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 144MHz 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 similar to 8 at z similar to 2. 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 RRM0,f = 0.71 +/- 0.07 rad m(-2) and a magnetic field per filament of B-f = 32 +/- 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 RRM0, f supports the presence of diffuse baryonic gas in filaments. We also estimated a conservative upper limit of the filament magnetic turbulence of sigma(RRM0,f) = 0.039 +/- 0.001 rad m(-2), concluding that the ordered magnetic field component dominates in filaments.