Cyclic sunspot activity during the first millennium CE as reconstructed from radiocarbon

¹ Space Physics and Astronomy research Unit, Sodankylä Geophysical Observatory, University of Oulu, Oulu, Finland
² Max-Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
³ Institute for Space-Earth Environmental Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 January 2026
Accepted: 16 March 2026

Abstract

Context. Solar activity, dominated by 11-year cyclic evolution, has been observed directly since 1610 CE. Indirect cosmogenic proxy data have been used to reconstruct solar activity for millennia prior to 1610. The precision of radiocarbon Δ¹⁴C measurements has recently improved enough to allow cyclic solar activity to be reconstructed over millennia.

Aims. We present the first detailed reconstruction of solar activity, represented here by annual sunspot numbers, during the first millennium, 1–969 CE.

Methods. The reconstruction of sunspot numbers from Δ¹⁴C was performed using a physics-based method that involves several steps: First, using the modern carbon-cycle box model, the ¹⁴C production rate, corrected for the contemporary geomagnetic shielding, was computed from the measured concentrations. The open solar magnetic flux was then computed using a model of the heliospheric cosmic-ray modulation. Sunspot numbers were calculated by inverting a model of the evolution of the Sun’s magnetic field. Lastly, the Markov chain Monte Carlo approach was used to directly account for different sources of uncertainty.

Results. Annual sunspot numbers were reconstructed for the first millennium CE. This period includes one extreme solar event that occurred in 774 CE and one grand solar minimum, from 650 to 730 CE. We were able to identify 91 solar cycles, of which 26 were well defined, 24 were reasonably well defined, and 41 were poorly defined. The mean cycle length was 10.6 years, but the lengths of individual cycles vary between 8 and 15 years. The existence of empirical Waldmeier relations remains inconclusive with this dataset. No significant periodicities were found beyond the 11-year cycle.

Conclusions. This work fills the gap in the solar cycle statistics between the previously reconstructed first millennium BCE and the second millennium CE, providing vital constraints for solar dynamo and irradiance models. A consistent 3-millennium-long reconstruction of sunspot numbers, based on a composite multi-proxy cosmogenic record, is pending.