An Attempt to Describe Frequency-Correlations among kHz QPOs and HBOs by Two-Armed Vertical p-Mode Oscillations: Case of No Magnetic Field

Abstract

The trapping of two-armed ($ m$$ =$ 2) vertical p-mode oscillations in relativistic disks is examined. The disks are assumed to be isothermal in the vertical direction, but are truncated at a certain height by the presence of corona. The same issues were examined in a previous paper (Kato 2012a). In this paper, unlike the previous paper, however, we do not use the approximation that the oscillations are nearly vertical, but limit to a simpler case of no magnetic field. As in the previous paper, the results suggest that the two basic oscillation modes [both are the fundamental ($ n$$ =$ 1) in the vertical direction, but in the horizontal direction one is the fundamental ($ n_{\rm r}$$ =$ 0) and the other the first overtone ($ n_{\rm r}$$ =$ 1)] correspond to the twin kHz QPOs. Second, the oscillation mode, which is the first overtone ($ n$$ =$ 2) in the vertical direction and the fundamental in the horizontal direction ($ n_{\rm r}$$ =$ 0), will correspond to the horizontal branch oscillation (HBO) of Z-sources. The latter suggests that the horizontal branch of Z-sources is a sequence of temperature change in disks whose vertical thickness is strongly terminated. The temperature increases leftward along the sequence from the apex between the normal and horizontal branches.