Post-merger Simulations of Neutron Star Systems with Improved Axisymmetryic Hydrodynamics

Simulations of binary neutron star (BNS) merger remnants are crucial to understanding processes like post-merger jet formation, gamma-ray burst, kilonova, and heavy element nucleosynthesis. Evolving the remnant accurately requires General Relativistic Magnetohydrodynamic (GRMHD) simulations, which are computationally expensive and challenging to carry out on a secular timescale. The Spectral Einstein Code (SpEC) can use the approximate axisymmetry of the BNS merger remnant, making it computationally cheaper and feasible to evolve on a second-timescale. In the past, we have implemented methods that remove non-smoothness close to the symmetry axis due to coordinate singularities but come at the cost of breaking the conservative form of hydrodynamic equations. Here, we present an improved implementation that preserves the conservative form and mitigates the non-smooth features. The remnant is also affected by angular momentum transport due to turbulence created by magnetohydrodynamic instabilities. These instabilities can act on different timescales and regions of the star, affecting outcomes like ejecta mass, ejecta speed, and the presence or absence of collapse. We discuss different momentum transport models for modeling these instabilities that can be a cheap and reasonable alternative to GRMHD simulations.