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

TL;DR

This study models two-armed vertical p-mode oscillations in relativistic disks without magnetic fields to explain correlations among kHz QPOs and HBOs, suggesting specific oscillation modes correspond to observed phenomena.

Contribution

It introduces a simplified model of disk oscillations without magnetic fields, linking specific modes to kHz QPOs and HBOs, expanding previous work with new assumptions.

Findings

Fundamental horizontal and vertical modes correspond to twin kHz QPOs.

First overtone vertical mode corresponds to HBOs.

Sequence of temperature changes relates to the horizontal branch in Z-sources.

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.