Trapped, two-armed, nearly vertical oscillations in disks with toroidal magnetic fields

摘要

We have examined the trapping of two-armed (m = 2) nearly vertical oscillations (vertical p-mode) in vertically isothermal (c_s = const.) relativistic disks with toroidal magnetic fields. The magnetic fields are stratified so that the Alfvén speed, cA, is constant in the vertical direction. The ratio c~2_A /c~2_s in the vertical direction is taken to be a parameter that examines the effects of magnetic fields on wave trapping. We find that the two-armed nearly vertical oscillations are trapped in the inner region of the disks, and their frequencies decrease with an increase of c~2_A =c~2_s The trapped regions of the fundamental (n = 1) and the first-overtone (n = 2) are narrow (less than the length of the Schwarzschild radius, rg), and their frequencies are relatively high (on the order of the angular frequency of disk rotation in the inner region). In contrast to this, the second overtone (n = 3) is trapped in a wide region (a few times rg), and the frequencies are low and tend to zero in the limit of c~2_A =c~2_s = 2.0.