# Beyond second-order convergence in simulations of magnetised binary neutron stars with realistic microphysics

## TL;DR

This paper demonstrates that high-order numerical methods improve the accuracy of simulating magnetised binary neutron star mergers, especially in gravitational-wave phase and ejecta modeling, compared to traditional second-order approaches.

## Contribution

The study introduces a fourth-order conservative finite-difference scheme for neutron star merger simulations with microphysics, showing enhanced convergence and more accurate ejecta and magnetic energy evolution.

## Key findings

- Higher than second-order convergence achieved in inspiral and post-merger phases.
- Second-order schemes overestimate proton-rich ejecta, affecting kilonova modeling.
- Low-resolution simulations with fourth-order schemes accurately resolve magnetic energy growth.

## Abstract

We investigate the impact of using high-order numerical methods to study the merger of magnetised neutron stars with finite-temperature microphysics and neutrino cooling in full general relativity. By implementing a fourth-order accurate conservative finite-difference scheme we model the inspiral together with the early post-merger and highlight the differences to traditional second-order approaches at the various stages of the simulation. We find that even for finite-temperature equations of state, convergence orders higher than second order can be achieved in the inspiral and post-merger for the gravitational-wave phase. We further demonstrate that the second-order scheme overestimates the amount of proton-rich shock-heated ejecta, which can have an impact on the modelling of the dynamical part of the kilonova emission. Finally, we show that already at low resolution the growth rate of the magnetic energy is consistently resolved by using a fourth-order scheme.