Riemann Solvers and Alfven Waves in Black Hole Magnetospheres

TL;DR

This paper introduces new Riemann solvers, HLLI and MuSIC, designed to reduce numerical dissipation of Alfven waves in black hole magnetosphere simulations, improving the accuracy of modeling plasma behavior near rotating black holes.

Contribution

The paper presents novel one-dimensional and multidimensional Riemann solvers, HLLI and MuSIC, specifically tailored to minimize Alfven wave dissipation in relativistic magnetosphere simulations.

Findings

HLLI effectively incorporates Alfven and contact discontinuities.

MuSIC enables low dissipation propagation of Alfven waves in multiple dimensions.

Higher order schemes further reduce numerical dissipation.

Abstract

In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.