Numerical methods for 3D magneto-rotational core-collapse supernova simulation with jet formation

摘要

The work presented in this thesis is devoted to the development ofuda numerical model for the three dimensional simulation of magneto-rotationaludcore-collapse supernovae (MHD-CCSNe) with jet formation.udThe numerical model then suggests that MHD-CCSNe naturally provide audpossible site for the strong rapid neutron capture process in agreement withudobservations of the early Galactic chemical evolution.ududIn the first part of this thesis, we develop several numerical methodsudand describe thoroughly their efficient implementations on currentudhigh-performance computer architectures.udWe develop a fast and simple computer code exttt{FISH} that solvesudthe equations of magnetohydrodynamics.udThe code is parallelized with an optimal combination of shared anduddistributed memory paradigms and scales to several thousands processesudon high-performance computer clusters.udWe develop a novel well-balanced numerical scheme for the Eulerudequations with gravitational source terms to preserve a discrete hydrostaticudequilibrium exactly.udBeing able to accurately represent hydrostatic equilibria is of particularudinterest for the simulation of CCSN, because a large part of the newlyudforming neutron star evolves in a quasi-hydrostatic manner.udWe include an approximate and computationally efficient treatment ofudneutrino physics in the form of a spectral leakage scheme.udIt enables us to capture approximately the most important neutrino coolingudeffects, which are responsible for the shock stall and for theudneutronisation of matter behind the shock.udThe latter is crucial for the nucleosynthesis yields.udTo fit into our multidimensional MHD-CCSN model, the spectral leakageudscheme is implemented in a ray-by-ray approach.ududIn the second part of this thesis, we apply our three-dimensionaludnumerical model to the study of the MHD-CCSN explosion mechanism.udWe investigate a series of models with poloidal magnetic field and varyingudinitial angular momentum distribution through the collapse, bounce andudjet formation phase.udFor all computed models, we investigate the process of magnetic fieldudamplification, angular momentum redisribution and the formation anduddriving mechanism of the bipolar outflow.ududIn a representative model we follow the jet for a longer time and largeruddistance.udWe find that the bipolar outflow features a significant amount of veryudneutron rich matter and is therefore a promising site for the rapidudneutron capture process (r-process).udThe computations show that under the prevailing conditions in the bipolarlyudejected matter the global solar r-process pattern could be reproduced.udThe computed amount of ejected matter and pecularity of the progenitorud(featuring large enough rotation and magnetic fields to induce MHD-CCSNudexplosion mechanism) indicates that only a fraction (perhaps 0.1 - 1%) ofudCCSN explode with the MHD mechanism.udThis is also in agreement with the observed large star-to-star scatter ofudr-process element abundances in very old halo stars indicating theudscarcity of these events in the early Galactic chemical evolution.udud