Amplification and Dissipation of Magnetic Fields in Accreting Compact Objects

Magnetic fields play a crucial role in shaping the dynamics of accreting compact objects. Whether we consider the formation of a proto-neutron star during the gravitational collapse of a massive star or the accretion disk around a black hole after a compact binary merger, a key process that remains challenging to include in large-scale simulations is the amplification and dissipation of magnetic fields driven by turbulent fluid motions. Despite the enormous increase in computational power currently available, the large separation between all the relevant spatial and temporal scales still poses severe limits to what can be achieved with ideal fluid simulations. One way to tackle such issue is to rely on sub-grid models, which however need to be appropriately tuned in light of models probing the small-scale dynamics. In this work we present the current state-of-the-art of dynamo models in proto-neutron stars, which aim at describing the amplification of magnetar-like magnetic fields during the gravitational collapse of a massive star. We also review some of the works from the past few years that included turbulent dynamos in accretion disks around a black holes, relying on a mean-field formalism. Finally, we will present a recent study on polar jets with explicit turbulent resistivity which showcases the importance of employing highly accurate numerical schemes.