Magnetorotational instability in eccentric disks

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 and threaded with a vertical background magnetic field. Much like in circular disks, MRI grows when the field is weak, but the growth per orbit declines slightly with increasing eccentricity; unlike in circular disks, MRI grows in highly eccentric disks even when the field is extremely strong. Eccentric MRI can be understood either as the competition between orbital shear and magnetic tension; or as the parametric destabilization of magnetic modes by eccentric orbital motion, which is resonant at small eccentricities.