Riemann solvers and Alfven waves in black hole magnetospheres

Area of Science:

• Plasma physics
• Astrophysical fluid dynamics
• Numerical relativity

Background:

• Plasma inflowing into rotating black hole magnetospheres must cross the inner Alfven critical surface (IACS).
• Inside the IACS, Alfven waves propagate inward, and the ergosphere is predominantly located.
• Alfven wave polarization dictates charge and transverse momentum flux, crucial for black hole magnetosphere dynamics.

Purpose of the Study:

• To minimize numerical dissipation of Alfven waves in relativistic simulations of black hole magnetospheres.
• To ensure accurate simulation of Goldreich-Julian charge density and Alfvenic information propagation.
• To develop advanced numerical methods for handling Alfven waves.

Main Methods:

• Formulation of a one-dimensional Riemann solver (HLLI) incorporating Alfven and contact discontinuities.
• Development of a multidimensional Riemann solver (MuSIC) for low-dissipation Alfven wave propagation.
• Cataloguing the importance of higher-order schemes in reducing numerical dissipation.

Main Results:

• The HLLI and MuSIC Riemann solvers enable low-dissipation propagation of Alfven waves.
• Numerical dissipation can hinder the accurate attainment of Goldreich-Julian charge density.
• Dissipated Alfvenic information can propagate outward, irrespective of the IACS.

Conclusions:

• The developed HLLI and MuSIC solvers are crucial for accurate relativistic numerical simulations of black hole magnetospheres.
• Minimizing numerical dissipation is essential for correctly simulating plasma behavior and charge density.
• Higher-order numerical schemes are vital for reducing Alfven wave dissipation.