⚛️ phenomenology

The phenomenology of Axion Relic Pockets

This paper investigates the phenomenology of axion relic pockets as dark matter by deriving axion-to-photon conversion rates in their compact, spherical geometry, demonstrating that interactions with atomic electric fields produce isotropic high-energy electromagnetic cascades, and using IceCube data to establish the first terrestrial constraints on this model while outlining future detection prospects.

Original authors: Wafaa Khater, M. C. David Marsh, Charalampos Nikolis

Published 2026-09-22

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Wafaa Khater, M. C. David Marsh, Charalampos Nikolis

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 universe is filled with invisible matter that holds galaxies together, yet we have never directly seen a single particle of it. For decades, physicists have proposed that this "dark matter" might be made of axions, hypothetical particles that are incredibly light and interact very weakly with ordinary matter. While these particles are a leading candidate for the missing mass of the cosmos, they have remained elusive in experiments designed to catch them. A different possibility has recently emerged: perhaps dark matter is not a sea of individual particles, but rather a collection of tiny, dense pockets of trapped energy. These "axion relic pockets" would be remnants of a phase transition in the early universe, where regions of false vacuum were stabilized by a hot gas of axions. If such pockets exist and drift through our solar system, they would carry immense energy, but detecting them would require a new kind of search, one that looks for the specific way these pockets interact with the electric fields of atoms.

A team of researchers has now taken the first major step toward finding these objects by calculating exactly how they would behave if they passed through the Earth. In their study, they focused on the interaction between the trapped axions inside a pocket and the electric fields surrounding atoms. When an axion relic pocket moves through a material like ice or air, the axions inside it can convert into photons, which are particles of light. Because the pocket is a confined sphere rather than a stream of free particles, the researchers had to develop new mathematical tools to describe this conversion. They found that as a pocket travels through the electric field of an atom, it emits a burst of high-energy photons. These photons do not travel in a single beam; instead, they scatter in all directions, creating a spherical spray of radiation.

The researchers applied their new calculations to real-world detectors to see if such a signal could be spotted. They discovered that if these pockets exist, they would create a very specific type of event: a shower of high-energy particles moving upward through the Earth. This upward direction is crucial because most natural high-energy particles, such as cosmic rays, come from space and travel downward. The only way for a shower to move upward is if it was triggered by something passing through the Earth from the other side. The team calculated that a pocket passing through the massive IceCube neutrino telescope in Antarctica would generate such an upward-moving shower of particles. By analyzing data from IceCube, they were able to place the first experimental limits on the existence of these pockets. Their results show that while the theory is still viable, the pockets cannot be too large or too heavy, or we would have already seen them.

The study also looked at other ways to find these pockets, including using balloon-borne instruments floating high in the atmosphere and large ground-based observatories that watch for flashes of light from particle showers. The researchers found that these atmospheric detectors are sensitive to the smallest, most energetic pockets, but the signals from such tiny objects are extremely faint and rare. Similarly, they examined underground experiments designed to detect dark matter directly, but concluded that these facilities are likely too small to catch the signal compared to the vast volume of the IceCube detector. The work provides a clear roadmap for future searches, showing that the most promising way to find these exotic pockets is to look for the unique signature of upward-moving particle showers in large detectors. While the current data has not yet confirmed their existence, the study proves that we now have the tools to hunt for them, turning a theoretical idea into a testable reality.

Technical Summary: The Phenomenology of Axion Relic Pockets

Problem Statement
Axion Relic Pockets (ARPs) are a proposed dark matter candidate consisting of spherical regions of false vacuum stabilized by a hot gas of trapped axions. While the formation mechanism of ARPs via first-order phase transitions involving a dilaton field has been established, their observational phenomenology remains largely unexplored. A critical gap exists in understanding how these confined axions interact with Standard Model fields, specifically electromagnetism. Standard axion-photon conversion calculations assume asymptotically free axions described by plane-wave solutions. However, axions trapped within ARPs are subject to reflective boundary conditions on the dilaton wall, rendering standard S-matrix and plane-wave approximations inapplicable. Consequently, there is no established framework for calculating the conversion rate of trapped axions into photons, nor for predicting the resulting experimental signatures in terrestrial or astrophysical detectors.

Methodology
The authors develop a theoretical framework to calculate the axion-photon conversion rate for axions confined within a spherical pocket of radius $R_{pocket}$ .

Modified Electrodynamics and Boundary Conditions: The authors solve the modified Maxwell equations coupled to the axion field, treating the axion field as a superposition of modes satisfying Dirichlet boundary conditions at the pocket wall ( $a(R_{pocket}) = 0$ ). The axion field is expanded in terms of spherical Bessel functions and spherical harmonics.
Classical and Quantum Derivations:
- Classical Approach: By linearizing the modified Maxwell equations around a background electric field, the authors derive the Poynting vector to calculate the emitted power. This involves computing an overlap integral over the pocket volume between the axion mode functions and the background field.
- Quantum Approach: Using Fermi's Golden Rule, the authors calculate the transition matrix element for single axion-to-photon conversion. They confirm that the quantum result matches the classical power emission rate in the appropriate limit.
Atomic Field Reconstruction: To apply these results to terrestrial detectors, the authors reconstruct the electric fields inside atoms (specifically Oxygen and Nitrogen) using relativistic Hartree-Fock atomic form factors. They treat the ARP as a subatomic object traversing these fields, approximating the field as homogeneous over the pocket volume during the interaction.
Event Rate Calculations: The derived conversion rates are integrated over the trajectories of ARPs passing through detector volumes. The authors calculate expected event rates for:
- IceCube: A neutrino telescope in Antarctic ice, sensitive to electromagnetic cascades from axion-photon conversion in oxygen atoms.
- Atmospheric Detectors: Balloon-borne payloads (modeled on ANITA) and ground-based fluorescence detectors (Pierre Auger Observatory), sensitive to upward-going electromagnetic showers in the atmosphere.
- Direct Detection: Liquid noble-gas detectors (modeled on XENONnT/LZ and future XLZD), though the authors note these are less sensitive due to smaller target masses.

Key Contributions

Analytical Conversion Rates: The paper derives the first analytical formulas for axion-photon conversion rates in spherical pockets with reflective boundary conditions. The primary results are the emitted power equation (Eq. 3.36) and the high-energy limit conversion rate (Eq. 3.48), which scales as $\Gamma \propto g_{a\gamma\gamma}^2 E_0^2 R_{pocket}$ .
Smoking-Gun Signal Identification: The authors identify "upward-going" electromagnetic cascades as a distinctive signature. Since ARPs move non-relativistically and the trapped axions are ultra-relativistic, the emitted photons are isotropic in the ARP rest frame. In the lab frame, this results in a significant fraction of upward-going high-energy showers, a feature strongly suppressed for Standard Model backgrounds (e.g., atmospheric neutrinos) at high energies due to Earth's absorption.
First Experimental Constraints: Using 11.4 years of IceCube "Medium Energy Starting Events" (MESE) data, the authors derive the first experimental limits on the ARP parameter space (specifically the axion-photon coupling $g_{a\gamma\gamma}$ versus pocket radius/mass).

Results

IceCube Constraints: The analysis places constraints on ARPs formed at transition temperatures $0.5 \cdot 10^4 \text{ TeV} \lesssim T_t \lesssim 8 \cdot 10^7 \text{ TeV}$ . These correspond to pockets with masses $M \sim \mathcal{O}(\text{kg})$ and radii $R \sim \text{atomic scale}$ . The authors find that for the simplest realization of the model (where axions do not co-thermalize with the Standard Model), only a small fraction of the parameter space yields signals strong enough to be constrained by current IceCube data.
Atmospheric Detectors: The event rates for balloon-borne (ANITA) and ground-based (Pierre Auger) detectors are calculated. The authors conclude that these observatories are primarily sensitive to the smallest, highest-energy pockets. However, for the models considered, the event rates are highly suppressed, and the authors state that ARPs cannot explain the previously reported "anomalous" upward-going events observed by ANITA.
Direct Detection: The event rates for liquid noble-gas detectors are found to be suppressed compared to IceCube due to the significantly smaller number of target atoms (by $\sim 8$ orders of magnitude). Furthermore, the signal morphology (a single high-energy photon triggering a cascade) differs from the electron/nuclear recoil signals these experiments are optimized for, making detection unlikely without specific trigger modifications.

Significance and Claims
The paper claims to provide the "necessary tools to initiate phenomenological studies of axion relic pockets across different environments." Its significance lies in:

Bridging Theory and Observation: It moves the ARP model from a purely theoretical cosmological construct to a testable phenomenological framework by deriving specific, calculable interaction rates.
Distinctive Signatures: It highlights that the isotropic nature of the emission and the resulting upward-going cascades offer a unique "smoking gun" that distinguishes ARPs from other dark matter candidates and standard backgrounds.
Modest Constraints: The authors are modest in their claims, noting that current data only constrains a "small part of the parameter space." They emphasize that existing axion constraints do not directly apply to ARPs, as ARP signals arise from light, relativistic false-vacuum axions rather than the true-vacuum axions probed by other experiments.
Future Directions: The work sets the stage for future investigations into more complex scenarios, such as strongly coupled axions that co-thermalize with the Standard Model, and the application of these methods to astrophysical environments with strong magnetic fields.

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