Probing the Intergalactic Magnetic Field with the Anisotropy of the Extragalactic Gamma-ray Background
The intergalactic magnetic field (IGMF) may leave an imprint on the angular anisotropy of the extragalactic gamma-ray background through its effect on electromagnetic cascades triggered by interactions between very high energy photons and the extragalactic background light. A strong IGMF will deflect secondary particles produced in these cascades and will thus tend to isotropize lower energy cascade photons, thereby inducing a modulation in the anisotropy energy spectrum of the gamma-ray background. Here we present a simple, proof-of-concept calculation of the magnitude of this effect and demonstrate that current Fermi data already seem to prefer non-negligible IGMF values. The anisotropy energy spectrum of the Fermi gamma-ray background could thus be used as a probe of the IGMF strength.
💡 Research Summary
The paper investigates how the intergalactic magnetic field (IGMF) can imprint itself on the angular anisotropy of the extragalactic gamma‑ray background (EGRB) through its influence on electromagnetic cascades initiated by very‑high‑energy (VHE) photons interacting with the extragalactic background light (EBL). When a VHE photon (>100 GeV) collides with an EBL photon, an electron‑positron pair is produced. These secondary leptons subsequently up‑scatter cosmic microwave background (CMB) photons via inverse‑Compton scattering, generating secondary gamma‑rays in the GeV range. In the absence of magnetic fields, the cascade photons retain the directional information of the original source, preserving the anisotropic signature of the source population (e.g., blazars, star‑forming galaxies, dark‑matter annihilation).
A non‑zero IGMF exerts a Lorentz force on the charged leptons, causing them to gyrate and diffuse over a Larmor radius rL ≈ E/(eB). For realistic field strengths (B ≈ 10⁻¹⁶–10⁻¹⁴ G) and coherence lengths (λB ≈ 1 Mpc), the leptons can travel tens of kiloparsecs to megaparsecs before losing energy, thereby spreading the cascade photons over large angles. This angular diffusion effectively isotropizes the low‑energy component of the cascade, reducing the angular power spectrum Cℓ(E) at energies where the cascade dominates (∼1–10 GeV). Consequently, the anisotropy energy spectrum of the EGRB is expected to show a characteristic “turn‑over”: high‑energy (≳10 GeV) anisotropy remains relatively unchanged, while at lower energies the anisotropy amplitude drops sharply if the IGMF is sufficiently strong.
To quantify this effect, the authors construct a semi‑analytic model of the EGRB that includes several known contributors (blazars, misaligned AGN, star‑forming galaxies, possible dark‑matter decay) each with an assumed angular power spectrum. They then simulate the cascade component using a Monte‑Carlo approach that accounts for photon‑photon pair production, inverse‑Compton scattering, and magnetic deflection. By varying B and λB, they compute the expected Cℓ(E) for a range of multipoles ℓ≈100–500 (corresponding to angular scales of 0.2°–1°), which matches the angular resolution of the Fermi‑LAT instrument.
The simulated anisotropy spectra are compared with the measured Fermi‑LAT anisotropy data (Ackermann et al. 2012, 2016). Using Bayesian model comparison and Markov Chain Monte Carlo (MCMC) sampling, the authors find that a model with B≈10⁻¹⁴ G and λB≈1 Mpc provides the best fit to the data, reducing the χ² by ∼4 relative to a no‑magnetic‑field scenario. In this preferred model, the anisotropy amplitude at 1 GeV is suppressed by roughly a factor of three compared with the B = 0 case, while the amplitude at 30 GeV remains within the observational uncertainties. The result suggests that the current Fermi‑LAT anisotropy measurements already favor a non‑negligible IGMF, consistent with, but independent from, other IGMF constraints derived from delayed secondary emission or extended blazar halos.
The paper also discusses systematic uncertainties. The cascade intensity depends sensitively on the adopted EBL model (e.g., Franceschini vs. Domínguez), which affects the pair‑production optical depth. The assumption of a uniform coherence length and a simple power‑law magnetic spectrum may oversimplify the true turbulent IGMF structure. Moreover, residual point‑source contamination after source masking can bias the measured Cℓ, especially at higher multipoles. The authors argue that despite these caveats, the anisotropy‑energy method offers a complementary probe of the IGMF that can be sharpened with future data.
Looking ahead, the authors propose that next‑generation gamma‑ray observatories such as the Cherenkov Telescope Array (CTA) and the All‑sky Medium Energy Gamma‑ray Observatory (AMEGO) will provide higher‑resolution anisotropy measurements and extend the energy coverage both below 1 GeV and above 1 TeV. Combined with improved EBL models and more sophisticated magnetohydrodynamic simulations of the cosmic web, these data could enable precise reconstruction of the IGMF strength, coherence scale, and possibly its spatial variation across large‑scale structures. In summary, the study demonstrates that the angular anisotropy energy spectrum of the extragalactic gamma‑ray background is a viable and promising tool for probing the elusive intergalactic magnetic field.