Magnetic fields in galaxy clusters in the Square Kilometre Array era

A new era for radio astronomy is coming. The Square Kilometre Array, with its unprecedented capabilities will revolutionize our knowledge of the Universe, opening new challenges to many fields of research: from astronomy to technology, passing by the big data problem. As astrophysicists, to be ready for this revolution, we have to understand how to manage in the best way the data that the SKA will collect. The purpose of this work is to address what is the origin of magnetic fields in the Universe and it is mainly focussed on the characterization of magnetic fields in galaxy clusters. These are ideal systems to study the properties of large scale magnetic fields as well as the relativistic particles that populate the intracluster medium. Indeed, direct manifestations of the aforementioned non-thermal components in clusters are given by the diffuse synchrotron sources named radio haloes, relics, and mini-haloes. All of these sources present low-surface brightness that makes them very elusive for the current radio telescopes. With the high sensitivity level expected for the SKA, the number of detected diffuse synchrotron sources will grow giving us the chance to characterize intracluster magnetic fields in a bigger sample of clusters. Going to kpc scales, polarized discrete radio sources play a decisive role in determining the strength and the structure of large scale magnetic fields. The Faraday rotation of the polarization plane of these sources, caused by the passage through a magneto-ionic medium, depends on the medium itself and can be used to constrain the properties of the magnetic field responsible for the rotation. So far, this approach has been applied in a limited number of galaxy clusters but the expectations for the SKA are extremely promising. To investigate how the study of the diffuse and discrete sources can help to shed light on cosmic magnetism, I pursued a two approaches: on one side, I conducted and analysed radio observations of galaxy clusters to infer the properties of their non-thermal component, on the other side, I realized a framework to produce the polarized sky that the SKA will detect. The combination of these two approaches let us understand what are the best strategies to constrain large scale magnetic fields and it is the starting point to get prepared for the SKA.