Accretion disks are both ubiquitous in astrophysics, and essential to many of the phenomenon observed in our universe. Appearing around young stars, compact objects like black holes, and even Saturn, astrophysical disks provide a host of interesting problems to consider. In my PhD, I focused on magnetohydrodynamic (MHD) oscillations and instabilities in accretion disks. Much of my recent and current work focuses on how these phenomena manifest in accretion disks which have been deformed to become eccentric.

Deformed disk dynamics

Accreting compact objects and stars do not exist in isolation, and many external influences likely induce deviations from the classical picture of a flat, circular disk. Tidal interaction with a companion star, for example, will cause streamlines to become eccentric. A misalignment of the spin axis of a black hole with the angular momentum of its surrounding accretion flow will cause the disc to become warped. While warp and eccentricity evolution itself has been studied in some detail, many of the phenomena which the long-lived deformations in turn excite have yet to be fully characterized.

Elliptical streamlines in an eccentric disk, overlaid
on top of a color-map showing the radial velocity
in the flow.

Diskoseismic oscillations

Trapped oscillations excited in relativistic disks around low-mass black holes present one potentially observable consequence of disc distortion. High-frequency quasi-periodic oscillations (HFQPOs) seen in the emission from black hole X-ray binaries promise insight into strongly curved spacetime. HFQPO frequencies are likely set by the intrinsic properties of the central black hole, so a robust model for them would provide a method for measuring spin angular momentum. In hydrodynamic models, relativistic effects on orbital motion give rise to a trapping cavity for inertial waves which may allow them to form as coherent ‘r-modes,' if sufficiently excited via a non-linear coupling with a warp or eccentricity. During my PhD, I quantified the effects of large-scale magnetic fields on the r-mode trapping region, finding that such fields have less of a negative impact than previously predicted.

Illustration of a hydromagnetic r-mode's distortion
of a vertically aligned magnetic field.

However, MHD turbulence driven by the magnetorotational instability (MRI) likely damps r-modes. Recently, I have used numerical simulations of relativistic accretion disks to investigate the competition between damping by MRI-turbulence and driving by eccentric deformations in the flow. These simulations demonstrate the efficacy of disk eccentricity in exciting trapped inertial waves, even in the presence of magnetic fields and magnetohydrodynamic turbulence.

This color-map of azimuthally averaged mass flux shows a trapped inertial wave excited in a simulation of an eccentric, relativistic disk.

Parametric instability

I also study the stability of eccentric accretion discs in more general, non-relativistic contexts. Eccentric accretion disks are generically unstable even in Newtonian gravity, without magnetic fields. I am using both numerical simulations and analysis to investigate global and local aspects of this instability.

Snapshot showing mid-plane vertical
velocity in a hydrodynamic simulation of
an eccentric, parametrically unstable disk.

Magnetorotational instability

The magnetorotational instability provides a widely accepted explanation for turbulent accretion in astrophysical disks. Although studied extensively in local simulations, numerical capabilities have only recently permitted explorations of the dynamics of MRI turbulence on a truly global scale. My recent global simulations of MHD turbulent, eccentric accretion disks indicate a nuanced interplay between disk eccentricity and the MRI.

Snapshot showing mid-plane azimuthal
magnetic field in a simulation of an
MHD-turbulent, eccentric disk.