The Axion-Photon Mixing and the Extragalactic Magnetic Background: Plateau Regimes, Resonances, and Non-Gaussian Boosts

Abstract

We present an analytical treatment of Axion-Like-Particle (ALP)--photon mixing with extragalactic background light (EBL) attenuation for constant, Gaussian-stochastic, and non-Gaussian magnetic field configurations--with direct implications for Very High Energy (VHE) gamma-ray observations such as LHAASO, HAWC, and CTA experiments. For constant fields, we derive exact probabilities and identify a perturbative plateau regime where photon survival scales as quartic order of magnetic field, isolating the four-point magnetic correlation as a sensitive probe of non-Gaussianity. For Gaussian stochastic fields, we obtain--for the first time--analytical formulas for non-exponential-decay components in the strong-attenuation regime. Contrary to the widely used domain-like model, photon survival is suppressed by 4-6 orders of magnitude, while both conversion and survival probabilities exhibit distinct multi-peak structures from mass-equal resonance, stochastic resonance, and EBL attenuation. Extending to non-Gaussian fields, we show that non-Gaussianity can enhance photon survival by several orders of magnitude relative to the Gaussian case, potentially explaining the unexpectedly VHE photon event observed by LHAASO. Our results demonstrate that stochastic magnetic fields cannot be reduced to domain-like coherence without losing essential physics, and that VHE gamma-ray spectra encode observable information about both the power spectrum and non-Gaussian structure of intergalactic magnetic fields--critical as next-generation observatories push toward PeV sensitivities.

Figures (5)

• Figure 1: The ALP-photon conversion probability $\mathcal{P}_{a\rightarrow\gamma}$ (upper panels) and the photon survival probability $\mathcal{P}_{\gamma\rightarrow\gamma}$ (lower panels) in a constant magnetic field for various parameter sets. All dimensional quantities are normalized to $\lambda_{\gamma}$. In the regime $d \ll \lambda_{\gamma}$, the probabilities reproduce the conventional ALP-photon mixing results in the absence of EBL attenuation. For $\lambda_{\gamma} \ll d \ll \left(1 + A^{2}\lambda_{\gamma}^{2}\right) / \left(\Delta_{B}^{2}\lambda_{\gamma}\right)$, both probabilities lie within the perturbative regime and remain approximately constant, exhibiting power-law scaling with the magnetic field as $\mathcal{P}_{a\rightarrow\gamma} \sim B^{2}$ and $\mathcal{P}_{\gamma\rightarrow\gamma} \sim B^{4}$. At larger distances, the probabilities decay exponentially due to EBL absorption.
• Figure 2: The ALP-photon mixing probabilities $\mathcal{P}_{a\rightarrow\gamma}$ and $\mathcal{P}_{\gamma\rightarrow\gamma}$ in the stochastic magnetic field with Gaussian distribution and the monochromatic spectrum. All dimensional quantities are properly normalized to $\lambda_{\gamma}$. Eq.\ref{['eq:P-parameterization']} provides an approximation (colored dash lines) which that holds in the regime $d/\lambda_{\gamma} \gg 1$. In the first plot illustrating ALP-photon conversion, the initial linear growth is a signature of stochastic resonance (see Section III for further details). The gray dashed lines correspond to $e^{-d/\lambda_{\gamma}}$ and $e^{-d/(2\lambda_{\gamma})}$, above which the exponential-decay component of the $\mathcal{P}_{\gamma\rightarrow\gamma}$ becomes subdominant and can be safely neglected compared to the non exponential-decay contribution.
• Figure 3: Left: The characteristic length scale $1/|A|$, in the oscillation Hamiltonian, for different ALP mass cases and photon mean free path $\lambda_{\gamma}$ as a function of energy. Middle and Right: the ALP-photon mixing probabilities $\mathcal{P}_{a\rightarrow\gamma}$ and $\mathcal{P}_{\gamma\rightarrow\gamma}$ in three magnetic field configurations: a constant magnetic field filling the entire space, a simplified domain-like model, and a stochastic magnetic field. The parameters are set to $B_{rms}=10^{-9}\textrm{Gs}$, $g_{a\gamma}=10^{-12}\textrm{GeV}^{-1}$ and $d=\textrm{Gpc}$. For the stochastic magnetic field, its distribution is Gaussian and the spectrum is monochromatic with correlation length $\lambda_{B}=1\textrm{Mpc}$. The black dotted line in right panel denotes the photon survival probability in the absence of ALP mixing. The thick curves are constrained to $\omega\gtrsim20\textrm{TeV}$ where the perturbative condition is well satisfied in the stochastic case.
• Figure 4: The photon survival probability $\mathcal{P}_{\gamma\rightarrow\gamma}$ in the stochastic magnetic field with a monochromatic spectrum with $\lambda_{B}=1\, \textrm{Mpc}$, for Gaussian (thick line) and non-Gaussian distributions (case-1 for dashed line, case-2 for dotted line and case-3 for thin line). The left panel is at fixed $\omega=100\textrm{TeV}$, and the middle and right panels is fixed at $d=\textrm{Gpc}$. The middle panel corresponds to the weak non-Gaussianity, where parameters are set to $\kappa=0.01$ for case-1, $\kappa=0.01,\lambda_{\rho}=0.1\textrm{Mpc}$ for case-2, and $g_{NL}=0.01$ for case-3. The right panel corresponds to strong non-Gaussianity, where parameters are set to $\kappa=100$ for case-1, $\kappa=1, \lambda_{\rho}=50\textrm{Mpc}$ for case-2, and $g_{NL}=100$ for case-3. Note that non-gaussianities highly boost the photon survival probability with model dependent profiles.
• Figure 5: The photon survival probability $\mathcal{P}_{\gamma\rightarrow\gamma}$ in the non-Gaussian magnetic field as a function of corresponding non-Gaussian parameters in Case 1 (left), Case 2 (right) and Case 3 (right). In Case 2 the probability depends on two non-Gaussian parameters $\kappa$ and $\lambda_\rho$, whereas independent of ALP mass. The dashed black line $\mathcal{P}_{\gamma\rightarrow\gamma}=10^{-5}$ denotes the marginal required probability to explain the 13 TeV photon observed by LHAASO. Such a high energetic photon can be explained by ALP-photon mixing in a strong non-Gaussian magnetic background.