Trapped, Two-Armed, Nearly Vertical Oscillations in Disks with Toroidal Magnetic Fields

Abstract

We have examined trapping of two-armed ($m=2$) nearly vertical oscillations (vertical p-mode) in vertically isothermal ($c_{\mathrm{s}}=$ const.) relativistic disks with toroidal magnetic fields. The magnetic fields are stratified so that the Alfv{é}n speed, $c_{\mathrm{A}}$, is constant in the vertical direction. The ratio of $c_{\mathrm{A}}^2/c_{\mathrm{s}}^2$ in the vertical direction is taken as a parameter examining the effects of magnetic fields on wave trapping. We find that the two-armed nearly vertical oscillations are trapped in the inner region of disks and their frequencies decrease with increase of $c_{\mathrm{A}}^2/c_{\mathrm{s}}^2$. The trapped regions of the fundamental ($n=1$) and the first-overtone ($n=2$) are narrow (less than the length of the Schwarzschild radius, $r_{\mathrm{g}}$) and their frequencies are relatively high (on the order of the angular frequency of disk rotation in the inner region). On contrast to this, the second-overtone ($n=3$) are trapped in a wide region (a few times $r_{\mathrm{g}}$), and their frequencies are low and tend to zero in the limit of $c_{\mathrm{A}}^2/c_{\mathrm{s}}^2=2.0$.

18 pages, 6 figures, accepted PASJ 63, No.1 (2011)

References in corpus (1)

• Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations

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• An Attempt to Describe Frequency-Correlations among kHz QPOs and HBOs by Two-Armed Vertical p-mode Oscillations: Case of No Magnetic Field
• Trapped, Two-Armed, Nearly Vertical Oscillations in Disks with Toroidal Magnetic Fields II: Effects of Finite Thickness
• A Possible Origin of kHZ QPOs in Low-Mass X-ray Binaries
• Correlated Frequency-Changes of Trapped Vertical p-mode Oscillations and kHz QPOs