On the Low and High Frequency Correlation in Quasi-periodic Oscillations among White Dwarf, Neutron Star, and Black Hole Binaries

Abstract

We interpret the correlation over 5 orders of magnitude between high frequency νhigh and low frequency νlow in quasi-periodic oscillations (QPOs) found by Psaltis, Belloni, & van der Klis for black hole (BH) and neutron star (NS) systems and then extended by Mauche to white dwarf (WD) binaries. The observed correlation strongly constrains theoretical models and provides clues to understanding the nature of the QPO phenomena at large. We argue that the observed correlation is a natural consequence of the Keplerian disk flow adjustment to the innermost sub-Keplerian boundary conditions near the central object that ultimately leads to the formation of the sub-Keplerian transition layer (TL) between the adjustment radius and the innermost boundary (the star surface for the NS and WD and the horizon for the BH). In the frameworks of the TL model, νhigh is related to the Keplerian frequency at the outer (adjustment) radius νK, and νlow is related to the magnetoacoustic oscillation frequency νMA. Using a relation between νMA, the magnetic and gas pressure, and the density and the hydrostatic equilibrium condition in the disk, we infer a linear correlation between νK and νMA. Identification of νhigh, νlow with νK, νMA, respectively, leads us to the determination of H/rout = 1.5 × 10-2 and β = 0.1 (where H is the half-width of the disk and β is a ratio of magnetic pressure to gas pressure). We estimate the magnetic field strength near the TL outer radius for BHs, NSs, and WDs. The fact that the observed high-low frequency correlation over 5 orders of magnitude is valid for BHs, NSs, and down to WDs strongly rules out relativistic models for QPO phenomena. We come to the conclusion that the QPO observations indicate the adjustment of the geometrically thin disk to sub-Keplerian motion near the central object. This effect is a common feature for a wide class of systems, starting from WD binaries up to BH binaries.