Binary neutron star mergers with SPHINCS_BSSN: temperature-dependent equations of state and damping of constraint violations

Abstract: Neutron star mergers hold the key to several grand challenges of contemporary (astro-)physics. In view of the upcoming next generation of ground-based detectors, it is crucial to keep improving theoretical predictions to harvest the full scientific returns from these investments. We introduce here a substantial update of our Lagrangian numerical relativity code SPHINCS_BSSN. Apart from changing our unit system, we add constraint damping terms to the BSSN spacetime evolution equations. We demonstrate that this measure reduces, without noteworthy computational cost, the Hamiltonian constraint violations by more than an order of magnitude. We further implement contributions to thermal energy and pressure that are based on Fermi liquid theory and contain a parametrization of the Dirac effective mass. These terms can be combined with any cold equation of state, and they enhance the physical realism of our simulations and introduce a physics-based concept of a temperature. In a set of merger simulations, we demonstrate good agreement with other temperature-dependent numerical relativity simulations. We find that different parametrizations of the Dirac effective mass can translate into shifts of $\sim 150$ Hz in the dominant post-merger gravitational wave peak frequency.