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

Abstract

We examine the radial trapping of two-armed ($ m$$ =$ 2) vertical p-mode oscillations in geometrically thin relativistic disks that are vertically isothermal, but terminated at a certain height by the presence of hot and low-density corona. The disks are assumed to be subject to toroidal magnetic fields. The oscillations are classified by $ n$ , a number related to the node number of oscillations in the vertical direction, and starting from $ n$$ =$ 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, $ \cdots$ the frequencies decrease and the radial extentions of the 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 oscillations (HBOs), and their correlations.