We measure the centroid frequency ratios of simultaneous quasi-periodic oscillations (QPOs) that occur at low frequency (0.1–30 Hz) in a selection of accreting black hole (BH) low-mass X-ray binaries. We use all data in the RXTE archive on GX 339–4, GRO J1655–40, 4U 1630–47, XTE J1550–564, and H 1743–322. We select the power spectra that show at least two simultaneous QPOs, and empirically divide them into four main categories, whose occurrence correlates systematically to X-ray spectral state. In the hard/hard-intermediate state, all sources show sets of QPO peaks with near-harmonic frequency relations, which we measure as precisely as possible using an improved analysis method. We find small but significant offsets from purely harmonic frequency relations that in most cases can be explained by the fit function not describing the QPOs accurately; for some QPO pairs, however, the ‘sub-harmonic’ is at a higher frequency than expected. In the intermediate and ultraluminous states, in all sources we find non-harmonic QPO pairs, some previously reported. We distinguish several different types of non-harmonic QPO pairs that occur across sources. We discuss these findings in the framework of classification schemes and models proposed for black hole low-frequency QPOs. We conclude that the phenomenology of the frequency ratios indicates that in addition to the physical mechanism (possibly precession) explaining the common harmonically related sets of (Type B and C) QPO peaks, at least one additional mechanism is required to explain the occurrence of pairs of QPOs in other states that are not only not harmonically related, but also stand out by the absence of harmonics to either of them.

中文翻译：

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黑洞低质量X射线双星中同时发生的低频QPO的质心频率比

我们在选择吸积黑洞（BH）低质量X射线双星的过程中，测量在低频（0.1–30 Hz）处同时发生的准周期振荡（QPO）的质心频率比。我们使用GX 339-4，GRO J1655-40、4U 1630-47，XTE J1550-564和H 1743-322上RXTE归档中的所有数据。我们选择能同时显示至少两个QPO的功率谱，并根据经验将它们分为四个主要类别，它们的出现与X射线光谱状态系统地相关。在硬/硬中间状态下，所有源均显示具有接近谐波频率关系的QPO峰集，我们使用改进的分析方法尽可能精确地对其进行测量。我们发现纯谐波频率关系有很小但很明显的偏移，在大多数情况下，拟合函数不能准确地描述QPO，可以解释这种偏移。但是，对于某些QPO对，“次谐波”的频率比预期的高。在中间和超发光状态下，在所有来源中我们都发现了非谐波QPO对，一些先前已经报道过。我们区分了跨源出现的几种不同类型的非谐波QPO对。我们在为黑洞低频QPO提出的分类方案和模型的框架中讨论这些发现。我们得出结论，频率比的现象学表明，除了解释（B和C型）QPO峰值的常见谐波相关集合的物理机制（可能是进动）之外，还需要至少一种其他机制来解释对的出现处于其他状态的QPO中，它们不仅与谐波无关，而且由于它们中的任何一个都不存在谐波而脱颖而出。