Sardinia Radio Telescope observations of Abell 194: The intra-cluster magnetic field power spectrum

Aims. We study the intra-cluster magnetic field in the poor galaxy cluster Abell 194 by complementing radio data, at different frequencies, with data in the optical and X-ray bands. Methods. We analyzed new total intensity and polarization observations of Abell 194 obtained with the Sardinia Radio Telescope (SRT). We used the SRT data in combination with archival Very Large Array observations to derive both the spectral aging and rotation measure (RM) images of the radio galaxies 3C 40A and 3C 40B embedded in Abell 194. To obtain new additional insights into the cluster structure, we investigated the redshifts of 1893 galaxies, resulting in a sample of 143 fiducial cluster members. We analyzed the available ROSAT and Chandra observations to measure the electron density profile of the galaxy cluster. Results. The optical analysis indicates that Abell 194 does not show a major and recent cluster merger, but rather agrees with a scenario of accretion of small groups, mainly along the NE-SW direction. Under the minimum energy assumption, the lifetimes of synchrotron electrons in 3C 40 B measured from the spectral break are found to be 157 ± 11 Myr. The break frequency image and the electron density profile inferred from the X-ray emission are used in combination with the RM data to constrain the intra-cluster magnetic field power spectrum. By assuming a Kolmogorov power-law power spectrum with a minimum scale of fluctuations of Λmin= 1 kpc, we find that the RM data in Abell 194 are well described by a magnetic field with a maximum scale of fluctuations of Λmax= (64 ± 24) kpc. We find a central magnetic field strength of < B0> = (1.5 ± 0.2) μG, which is the lowest ever measured so far in galaxy clusters based on Faraday rotation analysis. Further out, the field decreases with the radius following the gas density to the power of η = 1.1 ± 0.2. Comparing Abell 194 with a small sample of galaxy clusters, there is a hint of a trend between central electron densities and magnetic field strengths.