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

Ilya Usoskin, Sami K. Solanki, Natalie A. Krivova, Theodosis Chatzistergos

TL;DR

This study delivers the first detailed annual sunspot-number reconstruction for 1–969 CE by translating high-resolution radiocarbon ($\Delta^{14}$C) measurements into solar activity through a physics-based, four-step MCMC framework that accounts for geomagnetic shielding and ESPE events. The resulting series reveals an 11-year Schwabe-cycle-dominated variability, a Horrebow Grand minimum around 650–730 CE, and a notable ESPE in 774 CE, with 91 identified cycles and varying confidence levels. No robust long-period quasi-cycles beyond the 11-year cycle emerge, and Waldmeier-type relations remain inconclusive within this millennium. The work bridges gap in solar cycle statistics between the first millennium BCE and the second millennium CE, providing important constraints for solar dynamo and irradiance models, while highlighting the need for a consistent 3-millennium reconstruction from a composite multi-proxy cosmogenic record.

Abstract

Context. Solar activity, dominated by the 11-year cyclic evolution, has been observed directly since 1610. Before that, indirect cosmogenic proxy data are used to reconstruct it over millennia. Recently, the precision of radiocarbon measurements has improved sufficiently to allow reconstructing solar activity over millennia. Aims. The first detailed reconstruction of solar activity, represented by annual sunspot numbers, is presented for 1-969 CE. Methods. The reconstruction of sunspot numbers from D14C was performed using a physics-based method involving several steps: using a carbon-cycle box model, the 14C production rate, corrected for the geomagnetic shielding, was computed from the measured data; The open solar magnetic flux was computed using a model of the heliospheric cosmic-ray modulation; Sunspot numbers were calculated using a model of the evolution of the Sun's magnetic field. The Markov Chain Monte Carlo approach was used to account for different sources of uncertainty. Results. Annual sunspot numbers were reconstructed for the first millennium CE. This period includes one extreme solar event of 774 CE and one Grand solar minimum of 650-730 CE. We could identify 91 solar cycles, of which 26 were well-defined, while 24 and 41 were reasonably and poorly defined, respectively. 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's relations remains inconclusive. 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 the solar dynamo and irradiance models. A consistent 3-millennium-long reconstruction of sunspot numbers, based on a composite multi-proxy cosmogenic record, is pending.

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

TL;DR

This study delivers the first detailed annual sunspot-number reconstruction for 1–969 CE by translating high-resolution radiocarbon (C) measurements into solar activity through a physics-based, four-step MCMC framework that accounts for geomagnetic shielding and ESPE events. The resulting series reveals an 11-year Schwabe-cycle-dominated variability, a Horrebow Grand minimum around 650–730 CE, and a notable ESPE in 774 CE, with 91 identified cycles and varying confidence levels. No robust long-period quasi-cycles beyond the 11-year cycle emerge, and Waldmeier-type relations remain inconclusive within this millennium. The work bridges gap in solar cycle statistics between the first millennium BCE and the second millennium CE, providing important constraints for solar dynamo and irradiance models, while highlighting the need for a consistent 3-millennium reconstruction from a composite multi-proxy cosmogenic record.

Abstract

Context. Solar activity, dominated by the 11-year cyclic evolution, has been observed directly since 1610. Before that, indirect cosmogenic proxy data are used to reconstruct it over millennia. Recently, the precision of radiocarbon measurements has improved sufficiently to allow reconstructing solar activity over millennia. Aims. The first detailed reconstruction of solar activity, represented by annual sunspot numbers, is presented for 1-969 CE. Methods. The reconstruction of sunspot numbers from D14C was performed using a physics-based method involving several steps: using a carbon-cycle box model, the 14C production rate, corrected for the geomagnetic shielding, was computed from the measured data; The open solar magnetic flux was computed using a model of the heliospheric cosmic-ray modulation; Sunspot numbers were calculated using a model of the evolution of the Sun's magnetic field. The Markov Chain Monte Carlo approach was used to account for different sources of uncertainty. Results. Annual sunspot numbers were reconstructed for the first millennium CE. This period includes one extreme solar event of 774 CE and one Grand solar minimum of 650-730 CE. We could identify 91 solar cycles, of which 26 were well-defined, while 24 and 41 were reasonably and poorly defined, respectively. 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's relations remains inconclusive. 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 the solar dynamo and irradiance models. A consistent 3-millennium-long reconstruction of sunspot numbers, based on a composite multi-proxy cosmogenic record, is pending.
Paper Structure (9 sections, 2 equations, 7 figures, 1 table)

This paper contains 9 sections, 2 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data
  3. Methodology
  4. Reconstruction
  5. Uncertainties of the reconstruction
  6. Results and analyses
  7. Reconstructed sunspot numbers
  8. Solar cycles
  9. Conclusions

Figures (7)

  • Figure 1: Sequential steps of the annual solar activity reconstructions for the first millennium CE. Panel a) Raw $\Delta^{14}$C data wang_14C_26. The red arrow indicates the signature of the extreme solar particle event (ESPE) of 774 CE. Panel b) $^{14}$C production rate $Q^*$ corrected for the geomagnetic shielding and ESPE effects. Panel c) Open solar flux $F_{\rm o}$. Panel d) Sunspot number. Black curves, grey shading and red curves depict the annual values, 1$\sigma$ (68% confidence interval) uncertainties, and 22-year smoothed data, respectively.
  • Figure 2: Recent reconstructions of the geomagnetic virtual dipole moment VDM for the first millennium CE. The models are: P23 panovska23; K08 knudsen08; PAV14 pavon14; N22 nilsson22; U16 usoskin_AA_16; AK schanner22.
  • Figure 3: Correction of the dataset for the ESPE of 774 CE. Panel a) Mean raw $\Delta^{14}$C annual data (black curve); the modelled 774 response golubenko25; detrended $\Delta^{14}$C data (red dash-dotted curve). Panel b) Sunspot numbers reconstructed from the raw $\Delta^{14}$C (black) and detrended (red) datasets. Error bars are omitted for clarity in all panels.
  • Figure 4: Different sources of uncertainties of the sunspot number reconstruction plotted at the $1\sigma$ level: radiocarbon measurement errors (red $\Delta^{14}$C line); geomagnetic models (blue VDM line); model uncertainties (magenta line) including both the computation of the OSF and OSF-to-SSN conversion; and the total uncertainty (green line), which is close to the geometrical sum of the individual ones. The black dashed line represents the diagonal.
  • Figure 5: Sunspot numbers (ISN_v2 normalisation) reconstructed here for 1 -- 969 CE, split into two panels for clarity. The black curve, grey shading, and red curve depict the mean annual reconstructed SN, its 68% confidence interval, and the 22-year smoothed evolution (see main text), respectively. These data are identical to those in Figure \ref{['fig:1000']}d. The digital version of these data is available in CDS. The green curve depicts the smooth decadal SN values reconstructed from multi-proxy cosmogenic isotope data wu18.
  • ...and 2 more figures