Simulating neutron star mergers with the Lagrangian Numerical Relativity code SPHINCS_BSSN

Abstract: We present the first neutron star merger simulations performed with the newly developed Numerical Relativity code SPHINCS_BSSN. This code evolves the spacetime on a mesh using the BSSN formulation, but matter is evolved via Lagrangian particles according to a high-accuracy version of general-relativistic Smooth Particle Hydrodynamics (SPH). Our code contains a number of new methodological elements compared to other Numerical Relativity codes. The main focus here is on the new elements that were introduced to model neutron star mergers. These include a) a refinement (fixed in time) of the spacetime-mesh, b) corresponding changes in the particle--mesh mapping algorithm and c) a novel way to construct SPH initial data for binary systems via the recently developed "Artificial Pressure Method." This latter method makes use of the spectral initial data produced by the library LORENE, and is implemented in a new code called SPHINCS_ID. While our main focus is on introducing these new methodological elements and documenting the current status of SPHINCS_BSSN, we also show as a first application a set of neutron star merger simulations employing "soft" ($\Gamma=2.00$) and "stiff" ($\Gamma=2.75$) polytropic equations of state.