Alfven Wave Oscillation Mechanism For the Low and High Frequency QPO Correlations of X-ray Sources Among White Dwarfs, Neutron Stars and Black Holes

We interpret the correlation over five orders of magnitude between high frequency νhigh and low frequency νlow in a quasi-periodic oscillation (QPO) found by Psaltis, Belloni & van der Klis (1999, 2002) for black hole candidate (BHC) and neutron star (NS) systems and then extended by Mauche (2002), Warner et al (2003) and Warner & Woudt (2004) to white dwarf (WD) binaries. As declaimed, νhigh and νlow are identified as the lower kHz QPO frequency and the horizontal branch oscillations (HBOs) νHBO in Z sources or broad noise components in Atoll sources respectively, and in our model we ascribe νhigh to the Alfven wave oscillation frequency at a preferred radius ≃ 1.2RA and νlow to the same mechanism at the doubled Alfven radius ≃ 2RA. We obtain that the theoretical correlation between the low and high frequencies is νlow = 0.08 νhigh and the quadratic correlation between the low frequency νlow (or HBO νHBO) and the upper kHz QPO frequency ν2 is νHBO ≃ 57 (Hz) (ν2/kHz), which are in accordance with the observed empirical relations. Furthermore, some theoretical implications are discussed, including why QPO frequencies of white dwarfs and neutron stars span five orders of magnitude. Subject headings: accretion, accretion disks —stars: neutron—(stars:) white dwarfs—stars: oscillations (including pulsations)—X-ray: binaries—(magnetohydrodynamics:) MHD