The intra-cluster magnetic field in the double relic galaxy cluster
  Abell 2345
  Magnetic fields are ubiquitous in galaxy clusters, yet their radial profile,
power spectrum, and connection to host cluster properties are poorly known.
Merging galaxy clusters hosting diffuse polarized emission in the form of radio
relics offer a unique possibility to study the magnetic fields in these complex
systems. In this paper, we investigate the intra-cluster magnetic field in
Abell 2345. This cluster hosts two radio relics that we detected in
polarization with 1-2 GHz JVLA observations. X-ray XMM-Newton images show a
very disturbed morphology. We derived the Rotation Measure (RM) of five
polarized sources within $\sim$ 1 Mpc from the cluster center applying the RM
synthesis. Both, the average RM and the RM dispersion radial profiles probe the
presence of intra-cluster magnetic fields. Using the thermal electron density
profile derived from X-ray analysis and simulating a 3D magnetic field with
fluctuations following a power spectrum derived from magneto-hydrodynamical
cosmological simulations, we build mock RM images of the cluster. We
constrained the magnetic field profile in the eastern radio relic sector by
comparing simulated and observed RM images. We find that, within the framework
of our model, the data require a magnetic field scaling with thermal electron
density as $B(r)\propto n_e(r)$. The best model has a central magnetic field
(within a 200 kpc radius) of $2.8\pm0.1$ $\mu$G. The average magnetic field at
the position of the eastern relic is $\sim$0.3 $\mu$G, a factor 2.7 lower than
the equipartition estimate.
