Trapped, Two-Armed, Nearly Vertical Oscillations in Disks with Toroidal Magnetic Fields II: Effects of Finite Thickness

We examine radial trapping of two-armed ($m=2$) vertical p-mode oscillations in geometrically thin relativistic disks which are vertically isothermal but terminated at a certain height by the presence of hot and low-density corona. The disks are assumed to be subject to toroidal magnetic fields. The oscillations are classified by $n$, a number related to the node number of oscillations in the vertical direction and starting from $n=1$. In modes with $n=1$, the frequencies of trapped oscillations depend little on the height of termination, but in modes with $n=2,3,...$ the frequencies decrease and the radial extends of trapped region become wide, as the termination height decreases. This study is a preparation to examine whether these oscillations can describe kilo-hertz quasi-periodic oscillations (kHz QPOs), horizontal branch oscillation (HBOs), and their correlations.