Magnetic field strength in cosmic web filaments

We used the Rotation Measure (RM) catalogue derived from the LOFAR Two-metre Sky Survey Data Release 2 (LoTSS DR2) at 144-MHz to measure the evolution with redshift of the extragalactic RM (RRM: Residual RM) and the polarization fraction ($p$) of sources in low density environments. We also measured the same at 1.4-GHz by cross-matching with the NRAO VLA Sky Survey RM catalogue. We find that RRM versus redshift is flat at 144-MHz, but, once redshift-corrected, it shows evolution at high significance. Also $p$ evolves with redshift with a decrement by a factor of $\sim$8 at $z\sim2$. Comparing the 144-MHz and 1.4-GHz data, we find that the observed RRM and $p$ are most likely to have an origin local to the source at 1.4-GHz, while a cosmic web filament origin is favoured at 144-MHz. If we attribute the entire signal to filaments, we infer a mean rest frame RRM per filament of RRM_{0,f} = 0.71 \pm 0.07 rad m^{-2} and a magnetic field per filament of B_f = 32 \pm 3 nG. This is in agreement with estimates obtained with a complementary method based on synchrotron emission stacking, and with cosmological simulations if primordial magnetic fields are amplified by astrophysical source field seeding. The measurement of an RRM_{0,f} supports the presence of diffuse baryonic gas in filaments. We also estimated a conservative upper limit of the filament magnetic turbulence of σ_{ RRM_{0,f}} =0.039 \pm 0.001 rad m^{-2}, concluding that the ordered magnetic field component dominates in filaments.