Simulated Rotation Measure Sky from Primordial Magnetic Fields

TL;DR

This study tackles how primordial magnetic fields (PMFs) imprint on the intergalactic rotation measure (RM) by simulating PMFs with varied coherence scales and generating full-sky RM$_{IGM}$ maps through light-cone cosmological MHD simulations. By introducing a new RM sampling method and analyzing the RM$_{IGM}$ autocorrelation, the authors show that PMF coherence leaves distinct signatures: large-scale, horizon-length coherence yields enduring angular correlations, while small-scale coherent fields produce rapid, angle-dependent decorrelation. Comparisons with LOFAR RM data indicate consistency with PMF-strength upper limits and favor a model with larger coherence scales (km1) for reproducing mean RM trends, though uniform and other configurations cannot be ruled out given current uncertainties. The work highlights the potential of future all-sky RM surveys, with improved Galactic foreground removal, to constrain PMF structure and inform the origin of cosmic magnetism.

Abstract

Primordial Magnetic Fields (PMFs) -- magnetic fields originating in the early Universe and permeating the cosmological scales today -- can explain the observed microGauss-level magnetisation of galaxies and their clusters. In light of current and upcoming all-sky radio surveys, PMFs have drawn attention not only as major candidates for explaining the large-scale magnetisation of the Universe, but also as potential probes of early-Universe physics. In this paper, using cosmological simulations coupled with light-cone analysis, we study for the first time the imprints of the PMF structure on the mean rotation measure (RM) originating in the intergalactic medium (IGM), $\langle \mathrm{RM_{IGM}}\rangle$. We introduce a new method for producing full-sky $\mathrm{RM_{IGM}}$ distributions and analyse the autocorrelation of $\mathrm{RM_{IGM}}$ on small and large angular scales; we find that PMF structures indeed show distinct signatures. The large-scale uniform model (characterised by an initially unlimited coherence scale) leads to correlations up to 90 degrees, while correlations for small-scale stochastic PMF models drop by factor of $100$ at $ 0.17, 0.13$ and 0.11 degrees angular scales, corresponding to $5.24, 4.03$ and $3.52$ Mpc scales (at $z=2$ redshift) for magnetic fields with comoving $3.49, 1.81, 1.00 $ Mpc/h coherence scales, respectively; the correlation amplitude of the PMF model with comoving $\sim 19$ Mpc/h coherence scale drops only by factor of $10$ at 1 degree (30.6 Mpc). These results suggests that improvements in the modelling of Galactic RM will be necessary to investigate the signature of large-scale correlated PMFs. A comparison of $\langle \mathrm{RM_{IGM}}\rangle$ redshift dependence obtained from our simulations with that from the LOFAR Two-metre Sky Survey shows agreement with our previous upper limits' estimates on the PMF strength derived from RM-rms analysis.

Figures (6)

• Figure 1: Illustration of light cone (direction indicated with dashed lines) realisations within stacked comoving boxes. Blue and green vectors indicate the magnetic field and the $\hat{\mathbf{e}}$ unit vectors (Equation \ref{['eq:RM']}), respectively.
• Figure 2: Average of $\mathrm{RM_{IGM}}$ autocorrelation functions obtained from $10^4$ light cone realisations for each model at $z=2$ redshift depth; coherence scales of the PMF models are also indicated in the legend.
• Figure 3: Constructed $\mathrm{RM}_{\text{IGM}}$ maps [rad/m$^2$] for three PMF models studied in this work at $z=2$ redshift depth. The left part of the figure depicts mean $\mathrm{\langle RM_{\text{IGM}} \rangle}$ distribution in Galactic coordinates with 10000 and $\sim 3300$ light cone realisations in the uniform, and km1 and k25 cases, respectively (in the latter cases smaller number of realisations are chosen for a better visualisation). The right part shows example 2D light cone maps (having $2°$ FOVs and 20″ image resolution) used for calculating $\mathrm{RM_{IGM}}$ statistics.
• Figure 4: Angular autocorrelation of full-sky mean $\mathrm{RM_{IGM}}$ (Figure \ref{['fig:SkyMaps']}) for the uniform and stochastic PMF models (with coherence scales indicated in the legend). Cosine function is also shown for reference, with $\Phi$ indicating the angular separation.
• Figure 5: Mean $\mathrm{RM_{IGM}}$ trends of PMFs and mean RRM from LoTSS data (grey lines); error for the latter is calculated with bootstrapping, while for the simulated RMs standard deviations are shown (lower-opacity filled colour lines).