Geometric analysis of variability of radiocarbon abundances and solar activity

Abstract

This paper discusses a geometric time series analysis of variability of radiocarbon abundances and solar activity. Cosmic rays sometimes have a severe impact on the Earth’s environment. They interact with atoms in the atmosphere, producing radionuclides such as radiocarbon. Consequently, the ratio of radiocarbon to stable carbon in the atmosphere fluctuates on the basis of the influx of cosmic rays. Consequently, historical records of radiocarbon abundances show the intensity of cosmic rays in the past. The International Calibration (IntCal) curve widely used for radiocarbon dating is also used as a reference for such records. From a statistical point of view, detecting rapid changes in radiocarbon abundances, which are considered indicators of intense cosmic rays, from the IntCal data is challenging because such variations are generally smoothed out during the calibration process. However, in this study, we used a geometric time series analysis method to identify several rapid changes directly from the IntCal data. These variations in radiocarbon abundances also serve as indicators of solar activity. We also detected signals corresponding to solar grand minima and grand maxima by correlating them with temporal changes in the vector field derived from the dynamical system characterized by a second-order random oscillation.