A new correlation with lower kilohertz quasi-periodic oscillation frequency in the ensemble of low-mass X-ray binaries

We study the dependence of kilohertz quasi-periodic oscillation (kHz QPO) frequency on accretion-related parameters in the ensemble of neutron-star low-mass X-ray binaries. Based on the mass accretion rate, $\dot{M}$, and the magnetic field strength, B, on the surface of the neutron star, we find a correlation between the lower kHz QPO frequency and $\dot{M}/B^2$. The correlation holds in the current ensemble of Z and atoll sources and therefore can explain the lack of correlation between the kHz QPO frequency and X-ray luminosity in the same ensemble. The average run of lower kHz QPO frequencies throughout the correlation can be described by a power-law fit to source data. The simple power law, however, cannot describe the frequency distribution in an individual source. The model function fit to frequency data, on the other hand, can account for the observed distribution of lower kHz QPO frequencies in the case of individual sources as well as the ensemble of sources. The model function depends on the basic length scales, such as the magnetospheric radius and the radial width of the boundary region, both of which are expected to vary with $\dot{M}$ to determine the QPO frequencies. In addition to modifying the length scales, and hence the QPO frequencies, the variation in $\dot{M}$, being sufficiently large, may also lead to distinct accretion regimes, which would be characterized by Z and atoll phases.