delta-invariant for quasi-periodic oscillations and physical parameters ofthe 4U 0614+09 binary

The recently formulated two-oscillator (TO) model interprets the lowest of the kilohertz frequencies of the twin-peak quasi-periodic oscillations in X -ray binaries as the Keplerian frequency v(K). The high twin frequency v(h) in this model holds the upper hybrid frequency relation to the rotational frequency of the neutron star's magnetosphere Omega: v(h)(2) = v(K)(2) + 43 (Omega/2 pi)(2). The vector Omega is assumed to have an angle delta with th e normal to the disk. The first oscillator in the TO model allows one to in terpret the horizontal branch observed below 100 Hz as the lower mode of th e Keplerian oscillator under the influence of the Coriolis force, with freq uency v(L) being dependent on v(h), v(K), and delta. For some stars such as 4U 0614+09, Scorpius X-1, and 4U 1702-42, v(h), v(K), and v(L) have been o bserved simultaneously, thus providing the opportunity to check the central prediction of the TO model, i.e., the constancy of delta for a particular source. Given the considerable variation of each of these three frequencies , the existence of an observational invariant with a clear physical interpr etation as a global parameter of the neutron star magnetosphere is an impor tant test of the TO model. Using the results of recent observations of 4U 0 614+09, we verify the existence of this invariant and determine the angle d elta = 15 degrees.6 + 0 degrees.5 for this star. The second oscillator in t he model deals with both a radial (presumably sound) oscillation and a diff use process in the viscous layer surrounding the neutron star. Our analysis of the viscous oscillation frequency v(V) and the break frequency v(b) of the diffusion shows that the spin value of the inner boundary of the transi tion layer for 4U 0614+09 is at least 2 times more than the values for 4U 1 728-34 and Sco X-1.