Improving the treatment of AGN feedback and accretion in galaxy formation simulations.

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X-ray observations indicate that a significant fraction of galaxy clusters have short central cooling times. The degree of star formation and amount of cold gas that should then be present is not observed, however, implying that heating mechanisms are at work. Feedback from the central AGN in the form of relativistic jets is expected to play a dominant role here, however the relative importance of mechanisms through which the feedback energy couples to the ICM is still an open question.The complex nature of the interactions between the physical processes manifest in these clusters makes analytic models intractable. This puts galaxy formation simulations in a unique position as they provide insight into how heating and cooling are regulated by AGN jet feedback in a realistic environment. The scales on which the relevant processes act, however, span many orders of magnitude. Jets are launched close to the BH horizon and propagate to large distances. Gas is funnelled in from the ICM where, ultimately, it is micro-scale processes in the accretion disc that determine the rate at which this gas feeds the BH. The dynamic range required to simulate this from first-principles is therefore computationally unfeasible making it necessary to invoke so-called "sub-grid" models.During my PhD studies, I aim to advance current understanding of AGN accretion and feedback as well as the mechanisms by which this feedback energy couples to the ICM, which I will do by developing new methods to improve their modelling in hydrodynamic simulations of galaxy formation.Using the state-of-the-art moving-mesh code, AREPO, I will take advantage of: a) A new AGN accretion model whereby super-Lagrangian refinement techniques allow mass and angular momentum flows to be followed all the way from galaxy scales down to the outer edge of the accretion disc. The BH mass and spin are then tracked self-consistently by coupling this with a sub-grid thin alpha-disc. b) A new AGN jet model which also utilises super-Lagrangian refinement, here enabling the injection of the jet on parsec scales and its subsequent evolution to be followed to hundreds of kiloparsecs.I will use these models as a framework to couple the jet to the BH spin, taking advantage of the Blandford-Znajek (BZ) mechanism to self-consistently predict its power. So, for the first time, we will be in a position to study how feedback from a BZ jet affects structure on cluster scales.I will first test the model it in an isolated circumnuclear disc, accurately following the evolution of the sub-grid accretion disc, the BH mass and spin as well as the propagation of the jet. Following on from this, I will consider major mergers of isolated galaxy clusters harbouring accreting supermassive BHs at their centre to study how jet power and orientations changes during the merging event and if this can explain the occurrence of X-shaped radio galaxies. As a final step, I will perform fully self-consistent cosmological simulations of cluster formation with a BZ jet to study the cosmic evolution of radio power of these sources and a possible transition from FRII to FRI radio galaxies. My simulations will allow to make unique predictions for a wealth of upcoming radio data including the forecasts for the SKA telescope.