In the era of gravitational wave and multimessenger astronomy of binary neutron stars accurate numerical modelling of neutron-star mergers and their remnants on long time-scales $\simeq 1\, \rm s$ has never been more important. The coincident detection of a gravitational-wave signal from a neutron-star merger (The LIGO Scientific Collaboration & The Virgo Collaboration 2017) and an accompanying electromagnetic counterpart in form of a short gamma-ray burst (LIGO Scientific Collaboration et al. 2017) and kilonova afterglow (Kasen et al. 2017; Drout et al. 2017) has established a firm connection with electromagnetic counterparts and highlights the need for multiphysics modelling of neutron-star mergers. A neutron-star merger consists of several stages starting from the late inspiral, where accurate numerical waveforms are needed to calibrate analytical models for waveforms, through merger (Kawaguchi et al. 2018; Nagar et al. 2018; Dietrich et al. 2019), which requires sophisticated microphysics in terms of finite-temperature equations of state (EOS) satisfying recent observational constraints (Annala et al. 2018; Most et al. 2018; Tews, Margueron & Reddy 2018; Burgio et al. 2018; Raithel, Özel & Psaltis 2018) until the post-merger phase where neutrino and magnetic viscosity can drive large amounts of mass ejection (Just et al. 2015; Siegel & Metzger 2017, 2018; Fernández et al. 2019; Fujibayashi et al. 2018), that are needed to make a connection to the kilonova afterglow produced by the decay of heavy elements in the matter outflow. The modelling of this complicated multiphysics system requires both the use of numerical relativity (Baiotti & Rezzolla 2017; Duez & Zlochower 2019) and of an accurate modelling of the fluid, the electromagnetic fields as well as the microphysics. Considerable effort has been placed on improved and highly accurate methods to solve Einstein field equations numerically (Baumgarte & Shapiro 2010; Shibata 2016) and to couple them with high-order methods for relativistic hydrodynamics (Radice, Rezzolla & Galeazzi 2014a; Bernuzzi & Dietrich 2016). At the same time, mainly driven by an effort to model core-collapse supernovae, very sophisticated numerical schemes for neutrino transport have been developed (Ruffert, Janka & Schaefer 1996; Buras et al. 2006; Shibata et al. 2011; Sumiyoshi & Yamada 2012; Foucart et al. 2015; Just et al. 2015). When considering the late stages of the evolution of the system not only is it important to account for the various relevant physics contributions, such as neutrino interactions, but it is also crucial to understand how numerical errors at finite-numerical resolution accumulate over time. This is even highlighted by the fact that current simulations of neutron-star mergers sometimes show non-convergent behaviour in the magnetic field evolution (Endrizzi et al. 2016; Ciolfi et al. 2017) even when small resolution changes are used. Notwithstanding, that with current computational efficiencies and available resources not even all relevant physical scales involving magnetic turbulence can be resolved (Kiuchi et al. 2015b, 2018), studying the late-time evolution of the remnants accretion disc is not only feasible but has been the subject of recent investigations (Siegel & Metzger 2017, 2018; Fernández et al. 2019). While all such simulations so far have used traditional second-order accurate finite-volume schemes to model the evolution of the general-relativistic magnetohydrodynamics system (GRMHD), earlier works have already indicated the benefit of using more accurate high-order methods in this context (Del Zanna et al. 2007; Tchekhovskoy, McKinney & Narayan 2007; Radice et al. 2014a), while even more recent studies have already started to consider advanced finite-element approaches (Kidder et al. 2017; Fambri et al. 2018). Taking an intermediate approach similar to Del Zanna et al. (2007), McCorquodale & Colella (2011), Chen, Tóth & Gombosi (2016), and Felker & Stone (2018), we will consider the impact of using a fourth-order accurate numerical scheme to model the merger of magnetized binary neutron stars and show the advantages gained when additionally finite-temperature effects and neutrino cooling are included.
Citation: Burgio et al. 2018
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