An Attempt to Describe Frequency Correlations among kHz QPOs and HBOs by Two-Armed Nearly Vertical Oscillations

We examine whether the two-armed (m = 2) vertical p-mode oscillations trapped in the innermost region of magnetized accretion disks with finite disk thickness can describe kHz quasi-periodic oscillations (QPOs) and horizontal branch oscillations (HBOs) in low-mass X-ray binaries (LMXBs). First, we derive the frequency-frequency correlation of the two basic oscillations (both are fundamental modes in the vertical direction, but one is the fundamental and the other the first overtone in the radial direction), and compare it with the observed frequency correlation of twin kHz QPOs. Results show that the calculated frequency correlation can well describe the observed frequency one with reasonable values of the parameters. Second, we examine whether the observed frequency correlation between kHz QPOs and HBO can be described by regarding HBO as the first overtone oscillation in the vertical direction (and the fundamental in the radial direction). The results suggest that (i) the innermost parts of disks on the horizontal branch are strongly diminished in their vertical thickness (presumably by hot coronae) and (ii) the branch is roughly a sequence of variations of magnetic fields or disk temperature.