Improving numerical simulations of binary neutron star mergers (BNSM) is essential for advancing our understanding of and ability to interpret observations of these events. We demonstrate that smoothed particle hydrodynamic simulations of BNSM yield differing outcomes for identical merger events. This thesis is the first study to explore these variations, considering the possibility that they may be physical stochastic effects arising from small initial perturbations. We perform simulations of a 1.35-1.35 solar mass binary system with the same physical and numerical setup and discuss the observed variation in ejecta properties and the post-merger gravitational wave signal. We find an antiproportional correlation between the ejecta mass and the amplitude of the main feature fₚₑₐₖ of the gravitational wave frequency spectrum. We show that these fluctuations depend on how the double core structure evolves after merging. Our simulations do not yield a reduction of these variations when increasing the resolution, which might be an indication that these fluctuations are a physical effect. To make reliable predictions for the electromagnetic signal of merger events, it is necessary to evolve the mass-outflows on timescales which are significantly longer than the merger itself. Over this time, the ejecta dilutes and cools down over several orders of magnitude. We present a method to extend tabulated equation of states (EoS) to encompass lower rest-mass densities and temperatures. We investigate the issue that outflowing matter evolve towards negative internal energies in regions of low resolution in our simulations. We improve the discretization of the general-relativistic energy evolution equation to reduce the occurrence of this issue. Utilizing the extended EoS and the improved discretization of the energy equation, we perform a long-term BNSM simulation up to 250 milliseconds after merger. We estimate how much material reaches homologous expansion within this time. Our analysis indicates that the majority of the material expelled during the first 25 milliseconds nearly exhibits homologous expansion, and we estimate an upper bound of 10 % for the alteration in its radial velocity. For later ejecta, we observe that they attain a reduced velocity, requiring a duration on the order of seconds to reach homologous expansion. BNSM simulations of this length require a sufficient resolution of the expanding ejecta. We present a method to efficiently increase the resolution of BNSM ejecta in smoothed particle hydrodynamic simulations. We implement particle splitting, test different splitting criteria, and conduct a comparative study between simulations with and without particle splitting. Our findings indicate that the resolution of the BNSM ejecta can be enhanced by a factor of five using our proposed method while maintaining similar computational expenses.
Christian Schwebler (Wed,) studied this question.