Executive hypothesis

Hypothesis: A distributed array of well-calibrated, repeating fast radio bursts (an FRB Timing Array, FRB-TA) can detect and characterize the statistical properties of intergalactic magnetic fields (IGMF) — their rms strength, coherence scale, and power spectrum — through cross-correlated fluctuations in dispersion measure (DM), rotation measure (RM), scattering, and arrival-time structure across many sightlines.

Why this is plausible

FRBs are bright, cosmological, and often highly polarized; many repeat and can be monitored with high cadence. DM and RM encode integrated electron column and line-of-sight magnetic fields, respectively. Observed FRB RMs span a wide range — from nearly zero to >10^5 rad m−2 in extreme local environments — demonstrating sensitivity to magnetized plasma along cosmological sightlines (Michilli et al. 2018). The intergalactic medium (IGM) contributes a modest but coherent RM and DM signal whose statistical imprint across multiple nearby sightlines is set by the IGMF strength and coherence length (Akahori & Ryu 2011). A controlled, statistical measurement across many repeaters can separate IGM contributions from dominant, but largely uncorrelated, host- and Milky Way-induced effects.

Mechanistic sketch

Monitor a network of N repeating FRBs distributed across the sky. For each source, obtain high-time-resolution, wideband, fully polarized dynamic spectra on a regular cadence (weekly to monthly). From each epoch extract:

  • DM(t): frequency-dependent group delay integrated along the sightline.
  • RM(t): Faraday rotation of linear polarization as a function of λ2 (after careful polarization calibration).
  • High-resolution arrival-time structure and scintillation properties (to probe small-scale plasma inhomogeneities).

Construct two-point statistics (auto- and cross-correlation functions, structure functions) of DM and RM residuals after subtracting best-fit secular and local models. The IGM induces correlated fluctuations between sightlines that intersect the same large-scale structures (filaments, sheets). The angular correlation length of RM/DM fluctuations maps to the transverse coherence scale of the magnetized plasma; the amplitude constrains the line-of-sight magnetic field component convolved with electron density fluctuations. Combining redshift information for repeaters enables tomographic stacking and a redshift-dependent reconstruction of IGMF evolution.

Falsifiable predictions

  • If the IGMF has rms strength B_rms ≳ 0.1–1 nG with coherence scales of ~0.1–10 Mpc, then an FRB-TA of ≳100 well-measured repeaters (RM precision ≲0.1–1 rad m−2 per epoch) monitored for several years will detect a non-zero angular cross-correlation of RM and DM residuals above astrophysical foregrounds at >3σ.
  • If the IGMF is ≪0.1 nG or coherent only on scales ≪0.1 Mpc, the cross-correlation signal will be consistent with zero within the same data set; residual RM/DM variance will be dominated by host, Milky Way, and instrumental terms and show no redshift dependence traceable to large-scale structure.
  • Angular scale dependence: the correlation amplitude will fall with increasing separation in a way characteristic of the magnetic power spectrum (e.g., power-law or broken power-law), enabling model discrimination between primordial-seeding and astrophysical-outflow scenarios.

Experimental roadmap

  • Assemble a target sample of ≳100 bright repeaters spanning redshift 0.1–2. Prioritize sources with stable polarization fractions and minimal extreme local RM variability.
  • Instrumental requirements: wide instantaneous bandwidth (preferably 0.4–8 GHz or multi-band coverage) for robust DM and RM fits; sub-ms timing precision; polarization calibration stability to ≲0.1% over years; high S/N per epoch to reach RM precision ≲0.1–1 rad m−2.
  • Cadence: weekly-to-monthly monitoring for 3–5 years to sample relevant timescales of IGM turbulence and cosmological structure change in projection.
  • Analysis: compute RM/DM residuals after modeling host and Milky Way contributions; measure angular cross-correlation functions as a function of source separation and redshift; jointly fit for magnetic field power spectrum parameters with priors from cosmological simulations and galaxy/filament density maps.
  • Synergies: combine with large-scale structure surveys (e.g., DESI, Euclid) and RM catalogs for extragalactic sources to cross-validate filament associations and to perform targeted sightline stacks through known structures.

Controls and pitfalls

  • Host-local contamination: Many repeaters exhibit large, rapidly varying RM from their immediate environment. Mitigation: select subsets with stable local behavior; model and marginalize local terms; exploit angular correlation (host terms are uncorrelated between widely separated sources).
  • Milky Way foregrounds and ionosphere: use existing Galactic RM maps and contemporaneous ionospheric monitoring to remove foreground structure; perform null tests by scrambling source positions.
  • Instrumental polarization drift and RFI: maintain rigorous polarization calibration and include calibration sources each epoch; develop robust RFI excision pipelines.
  • Theoretical degeneracies: DM and RM are integrals over n_e and B_parallel; degeneracy with density fluctuations can be broken using scattering and scintillation measurements and by correlating with galaxy/filament density.

Implications

Detecting and characterizing the IGMF with an FRB-TA would constrain seeding scenarios (primordial vs astrophysical), inform models of structure formation, and quantify magnetic deflections relevant to ultra-high-energy cosmic ray propagation. A null result at the sensitivity limits would place stringent upper bounds on pervasive cosmological magnetic fields and guide theoretical models that invoke significant IGM magnetization.

In short: FRBs provide a scalable, high-precision toolset — DM, RM, scattering, and timing — that, when deployed in a coordinated timing array, can reveal the statistical fingerprint of magnetic fields in the vast intergalactic web.