Numerical evolution of binary neutron star mergers

Binary neutron star mergers feature some of the most extreme physical conditions known throughout the universe: densities exceeding that of atomic nuclei, temperatures in excess of 1011K, and speeds approaching 0.5c. Due to these conditions, they provide an excellent test bed for theoretical physics at the limit of our current understanding, and beyond. In order to learn about these phenomena through observation we need to first obtain an idea of what sorts of signals we should be looking for, and then we need to determine what we can learn from analysing this data. Numerical simulations of neutron star mergers can give us answers to these questions. However, binary neutron star mergers pose a significant computational challenge: they involve physics on greatly differing length scales, and systems of highly non-linear coupled partial differential equations. In this thesis we present state-of-the-art simulations of binary neutron star mergers. We cover: the theoretical background of these simulations, the software we use to perform simulations, analysis and visualisation techniques used for studying simulations, our work on the extension of the simulations to include new physics, and results from such simulations. Through these simulations we explore concepts central to the extraction of information from multi-messenger observation of binary neutron star mergers, namely the reactions between protons, neutrons, and electrons in neutron star fluid, the equilibrium they work to establish, and the bulk viscosity resulting from out-of-equilibrium conditions. We show these reactions affect not only electromagnetic and neutrino radiation observed in merger simulations, they need to be implemented to ensure accurate gravitational waveform templates are produced for third generation detectors. We go on to show that the notion of equilibrium between species in the fluid is complex, depending on both local conditions (particularly the temperature of the fluid), and also on the behaviour of surrounding matter. Finally, we discuss the difficulty in implementing reactions in simulations, with a view of modelling bulk viscosity. We show that the timescales involved vary over several orders of magnitude, with the slower behaviour being easily resolvable in current simulations, and the fast behaviour being far out of reach. An approach that includes the effects of both resolvable and unresolvable reactions, with a consistent treatment of the crossover, is therefore needed to properly model bulk viscosity