Lost Light, Hidden Fields: How Magnetic Chaos Could Unlock Gamma-Ray Mysteries

Author: Denis Avetisyan

A new analysis reveals that complex intergalactic magnetic fields may dramatically increase the survival of high-energy photons, potentially explaining observed gamma-ray fluxes and opening a window into elusive axion-like particles.

The study demonstrates that highly energetic photons observed by LHAASO can be explained through the mixing of axion-like particles and photons within strong, non-Gaussian magnetic fields, with survival probability <span class="katex-eq" data-katex-display="false">\mathcal{P}\_{\gamma\rightarrow\gamma}</span> dependent on parameters κ and <span class="katex-eq" data-katex-display="false">\lambda\_{\rho}</span> but independent of axion-like particle mass, suggesting a mechanism where even established theoretical frameworks are vulnerable beyond certain thresholds. — The study demonstrates that highly energetic photons observed by LHAASO can be explained through the mixing of axion-like particles and photons within strong, non-Gaussian magnetic fields, with survival probability $\mathcal{P}\_{\gamma\rightarrow\gamma}$ dependent on parameters κ and $\lambda\_{\rho}$ but independent of axion-like particle mass, suggesting a mechanism where even established theoretical frameworks are vulnerable beyond certain thresholds.

This review details how non-Gaussian stochastic magnetic fields in the intergalactic medium influence axion-photon mixing and affect the attenuation of very-high-energy gamma rays.

The standard treatment of very-high-energy (VHE) gamma-ray propagation through intergalactic space often relies on simplified models of magnetic field coherence. This work, ‘The Axion-Photon Mixing and the Extragalactic Magnetic Background: Plateau Regimes, Resonances, and Non-Gaussian Boosts’, presents a detailed analytical investigation of axion-like particle (ALP)-photon mixing, revealing that non-Gaussian magnetic field structures can significantly enhance photon survival probabilities-potentially explaining unexpectedly high fluxes observed by experiments like LHAASO. Specifically, we demonstrate that stochastic magnetic fields exhibit distinct resonant features and non-exponential attenuation, with non-Gaussianity boosting survival by several orders of magnitude compared to Gaussian models. As next-generation observatories approach PeV sensitivities, can detailed analyses of VHE gamma-ray spectra unlock a comprehensive understanding of the power spectrum and non-Gaussianity of intergalactic magnetic fields?

The Universe’s Veil: A Transparency Crisis

Recent observations of gamma-ray burst GRB221009A, captured by the Large High Altitude Air Shower Observatory (LHAASO), have presented a significant challenge to current understandings of high-energy photon propagation. LHAASO detected photons with energies exceeding 10 TeV, far surpassing expectations based on established models. These models predict substantial attenuation of such high-energy photons during their journey across vast cosmic distances due to interactions with the extragalactic background light. The unexpectedly high flux of these photons suggests either a fundamental flaw in the current theoretical framework governing gamma-ray burst propagation, or a previously underestimated mechanism allowing these photons to traverse intergalactic space with minimal interaction. This discovery necessitates a re-evaluation of assumptions regarding the density of the extragalactic background light and potentially points towards the involvement of novel physical processes at play during these energetic events.

The unexpectedly clear passage of extremely high-energy photons across vast cosmic distances, as observed in events like GRB221009A, presents a significant challenge to established astrophysical models. Current understanding dictates that these photons should interact with the extragalactic background light – the cumulative glow of all galaxies – losing energy through pair production and becoming significantly attenuated over such distances. The fact that a substantial flux of these photons reaches Earth suggests one of two possibilities: either the universe’s background light is less dense than previously estimated, requiring a re-evaluation of galaxy formation and evolution models, or fundamental aspects of photon propagation – potentially involving previously unknown physical processes or the influence of complex intergalactic magnetic fields – are not fully understood and demand a revision of existing theoretical frameworks. This discrepancy isn’t merely a refinement of existing data; it hints at a potential gap in the standard model of cosmology and particle physics.

The journey of high-energy photons across vast cosmic distances isn’t unimpeded; these particles interact with the extragalactic background light (EBL), a faint afterglow of all the stars and galaxies that have ever formed. This interaction isn’t a simple scattering, but a process called pair production, where a high-energy photon collides with a low-energy photon from the EBL, converting both into an electron and a positron. This effectively diminishes the intensity of the original, high-energy photon – a phenomenon known as attenuation. The higher the energy of the photon and the longer the distance it travels, the more significant this attenuation becomes, creating an expected dimming of very high-energy emissions. Consequently, the unexpectedly bright detection of extremely energetic photons from events like GRB221009A challenges current understanding, as these photons should have been substantially absorbed by the EBL if standard models are accurate.

The unexpectedly high flux of very-high-energy photons reaching Earth from GRB221009A presents a significant challenge to current understandings of cosmic propagation. Existing models predict substantial attenuation of these photons due to interaction with the extragalactic background light (EBL) – the cumulative glow of all galaxies – via a process called pair production. However, the observed signal suggests the EBL may be considerably less dense than previously estimated, potentially requiring a reassessment of galaxy formation and evolution models. Alternatively, the photons may be propagating more freely than anticipated due to previously unconsidered effects, such as complex, non-Gaussian distributions of magnetic fields within the intergalactic medium; these structures could deflect and guide high-energy particles, reducing the likelihood of interaction with the EBL and allowing a greater proportion to reach detectors. Further investigation into both the EBL’s density and the topology of intergalactic magnetic fields is now crucial to resolve this cosmic transparency puzzle.

Axion-to-photon (<span class="katex-eq" data-katex-display="false">\mathcal{P}_{a\rightarrow\gamma}</span>) and photon survival (<span class="katex-eq" data-katex-display="false">\mathcal{P}_{\gamma\rightarrow\gamma}</span>) probabilities, normalized to <span class="katex-eq" data-katex-display="false">\lambda_{\gamma}</span>, exhibit power-law scaling with the magnetic field (<span class="katex-eq" data-katex-display="false">\sim B^2</span> and <span class="katex-eq" data-katex-display="false">\sim B^4</span>, respectively) at intermediate distances before decaying exponentially due to extragalactic background light absorption. — Axion-to-photon ( $\mathcal{P}_{a\rightarrow\gamma}$ ) and photon survival ( $\mathcal{P}_{\gamma\rightarrow\gamma}$ ) probabilities, normalized to $\lambda_{\gamma}$ , exhibit power-law scaling with the magnetic field ( $\sim B^2$ and $\sim B^4$ , respectively) at intermediate distances before decaying exponentially due to extragalactic background light absorption.

Whispers of Hidden Particles: The ALP Solution

Axion-like particles (ALPs) propose a solution to photon propagation through opaque media via a process known as ALP-photon mixing. This mechanism postulates that photons can oscillate into ALPs within regions where they would normally be absorbed or scattered, effectively circumventing opacity. The probability of this oscillation, and thus the photon’s ability to traverse the region, is dependent on the ALP’s coupling strength to photons and the distance traveled within the opaque medium. When a photon interacts with a magnetic field, it can transition into an ALP, travel through the opaque region without interaction, and then transition back into a photon on the other side, effectively “regenerating” the original signal. This process allows photons to traverse distances that would otherwise be impossible, offering a potential explanation for observed transparency in certain astrophysical environments and providing a means to search for these weakly interacting particles.

The interaction between photons and axion-like particles (ALPs) leading to photon-ALP mixing is fundamentally dependent on the presence of external magnetic fields. This is because the mixing process arises from the effective coupling between the electromagnetic field and the ALP field, a coupling that is directly proportional to the magnetic field strength. Specifically, the magnetic field component perpendicular to the photon’s propagation direction drives transitions between photons and ALPs; this transition probability is parameterized by a mixing angle that is proportional to the magnetic field strength $B$ . Without an external magnetic field, this coupling is absent, and photon-ALP mixing cannot occur, effectively preventing photons from traversing regions of space otherwise opaque to them.

ALP-photon mixing can be induced by both coherent, constant magnetic fields and incoherent, stochastic magnetic fields. Constant fields drive a predictable oscillation between photons and ALPs, resulting in a resonant suppression of photon flux at specific energies dependent on the field strength and ALP mass. Stochastic magnetic fields, conversely, induce mixing through a cumulative effect of numerous small-scale field interactions; this leads to a depolarization of the photon polarization and an effective reduction in photon survival probability that is less energy-dependent than in the constant field case. The differing propagation signatures arising from these two magnetic field types allow for potential discrimination between ALP models and provide complementary probes of astrophysical magnetic field structures.

The probability of photon survival during ALP-photon mixing is strongly dependent on both the magnetic field strength (B) and the mass of the ALP. In the perturbative regime, where the mixing is relatively weak, the photon survival probability scales as $B^{-4}$ . This means that a stronger magnetic field significantly suppresses photon propagation due to increased mixing into ALPs. The ALP mass also plays a critical role; for a given magnetic field strength, the mixing probability is inversely proportional to the fourth power of the ALP mass. Therefore, lighter ALPs are more easily mixed into, and heavier ALPs require stronger magnetic fields to induce comparable mixing effects.

The characteristic length scale of oscillation and the resulting ALP-photon mixing probabilities <span class="katex-eq" data-katex-display="false">\mathcal{P}_{a\rightarrow\gamma}</span> and <span class="katex-eq" data-katex-display="false">\mathcal{P}_{\gamma\rightarrow\gamma}</span> vary with ALP mass and photon mean free path, being significantly affected by the configuration of the magnetic field (constant, domain-like, or stochastic with <span class="katex-eq" data-katex-display="false">\lambda_B = 1\,\textrm{Mpc}</span>), and are reliable above <span class="katex-eq" data-katex-display="false">\omega \gtrsim 20\,\textrm{TeV}</span> under perturbative conditions. — The characteristic length scale of oscillation and the resulting ALP-photon mixing probabilities $\mathcal{P}_{a\rightarrow\gamma}$ and $\mathcal{P}_{\gamma\rightarrow\gamma}$ vary with ALP mass and photon mean free path, being significantly affected by the configuration of the magnetic field (constant, domain-like, or stochastic with $\lambda_B = 1\,\textrm{Mpc}$ ), and are reliable above $\omega \gtrsim 20\,\textrm{TeV}$ under perturbative conditions.

Dissecting the Void: Perturbation Theory and Resonance

Integral Perturbation Theory (IPT) offers a mathematical approach to determine the probability of Axion-Like Particle (ALP) to photon conversion within a background stochastic magnetic field. The governing equations for ALP-photon mixing are typically intractable analytically; IPT provides an iterative solution by treating the magnetic field as a perturbation to the ALP propagation. This method involves expressing the mixing amplitude as a series expansion in terms of the magnetic field strength, allowing for calculation of successive contributions to the conversion probability. The resultant integral equations are then solved numerically, requiring the specification of the magnetic field’s statistical properties, such as its power spectrum, to accurately model the mixing process and determine the overall conversion rate. $P(\gamma \rightarrow a)$ , the probability of photon to ALP conversion, is directly calculated via this iterative process.

Integral Perturbation Theory facilitates the systematic examination of how variations in magnetic field distribution affect the probability of Axion-Like Particle (ALP) to photon mixing. Specifically, the theory allows for the modeling of mixing probabilities across a range of magnetic field power spectra and coherence lengths. By altering parameters defining the magnetic field distribution – such as its average strength, spatial variations, and correlation function – researchers can quantify the resulting changes in mixing probability. This capability is essential for determining how the characteristics of astrophysical magnetic fields, or those present in laboratory experiments, influence the detectability of ALPs, and for distinguishing between different models of ALP-photon interaction.

Resonance conditions play a critical role in amplifying Axion-Like Particle (ALP)-photon mixing. Mass-equal resonance occurs when the ALP mass $m_{\alpha}$ equals the photon energy $E$ , maximizing the mixing probability. Stochastic resonance, however, arises from the interaction of the ALP with a fluctuating magnetic field; even in the absence of a strict mass equality, specific statistical properties of the magnetic field fluctuations can induce significant mixing. These resonance conditions effectively overcome suppression factors in the mixing amplitude, leading to observable enhancements in the conversion rate between ALPs and photons that would otherwise be negligible. The magnitude of enhancement is dependent on the specific characteristics of the magnetic field and the proximity to the resonance condition.

Accurate modeling of Axion-Like Particle (ALP)-photon mixing necessitates a detailed characterization of the stochastic magnetic field beyond simple average field strengths. The four-point correlation function, specifically, describes the statistical relationship between magnetic field fluctuations at different spatial locations and provides critical information for calculating the mixing probability. Deviations from a purely Gaussian magnetic field distribution, as captured by higher-order correlation functions, can significantly alter the predicted mixing rates. Simulations and analytical calculations demonstrate that specific configurations of magnetic field correlations can lead to photon survival probability enhancements ranging from ten to several orders of magnitude compared to scenarios assuming uncorrelated fields, highlighting the importance of incorporating these statistical properties into theoretical models and observational analyses.

ALP-photon mixing probabilities <span class="katex-eq" data-katex-display="false">\mathcal{P}_{a\rightarrow\gamma}</span> and <span class="katex-eq" data-katex-display="false">\mathcal{P}_{\gamma\rightarrow\gamma}</span> exhibit stochastic resonance in a Gaussian magnetic field, with an approximate analytical solution (dashed lines) valid when the coherence length exceeds the scattering length, and the exponential decay component of <span class="katex-eq" data-katex-display="false">\mathcal{P}_{\gamma\rightarrow\gamma}</span> becomes negligible beyond <span class="katex-eq" data-katex-display="false">e^{-d/\lambda_\gamma}</span>. — ALP-photon mixing probabilities $\mathcal{P}_{a\rightarrow\gamma}$ and $\mathcal{P}_{\gamma\rightarrow\gamma}$ exhibit stochastic resonance in a Gaussian magnetic field, with an approximate analytical solution (dashed lines) valid when the coherence length exceeds the scattering length, and the exponential decay component of $\mathcal{P}_{\gamma\rightarrow\gamma}$ becomes negligible beyond $e^{-d/\lambda_\gamma}$ .

Mapping the Invisible: From Gaussian to Domain-Like Fields

Gaussian stochastic fields represent random magnetic fields as a statistical ensemble where the field at any given point follows a normal (Gaussian) distribution. This approach simplifies analysis by fully characterizing the field through its mean and covariance function, typically defined by a correlation length and field strength. While computationally efficient and serving as a foundational model, the Gaussian assumption implies that fluctuations are entirely random and lacks any inherent coherence or scale beyond the correlation length. Consequently, it often underestimates the suppression of high-energy photons traveling through magnetized plasmas, requiring refinement with more complex, non-Gaussian models to accurately represent observed photon survival probabilities and account for localized coherence effects in realistic intergalactic magnetic fields.

Domain-like models of intergalactic magnetic fields posit that magnetic field coherence is not uniform across vast distances, but rather is limited to localized regions, or domains. This approach contrasts with Gaussian models which assume coherence extends indefinitely. These domains are characterized by a coherence length, defining the scale over which the field maintains a relatively consistent direction. Within a domain, the magnetic field can be approximated as constant or slowly varying, while transitions between domains introduce discontinuities or rapid changes in field direction. The assumption of localized coherence is motivated by astrophysical processes likely responsible for field generation and amplification, which often operate on limited scales. Consequently, domain-like models offer a more physically realistic representation of the magnetic field structure than models assuming infinite coherence, impacting calculations of photon propagation and survival probabilities.

The accurate modeling of stochastic magnetic fields necessitates precise definition of the correlation length and field strength of the fluctuations. The correlation length, λ, determines the spatial scale over which the magnetic field is correlated; shorter correlation lengths imply more rapidly varying fields. Field strength, typically quantified as a root-mean-square value, dictates the amplitude of the random fluctuations. Both parameters significantly influence calculations of photon propagation, as the probability of photon survival is directly related to the coherence of the magnetic field over the traversed distance. Insufficiently constrained values for these parameters introduce uncertainty into models and can lead to inaccurate predictions regarding the attenuation or deflection of high-energy particles and photons.

Comparison of model predictions with observational data allows for the constraint of intergalactic magnetic field properties. Specifically, non-Gaussian models have demonstrated the potential to achieve photon survival probabilities of up to approximately 10^-5. This represents a significant suppression – by several orders of magnitude – when contrasted with predictions derived from employing Gaussian fields or domain-like models relying on Gaussian statistics. These findings suggest that the statistical properties of the intergalactic magnetic field may deviate substantially from Gaussianity, influencing the propagation of high-energy photons.

Photon survival probability <span class="katex-eq" data-katex-display="false">\mathcal{P}_{\gamma\rightarrow\gamma}</span> is significantly enhanced by non-Gaussian magnetic field distributions-varying with parameters like κ, <span class="katex-eq" data-katex-display="false">\lambda_{\rho}</span>, and <span class="katex-eq" data-katex-display="false">g_{NL}</span>-compared to Gaussian fields, as demonstrated at <span class="katex-eq" data-katex-display="false">\omega=100\\,\\textrm{TeV}</span> and <span class="katex-eq" data-katex-display="false">d=\\textrm{Gpc}</span>. — Photon survival probability $\mathcal{P}_{\gamma\rightarrow\gamma}$ is significantly enhanced by non-Gaussian magnetic field distributions-varying with parameters like κ, $\lambda_{\rho}$ , and $g_{NL}$ -compared to Gaussian fields, as demonstrated at $\omega=100\\,\\textrm{TeV}$ and $d=\\textrm{Gpc}$ .

The pursuit of understanding very-high-energy gamma rays, as detailed in this analysis of axion-photon mixing, reveals a humbling truth about theoretical physics. It’s easy to construct elegant models predicting signal attenuation through the intergalactic medium, assuming perfectly ordered or even mildly turbulent magnetic fields. However, the possibility of significant non-Gaussian boosts, altering photon survival probabilities, suggests these assumptions are often… optimistic. As Pyotr Kapitsa once observed, “It is better to be disliked and truthful than to be liked and a liar.” The universe doesn’t care for beautiful equations; it presents data, and the theory must bend to it, even if it means admitting prior assumptions were, shall we say, a bit fanciful. Physics, after all, is the art of guessing under cosmic pressure.

What Lies Beyond the Horizon?

The presented perturbative analysis of axion-photon mixing, while illuminating the potential for enhanced gamma-ray survival within a turbulent extragalactic magnetic field, necessarily rests upon approximations. The Schwarzschild and Kerr metrics describe exact spacetime geometries around spherically and axially symmetric rotating bodies; however, the intergalactic medium is neither. Any discussion of quantum singularity requires careful interpretation of observables, and here, the ‘observables’ are photons that may, or may not, have traversed a probabilistic landscape sculpted by as-yet-unmapped magnetic fields. The calculated ‘plateau regimes’ and ‘non-Gaussian boosts’ are, therefore, contingent upon the validity of these assumptions-a validity that, like all extrapolations, diminishes with distance from the initial conditions.

Future investigations must confront the limitations of perturbative methods. Fully nonlinear simulations, while computationally expensive, are required to assess the robustness of the reported enhancements. Moreover, a more rigorous characterization of the extragalactic magnetic background is paramount. Current models, based on observations of Faraday rotation and synchrotron emission, provide only a fragmented picture. A unified theory connecting these observations with the underlying magnetohydrodynamic processes remains elusive.

Ultimately, this work serves as a reminder that the search for dark matter candidates, like axions, is not merely a quest to identify a particle, but a confrontation with the limits of knowledge. Each positive signal, each apparent detection, merely pushes the event horizon further away, revealing new layers of complexity and uncertainty. The true nature of the dark universe may, in the end, prove to be less a puzzle to be solved, and more a mirror reflecting the inherent limitations of the observing mind.

Original article: https://arxiv.org/pdf/2602.23249.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Universe’s Veil: A Transparency Crisis

Whispers of Hidden Particles: The ALP Solution

Dissecting the Void: Perturbation Theory and Resonance

Mapping the Invisible: From Gaussian to Domain-Like Fields

What Lies Beyond the Horizon?

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