Constraints on magnetic fields and particle acceleration in the inter-cluster bridge A399-A401

Galaxy clusters are the most massive gravitationally bound structures in the Universe. Diffuse non-thermal emission coming from these objects has unveiled complex internal structures and traced the presence of energetic particles and magnetic fields. However, many aspects of this cluster environment are still unclear, in particular regarding the magnetic field structure and origins. Beyond the cluster environment, elongated filaments of matter (galaxies, dark matter and magnetized gas) are located between clusters, forming an even larger unbound structure, known as the Cosmic Web. Galaxy clusters are located at the nodes of this web, and interact with each other through this network with matter accretion and merger events. With the advent of low frequency studies new features of this large scale structure have been discovered. In particular, recent observations have detected filaments of diffuse synchrotron emission connecting two merging galaxy clusters, Abell 399 and Abell 401 (Govoni et al., 2019). Such result is the first observational evidence of radio emission coming from an inter-cluster region, tracing the presence of relativistic particles and magnetic fields in-between clusters. In this thesis, we have used new LOFAR observations to study the polarized emission in the A399-A401 inter-cluster region. The non-detection of polarized emission from the bridge lead us to derive upper limits on it and comparing our results with a shock-driven emission model proposed to explain this peculiar object. The comparison between simulated and observational results allowed us to provide, for the first time, constrains on the magnetic field in inter-cluster region