Sunspot cycles for the first millennium BC reconstructed from radiocarbon

¹ Space Physics and Astronomy Research Unit and Sodankylä Geophysical Observatory, University of Oulu, Oulu, Finland
² Max Planck Institute for Solar System Research, Justus-Von-Liebig-Weg 3, D-37077 Göttingen, Germany
³ Ioffe Physical-Technical Institute, St. Petersburg, Russia
⁴ Laboratory of Ion Beam Physics, ETH-Zürich, Zürich, Switzerland

^⋆ Corresponding authors: ilya.usoskin@oulu.fi; chatzistergos@mps.mpg.de

Received: 14 April 2025
Accepted: 9 May 2025

Abstract

Context. The relative sunspot number (SN) is the primary index of solar activity since 1610. For earlier periods, the SN can be reconstructed from the concentrations of cosmogenic isotopes, in particular, ¹⁴C and ¹⁰Be in natural archives. Because the measurement techniques are limited, however, these reconstructions typically provide the SN with a resolution of decades only.

Aims. We reconstruct the first annually resolved SNs for the first millennium BC. They provide a detailed view of the solar cycles over a period for which this was not possible before.

Methods. We reconstructed the SN from high-precision annual measurements of relative decay-corrected ¹⁴C concentrations, Δ¹⁴C, that cover 1000 to 2 BC. The process is based on the physics-based approach we developed earlier and has the following four steps: (1) The carbon-cycle model is inverted to reconstruct the production rate of ¹⁴C, Q. (2) The effect of the varying geomagnetic field on Q is accounted for. (3) The open solar magnetic flux is computed. (4) The flux is converted into SN. A Monte Carlo approach is used to account for the uncertainty of the reconstruction.

Results. We reconstructed the annually resolved SN covering the first millennium BC. Over this period, we identified 93 complete solar cycles with a mean length of 10.5 years. Twenty-three of these cycles are well defined, 21 are reasonably well defined, and the remainder are poorly defined. Our reconstructed SN and previous decadal reconstructions agree very well, but the SN around 1000–920 BC is higher. We found no significant long-term periodicities beyond the 11-year solar cycle.

Conclusions. This reconstruction offers unique insights into the cyclic solar activity for this period of time. This is valuable information for solar dynamo studies and irradiance modelling.