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

Abstract

Trapping of two-armed ($m=2$) vertical p-mode oscillations in relativistic disks are 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 have been 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 normal and horizontal branches.