Measuring the magnetization profiles of galaxy groups and clusters

Magnetic fields are vital in determining the physical conditions of baryons in massive halos. They are, however, notoriously difficult to observe. This impacts problems from our understanding of galaxy formation, to the observed deficit in the amplitude of thermal Sunyaev-Zel'dovich (tSZ) power spectrum that affects cosmological inferences. Although Faraday rotation measures (RMs) offer a direct probe of magnetic fields, it weights magnetic fields by the free-electron density. Several probes of free electrons, including fast radio burst (FRB) dispersion measures (DMs) and kinematic SZ (kSZ) effect, are now maturing into precision tools. We combine RM$^2$ stacks from SPICE-RACS around DESI galaxy groups and ROSAT clusters with optical depth profiles constrained jointly by the FRB DM-redshift relation and the kSZ effect, and obtain 95% upper limits on the rms line-of-sight magnetic field of $<3.9$-$11.6~μ$G ($<2.3$-$6.4~μ$G) in groups (clusters) for a 10~kpc coherence length. Combining these with thermal pressure profiles inferred from tSZ-shear cross-correlations, we obtain 95% lower limits on the plasma $β$ of $>0.31$ ($>11$) in groups (clusters). Although current constraints are only limits, we forecast a first detection with larger datasets from the Deep Synoptic Array (DSA). We present the first forecast of the DSA RM grid density ($\sim365$ RMs deg$^{-2}$), which when combined with 10$^4$ FRBs would measure the field in groups to $3$-$13\%$ precision, compared to current constraints of $38$-$75\%$. Although the interpretation of current measurements remains challenging owing to depolarization along turbulent halo sightlines and the unknown coherence length, larger samples and DSA/Square Kilometer Array observations may resolve these uncertainties by measuring polarization-fraction profiles and the RM structure function using extended radio sources, respectively.