Distribution of Kilohertz QPO Frequencies and Their Ratios in the Atoll Source 4U 1636-53

A recently published study on long term evolution of the frequencies of the kilohertz quasi-periodic oscillations (QPOs) in the atoll source 4U 1636-53 concluded that there is no preferred frequency ratio in a distribution of twin QPOs that was inferred from the distribution of a single frequency alone. However, we find that the distribution of the ratio of actually observed pairs of kHz QPO frequencies is peaked close to the 3/2 value, and possibly also close to the 5/4 ratio. To resolve the apparent contradiction between the two studies, we examine in detail the frequency distributions of the lower kHz QPO and the upper kHz QPO detected in our data set. We demonstrate that for each of the two kHz QPOs (the lower or the upper), the frequency distribution in all detections of a QPO differs from the distribution of frequency of the same QPO in the subset of observations where both the kHz QPOs are detected. We conclude that detections of individual QPOs alone should not be used for calculation of the distribution of the frequency ratios.