Magnetic fields of order a few to tens of nanogauss are predicted to permeate the cosmic web — the network of galaxy clusters, filaments, and sheets surrounding cosmic voids — but measuring them through the Faraday rotation they imprint on polarized background radio sources is exceptionally difficult: the expected signature, of order 1 rad m−21\ \mathrm{rad\ m^{-2}}, is comparable to residual Galactic Faraday-rotation fluctuations, typical rotation-measure (RM) errors at GHz frequencies, and intrinsic source contributions. Building on the 2018 review by Vacca and collaborators, the problem is to move from candidate detections and statistical upper limits to robust measurements of cosmic-web magnetic fields using RM grids: detect the weak cosmic-web RM signature with systematics under control, and statistically separate it into distinct large-scale-structure environments (clusters, filaments, sheets, voids). Subsequent work has achieved major partial progress — stacked LOFAR and ASKAP RM analyses now yield statistical detections of magnetized filaments (rest-frame RM of about 0.7 rad m−20.7\ \mathrm{rad\ m^{-2}} per filament and B≈11B\approx 11–15 nG15\ \mathrm{nG}) and of magnetized gas around galaxy groups — but these are stacked statistical inferences whose amplitudes shift under analysis choices, sheets and voids remain observationally unconstrained, and modeling-assumption biases are unquantified. The problem therefore remains open, and its resolution bears directly on the origin of cosmic magnetism.

Background

On scales of tens of megaparsecs, matter in the Universe is organized into the cosmic web: dense galaxy clusters at the nodes, elongated filaments and planar sheets connecting them, and near-empty voids in between. Most baryons outside galaxies reside in the warm-hot intergalactic medium (WHIM), a tenuous million-kelvin plasma permeating filaments and sheets. Whether, and how strongly, these structures are magnetized is a central open question of cosmic magnetism: measured cosmic-web fields would discriminate magnetogenesis scenarios — whether seed fields originated in the early Universe (primordial origin) or were produced astrophysically by galaxies and their outflows, later amplified by turbulent dynamos.

Faraday rotation is the standard probe of magnetized plasma along the line of sight: the polarization angle of linearly polarized radio emission rotates by an angle proportional to the square of the wavelength, with the rotation measure

RM [rad m−2]=0.812∫ne [cm−3]  B∥ [μG]  dl [pc],\mathrm{RM}\ [\mathrm{rad\ m^{-2}}] = 0.812 \int n_e\ [\mathrm{cm^{-3}}]\; B_\parallel\ [\mu\mathrm{G}]\; dl\ [\mathrm{pc}],

an integral of the thermal electron density nen_e times the line-of-sight magnetic field B∥B_\parallel along the path. Measuring RM for a large grid of polarized background radio galaxies (an 'RM grid') samples all magnetoionic material along each line of sight — Galactic foreground, galaxy clusters, the WHIM, and the sources' own environments.

The difficulty posed by the cosmic web is one of dynamic range. Cluster fields of a few μG\mu\mathrm{G} over megaparsec paths produce RMs of tens to thousands of rad m−2\mathrm{rad\ m^{-2}}, but the cosmic web outside clusters — with ne∼10−5 cm−3n_e\sim 10^{-5}\ \mathrm{cm^{-3}} and fields of a few to tens of nanogauss over paths of order 10 Mpc — is expected to contribute only of order 1 rad m−21\ \mathrm{rad\ m^{-2}}, comparable to residual fluctuations of the Galactic foreground RM, to typical per-source RM errors at GHz frequencies, and to intrinsic source RM contributions. Low-frequency observations (e.g. with LOFAR, a low-frequency radio interferometer, at 144 MHz) reduce the per-source RM error but face ionospheric-calibration challenges and depolarization — the wavelength-dependent scrambling of polarization angle within sources and screens that reduces polarized flux — which thins the usable background-source grid.

Inference from RM data is also model-dependent. Forward-modeling approaches represent fields as Gaussian random realizations with power-law magnetic power spectra, assume electron-density profiles such as the β-model (ne∝[1+(r/rc)2]−3β/2n_e\propto[1+(r/r_c)^2]^{-3\beta/2}, the standard parametrization of intracluster gas), and often adopt equipartition (equal magnetic and cosmic-ray energy densities) or other assumed scaling relations; the bias these assumptions introduce in inferred field amplitudes and spectra has not been systematically quantified.

As of the 2018 source review (Vacca et al. 2018, Galaxies 6, 142), the state of the art consisted of statistical upper limits from diffuse synchrotron emission (Brown et al. 2017; Vernstrom et al. 2017), Bayesian RM-grid inference frameworks — which fit magnetic-field parameters by posterior probability distributions conditioned on the RM data — validated only on simulations (Vacca et al. 2016, A&A 591, A13), and Sardinia Radio Telescope (SRT) observations that had found 28 candidate diffuse radio sources possibly associated with a z≈0.1z\approx 0.1 cluster filament, with their polarized properties unestablished (Vacca et al. 2018, MNRAS 479, 776). A subsequent RM-statistics study of adjacent radio sources likewise found no significant excess (Vernstrom et al. 2019, ApJ 878, 92).

Problem Statement

The problem is to move from candidate detections and statistical upper limits to robust measurements of magnetic fields in the cosmic web outside galaxy clusters, using Faraday rotation, through two jointly required components whose common objective is a trustworthy measurement of cosmic-web magnetism:

  1. Detection of the weak cosmic-web RM signature. Detect the expected order-1 rad m−21\ \mathrm{rad\ m^{-2}} rotation-measure contribution of the cosmic web, controlling the confounders of comparable size: residual Galactic foreground RM fluctuations, per-source observational RM errors at GHz frequencies, intrinsic source contributions, and — at low radio frequencies — ionospheric calibration systematics and depolarization-driven loss of background sources. This requires very large, well-calibrated RM catalogs with accurate source redshifts and reliable large-scale-structure path-length information.

  2. Environmental separation. Statistically separate the extragalactic RM contribution into distinct large-scale-structure components — clusters, filaments, sheets, and voids — using joint datasets (deep polarization surveys, source redshifts, and reconstructed cosmic-web maps) together with Bayesian or forward-modeling inference pipelines validated against realistic mock skies (simulated skies whose true magnetic fields and foregrounds are known).

Confirming the cosmic-web nature of candidate diffuse radio sources (for example, establishing the polarized properties of the SRT-discovered candidate filament sources) is supporting context for component 1, not a separate required deliverable. Success is a robust — and ultimately spatially resolved — measurement of the strength and structure of cosmic-web magnetic fields of sufficient fidelity to discriminate primordial versus astrophysical magnetogenesis scenarios.

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