On the distribution of frequency ratios of kHz quasi-periodic oscillations

The width (Delta nu) and root mean squared amplitude (r(S)) of lower and upper kHz quasi-periodic oscillations (QPOs) from accreting neutron stars vary with frequency. Similarly, the QPO frequency varies with the source count rate (S). Hence, the significance of a QPO, scaling as S x r(S)(2)/root Delta nu, will also depend on frequency. In addition, the significance also scales up with the square root of the integration time of the Fourier power-density spectrum (T). In practice and in most analysis, T is constrained (e. g. limited by the Rossi X-ray Timing Explorer (RXTE) orbital period if the source is occulted by the Earth) or minimized to increase the number of detections. Consequently, depending on the way data are considered, kHz QPOs (the lower, the upper or both kHz QPOs) may be detected only over a limited range of their frequency spans or detected predominantly at some frequencies, leading potentially to biases in the observed distributions of frequencies or frequency ratios. Although subject of much controversy, an observed clustering of QPO frequency ratios around 3/2 in Sco X-1, also seen in other sources, has been previously used as an argument supporting resonance-based models of neutron star QPOs. In this paper, we measure how the statistical significances of both kHz QPOs vary with frequency. For this purpose, we consider three prototype neutron star kHz QPO sources, namely 4U1636-536, 4U0614+091 and Sco X-1, whose QPO parameters have different, though representative, dependence with frequency. As the significance of QPO detection depends on frequency, we show that in sensitivity-limited observations (as in the case of the RXTE/Proportional Counter Array), a simultaneous detection of both the lower and upper kHz QPOs can only be achieved over limited frequency ranges. As a result, even a uniform distribution of QPO frequencies will lead to peaks (in particular around 3/2) in the histogram of ratios of simultaneous kHz QPO frequencies. This implies that the observed clustering of ratios of twin QPO frequencies does not provide any evidence for intrinsically preferred frequency ratios in those systems, thus weakening the case for a resonance mechanism at the origin of neutron star kHz QPOs.