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The new generation of broad-band radio continuum surveys will provide largedata sets with polarization information. New algorithms need to be developed toextract reliable catalogs of linearly polarized sources that can be used tocharacterize those sources and produce a dense rotation measure (RM) grid toprobe magneto-ionized structures along the line of sight via Faraday rotation.The aim of the paper is to develop a computationally efficient and rigorouslydefined source-finding algorithm for linearly polarized sources. We used acalibrated data set from the LOw Frequency ARray (LOFAR) at 150 MHz centered onthe nearby galaxy M51 to search for polarized background sources. With a newimaging software, we re-imaged the field at a resolution of 18''x15'' andcataloged a total of about 3000 continuum sources within 2.5 degrees of thecenter of M51. We made small Stokes Q and U images centered on each sourcebrighter than 100 mJy in total intensity (201 sources) and used RM synthesis tocreate corresponding Faraday cubes that were analyzed individually. For eachsource, the noise distribution function was determined from a subset ofmeasurements at high Faraday depths where no polarization is expected; thepeaks in polarized intensity in the Faraday spectrum were identified and thep-value of each source was calculated. Finally, the false discovery rate methodwas applied to the list of p-values to produce a list of polarized sources andquantify the reliability of the detections. We also analyzed sources fainterthan 100 mJy but that were reported as polarized in the literature at at leastanother radio frequency. Of the 201 sources that were searched forpolarization, 6 polarized sources were detected confidently (with a falsediscovery rate of 5 percent). This corresponds to a number density of 1polarized source per 3.3 square degrees, or 0.3 source/square degree.[Abridged]

Reliable detection and characterization of low-frequency polarized sources in the LOFAR M51 field