General Relativistic Resistive Magnetohydrodynamics in Neutron Stars: Development and Application of the MIR Code

On August 17, 2017, a gravitational wave (GW) signal (GW170814), produced by two neutron stars spiraling closer to each other and finally merging, was detected by the Advanced Virgo detector and the two Advanced LIGO detectors. This is the first GW observation confirmed by non-gravitational means, setting a real milestone in the history of multi-messenger astronomy. The post-merger GW emission depends on the magnetic field strength of the remnant. In General Relativity, describing the evolution of a magnetized fluid requires simultaneously solving the Einstein, Euler, and Maxwell equations. For this purpose, several numerical codes have been developed to date. These codes operate in the so-called Ideal MHD (magnetohydrodynamics) regime, where the fluid is assumed to be a perfect conductor. However, the combination of fast rotations and intense magnetic fields can generate anisotropies in the distribution of currents, thus dropping the conditions of validity of the Ideal MHD regime. This can lead to the development of instabilities that can increase the effective resistivity of the plasma. An optimal choice to include resistive effects in numerical simulations is the so-called IMEX (IMplicit EXplicit) scheme, which can guarantee stability in reasonable computation times. The PhD research project’s main goal was to develop (from scratch) a new numerical code (MIR) capable of solving the equations of the general relativistic resistive MHD. The code has been validated against standard test cases and yields the expected results. Finally, the code has been used to perform the first study of a bar-mode instability in the resistive regime, which helps understand the effects of electrical resistivity in a post-merger-like configuration and the evolution of the magnetic field during a strongly dynamic evolution of the matter component.