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 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 the normal to the disk. The first oscillator in the TO model allows one to interpret the horizontal branch observed below 100 Hz as the lower mode of the Keplerian oscillator under the influence of the Coriolis force, with frequency 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 observed 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 interpretation as a global parameter of the neutron star magnetosphere is an important test of the TO model. Using the results of recent observations of 4U 0614+09, we verify the existence of this invariant and determine the angle delta = 15 degrees.6 + 0 degrees.5 for this star. The second oscillator in the model deals with both a radial (presumably sound) oscillation and a diffuse 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 transition layer for 4U 0614+09 is at least 2 times more than the values for 4U 1728-34 and Sco X-1.