Multi-tracer analysis of straight depolarisation canals in the
  surroundings of the 3C 196 field
  Faraday tomography of a field centred on the extragalactic point source 3C
196 with the LOw Frequency ARray (LOFAR) revealed an intertwined structure of
diffuse polarised emission with straight depolarisation canals and tracers of
the magnetized and multi-phase interstellar medium (ISM), such as dust and line
emission from atomic hydrogen (HI). This study aims at extending the
multi-tracer analysis of LOFAR data to three additional fields in the
surroundings of the 3C 196 field. For the first time, we study the
three-dimensional structure of the LOFAR emission by determining the distance
to the depolarisation canals. We use the Rolling Hough Transform to compare the
orientation of the depolarisation canals with that of the filamentary structure
seen in HI and, based on starlight and dust polarisation data, with that of the
plane-of-the-sky magnetic field. Stellar parallaxes from $Gaia$ complement the
starlight polarisation with the corresponding distances. Faraday tomography of
the three fields shows a rich network of diffuse polarised emission at Faraday
depths between $-10~{\rm rad~m^{-2}}$ and $+15~{\rm rad~m^{-2}}$. A complex
system of straight depolarisation canals resembles that of the 3C 196 field.
The depolarisation canals align both with the HI filaments and with the
magnetic field probed by dust. The observed alignment suggests that an ordered
magnetic field organises the multiphase ISM over a large area
($\sim$20$^{\circ}$). In one field, two groups of stars at distances below and
above 200 pc, respectively, show distinct magnetic-field orientations. These
are both comparable with the orientations of the depolarisation canals in the
same field. We conclude that the depolarisation canals likely trace the same
change of the magnetic field as probed by the stars, which corresponds to the
edge of the Local Bubble.
