Reversal of the amplitude difference of kHz QPOs in six atoll sources

Context. Several models have been proposed to explain the twin kilohertz quasi-periodic oscillations (kHz QPOs) detected in neutron-star low-mass X-ray binaries; but when confronting theory with observations, not much attention has been paid so far to the relation between their amplitudes. Aims. For six neutron-star atoll sources (namely 4U 1608-52, 4U 1636-53, 4U 0614+09, 4U 1728-34, 4U 1820-30, and 4U 1735-44), we investigate the relationship between the observed fractional rms amplitudes of the twin kHz QPOs. We discuss whether this relationship displays features that could have a physical meaning in terms of the proposed QPO models. Methods. We consider the difference in rms amplitude between the upper and lower kHz QPOs as a function of the frequency ratio R = $\nu_U/\nu_L$. We compared two data sets. Set I is a collection taken from published data. Set II has values for the rms amplitudes obtained by automatic fitting of all RXTE-PCA observations available up to the end of 2004, corresponding to continuous segments of observation. Results. For each of the six sources, we find that there is a point in the R domain around which the amplitudes of the two twin kilohertz QPOs are the same. We find such a point located inside a narrow interval R = 1.5 ± 3%. Further investigation is needed in the case of 4U 1820-30 and 4U 1735-44 to explore this finding, since we have not determined this point in Set II. There is evidence of a similar point close to R = 1.33 or R = 1.25 in the four sources 4U 1820-30, 4U 1735-44, 4U 1608-52, and 4U 1636-53. We suggest that some of these special points may correspond to the documented clustering of the twin kHz QPO frequency ratios. Conclusions. For the sources studied, the rms amplitudes of the two twin peaks become equal when the frequencies of the oscillations pass through a certain ratio R, which is roughly the same for each of the sources. In terms of the orbital QPO models (of both the hot-spot and disc-oscillation types), with some assumptions concerning the QPO modulation mechanism, this finding implies the existence of a specific orbit at a particular common value of the dimensionless radius, at which the oscillations corresponding to the two twin peaks come into balance. In a more general context, the amplitude difference behaviour suggests a possible energy interchange between the upper and lower QPO modes.