Resonant Excitation of Disk Oscillations in Deformed Disks VI: Stability Criterion Revisited

Abstract

We re-examine excitation of a set of disk oscillations in a deformed disk by a resonant process. We assume that the disk is deformed from an axisymmetric steady state by an oscillatory deformation with frequency ${\omega }_{\mathrm{D}}$ and azimuthal wavenumber $m_{\mathrm{D}}$. Then, we consider two normal mode oscillations with a set of frequencies and azimuthal wavenumber being (${\omega }_1$, $m_1$) and (${\omega }_2$, $m_2$) and satisfying the resonant conditions (${\omega }_1+{\omega }_2+{\omega }_{\mathrm{D}}=0$ and $m_1+m_2+m_{\mathrm{D}}=0$). These oscillations are resonantly excited if $(E_1/{\omega }_1)(E_2/{\omega }_2)>0$, where $E_1$ and $E_2$ are wave energies of the above two oscillations, when the deformation is maintained by external forces or has a large amplitude compared with the oscillations. This instability condition is rather general as long as unperturbed density and pressure vanish on the surface of the system. Possibility of application to superhump and negative superhump in superoutburst state of dwarf novae are briefly discussed.

16 pages, 2 figures, typo errors corrected (Aug. 27, 2013), published in PASJ 65, 75 (2013)

References in corpus (5)

• The Cause of the Superoutburst in SU UMa Stars is Finally Revealed by Kepler Light Curve of V1504 Cygni
• On an excitation mechanism for trapped inertial waves in discs around black holes
• Discovery of Negative Superhumps during a Superoutburst of January 2011 in ER Ursae Majoris
• A Resonantly-Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars
• Tidal Instability and Superhump by a Wave-Wave Resonant Model

Cited by in corpus (4)

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• Resonant Excitation of Tilt Mode in Tidally Deformed Disks
• Resonant Excitation of Disk Oscillations in Deformed Disks VII: Stability Criterion in MHD Systems
• Simultaneous Resonant Excitation of Low-frequency Eccentric Wave and Tilt Wave on Tidally Deformed Disks