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The $\tau$ of Neutral Hydrogen: Increased CMB Optical Depth at Long Wavelengths

This paper proposes that the absorption of long-wavelength CMB photons by neutral hydrogen during the cosmic "dark ages" creates a measurable, frequency-dependent optical depth that, when cross-correlated with millimeter-wave maps, offers a novel method to directly probe the evolution of the neutral fraction and spin temperature of cosmic gas.

Original authors: Gilbert Holder, Adrian Liu, Tzu-Ching Chang, David Zegeye

Published 2026-05-25

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CC BY 4.0

Original authors: Gilbert Holder, Adrian Liu, Tzu-Ching Chang, David Zegeye

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 Idea: A "Fog" on the Cosmic Microwave Background

Imagine the Cosmic Microwave Background (CMB) as a giant, ancient photograph of the universe taken just after the Big Bang. For decades, astronomers have studied this photo using "cameras" that see in millimeter waves (like a very high-resolution digital camera). They know exactly what this photo should look like.

This paper suggests that if we look at this same ancient photo using radio waves (which have much longer wavelengths, like the radio waves that carry music to your car), the photo will look slightly different. It won't be as sharp or bright.

Why? Because between the time the photo was taken and now, the light had to pass through a vast, invisible "fog" made of neutral hydrogen gas.

The Analogy: The "Absorption Filter"

Think of the CMB light as a beam of white light shining through a room.

Standard View (Millimeter waves): In the room, the air is clear. The light passes through perfectly, and you see the original image clearly.
Radio View (Long wavelengths): Now, imagine the room is filled with a very specific type of mist. This mist doesn't block all the light, but it acts like a filter that catches a tiny bit of the light at specific colors (frequencies).

The paper argues that this "mist" is neutral hydrogen gas from the early universe. As the light travels through it, some photons (particles of light) get absorbed. This makes the radio version of the CMB look about 3% to 4% dimmer than the millimeter version.

The "Spin Temperature" Mystery

The amount of light this "fog" absorbs depends on how cold the gas is. The authors call this the spin temperature.

The Cold Gas: In the early universe (before stars formed), the gas was very cold. Cold gas is like a hungry sponge; it soaks up a lot of light. This creates a strong "dimming" effect.
The Warming Gas: Later, as the first stars ignited, they heated the gas up. Warm gas is less "hungry" and absorbs less light.

By measuring exactly how much the CMB is dimmed at different radio frequencies, we can figure out how cold or warm the gas was at different times in history. It's like looking at the dimming of a lightbulb through a window to guess the temperature of the glass.

The Challenge: The "Static" Problem

You might ask, "Why haven't we seen this yet?"

Imagine trying to hear a whisper (the CMB) in a room where a rock concert is playing (the radio sky).

At the radio frequencies needed to see this effect, the sky is incredibly bright with "static" from our own galaxy and other sources. This static is thousands of times louder than the CMB whisper.
Usually, this would make the CMB impossible to detect.

The Solution: The "Template" Trick

Here is the clever part of the paper. The authors propose a way to hear the whisper even with the rock concert playing.

The Template: We already have a perfect, high-quality map of the CMB from the millimeter-wave cameras (the "clear room" photo). We know exactly where the bright spots and dark spots are.
The Cross-Check: Instead of trying to find the CMB in the noisy radio data on its own, we take our perfect "template" and slide it over the noisy radio map. We ask: "Does the pattern of the radio noise match the pattern of our template, just slightly dimmer?"

Because we know the pattern so well, we can ignore the random "rock concert" noise and focus only on the parts that match our template. This allows us to detect the tiny 3-4% dimming effect even if the radio map is very noisy.

The "Dark Ages" Discovery

The paper calculates that this method might actually be easier than trying to detect the hydrogen gas directly (which is the goal of many other experiments).

Direct Detection: Trying to see the hydrogen gas itself is like trying to see a ghost in a dark room. The signal is weak and buried in noise.
CMB Cross-Correlation: Using the CMB template is like shining a flashlight on the ghost. The paper suggests that for the era known as the "Dark Ages" (before the first stars), we could detect the CMB's dimming effect before we are good enough to see the hydrogen gas itself.

What This Means for Science

If we can measure this dimming effect, we get a new, direct way to measure the combination of how much hydrogen was neutral and how cold it was at different points in time.

Currently, scientists have to guess these numbers based on complex theories. This paper offers a way to measure them directly, like taking a direct reading on a thermometer rather than guessing the temperature by looking at the weather.

Summary

The Problem: The early universe's hydrogen gas absorbs a tiny bit of the ancient CMB light at long radio wavelengths, making it look slightly dimmer.
The Obstacle: The radio sky is incredibly noisy, making the CMB hard to see.
The Fix: Use our perfect knowledge of the CMB from other wavelengths as a "template" to find the pattern in the noisy radio data.
The Result: This might allow us to measure the temperature and state of the early universe's gas even before we can see the gas itself directly.

Technical Summary: The $\tau$ of Neutral Hydrogen: Increased CMB Optical Depth at Long Wavelengths

Problem Statement
The Cosmic Microwave Background (CMB) is typically observed at millimeter wavelengths, where its fluctuations provide a wealth of cosmological information. However, at longer radio wavelengths (specifically below the 21 cm rest frequency of 1420 MHz), CMB photons traversing the universe encounter a non-zero probability of absorption by neutral hydrogen (HI) in the intergalactic medium. This resonant absorption introduces an additional optical depth, $\tau_{HI}$ , distinct from the frequency-independent Thomson scattering optical depth ( $\tau_e$ ) caused by free electrons.

This absorption suppresses the observed CMB angular power spectrum at radio wavelengths relative to the spectrum measured at millimeter wavelengths. The magnitude of this suppression depends on the neutral fraction of hydrogen ( $x_{HI}$ ) and the 21 cm spin temperature ( $T_s$ ) of the gas as a function of cosmic time (redshift). While the "dark ages" and "cosmic dawn" are primary targets for 21 cm cosmology experiments aiming to detect intrinsic HI fluctuations, this paper investigates the feasibility of detecting the suppression of the primary CMB signal itself as a probe of the $x_{HI}/T_s$ combination.

Methodology
The authors calculate the expected frequency-dependent optical depth $\tau_{HI}(\nu)$ using standard cosmological parameters (Planck 2020) and models for the evolution of the spin temperature $T_s$ . The calculation assumes a uniform background of gas at the cosmological mean density, ignoring small-scale density and velocity perturbations to focus on the global absorption effect.

The core methodology involves:

Analytical Modeling: Deriving the relationship between observed frequency, redshift, and optical depth using the standard 21 cm absorption formalism (Furlanetto et al. 2006).
Cross-Correlation Analysis: Proposing that the CMB fluctuations at radio wavelengths be cross-correlated with high-precision mm-wave CMB maps (e.g., from Planck). Since the mm-wave CMB template is known with high signal-to-noise, the radio map can be treated as a noisy realization of this template attenuated by $e^{-\tau_{HI}}$ .
Signal-to-Noise Estimation: Comparing the detectability of the radio CMB via cross-correlation against the detectability of intrinsic 21 cm fluctuations via auto-correlation. The authors utilize standard estimators for signal-to-noise ( $S/N$ ) in both auto- and cross-power spectra, accounting for white noise and foreground limitations.
Instrumental Sensitivity Forecasting: Developing a sensitivity estimator for a hypothetical interferometric array (30 $\times$ 30 array of 6 m dishes) to determine the required integration time and array configuration to measure the template amplitude $\alpha$ (where $\alpha \approx e^{-\tau_{HI}}$ ).

Key Results

Magnitude of Effect: The excess optical depth $\tau_{HI}$ peaks at the level of a few percent around 100 MHz (corresponding to the "cosmic dawn" era, $z \sim 10-20$ ) and reaches slightly higher levels during the "dark ages" ( $z \sim 40-150$ ). This results in a suppression of the radio CMB power spectrum by approximately 3.5% to 4% relative to the mm-wave spectrum.
Detectability via Cross-Correlation: The paper demonstrates that detecting the radio CMB fluctuations via cross-correlation with mm-wave templates is significantly easier than detecting the intrinsic 21 cm fluctuations.
- At $z \sim 50$ (dark ages, $\nu \sim 28$ MHz), achieving a $25\sigma$ detection of the CMB cross-correlation requires a 21 cm auto-correlation detection significance of only $\sim 12\sigma$ .
- At $z \sim 15$ (cosmic dawn, $\nu \sim 89$ MHz), the 21 cm auto-correlation signal is much stronger than the CMB, making the CMB cross-correlation a more accessible intermediate target.
Instrumental Requirements: Sensitivity calculations suggest that a compact interferometric array (e.g., 30 $\times$ 30 dishes) observing for $\sim 4000$ hours could achieve a total significance of $\gtrsim 100\sigma$ for the template amplitude measurement, sufficient to detect percent-level effects. The sensitivity scales favorably with the number of dishes and baseline length, favoring compact arrays to probe the large angular scales where CMB fluctuations are strongest.
Foreground Challenges: The primary obstacle remains foreground removal. The radio sky is dominated by bright synchrotron emission (order of 1000 K). While the foregrounds are spectrally smooth, the signal of interest ( $\tau_{HI}$ ) is also a relatively smooth function of frequency. Aggressive foreground filtering risks removing the signal. The authors note that new methods not relying solely on spectral smoothness (e.g., component separation, Bayesian forward modeling) are necessary.

Significance and Claims
The paper claims that measuring the amplitude of CMB fluctuations as a function of radio wavelength provides a novel, direct path to measuring the combination $x_{HI}/T_s$ as a function of redshift. This approach offers several distinct advantages over traditional 21 cm intensity mapping:

Template Advantage: The use of a well-characterized mm-wave CMB template allows for a weighted average of the entire radio map, effectively squeezing map information into a single amplitude measurement. This mitigates the impact of per-pixel noise that plagues auto-correlation studies.
Alternative to Global Signal: Unlike global 21 cm experiments that measure the monopole (mean brightness temperature) and struggle with foreground subtraction and systematics, this mapping experiment utilizes spatial fluctuations and cross-correlation, offering more varied opportunities for null tests and jackknife analyses.
Feasibility: The authors argue that it may be easier to detect the CMB in cross-correlation than the intrinsic 21 cm fluctuations themselves, particularly for "dark ages" experiments. Consequently, the measurement of $\tau_{HI}$ could serve as a useful intermediate science goal for low-frequency radio arrays, potentially providing constraints on the physics of the "dark ages" and "cosmic dawn" (including the EDGES anomaly) before the intrinsic 21 cm signal is fully resolved.

The paper concludes that while foreground separation remains a significant challenge requiring advanced mitigation strategies, the cross-correlation technique presents a viable and potentially more robust pathway to probing the thermal and ionization history of the early universe via the CMB's interaction with neutral hydrogen.