δ-Invariant for Quasi-periodic Oscillations and Physical Parameters of the 4U 0614+09 Binary

The recently formulated Two Oscillator (TO) model interprets the lowest ofthe kilohertz frequencies of the twin peak quasi-periodic oscillations in X-ray binaries as the Keplerian frequency nu_K. The high twin frequency nu_h inthis model holds the upper hybrid frequency relation to the rotationalfrequency of the neutron star's magnetosphere Omega: nu_h^2=nu_K^2+4(Omega/2pi)^2. The vector Omega is assumed to have an angle delta with thenormal to the disk. The first oscillator in the TO model allows one tointerpret the horizontal branch observed below 100 Hz as the lower mode of theKeplerian oscillator under the influence of the Coriolis force, with frequencynu_L being dependent on nu_h, nu_K and delta. For some stars such as 4U0614+09, Sco X-1 and 4U 1702-42, nu_h, nu_K and nu_L have been observedsimultaneously providing the opportunity to check the central prediction of theTO model: the constancy of delta for a particular source. Given theconsiderable variation of each of these three frequencies, the existence of anobservational invariant with a clear physical interpretation as a globalparameter of the neutron star magnetosphere is an important test of the TOmodel. Using the results of recent observations of 4U 0614+09 we verify theexistence of this invariant and determine the angle delta=15^o.6+/- 0.^o5 forthis star. The second oscillator in the model deals with a radial (presumablysound) oscillation and diffuse process in the viscous layer surrounding theneutron star. Our analysis of the viscous oscillation frequency nu_V and thebreak frequency nu_b of the diffusion shows that the spin value of the innerboundary of the transition layer for 4U 0614+09 is at least two times more thanvalues for 4U 1728-34 and Sco X-1.Comment: 13 pages, 4 figures, accepted for publications in ApJ Letter