The intracluster 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 intracluster magnetic field in Abell 2345. This cluster hosts two radio relics that we detected in polarization with 1-2 GHz Jansky Very Large Array observations. X-ray XMM-Newton images show a very disturbed morphology. We derived the rotation measure (RM) of five polarized sources within similar to 1Mpc from the cluster centre applying the RMsynthesis. Both, the averageRMand the RMdispersion radial profiles probe the presence of intracluster 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 frommagneto-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) proportional to n(e)(r). The best model has a central magnetic field (within a 200 kpc radius) of 2.8 +/- 0.1 mu G. The average magnetic field at the position of the eastern relic is similar to 0.3 mu G, a factor 2.7 lower than the equipartition estimate.