Polarization measurements at low radio frequencies allow detection of small Faraday rotation measures caused by regular magnetic fields in galaxies and in the foreground of the Milky Way. The galaxy M31 was observed in two overlapping pointings with the Westerbork Synthesis Radio Telescope (WSRT) resulting in ~4 resolution in total intensity and linearly polarized emission. The frequency range 310-376 MHz was covered by 1024 channels which allowed the application of RM synthesis. We derived a data cube in Faraday depth and compared two symmetric ranges of negative and positive Faraday depths. This new method avoids the range of high instrumental polarization and allows the detection of very low degrees of polarization. For the first time, diffuse polarized emission from a nearby galaxy is detected below 1 GHz. The degree of polarization is only 0.21 +/- 0.05 %, consistent with extrapolation of internal depolarization from data at higher radio frequency. A catalogue of 33 polarized sources and their Faraday rotation in the M31 field is presented. Their average depolarization is DP(90,20) = 0.14 +/- 0.02, 7 times stronger depolarized than at 1.4 GHz. We argue that this strong depolarization originates within the sources, e.g. in their radio lobes, or in intervening galaxies on the line of sight. On the other hand, the Faraday rotation of the sources is mostly produced in the foreground of the Milky Way and varies significantly across the ~9 square degree M31 field. As expected, polarized emission from M31 and extragalactic background sources is much weaker at low frequencies compared to the GHz range. Future observations with LOFAR, with high sensitivity and high angular resolution to reduce depolarization, may reveal diffuse polarization from the outer disks and halos of galaxies.
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