Testing the transition layer model of quasi-periodic oscillations in neutron star X-ray binarie

We compare the theoretical predictions of the transition layer model with some observational features of quasi-periodic oscillations (QPOs) in neutron star X-ray binaries. We found that the correlation between horizontal branch oscillation (HBO) frequencies and kilohertz (kHz) QPO frequencies, the difference between the low-frequency QPOs in atoll sources and HBOs in Z sources, and the correlation between the frequencies of low-frequency QPOs and break frequencies can be well explained by the transition layer model, provided the neutron star mass is around 1.4 solar mass and the angle between magnetosphere equator and accretion disk plane is around 6 degree. The observed decrease of peak separation between two kHz QPO frequencies with the increase of kHz QPO frequencies and the increase of QPO frequencies with the increase of inferred mass accretion rate are also consistent with the theoretical predictions of transition layer model. In addition, we derive a simple equation that can be adopted to estimate the angle ($\delta$) between magnetosphere equator and accretion disk plane by use of the simultaneously observed QPO frequency data. We estimate these angles, in the range of 4 to 8 degrees, for five Z sources and two atoll sources. The nearly constant $\delta$ value for each source, derived from the different sets of simultaneously observed QPO frequency data, provides a strong test of the theoretical model. Finally, we suggest that the similar transition layer oscillations may be also responsible for the observed QPOs in accretion-powered millisecond X-ray pulsar and Galactic black hole candidates.