Abstract
Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the relativistic case, this requires the numerical solution of a system of nonlinear equations. Although several approaches are available, none has proven completely reliable. A recent study comparing different methods showed that all can fail, in particular for the important case of strong magnetization and moderate Lorentz factors. Here, we propose a new robust, efficient, and accurate solution scheme, along with a proof for the existence and uniqueness of a solution, and analytic bounds for the accuracy. Further, the scheme allows us to reliably detect evolution errors leading to unphysical states and automatically applies corrections for typical harmless cases. A reference implementation of the method is made publicly available as a software library. The aim of this library is to improve the reliability of binary neutron star merger simulations, in particular in the investigation of jet formation and magnetically driven winds.
Highlights
General relativistic magnetohydrodynamic (GRMHD) simulations are an important tool to study many astrophysical scenarios involving neutron stars (NSs) and black holes (BHs)
Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a longstanding technical problem given by the need to recover fundamental variables from those variables that are evolved in time
We solved the technical problem of primitive variable recovery in relativistic ideal magnetohydrodynamic evolution codes via a new fully reliable scheme
Summary
General relativistic magnetohydrodynamic (GRMHD) simulations are an important tool to study many astrophysical scenarios involving neutron stars (NSs) and black holes (BHs). GRMHD simulations of BNS and NS-BH mergers, while considerably more complex and expensive because of the inclusion of magnetic fields, become necessary to properly address the problem Recent studies in this direction already provide important hints, supporting a scenario where the central engine is an accreting BH [14,15] while disfavoring the massive NS scenario [16]. This kilonova was observed in unprecedented detail, the interpretation in terms of specific ejecta components and their physical origin is still under debate In this case, numerical relativity simulations represent the ideal approach to fully understand the different mass ejection processes occurring in a BNS (or a NS-BH) merger. The equations for the primitive variable recovery are very different for resistive GRMHD Another complication is that in regions with strong magnetic fields but low mass density, movement of the matter becomes dominated by the field.
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