Linear and nonlinear eccentric mode evolution in unstratified MHD discs

TL;DR

This paper develops a framework for studying the evolution of eccentric modes in unstratified magnetized discs, showing magnetic fields have minimal influence at certain strengths but can be enhanced by eccentricity, verified through 2D simulations.

Contribution

It introduces a new method for computing precessing eccentric modes in magnetized discs, useful for future instability and turbulence studies.

Findings

Magnetic field has negligible influence at MRI-relevant strengths.

Eccentric discs can significantly enhance magnetic field strength.

Simulated modes match theoretical expectations when adequately resolved.

Abstract

In this paper we develop a framework for studying unstratified, magnetised eccentric discs and compute uniformly precessing eccentric modes in a cylindrical annulus which provide convenient initial conditions for numerical simulations. The presence of a magnetic field in an eccentric disc can be described by an effective gas with a modified equation of state. At magnetic field strengths relevant to the magneto-rotational instability the magnetic field has negligible influence on the evolution of the eccentric disc, however the eccentric disc can significantly enhance the magnetic field strength over that in the a circular disc. We verify the suitability of these eccentric disc solutions by carrying out 2D simulations in RAMSES. Our simulated modes (in 2D) follow a similar evolution to the purely hydrodynamical modes, matching theoretical expectations, provided they are adequately resolved. Such solutions will provide equilibrium states for studies of the eccentric magneto-rotational instability and magnetised parametric instability in unstratified discs and are useful for exploring the response of disc turbulence on top of a fluid flow varying on the orbital timescale.