The intergalactic magnetic field probed by a giant radio galaxy
  Cosmological simulations predict that an intergalactic magnetic field (IGMF)
pervades the large scale structure (LSS) of the Universe. Measuring the IGMF is
important to determine its origin (i.e. primordial or otherwise). Using data
from the LOFAR Two Metre Sky Survey (LoTSS), we present the Faraday rotation
measure (RM) and depolarisation properties of the giant radio galaxy
J1235+5317, at a redshift of $z = 0.34$ and 3.38 Mpc in size. We find a mean RM
difference between the lobes of $2.5\pm0.1$ rad/m$^2$ , in addition to small
scale RM variations of ~0.1 rad/m$^2$ . From a catalogue of LSS filaments based
on optical spectroscopic observations in the local universe, we find an excess
of filaments intersecting the line of sight to only one of the lobes.
Associating the entire RM difference to these LSS filaments leads to a gas
density-weighted IGMF strength of ~0.3 {\mu}G. However, direct comparison with
cosmological simulations of the RM contribution from LSS filaments gives a low
probability (~5%) for an RM contribution as large as 2.5 rad/m$^2$ , for the
case of IGMF strengths of 10 to 50 nG. It is likely that variations in the RM
from the Milky Way (on 11' scales) contribute significantly to the mean RM
difference, and a denser RM grid is required to better constrain this
contribution. In general, this work demonstrates the potential of the LOFAR
telescope to probe the weak signature of the IGMF. Future studies, with
thousands of sources with high accuracy RMs from LoTSS, will enable more
stringent constraints on the nature of the IGMF.
