Correlated Frequency-Changes of Trapped Vertical p-mode Oscillations and kHz QPOs

We have examined the frequencies of trapped two-armed ($m=2$) nearly vertical oscillations (vertical p-mode) in vertically isothermal disks with toroidal magnetic fields. The magnetic fields are stratified so that the Alfv\'{e}n speed, $c_{\rm A}$, is constant in the vertical direction. We have particularly focused our attention on how frequencies of the fundamental mode ($n_{\rm r}=0$) and first overtone ($n_{\rm r}=1$) in the radial direction change with correlation, when the ratio $c_{\rm A}^2/c_{\rm s}^2$ changes, $c_{\rm s}$ being the isothermal acoustic speed. The results show that in the case where the oscillations are fundamental mode ($n=1$) in the vertical direction, the correlated frequency changes of the above-mentioned oscillations seem to well describe, with standard values of the mass and spin of the central sources, the frequency correlation of kHz QPOs observed in neutron-star X-ray binaries.