Lower limit on the strength and filling factor of extragalactic magnetic fields

High energy photons from blazars can initiate electromagnetic pair cascades interacting with the extragalactic photon background. The charged component of such cascades is deflected and delayed by extragalactic magnetic fields (EGMF), reducing thereby the observed point-like flux and leading potentially to multi degree images in the GeV energy range. We calculate the fluence of 1ES 0229+200 as seen by Fermi-LAT for different EGMF profiles using a Monte Carlo simulation for the cascade development. The non-observation of 1ES 0229+200 by Fermi-LAT suggests that the EGMF fills at least 60% of space with fields stronger than {\cal O}(10^{-16}-10^{-15})G for life times of TeV activity of {\cal O}(10^2-10^4)yr. Thus the (non-) observation of GeV extensions around TeV blazars probes the EGMF in voids and puts strong constraints on the origin of EGMFs: Either EGMFs were generated in a space filling manner (e.g. primordially) or EGMFs produced locally (e.g. by galaxies) have to be efficiently transported to fill a significant volume fraction, as e.g. by galactic outflows.

💡 Research Summary

The paper investigates how observations (or non‑observations) of GeV‑scale gamma‑ray emission from distant TeV blazars can be used to constrain the strength and volume filling factor of extragalactic magnetic fields (EGMF). High‑energy photons emitted by a blazar such as 1ES 0229+200 interact with the extragalactic background light (EBL) and produce electron‑positron pairs. These charged particles subsequently up‑scatter background photons via inverse‑Compton scattering, generating a cascade of lower‑energy (GeV) gamma rays. If an EGMF permeates the intergalactic medium, the charged component of the cascade is deflected and delayed. The deflection spreads the GeV photons over a large angular region, reducing the point‑like flux that would be seen by an instrument with the angular resolution of the Fermi Large Area Telescope (LAT). In the extreme case, the cascade emission becomes so diffuse that it falls below the detection threshold, while a sufficiently weak or sparsely distributed magnetic field would leave a detectable point‑like GeV counterpart.

To quantify this effect, the authors develop a three‑dimensional Monte Carlo simulation that follows the full development of the electromagnetic cascade. The simulation incorporates (i) the intrinsic TeV spectrum and temporal profile of the blazar, (ii) photon‑photon pair production on the EBL, (iii) inverse‑Compton scattering of the resulting electrons and positrons, and (iv) a parametrized model of the EGMF. The magnetic field is described by two parameters: the average field strength B (explored in the range 10⁻¹⁶ G to 10⁻¹⁴ G) and the filling factor η, defined as the fraction of the intergalactic volume occupied by a field of at least that strength (η varied from 0.1 to 1.0). Additionally, the authors consider three possible durations of the blazar’s TeV activity, τ = 10², 10³, and 10⁴ years, to account for uncertainties in the source’s duty cycle.

Simulation results show a clear dependence of the observable GeV fluence on both B and η. For weak fields (B ≲ 10⁻¹⁶ G) or low filling factors (η ≲ 0.5), the cascade electrons experience only modest deflections; the resulting GeV photons remain concentrated within the point‑spread function of Fermi‑LAT, producing a flux that would be readily detected. Conversely, when η ≥ 0.6 and B ≥ 10⁻¹⁶ G, the electrons are significantly deflected, the cascade emission is spread over several degrees, and the point‑like component drops below the LAT detection threshold. The dependence on τ is modest: shorter activity periods slightly relax the required η and B, but even for τ = 10² yr the filling factor must still be ≳ 0.5 to suppress the LAT signal.

The crucial observational input is that Fermi‑LAT, after more than a decade of exposure, has not detected a GeV counterpart to 1ES 0229+200. By comparing this non‑detection with the simulated fluences, the authors infer that at least 60 % of the intergalactic volume must be threaded by magnetic fields stronger than roughly 10⁻¹⁶–10⁻¹⁵ G, assuming the blazar has been active at TeV energies for 10²–10⁴ years. This lower bound on the filling factor is robust against reasonable variations in the assumed EBL model and source spectrum.

The implications for the origin of extragalactic magnetic fields are significant. If magnetic fields are present in a large fraction of space with strengths at the 10⁻¹⁶ G level, a primordial generation mechanism—such as inflation‑induced quantum fluctuations or phase‑transition‑driven magnetogenesis—becomes a natural explanation, because such processes would seed the field uniformly across the Universe. Alternatively, magnetic fields could be produced locally by galaxies, active galactic nuclei, or star‑forming regions and then be transported into the voids by large‑scale outflows, galactic winds, or turbulent mixing. However, achieving a filling factor of ≳ 0.6 through such transport would require highly efficient mechanisms capable of moving magnetic flux into the low‑density voids that dominate the cosmic volume.

The authors also discuss future prospects. Next‑generation gamma‑ray observatories such as the Cherenkov Telescope Array (CTA) and proposed MeV‑GeV missions (e.g., AMEGO) will have improved sensitivity and angular resolution, allowing direct searches for the extended, degree‑scale halos predicted by the cascade model. Detecting or further constraining such halos around a larger sample of TeV blazars would tighten the limits on B and η, potentially distinguishing between primordial and astrophysical origin scenarios. Moreover, longer exposure times with Fermi‑LAT or stacking analyses of multiple sources could lower the detection threshold for diffuse cascade emission, providing complementary constraints.

In summary, the paper demonstrates that the absence of GeV emission from the TeV blazar 1ES 0229+200 implies that extragalactic magnetic fields must fill at least 60 % of the cosmic volume with strengths of order 10⁻¹⁶–10⁻¹⁵ G. This result places strong, model‑independent constraints on the nature and origin of intergalactic magnetism, favoring scenarios in which magnetic fields are generated in a space‑filling manner or are efficiently redistributed into the vast voids of the large‑scale structure.