The distribution of kHz QPO frequencies in bright LMXBs

We analyzed all published frequencies, nu_1 and nu_2, of the twin kilohertz quasi-periodic oscillations (kHz QPOs) in bright neutron star low-mass X-ray binaries. The two frequencies are well correlated but, contrary to recent suggestions, the frequency-frequency correlation is significantly different from a nu_2 = (3/2) nu_1 relation. To check whether, although not following the the 3/2 relation, the QPO frequencies cluster around a region where nu_2/nu_1 ~ 3/2, we re-analyzed the Sco X-1 data that were used to report that ratio and show that, because the distribution of ratios of linearly correlated measurements is intrinsically biased, although the significance of the clustering around nu_2/nu_1 ~ 3/2 previously reported in the case of Sco X-1 is formally correct, it does not provide any useful information about a possible underlying resonance mechanism in this source. Using the same data, we then show that the (unbiased) distribution of QPO frequencies is consistent with a uniform distribution at a 2.4 sigma level. To investigate this further, we analyzed a larger data set of Sco X-1 and four other sources, 4U 1608-52, 4U 1636-53, 4U 1728-34 and 4U 1820-30. We find that for all five sources the distribution of the kHz QPO frequencies is not uniform and has multiple peaks, which have no analogy in the distribution of points in the spectral color-color diagrams of these sources. Finally, we demonstrate that a simple random walk of the QPO frequencies can reproduce qualitatively the observed distributions in frequency and frequency ratio. This result weakens the support for resonance models of kHz QPOs in neutron stars.