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Ringing of the Reionization: A first direct measurement of the intergalactic pressure smoothing scale at redshift z>4.2 as imprinted onto small-scale peculiar velocities in the Lyman-alpha forest

This study presents the first direct measurements of the intergalactic pressure smoothing scale at redshifts $z>4.2$ by identifying an acoustic feature in the Lyman- $\alpha$ forest's flux power spectrum that is imprinted by the thermal history of the epoch of reionization.

Original authors: Vid Iršič, Matteo Viel, Martin G. Haehnelt, James S. Bolton, Ewald Puchwein, Luke I. Gilmartin

Published 2026-07-23

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CC BY 4.0

Original authors: Vid Iršič, Matteo Viel, Martin G. Haehnelt, James S. Bolton, Ewald Puchwein, Luke I. Gilmartin

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

Imagine the Universe as a giant, invisible ocean made of gas, stretching between the stars and galaxies. For a long time, scientists thought this gas was mostly quiet and still, slowly cooling down as the Universe expanded. But about 13 billion years ago, something dramatic happened: the first stars and galaxies turned on like a cosmic floodlight. This event, called "reionization," blasted the cold gas with intense energy. Think of it like throwing a giant rock into a calm pond; the water doesn't just ripple; it gets heated up, pressurized, and starts to expand outward in a rush.

This paper is about listening to the "ringing" of that cosmic splash. When the gas gets heated and pushed, it doesn't just move randomly; it creates a specific kind of wave pattern, a pressure wave that smooths out the gas over a certain distance. Scientists have known for a while that this "pressure smoothing" exists, but they've mostly been guessing its size by looking at the shadows the gas casts on light from distant quasars. It's like trying to figure out the size of a stone by looking at the ripples it made in a pond hours later, without ever seeing the stone itself. This study tries to do something new: it looks directly at the "wind" of the gas itself—the tiny, invisible movements of the gas particles—to hear the echo of that ancient explosion and measure the size of the ripple it left behind.

The authors of this paper, led by Vid Iršic and Matteo Viel, have taken a fresh approach to this cosmic mystery. Instead of just looking at the gas density, they focused on the "peculiar velocities"—the specific, local speeds at which the gas is moving toward or away from us. They discovered a distinct "ringing" feature in the power spectrum of these velocities, a specific scale where the gas seems to be expanding in a coordinated way. To understand what this means, they built a simple "toy model" of the Universe. Imagine the gas as a collection of invisible, expanding balloons. As these balloons puff up, they push the gas around them, creating a specific pattern of movement. The authors found that this simple model of expanding spheres perfectly mimics the complex, messy data from their supercomputer simulations.

The key finding is that this "ringing" feature is a direct fingerprint of the pressure smoothing scale. In the simulations, the size of this feature changes depending on how much heat was injected into the gas during reionization. The authors then applied this method to real observations of the Lyman-alpha forest (the absorption lines in light from distant quasars) at very high redshifts, specifically between $z = 4.2$ and $z = 5.0$ . By comparing the real data to their simulations, they were able to provide the first direct measurements of this pressure smoothing scale at these early times. They found that at $z = 4.2$ , the scale is greater than $33.78$ comoving kiloparsecs (ckpc). At $z = 4.6$ , it is $32.36 \pm 8.35$ ckpc, and at $z = 5.0$ , it is $31.27 \pm 18.28$ ckpc.

It is important to note that these results are based on a "proof-of-concept" study. The authors used high-resolution hydrodynamical simulations to show that the method works and that the signal they see is likely real. They argue that the feature they found is strongly associated with the pressure smoothing scale caused by the hydrodynamic response of the gas to reionization. While the simulations show a clear link between the acoustic feature in the velocity field and the pressure smoothing, the paper acknowledges that this is a first step. The measurements on real data come with significant uncertainties (especially at $z=5.0$ ), and the authors suggest that future programs will need to refine these techniques to fully recover the thermal history of the Universe. However, the core idea—that we can hear the "ringing" of reionization in the small-scale movements of the gas—seems to hold up in their models, offering a new and exciting way to listen to the early Universe.

Technical Summary: Ringing of the Reionization

Problem Statement
The epoch of reionization imprints distinct signatures on the thermal history of the intergalactic medium (IGM). As ionization fronts swept across the cosmic web, they overpressurized cold gas, triggering a hydrodynamic response that smoothed gas density structures below a characteristic "pressure smoothing scale." While this effect has been indirectly inferred over the past decade through the power spectra of the Lyman- $\alpha$ forest, direct measurements of the typical scale associated with this physical process have been scarce. Existing methods typically rely on comparing observations to high-resolution hydrodynamical simulations to map flux power spectra onto parameter spaces, or utilize the phase power spectrum of close quasar pairs (effective at $2.0 \leq z \leq 3.6$ ). This work addresses the challenge of directly measuring the pressure smoothing scale at higher redshifts ( $z > 4.2$ ) by identifying a specific acoustic feature imprinted on small-scale peculiar velocities.

Methodology
The study utilizes a suite of high-resolution cosmological hydrodynamical simulations from the Sherwood-Relics project (Bolton et al. 2017; Puchwein et al. 2023). These simulations employ a flat $\Lambda$ CDM cosmology with varying thermal histories characterized by the cumulative injected heat parameter ( $u_0$ ), the IGM temperature at mean density ( $T_0$ ), and the redshift of the end of reionization ( $z_{\text{rei}}$ ).

The core methodology focuses on the small-scale clustering of the peculiar velocity gradient projected along the line of sight, denoted as $\eta$ :
$\eta = -\frac{(\mathbf{n} \cdot \nabla)(\mathbf{n} \cdot \mathbf{v})}{aH}$
where $\mathbf{n}$ is the line-of-sight unit vector, $\mathbf{v}$ is the gas velocity, and $H$ and $a$ are the Hubble rate and scale factor.

To interpret the simulation results, the authors employ two theoretical frameworks:

Toy Model (Expanding Spheres): A simplified model where a population of expanding spheres, representing the hydrodynamic response of gas to heat injection, is injected into a smoothed baseline velocity field. This model tests how parameters such as sphere number density ( $\bar{n}$ ), expansion velocity ( $v$ ), and size ( $R$ ) affect the power spectrum.
Linear Theory: The simulation results are compared to linear theory predictions (Gnedin & Hui 1998) which define a characteristic filtering cut-off ( $k_F$ ) in baryon density due to integrated pressure effects. This framework predicts damped acoustic oscillations in the peculiar velocity field driven by time-dependent sound speeds during reionization.

The study analyzes the 1D power spectrum of $\eta$ ( $P_{\eta\eta}$ ) and the flux power spectrum ( $P_{FF}$ ) across redshifts $z = 2.0$ to $5.6$. A methodology developed for simulations is then applied to the latest observational measurements of flux power spectra at $z = 4.2 - 5.0$ .

Key Contributions and Results

Identification of an Acoustic Feature: The authors identify a distinct peak in the power spectrum of the projected peculiar velocity gradient $\eta$ at scales $k \approx 0.1 - 1.0 \, \text{km}^{-1} \text{s}$ . This feature is shown to be strongly associated with the pressure smoothing scale.
Link to Thermal History: The position and amplitude of this peak in $P_{\eta\eta}$ are sensitive to the thermal history of the IGM. Specifically, models with lower cumulative injected heat ( $u_0$ ) exhibit the peak at smaller scales (higher $k$ ).
Validation via Toy Model and Linear Theory:
- The toy model of expanding spheres successfully reproduces the peak feature in the velocity power spectrum, confirming that the signal arises from expansion velocities of $\sim 10 \, \text{km/s}$ on scales of $\sim 40 \, \text{ckpc}/h$ .
- Linear theory calculations, incorporating time-dependent sound speeds from reionization, predict damped acoustic oscillations whose first peak coincides with the small-scale feature observed in simulations. This supports the interpretation that the feature is a "ringing" effect of the reionization process.
Redshift Evolution: The position of the peak systematically shifts to larger scales (lower $k$ ) as redshift decreases, tracking the growth of the underlying expanding structures. This dependence on astrophysics (reionization history) is prominent at high redshifts but is erased at lower redshifts ( $z < 3$ ) once reionization is complete.
Direct Measurements: Applying the simulation-derived methodology to observational data at $z = 4.2, 4.6,$ $z = 4.2, 4.6,$ and $5.0$, the authors provide the first direct measurements of the pressure smoothing scale ( $\lambda_p$ $λ_{p}$ ) at these high redshifts:
- $\lambda_p(z = 4.2) > 33.78 \, \text{ckpc}$ ( $1\sigma$ )
- $\lambda_p(z = 4.6) = 32.36 \pm 8.35 \, \text{ckpc}$
- $\lambda_p(z = 5.0) = 31.27 \pm 18.28 \, \text{ckpc}$

Significance and Claims
The paper presents this work as a "proof-of-concept" study. It claims to demonstrate a viable pathway for directly measuring the pressure smoothing scale at high redshifts ( $z > 4.2$ ) by analyzing small-scale peculiar velocities imprinted on the Lyman- $\alpha$ forest. The authors assert that this method provides an integral constraint over periods of reionization that are otherwise unobservable with traditional IGM methods.

The significance of the study lies in its potential to recover the thermal history of the Universe using small-scale observations. The authors note that understanding the hydrodynamic response and pressure smoothing is critical for next-generation searches for the nature of dark matter, as these astrophysical effects are tightly linked to the small-scale structure of the Lyman- $\alpha$ flux power spectrum. The study concludes that this approach paves the way for future observational programs aimed at constraining the thermal history of the IGM during the epoch of reionization.

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