标题： 在克尔黑洞场中振荡的弦环，作为微类星体中观测到的双高频准周期振荡的可能解释 显示英文标题

标题： String loops oscillating in the field of Kerr black holes as a possible explanation of twin high-frequency quasiperiodic oscillations observed in microquasars

摘要： 在Kerr黑洞赤道平面上有效势能的极小值处，研究了电流环在稳定平衡位置附近的微小振荡，使用了微扰方法。 在最低近似下，得到了两个解耦的简谐振子，分别描述径向和垂直方向的振荡；高阶项决定了非线性现象，并通过准周期阶段的振荡运动导致混沌运动。 给出了径向和垂直简谐振荡的频率径向分布，这些频率在振荡运动的准周期阶段也相关，且它们的特性取决于黑洞的自转以及弦环的角动量和张力。 结果表明，径向分布与地心轨道的径向和垂直频率的径向分布有显著不同；然而，它们具有相同的质量比例关系，其大小在同一数量级。 因此，我们能够证明，假设在径向和垂直弦环振荡频率比为3:2时共振现象的相关性，弦环的振荡频率可以很好地与在微类星体GRS 1915+105、XTE 1550-564和GRO 1655-40中观测到的双高频准周期振荡（HF QPOs）频率相关联。 我们可以得出结论，振荡的电流环必须被视为解释致密天体场中HF QPOs的可能解释之一。 显示英文摘要

摘要： Small oscillations of current-carrying string loops around stable equilibrium positions corresponding to minima of the effective potential in the equatorial plane of the Kerr black holes are studied using the perturbation method. In the lowest approximation, two uncoupled harmonic oscillators are obtained that govern the radial and vertical oscillations; the higher-order terms determine non-linear phenomena and transition to chaotic motion through quasi-periodic stages of the oscillatory motion. The radial profiles of frequencies of the radial and vertical harmonic oscillations that are relevant also in the quasi-periodic stages of the oscillatory motion are given, and their properties in dependence on the spin of the black holes and the angular momentum and tension of the string loops are determined. It is shown that the radial profiles differ substantially from those corresponding to the radial and vertical frequencies of the geodetical epicyclic motion; however, they have the same mass-scaling and their magnitude is of the same order. Therefore, we are able to demonstrate that assuming relevance of resonant phenomena of the radial and vertical string-loop oscillations at their frequency ratio 3:2, the oscillatory frequencies of string loops can be well related to the frequencies of the twin high-frequency quasi-periodic oscillations (HF QPOs) observed in the microquasars GRS 1915+105, XTE 1550-564, GRO 1655-40. We can conclude that oscillating current-carrying string loops have to be considered as one of the possible explanations of the HF QPOs occurring in the field of compact objects.