Tidal Instability of Accretion Disks

Details Tidal Instability of Accretion Disks Tidal Instability of Accretion Disks

Dec 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...419..758l&link_type=abstract

Astrophysical Journal v.419, p.758

Astronomy and Astrophysics

Astronomy

17

Accretion, Accretion Disks

Scientific paper

We analyze a parametric instability for tidally distorted disks, investigated by Goodman (1993). We consider the tidal stability of g-modes, using a perturbation method in which β, the relative distortion of streamlines in the disk, is the expansion parameter. We study in detail a model system which has a simplified form of the tidally distorted base state and treats the oscillations as incompressible. We indicate how the method can be extended to include the neglected effects. We conclude that m = 1 standing g-modes that are corotating with the binary are dynamically unstable with growth rate ˜βΩB for binary angular speed ΩB. The most unstable wave is the wave with n = 0 (where n is the number of vertical nodes in the wave) which corresponds to a local corrugation or buckling of the disk. Other waves, waves with n odd (symmetric distortions about the orbit plane) and with n even (corrugation waves), also grow.
We consider how these tightly wrapped waves can gain angular momentum from the smoothly varying tidal field. We show that an interaction between the leading and trailing components of the standing wave, in second order of the wave amplitude, is responsible for the net torque. Finally, consider whether the instability can survive losses due to imperfect reflection at the disk outer edge to form a global instability. We conclude that global instability is marginally possible, but a more detailed analysis is required.

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