Abstract

Magnetic fields in the Universe are found in almost all studied environments. In particular, their presence in the inter-galactic medium and in the intra-cluster medium is confirmed by diffuse radio emission as well as by observations of Faraday Rotation Measures towards polarized radio sources within or behind the magnetized medium. Besides the observations, their dynamical importance in astrophysical systems is poorly constrained, therefore there are still plenty of processes in which the role of magnetic fields are not fully understood. Astrophysical systems are complex and highly nonlinear. Therefore, numerical simulations have demonstrated to be a useful tool to study those problems. However, the inclusion of magnetic fields in numerical implementations is not easy to achieve. Mainly because of the difficulties to keep the ∇ · B constraint low, and to have a stable implementation in different circumstances. We study and developed a cosmological MHD code in SPH. We study different possible schemes to regularize the magnetic field, and avoid instabilities. Those schemes included the use of Euler potentials to build the magnetic field, as well as cleaning schemes for the numerical ∇ · B errors. We studied the magnetic field evolution in the context of cosmological structure formation of galaxy clusters. We compare different numerical schemes leading us to the conclusion that the ∇ · B terms do not drive the evolution and growth of the magnetic field in galaxy clusters. We made synthetic rotation measure maps and study the reversals of the magnetic field in comparison with observations. The comparison between observations and high resolution simulations, suggests that the physics may be described by a multi scale turbulence model. This means that the turbulent dynamo driven by the cosmological cluster formation process works effectively, reproducing basic properties from observations, even to details shown in structure functions and converging to the observation when we increase the resolution. We clearly demonstrates that using advanced schemes together with very high resolution allow to probe the properties of the ICM. Additionally, we investigate the magnetic fields and their relation with the cosmic structure in which they are embedded. In general, the observed rotation measure signal is strongly dominated by denser regions (e.g. those populated by galaxy clusters and groups), and in unclear how is their transition to low density regions, because there is difficult to acquire direct magnetic field information of those regions. Therefore statistical tools, such as correlation functions have to be used. To do so, we use cosmological simulations and try to mimic all the possible observation biases to constrain actual measurements. We find that the shape of the cross-correlation function using a normalized estimator (in absence of any noise or foreground signal) nicely reflects the underlying distribution of magnetic field within the large scale structure. However, current measurement errors suppress the signal in such a way that it is impossible to relate the amplitude of the cross-correlation function to the underlying magnetization of the large scale structure