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Sensitivity of the redshifted 21 cm signal from the Dark Ages to parameters of primordial magnetic fields

This paper analyzes how decaying magnetic turbulence and ambipolar diffusion from primordial magnetic fields alter the thermal and ionization history of the Dark Ages Universe, demonstrating that these effects produce distinct signatures in the global redshifted 21 cm signal that can be used to constrain primordial magnetic field parameters.

Original authors: Bohdan Novosyadlyj, Yurii Kulinich, Nazar Fortuna, Anton Rudakovskyi

Published 2026-02-04

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CC BY 4.0

Original authors: Bohdan Novosyadlyj, Yurii Kulinich, Nazar Fortuna, Anton Rudakovskyi

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: Listening to the Universe's "Baby Photos"

Imagine the Universe as a giant, expanding balloon. A long time ago, when the balloon was much smaller, the Universe was a hot, glowing fog. As it expanded and cooled, the fog cleared, leaving behind a vast, dark, and silent space known as the "Dark Ages."

During this time, there were no stars or galaxies yet. The only things floating around were clouds of hydrogen gas and the leftover heat from the Big Bang (called the Cosmic Microwave Background, or CMB).

Scientists want to "listen" to this era by looking for a specific radio signal: the 21 cm line. Think of this like a specific musical note that hydrogen gas naturally hums. If the gas is cold, it absorbs this note from the background heat, creating a dip in the sound. If the gas is warm, it might even add its own volume to the note.

This paper asks a simple question: What if there were invisible magnetic fields in the early Universe that acted like a hidden heater? Would they change the "song" of the hydrogen gas enough for us to hear them?

The Hidden Heater: Primordial Magnetic Fields

The authors are investigating Primordial Magnetic Fields (PMFs). These are magnetic fields that might have been created at the very birth of the Universe, long before stars existed.

Think of these magnetic fields like invisible elastic bands stretched across the early Universe. As the Universe expands, these bands get stretched and eventually snap or decay. When they decay, they release energy, much like a stretched rubber band snapping back and warming up your fingers.

The paper looks at two ways this "magnetic snapping" heats the gas:

Turbulence: Imagine the magnetic field is like a stormy ocean. As the waves (turbulence) die down, they churn up the water and create heat.
Ambipolar Diffusion: Imagine the gas is a crowd of people (neutral atoms) and a few dancers (charged particles). The magnetic field tries to make the dancers move, but they drag the crowd with them. The friction between the dancers and the crowd creates heat.

The Experiment: Turning Up the Volume

The researchers used a computer to simulate the Dark Ages. They started with the standard model of the Universe (which has no extra magnetic heating) and then turned up the "magnetic heater" to different levels.

They tested two main "knobs" on their magnetic heater:

Strength ( $B_0$ ): How strong are the magnetic fields? (Like turning up the volume on a heater).
Texture ( $n_B$ ): How is the energy distributed? (Is the heat spread out evenly, or is it concentrated in specific spots?).

What They Found: The Signal Changes

Here is what happened when they turned on the magnetic heater:

1. The "Cold" Signal Gets Warmer
In the standard model (no extra magnetic fields), the hydrogen gas is very cold. It acts like a sponge, soaking up the background radio waves. This creates a deep "dip" or absorption line in the signal (like a deep valley in a sound wave).

When the authors added magnetic fields:

Weak Fields: The gas got slightly warmer. The "valley" in the signal became shallower (less deep).
Strong Fields: The gas got so warm that it stopped absorbing the background noise and started emitting its own signal. The "valley" turned into a "hill" (an emission line).

2. The Shape Depends on the "Texture"
The paper found that the shape of this signal change depends heavily on the "texture" of the magnetic field (the spectral index, $n_B$ ).

If the magnetic field is "smooth" (low index), the heating is gentle.
If the magnetic field is "spiky" (high index), the heating can be much more intense, especially at certain times.

3. A New Way to Measure the Universe
The authors realized that by looking at the exact shape and depth of this 21 cm signal, we can figure out how strong those ancient magnetic fields were.

If we see a deep valley, the magnetic fields were weak.
If we see a shallow valley or a hill, the magnetic fields were strong.

The Challenge: Finding a Needle in a Haystack

The paper also discusses the difficulty of actually hearing this signal.

The Problem: The 21 cm signal from the Dark Ages is incredibly faint. It's like trying to hear a whisper in a stadium full of screaming fans. The "fans" are human-made radio waves (like TV and cell phones) and the natural noise from our own Milky Way galaxy.
The Solution: To hear this whisper, we need to go to a very quiet place. The paper suggests that telescopes on the far side of the Moon would be perfect because the Moon blocks the Earth's radio noise.

The Bottom Line

This paper is a "recipe book" for what the Universe's radio signal should look like if primordial magnetic fields exist.

If we find the signal exactly as predicted by the standard model (no magnetic fields), we know the early Universe was very quiet and calm.
If we find the signal is "warmer" or shaped differently, it's proof that invisible magnetic fields were heating up the gas back then.

The authors conclude that future telescopes (like the Square Kilometre Array or lunar telescopes) are sensitive enough to detect these differences. By measuring the 21 cm signal, we can finally "see" the invisible magnetic fields that shaped our Universe's childhood.

Technical Summary: Sensitivity of the redshifted 21 cm signal from the Dark Ages to parameters of primordial magnetic fields

Problem Statement
The existence of primordial magnetic fields (PMFs) is supported by various observational constraints, yet their origin and specific parameters (amplitude $B_0$ and spectral index $n_B$ ) remain undetermined. While PMFs are known to influence the Cosmic Microwave Background (CMB) and large-scale structure, their impact on the thermal and ionization history of the Universe during the "Dark Ages" ( $30 \le z \le 300$ ) requires further investigation. Specifically, the decay of PMFs through magnetic turbulence and ambipolar diffusion heats the intergalactic medium (IGM), potentially altering the global 21 cm hydrogen line signal. Previous studies have largely focused on the Cosmic Dawn epoch or assumed nearly scale-invariant spectra ( $n_B \approx -2.9$ ). This paper addresses the gap in understanding how a broader range of PMF parameters affects the 21 cm signal in the decametre wavelength range (10–50 MHz) and whether this signal can constrain PMF properties.

Methodology
The authors model the ionization and thermal history of the baryonic gas from cosmological recombination ( $z \approx 1088$ ) to the end of the Dark Ages ( $z=10$ ) within the $\Lambda$ CDM framework, augmented by PMF heating mechanisms.

Thermal Evolution: The evolution of the baryon temperature ( $T_b$ ) and ionization fractions ( $x_{HII}$ , $x_{HeII}$ ) is calculated by integrating a system of differential equations describing energy balance and ionization-recombination kinetics. The code utilizes a three-level atomic model (RecFast) for $z > 200$ and numerical integration for $z < 200$ .
PMF Heating Mechanisms: Two heating sources are included:
1. Decaying Magnetic Turbulence: Described by a heating function $\Gamma^{(dt)}_{pmf}$ that depends on the magnetic field strength and spectral index.
2. Ambipolar Diffusion: Described by $\Gamma^{(amd)}_{pmf}$ , which is significant in partially ionized plasmas.
Magnetic Field Evolution: The authors model the PMF as an isotropic, homogeneous random process with a power spectrum $P_B(k) \propto k^{n_B}$ . They calculate the evolution of the damping scale $k_D(z)$ due to magnetic dissipation, which determines the smoothed field strength $B_\lambda(z)$ at any redshift. The energy density decay includes both adiabatic expansion losses and non-adiabatic losses due to dissipation.
21 cm Signal Calculation: The differential brightness temperature $\delta T_{br}$ is computed using the spin temperature ( $T_s$ ), which is determined by the coupling between the CMB temperature, the kinetic gas temperature, and collisional de-excitation rates. The authors analyze the signal for $B_0 \in [0.05, 0.5]$ nG and $n_B \in [-2.9, 4]$ .

Key Contributions and Results

Heating Function Characteristics:
- The heating function from decaying magnetic turbulence decreases monotonically after recombination. Its amplitude is strongly dependent on $B_0$ but only weakly dependent on $n_B$ .
- In contrast, the heating from ambipolar diffusion is strongly dependent on $n_B$ (increasing significantly as $n_B$ rises) but is subdominant to turbulence heating for $B_0 \lesssim 0.5$ nG during the Dark Ages ( $z > 100$ ).
- The damping scale evolution factor $f_D(z)$ shows that PMF energy density decays faster than adiabatic expansion, with the rate depending on $n_B$ .
Thermal and Ionization History:
- PMFs with $B_0 \ge 0.05$ nG noticeably increase the baryon temperature $T_b$ compared to the standard $\Lambda$ CDM model for $z < 300$ .
- For $B_0 \gtrsim 0.35-0.40$ nG (with $n_B = -2.9$ ), the gas temperature exceeds the CMB temperature throughout the Dark Ages.
- The ionization fraction $x_{HII}$ remains low ( $<1\%$ ) and is only slightly elevated compared to the standard model, as the heating is insufficient to cause significant re-ionization in this epoch.
Sensitivity of the 21 cm Global Signal:
- Amplitude Dependence: The global 21 cm signal is highly sensitive to $B_0$ . In the standard model, the signal is an absorption line with $\delta T_{br} \approx -41$ mK at $\sim 16$ MHz. As $B_0$ increases, the absorption depth decreases, vanishes, and transitions into an emission line at $B_0 \approx 0.3$ nG.
- Spectral Index Dependence: The signal profile is also sensitive to $n_B$ . For a fixed $B_0 = 0.1$ nG, increasing $n_B$ from -2.9 to 4.0 makes the absorption line shallower (from -35 mK to -32 mK). For $B_0 = 0.5$ nG, increasing $n_B$ increases the emission line amplitude (from $\sim 20$ mK to $\sim 30$ mK).
- Degeneracy and Diagnostics: The authors propose using the ratios of the signal at different frequencies ( $R_{20/30}$ and $R_{40/30}$ ) to distinguish PMF models from the standard $\Lambda$ CDM. The distribution of PMF models in this ratio space deviates from the standard model, though the spread is wider than in other non-standard models.

Significance and Claims
The paper claims that the redshifted 21 cm signal from the Dark Ages is a viable probe for constraining PMF parameters.

Detection Potential: The authors note that ground-based telescopes like UTR-2 and GURT have sufficient sensitivity to detect these signals with integration times of $\sim 60$ days. Future lunar far-side missions (e.g., FARSIDE) could place upper limits on $B_0$ (e.g., $< 0.1$ nG) or detect emission signatures for stronger fields ( $B_0 = 0.5$ nG) with integration times of 3,600 to 10,000 hours.
Degeneracy Warning: The authors highlight a significant degeneracy between the 21 cm profiles generated by PMFs and those generated by decaying or self-annihilating dark matter. They assert that the 21 cm line alone cannot uniquely identify PMFs; it must be used in conjunction with other signals, such as ro-vibrational lines of the first molecules, CMB anisotropies, or Faraday rotation measurements, to break this degeneracy.
Model Constraints: The study establishes that for nearly scale-invariant spectra ( $n_B \approx -2.9$ ), the 21 cm signal is sensitive to fields as weak as $B_0 \approx 0.05$ nG, providing a potential lower bound for future observational constraints.