}$ ), while changes in the faint-end cutoff ( $M_{\text{lim}}$ ) have a weaker effect on the $R \ge 2.5$ cMpc tail.
- Lowering the duty cycle ( $f_{\text{duty}}$ ) suppresses the tail slightly by allowing recombination during inactive phases, but the high-R tail remains largely insensitive to $f_{\text{duty}}$ at fixed UVLF.
Global Consistency: The model reproduces a global reionization history consistent with current constraints, reaching $x_{\text{HI}} < 0.01$ by $z \simeq 5.6$ and yielding an electron scattering optical depth $\tau_e \simeq 0.056\text{--}0.059$ , consistent with Planck measurements.
Conservatism of the Model: The independent-sphere approximation is conservative. While mergers and percolation are rare at $z \gtrsim 13$ , they would increase the effective ionized path length around clustered sources at lower redshifts. The authors note that source clustering and anisotropic radiative transfer are neglected, meaning the reported incidence is a conservative baseline for connected ionized environments.

Significance and Claims
The paper concludes that the existence of Witstok-sized ionized regions at $z \approx 13$ is a plausible outcome of standard galaxy-driven models calibrated to JWST UVLFs, provided the bright end of the UVLF follows a double power-law form. The study emphasizes that while the environment (a large bubble) is statistically common in the population, the specific source (Witstok) may still represent an outlier in terms of effective ionizing efficiency or luminosity history. The work provides a population-level incidence statistic ( $\Sigma_{\ge 2.5}$ ) that can be compared against future Ly $\alpha$ detections and serves as an input for statistical 21 cm forecasts and topology studies, rather than a strict lower bound on every individual Ly $\alpha$ visibility statistic.