Resonant Excitation of Disk Oscillations in Deformed Disks VII: Stability Criterion in MHD Systems

Abstract

In a disk with an oscillatory deformation from an axisymmetric state with frequency ${\omega }_{\mathrm{D}}$ and azimuthal wavenumber $m_{\mathrm{D}}$, a set of two normal mode oscillations with frequency and azimuthal wavenumber being (${\omega }_1$, $m_1$) and (${\omega }_2$, $m_2$) resonantly couple through the disk deformation, when the resonant conditions (${\omega }_1+{\omega }_2+{\omega }_{\mathrm{D}}=0$ and $m_1+m_2+m_{\mathrm{D}}=0$) are satisfied. In the case of hydrodynamical disks, the resonance amplifies the set of the oscillations if $(E_1/{\omega }_1)(E_2/{\omega }_2)>0$ (Kato 2013b), where $E_1$ and $E_2$ are wave energies of the two oscillations with ${\omega }_1$ and ${\omega }_2$, respectively. In this paper we show that this instability criterion is still valid even when the oscillations are ideal MHD ones in magnetized disks, if the displacements associated with the oscillations vanish on the boundary of the system.

21 pages, 1 figure, to be published in PASJ 66, Vol. 1 (2014)

References in corpus (5)

• Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations
• Corotational Instability, Magnetic Resonances and Global Inertial-Acoustic Oscillations in Magnetized Black-Hole Accretion Discs
• A Resonantly-Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars
• Tidal Instability and Superhump by a Wave-Wave Resonant Model
• Resonant Excitation of Disk Oscillations in Deformed Disks VI: Stability Criterion Revisited

Cited by in corpus (2)

• A Possible Origin of kHZ QPOs in Low-Mass X-ray Binaries
• Simultaneous Resonant Excitation of Low-frequency Eccentric Wave and Tilt Wave on Tidally Deformed Disks