A Phenomenological Study of the Cosmic Ray Variations over the Past 9400 Years, and Their Implications Regarding Solar Activity and the Solar Dynamo

Abstract

Two 9400-year long ¹⁰Be data records from the Arctic and Antarctic and a ¹⁴C record of equal length were used to investigate the periodicities in the cosmic radiation incident on Earth throughout the past 9400 years. Fifteen significant periodicities between 40 and 2320 years are observed in the ¹⁰Be and ¹⁴C records, there being close agreement between the periodicities in each record. We found that the periodic variations in the galactic cosmic radiation are the primary cause for periods < 250 years, with minor contributions of terrestrial origin possible > 250 years. The spectral line for the Gleissberg (87-year) periodicity is narrow, indicating a stability of ≈ 0.5 %. The 9400-year record contains 26 Grand Minima (GM) similar to the Maunder Minimum, most of which occurred as sequences of 2 – 7 GM with intervals of 800 – 1200 years in between, in which there were no GM. The intervals between the GM sequences are characterised by high values of the modulation function. Periodicities < 150 years are observed in both the GM intervals and the intervals in between. The longer-period variations such as the de Vries (208-year) cycle have high amplitudes during the GM sequences and are undetectable in between. There are three harmonically related pairs of periodicities (65 and 130 years), (75 and 150 years), and (104 and 208 years). The long periodicities at 350, 510, and 708 years closely approximate 4, 6, and 8 times the Gleissberg period (87 years). The well-established properties of cosmic-ray modulation theory and the known dependence of the heliospheric magnetic field on the solar magnetic fields lead us to speculate that the periodicities evident in the paleo-cosmic-ray record are also present in the solar magnetic fields and in the solar dynamo. The stable, narrow natures of the Gleissberg and other periodicities suggest that there is a strong “frequency control” in the solar dynamo, in strong contrast to the variable nature (8 – 15 years) of the Schwabe (11-year) solar cycle.

Appendix: Terrestrial Contributions to the Variability of Δ14C

Global-scale climate change affects the interchange and storage of ¹⁴C in the atmosphere and the oceans, and hence the concentration in tree rings, which leads to long-term changes as a consequence of climate change (Beer et al. 2011). Mathematical models of the carbon cycle show that this effect is weak (see Section 13.5 of Beer, McCracken, and von Steiger, 2012). As an example, we considered changes in the two most important contributors: the gas-exchange rate between the atmosphere and the upper-most portion of the oceans [k _am], and the eddy diffusion constant [K] that quantifies the mixing of the water below the surface layer (Chapter 13.5.3, Beer, McCracken, and von Steiger, 2012). Variations in k _am are mainly controlled by the long-term climate-driven changes in the surface winds and by the extent of sea ice. During the past 60 years, the annual mean area of sea ice has varied by ≈ 0.8 % peak-to-peak (compared to the total area of the Earth’s oceans), implying a similar variation in k _am. To allow for winds and other factors we quadrupled this to an ≈ 3.2 % peak-to-peak change in k _am as a consequence of climate change in correlation with the Gleissberg cycle. Muscheler et al. (2004) used a 30 % change in K to model the carbon-cycle effects during the Younger Dryas transition from the glacial to inter-glacial epochs, and we used a tenth of that for the much smaller changes expected during the Holocene. Using these estimates in a box diffusion carbon-cycle model yields an amplitude of 4.5(1−e^{−T/(2⋅460)}) ‰ for the variation in Δ¹⁴C, where T is the period of the climate change in question. For the Gleissberg periodicity, this yields an amplitude of 0.4 ‰. The observed Gleissberg variation in Δ¹⁴C is approximately 7 ‰. That is, rather extreme assumptions regarding the variability in the carbon-cycle can only account for ≈ 5.7 % of the observed amplitude of the Gleissberg cycle in Δ¹⁴C. The exponential term in the above equation quantifies the rapidity with which the changes in k _am and K attain equilibrium, and this clearly means that the longer-period climatic changes will have a greater effect than we derived in the above example.