Gravitational planetary lensing of slow-moving matter streaming towards the Sun was suggested to explain puzzling solar-flare occurrences and other unexplained solar-emission phenomena (Bertolucci et al. in Phys. Dark Universe 17 , 13, 2017 ). If it is actually so, the effect of gravitational lensing of this stream by heavy planets (Jupiter, Saturn, Uranus and Neptune) could be manifested in solar activity changes on longer time scales too where solar records present specific oscillations known in the literature as the cycles of Bray–Hallstatt (2100–2500 yr), Eddy (800–1200 yr), Suess–de Vries (200–250 yr), Jose (155–185 yr), Gleissberg (80–100 year), the 55–65 yr spectral cluster and others. It is herein hypothesized that these oscillations emerge from specific periodic planetary orbital configurations that generate particular waves in the force-fields of the heliosphere which could be able to synchronize solar activity. These harmonics are defined by a subset of orbital frequencies herein labeled as “orbital invariant inequalities” of the solar system that derive from the synodical periods among the Jovian planets. Thus, they are associated with the repeating pattern of planetary alignment relative to the Sun when tidal forcing, interplanetary magnetic couplings and planetary lensing effects could be enhanced. These frequencies are physically relevant also because they are invariant relative to any spinning system centered on the Sun and, therefore, they and their combinations should characterize the spectrum of any forcing able to externally synchronizing the internal dynamics of the solar dynamo. Herein the orbital invariant inequalities of the solar system are determined and are demonstrated to cluster around specific spectral bands that exactly correspond to the above spectrum of solar activity. In particular, the orbital invariant inequality model is shown to predict, both in frequency and phase, the Bray–Hallstatt cycle (2100–2500 yr) found in Δ 14 C $\Delta ^{14}C$ and in climate records throughout the Holocene. The result suggests that some kind of planetary forcing is synchronizing solar internal dynamics.

中文翻译：

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太阳振荡和太阳系的轨道不变不等式

有人建议用缓慢移动的物质流向太阳的引力行星透镜来解释令人费解的太阳耀斑事件和其他无法解释的太阳辐射现象（Bertolucci 等人在 Phys. Dark Universe 17 , 13, 2017 中）。如果确实如此，那么重行星（木星、土星、天王星和海王星）对这条流的引力透镜效应也可以在更长时间尺度上的太阳活动变化中体现出来，其中太阳记录呈现出文献中称为Bray-Hallstatt（2100-2500 年）、Eddy（800-1200 年）、Suess-de Vries（200-250 年）、Jose（155-185 年）、Gleissberg（80-100 年）、55- 65 年光谱簇等。在此假设这些振荡来自特定的周期性行星轨道配置，这些配置会在日光层的力场中产生特定的波，从而能够同步太阳活动。这些谐波由这里标记为太阳系“轨道不变不等式”的轨道频率子集定义，这些轨道频率源自木星行星之间的会合周期。因此，当潮汐力、行星际磁耦合和行星透镜效应可以增强时，它们与行星相对于太阳的重复排列模式有关。这些频率也是物理相关的，因为它们相对于以太阳为中心的任何旋转系统都是不变的，因此，它们及其组合应该表征能够从外部同步太阳发电机内部动力学的任何强迫的频谱。在此确定了太阳系的轨道不变不等式，并证明它们聚集在与上述太阳活动光谱完全对应的特定光谱带周围。特别是，轨道不变不等式模型被证明可以在频率和相位上预测在 Δ 14 C$\Delta ^{14}C$ 和整个气候记录中发现的布雷-哈尔施塔特循环（2100-2500 年）。全新世。结果表明，某种行星强迫正在同步太阳内部动力学。在此确定了太阳系的轨道不变不等式，并证明它们聚集在与上述太阳活动光谱完全对应的特定光谱带周围。特别是，轨道不变不等式模型显示可以在频率和相位上预测在 Δ 14 C $\Delta ^{14}C$ 和整个气候记录中发现的布雷-哈尔施塔特循环（2100-2500 年）。全新世。结果表明，某种行星强迫正在同步太阳内部动力学。在此确定了太阳系的轨道不变不等式，并证明它们聚集在与上述太阳活动光谱完全对应的特定光谱带周围。特别是，轨道不变不等式模型显示可以在频率和相位上预测在 Δ 14 C $\Delta ^{14}C$ 和整个气候记录中发现的布雷-哈尔施塔特循环（2100-2500 年）。全新世。结果表明，某种行星强迫正在同步太阳内部动力学。