Abstract:

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.

Key words: solar inertial motion, solar activity, Hallstatt cycle, ensemble empirical mode decomposition (EEMD)