The Interpretations For the Low and High Frequency QPO Correlations of X-ray Sources Among White Dwarfs, Neutron Stars and Black Holes

It is found that there exists an empirical linear relation between the high frequency $\text{nhigh}$ and low frequency $\text{nlow}$ of quasi-periodic oscillations (QPOs) for black hole candidate (BHC), neutron star (NS) and white dwarf (WD) in the binary systems, which spans five orders of magnitude in frequency. For the NS Z (Atoll) sources, ${\nu }_{high}$ and ${\nu }_{low}$ are identified as the lower kHz QPO frequency and horizontal branch oscillations (HBOs) $\text{nh}$ (broad noise components); for the black hole candidates and low-luminosity neutron stars, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the ``dwarf nova oscillations’’ (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes ${\nu }_{high}$ to the Alfv'en wave oscillation frequency at a preferred radius and ${\nu }_{low}$ to the same mechanism at another radius. Then, we can obtain $\nlow = 0.08 \nhigh$andtherelationbetweentheupperkHzQPOfrequency$\nt$ and HBO to be $\text{nh}\simeq 56(\mathrm{H}\mathrm{z})(\text{nt}\mathrm{/}\mathrm{k}\mathrm{H}\mathrm{z}{)}^2$, which are in accordance with the observed empirical relations. Furthermore, some implications of model are discussed, including why QPO frequencies of white dwarfs and neutron stars span five orders of magnitude in frequency. \