Reliable detection and characterization of low-frequency polarized
  sources in the LOFAR M51 field
  The new generation of broad-band radio continuum surveys will provide large
data sets with polarization information. New algorithms need to be developed to
extract reliable catalogs of linearly polarized sources that can be used to
characterize those sources and produce a dense rotation measure (RM) grid to
probe magneto-ionized structures along the line of sight via Faraday rotation.
The aim of the paper is to develop a computationally efficient and rigorously
defined source-finding algorithm for linearly polarized sources. We used a
calibrated data set from the LOw Frequency ARray (LOFAR) at 150 MHz centered on
the nearby galaxy M51 to search for polarized background sources. With a new
imaging software, we re-imaged the field at a resolution of 18''x15'' and
cataloged a total of about 3000 continuum sources within 2.5 degrees of the
center of M51. We made small Stokes Q and U images centered on each source
brighter than 100 mJy in total intensity (201 sources) and used RM synthesis to
create corresponding Faraday cubes that were analyzed individually. For each
source, the noise distribution function was determined from a subset of
measurements at high Faraday depths where no polarization is expected; the
peaks in polarized intensity in the Faraday spectrum were identified and the
p-value of each source was calculated. Finally, the false discovery rate method
was applied to the list of p-values to produce a list of polarized sources and
quantify the reliability of the detections. We also analyzed sources fainter
than 100 mJy but that were reported as polarized in the literature at at least
another radio frequency. Of the 201 sources that were searched for
polarization, 6 polarized sources were detected confidently (with a false
discovery rate of 5 percent). This corresponds to a number density of 1
polarized source per 3.3 square degrees, or 0.3 source/square degree.
[Abridged]
