Solar activity during the Holocene: the Hallstatt cycle and its consequence for grand minima and maxima

Aims. Cosmugenic isotopes provide the only quantitative proxy for analyzing the long-term solar variability over a centennial timescale. While essential progress has been achieved in both measurements and modeling of the cosmogenic proxy, uncertainties still remain in the determination of the geomagnetic dipole moment evolution. Here we aim at improving the reconstruction of solar activity over the past nine millennia using a multi-proxy approach. Methods. We used records of the C-14 and Be-10 cosmogenic isotopes, current numerical models of the isotope production and transport in Earth's atmosphere, and available geomagnetic held reconstructions, including a new reconstruction relying on an updated archeo- and paleointensity database. The obtained series were analyzed using the singular spectrum analysis (SSA) method to study the millennial-scale trends. Results. A new reconstruction of the geomagnetic dipole field moment, referred to as GMAG.9k, is built for the last nine millennia. New reconstructions of solar activity covering the last nine millennia, quantified in terms of sunspot numbers, are presented and analyzed. A conservative list of grand minima and maxima is also provided. Conclusions. The primary components of the reconstructed solar activity, as determined using the SSA method, are different for the series that are based on C-14 and Be-10. This shows that these primary components can only be ascribed to long-term changes in the terrestrial system and not to the Sun. These components have therefore been removed from the reconstructed series. In contrast, the secondary SSA components of the reconstructed solar activity are found to be dominated by a common approximate to 2400-year quasi-periodicity, the so-called Hallstatt cycle, in both the C-14 and Be-10 based series. This Hallstatt cycle thus appears to be related to solar activity. Finally, we show that the grand minima and maxima occurred intermittently over the studied period, with clustering near lows and highs of the Hallstatt cycle, respectively.