The applications of the MHD Alfven wave oscillation model for kHz quasi-periodic oscillations

Abstract

In this paper, we improve the previous work on the MHD Alfven wave oscillation model for the neutron star (NS) kHz quasi-periodic oscillations (QPOs), and compare the model with the updated twin kHz QPO data. For the 17 NS X-ray sources with the simultaneously detected twin kHz QPO frequencies, the stellar mass M and radius R constraints are given by means of the derived parameter A in the model, which is associated with the averaged mass density of star as ${\rm \lan \rho \ran = 3M/(4\pi R^{3}) \simeq 2.4\times 10^{14} (g/cm^{3}) (A/0.7)^{2}}$, and we also compare the M-R constraints with the star equations of states. Moreover, we also discuss the theoretical maximum kHz QPO frequency and maximum twin peak separation, and some expectations on SAX J1808.4-3658 are mentioned, such as its highest kHz QPO frequency $\sim$~870 (Hz), which is about 1.4-1.5 times less than those of the other known kHz QPO sources. The estimated magnetic fields for both Z sources (about Eddington accretion rate $\med$) and Atoll sources ($ 1% \med$) are approximately $10^9$ G and $10^8$ G respectively.