基于行星会合指数运动学方程,推演出太阳质心到太阳系质心距离变化的计算公式,并利用该公式重建太阳质心相对于太阳系质心的距离变化时间序列,作为太阳轨道运动的替代性指标,使用聚合经验模态分解（Ensemble empirical mode decomposition,EEMD）方法分析0~25.0 ka BP太阳质心到太阳系质心的距离与Δ¹⁴C时间序列。结果显示：两者均存在蕴含~2300 a 周期（Hallstatt cycle）的IMF分量;互相关分析证实两者蕴含的Hallstatt周期分量间具有相关性,0~13.9 ka BP与13.9~25.0 ka BP年代相关系数分别可达0.52、0.44,并且太阳质心到太阳系质心距离的变化超前于太阳活动指标Δ¹⁴C的变化。表明太阳质心远离太阳系质心时,大气¹⁴C含量增加,对应于太阳活动较弱的时期;太阳质心靠近太阳系质心时,大气¹⁴C含量减小,对应于太阳活动较强的时期。这一认识对于进一步探究太阳活动Hallstatt周期的成因机制提供了新的依据和思路。

Solar activity, evidenced by ¹⁴C proxies, shows a period of ~2300 years (Hallstatt cycle). Its physical origin remains uncertain. Recent studies suggested that ~2300-year Hallstatt oscillations of solar activity may be caused by the solar inertial motion (the Sun motion around the center of mass of the solar system). In this study, a formula for calculating the distance between the solar centroid and the solar system’s centroid is deduced based on the kinematic equation of the planet juncture index. In the appropriate proxy of solar inertial motion, the time series of distance change is reconstructed using this formula. Ensemble empirical mode decomposition (EEMD) is a method with which any complicated signal can be decomposed into several intrinsic mode functions (IMFs). This decomposition method is adaptive and highly efficient. It applies to nonlinear and non-stationary processes since the decomposition is based on the local characteristic time scale of the data. To compare the radiocarbon series of INTCAL13 data with the variations of the distance between the solar centroid and the solar system’s centroid from 0 to 25.0 ka BP, we employ the empirical mode decomposition method. The analysis results are as follows: (1) Various components have been identified by decomposing the distance signal, including a significant component with a period of ~2300 years. (2) Following the analysis of the time series of distance change, there is also a component with ~2300-year Hallstatt cycle in the data on the production rate of radiocarbon. The traditional method of Δ¹⁴C record preprocessing, applying a pre-selected detrending function, amounts to injecting external information into data. Different from the traditional method the true and more physical meaningful component with the Hallstatt cycle is decomposed by the adaptive EEMD method. (3) Next, the ~2300-year variations of the two series considered are compared. The last 13900 years data in INTCAL13 record derive mostly from tree-ring chronologies, while the older data is made using mostly marine records. Thus, cross-correlation analysis is applied to the above two time-frames of the components with the Hallstatt cycle decomposed from the time series of the distance and Δ ¹⁴C. The cross-correlation coefficient is 0.52 from 0 to 13.9 ka BP, and 0.44 from 13.9 to 25.0 ka BP. The values confirm the assumption that the variations of the distance between the solar centroid and the solar system’s centroid and the production rate of radiocarbon are related. As discussed above, the study of the relationship between solar inertial motion and solar activity covers the Holocene and extends to 25.0 ka BP. (4) It appears that solar inertial motion is the cause of the Hallstatt cycle found in solar activity proxy. The¹⁴C concentration of the atmosphere increases when the solar centroid moves away from the solar system’s centroid, which corresponds to the period of weak solar activity. When the solar centroid is near the solar system’s centroid, the¹⁴C concentration decreases which corresponds to the period of strong solar activity.