Probing Cosmic Magnetism with Rotation Measure-Squared-Galaxy Cross-Correlations

TL;DR

This work introduces a novel RM-based probe of cosmic magnetism by measuring the cross-correlation between RM^2 maps toward background sources and the projected foreground galaxy density, enabling tomographic insights into the redshift evolution of large-scale magnetic fields. The statistic maps to a bispectrum of two electron-density–weighted magnetic-field components and a galaxy fluctuation, and is modeled with Illustris-TNG simulations as well as an analytic framework that links amplitude to the projected magnetic-field strength and to the electron–galaxy cross-power. Results show that the RM^2 × g signal grows by roughly three orders of magnitude from high to low redshift, driven by dynamo amplification and magnetized outflows in halos, with the signal's scale dependence governed by the electron–galaxy clustering. Forecasts indicate high-significance detections are achievable with current data in some bins and will be routinely detectable with SKA-era RM catalogs, offering a powerful tomographic census of the cosmic magnetic-energy density across cosmic time.

Abstract

We present a new approach for extracting information about cosmic magnetic fields using cross-correlations between extragalactic Faraday rotation measure (RM) catalogs and galaxy surveys. Specifically, we propose measuring the two-point cross-correlation between RM squared, ${\rm RM}^2$, towards background sources and the projected density field of foreground galaxies, $\langle {\rm RM}^2 \times {\rm g} \rangle$, as a function of transverse separation. This statistic is analogous to the ''projected fields'' estimator used for the kinetic Sunyaev-Zel'dovich (kSZ) effect, $\langle {\rm kSZ}^2 \times {\rm g} \rangle$. Our estimator avoids contamination, and is also free from the noise bias that arises when correlating the absolute value of the RMs with galaxies. Moreover, by binning in foreground galaxy redshifts, $\langle {\rm RM}^2 \times {\rm g} \rangle$ enables a tomographic reconstruction of the redshift evolution of large-scale cosmic magnetic fields. We model this statistic using the Illustris-TNG cosmological magnetohydrodynamic simulations and compare with approximate analytic predictions. We show that $\langle {\rm RM}^2 \times {\rm g} \rangle$ can be related to a bispectrum involving two copies of the electron-density--weighted magnetic field strength and one of the galaxy overdensity. In Illustris-TNG, the effective field strength is primarily set by the magnetic field amplitudes within the inner regions of galaxy-hosting dark matter halos. It increases towards low redshift, driven by dynamo amplification and magnetized outflows. Our forecasts suggest that $\langle {\rm RM}^2 \times {\rm g} \rangle$ is detectable at high significance with current galaxy surveys and future RM catalogs from the SKA, offering a tomographic probe of large-scale magnetic fields across cosmic time.

Figures (12)

• Figure 1: Projected fields in TNG300-3 at $z=0$. In each panel, the fields are projected along the full length of the simulation box, $L_{\rm box} = 205$$h^{-1}$ Mpc, and the slice widths match $L_{\rm box}$. Top left: the projected halo overdensity field. Top right: the electron overdensity field. Bottom left: the absolute value of the projected line-of-sight component of the magnetic field. Bottom right: the RM$^2$ contributions from magnetized plasma across the coeval box. The projected maps illustrate how the large-scale dark matter halo distribution, the electron density, magnetic field strength, and RM$^2$ fields all trace the same underlying distribution of large-scale structure. This motivates measuring cross-correlations between the halo (or galaxy) distribution and RM$^2$ measurements to infer some of the statistical properties of these fields. The ranges on the RM$^2$ and magnetic field strength color bars encapsulate 5%-95% of the simulation pixels.
• Figure 2: Schematic illustration of the stacking method and radial binning used in computing the coeval cross-correlation functions. The radial bins increase logarithmically from the halo center out to half of the box size (102.5 Mpc/$h$). Left: The RM$^2$ grid stacked around 391,144 halos from TNG300-3 at $z = 0$. Middle: The radial binning employed, showing rings from $r$ to $r+dr$. Right: Zoomed-in view of the stacked grid and inner radial bins near the stacking center. The excess $\rm{RM}^2$ around the stacked simulated halos is visible by eye. Measuring this signal in upcoming data sets as a function of scale, redshift, and potentially galaxy properties should help extract a wealth of information about cosmic magnetic fields.
• Figure 3: Two-point cross-correlation functions between the RM and halo overdensity fields, computed using two estimators: $w_{\mathrm{RM}^2,{\rm g}}(r_\perp;z)$ ( left panels) and $w_{|\mathrm{RM}|,{\rm g}}(r_\perp;z)$ ( right panels). Here we show coeval cross-correlations in narrow redshift bins (see text) from $z=0$ to $z=4$. Note that the scales considered here lie beyond the virial radius of most of the halos included in the stacks, and so the signal here reflects the large-scale correlated excess ${\rm RM}^2$ (or $|\mathrm{RM}|$ around the stacked halos. The cross-correlations increase strongly with decreasing redshift, as we will discuss. The two estimators show broadly similar scale dependence and redshift evolution trends.
• Figure 4: Power spectrum of the electron-density--weighted line-of-sight magnetic field as a function of redshift. Here we take only the $q_\parallel=0$ modes of this field, because line-of-sight Fourier modes are suppressed in projection. The quantity plotted shows the contribution to the electron-weighted magnetic field strength per $d\,\rm{ln} \,q_\perp$. The integral of this power spectrum, over all $q_\perp$, largely governs the amplitude of $w_{\mathrm{RM}^2,{\rm g}}(r_\perp;z)$. In Illustris-TNG the electron-density--weighted magnetic field strength increases strongly towards low redshift.
• Figure 5: The (3D) electron density–halo cross-power spectrum ( left panel) and the real-space projected electron-halo two-point cross-correlation function ( right panel). These functions characterize spatial correlations between the free electron and halo distributions, and largely determine the large-scale shape of the $w_{\mathrm{RM}^2,{\rm g}}(r_\perp;z)$ correlation function. We extrapolate the simulated 3D electron density-halo cross-power spectrum to large scales (beyond the fundamental mode of the simulation box) assuming a linear biasing model (dashed lines). The projected electron-halo cross-correlation function is computed based on the cross-power in the left panel, and the linear theory extrapolation to low $k$. The amplitude of the projected electron-halo correlation function increases towards low redshift.