Magnetorotational instability in eccentric disks

TL;DR

This paper investigates whether the magnetorotational instability (MRI), crucial for accretion in circular disks, also operates in eccentric disks, revealing mode behaviors, growth conditions, and the significance of pericenter regions.

Contribution

It provides the first linear analysis of MRI in eccentric disks, identifying mode families, growth conditions, and the role of orbital eccentricity in MRI behavior.

Findings

Two MRI mode families identified with different dominant components.

MRI growth is similar to circular disks for certain parameters, declining with eccentricity.

MRI and angular momentum transport are most active near pericenter.

Abstract

Eccentric disks arise in such astrophysical contexts as tidal disruption events, but it is unknown whether the magnetorotational instability (MRI), which powers accretion in circular disks, operates in eccentric disks as well. We examine the linear evolution of unstratified, incompressible MRI in an eccentric disk orbiting a point mass. We consider vertical modes of wavenumber $k$ on a background flow with uniform eccentricity $e$ and vertical Alfv\'en speed $v_\mathrm A$ along an orbit with mean motion $n$. We find two mode families, one with dominant magnetic components, the other with dominant velocity components; the former is unstable at $(1-e)^3f^2\lesssim3$, where $f\equiv kv_\mathrm A/n$, the latter at $e\gtrsim0.8$. For $f^2\lesssim3$, MRI behaves much like in circular disks, but the growth per orbit declines slowly with increasing $e$; for $f^2\gtrsim3$, modes grow by parametric amplification, which is resonant for $0<e\ll1$. MRI growth and the attendant angular momentum and energy transport happen chiefly near pericenter, where orbital shear dominates magnetic tension.