| Abstrakt: |
Magnetically polarized matter in astrophysical systems may be relevant in some magnetically dominated regions, for instance, in the funnel that is generated in some highly magnetized disk configurations where relativistic jets are thought to spread, or in pulsars where the fluids are subject to very intense magnetic fields. With the aim of dealing with magnetic media in the astrophysical context, we present for the first time the conservative form of the ideal general relativistic magnetohydrodynamics (GRMHD) equations with a non-zero magnetic polarization vector mμ. Then, we follow the Anile method to compute the eigenvalue structure in the case where the magnetic polarization is parallel to the magnetic field, and it is parameterized by the magnetic susceptibility χm. This approximation allows us to describe diamagnetic fluids, for which χm < 0, and paramagnetic fluids, for which χm > 0. The theoretical results were implemented in the CAFE code to study the role of magnetic polarization in several one-dimensional Riemann problems. We found that independent of the initial condition, the first waves that appear in the numerical solutions are faster in diamagnetic materials than in paramagnetic ones. Moreover, the constant states between the waves change notably for different magnetic susceptibilities. All of these effects are more appreciable if the magnetic pressure is much higher than the fluid pressure. Additionally, with the aim of analyzing magnetic media in a strong gravitational field, we carry out for the first time a test of the magnetized Michel accretion of a magnetically polarized fluid. With this test, we found that the numerical solution is effectively maintained over time (t > 4000), and that the global convergence of the code is ≳2 for χm ≲ 0.005 for all magnetic field strengths β we considered. Finally, when χm = 0.008 and β ≥ 10, the global convergence of the code is reduced to a value between the first and second orders. [ABSTRACT FROM AUTHOR] |
