J/A+A/708/A333 1000-year sunspot series (Usoskin+, 2026)
Cyclic sunspot activity during the first millennium CE as reconstructed from
radiocarbon.
Usoskin I., Solanki S.K., Krivova N.A., Chatzistergos T.
<Astron. Astrophys. 708, A333 (2026)>
=2026A&A...708A.333U 2026A&A...708A.333U (SIMBAD/NED BibCode)
ADC_Keywords: Sun
Keywords: Sun: activity - solar-terrestrial relations - sunspots
Abstract:
Solar activity, dominated by the 11-year cyclic evolution, has been
observed directly since 1610 CE. Before that, indirect cosmogenic
proxy data are used to reconstruct it over millennia. Recently, the
precision of radio-carbon {DELTA}14C measurements has improved
sufficiently to allow reconstructing cyclic solar activity over
millennia.
We present the first detailed reconstruction of solar activity,
represented here by annual sunspot numbers, during the first
millennium, 1-969, CE.
The reconstruction of sunspot numbers from {DELTA}14C was performed
using a physics-based method which involves several steps: 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 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. The Markov Chain Monte Carlo approach was used
to directly account for different sources of uncertainty.
Annual sunspot numbers were reconstructed for the first millennium CE.
This period includes one extreme solar event occurring in 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 with this dataset. No significant periodicities were
found beyond the 11-year cycle.
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.
Description:
Five tabular files are presented.
* File 'Q_1000CE.txt' contains annual reconstructions of the 14C
production rate [Q] along with its 1-sigma uncertainties [sQ] and the
smoothed (22-yr SSA -- see text) values [].
* File 'Qa_1000CE.txt' contains annual reconstructions of the 14C
production rate reduced to the present-day conditions [Q*] along with
its 1-sigma uncertainties [sQ*] and the smoothed (22-yr SSA) values
[<Q*>]. This table corresponds to Figure 1b in the text.
* File 'Fo_1000CE.txt' contains annual reconstructions of the open
solar flux (OSF) [Fo] along with its 1-sigma uncertainties [sF] and
the smoothed (22-yr SSA) values [<Fo>]. This table corresponds to
Figure 1c in the text.
* File 'SN_1000CE.txt' contains annual reconstructions of the sunspot
number (SN) [SN] along with its 1-sigma uncertainties [sSN] and the
smoothed (22-yr SSA) values []. This table corresponds to Figure
1d in the text.
* File 'Cycles.txt' presents a textual tabular version of Table 1 in
the text and contains the internal cycle number [n], years of minimum
[Ymin] and maximum [Ymax] of each cycle, cycle-averaged sunspot number
[], its 1-sigma uncertainty [sS], cycle length (min-to-min) [T],
and quality flag [q].
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
q1000ce.dat 21 969 Annual reconstructions of the 14C production rate
qa1000ce.dat 21 969 Annual reconstructions of the 14C production rate
reduced to the present-day conditions (Fig. 1b)
fo1000ce.dat 19 969 Annual reconstructions of the open solar flux
(Fig. 1c)
sn1000ce.dat 21 969 Annual reconstructions of the sunspot number
(Fig. 1d)
cycles.dat 22 91 Cycles (Table A1)
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See also:
VI/138 : Sunspots catalogues, 1853-1870 (Casas+, 2013)
J/A+A/390/707 : Hemispheric Sunspot Numbers 1975-2000 (Temmer+, 2002)
J/A+A/447/735 : Hemispheric Sunspot Numbers 1945-2004 (Temmer+, 2006)
J/A+A/584/A73 : Sunspot areas and tilt angles (Senthamizh Pavai+, 2015)
J/A+A/595/A104 : Scheiner drawing sunspot areas and tilt angles (Arlt+, 2016)
J/A+A/599/A131 : Butterfly diagram wings (Leussu+, 2017)
J/A+A/601/A106 : Sunspot on 1921-2011 (Mandal+, 2017)
J/A+A/601/A109 : Monthly numbers of sunspot groups 1749-1996 (Willamo+, 2017)
J/A+A/602/A69 : Group sunspot number series since 1739 (Chatzistergos+, 2017)
J/A+A/615/A93 : Reconstructed decadal sunspot numbers (Wu+, 2018)
J/A+A/627/A46 : Sunspot penumbra and umbral flashes models (Bose+, 2019)
J/A+A/628/A103 : Mt Wilson sunspot magnetic field measurements (Pevtsov+, 2019)
J/A+A/640/A78 : Sunspot area catalogue revisited (1874-2019) (Mandal+, 2020)
J/A+A/649/A141 : 1000-year sunspot series (Usoskin+, 2021)
J/A+A/652/A56 : Hemispheric Sunspot Numbers 1874-2020 (Veronig+, 2021)
J/ApJS/256/38 : SCO daily sunspot area measurements (1886-1940)
(Carrasco+, 2021)
J/ApJS/269/53 : Solar observations by Angelo Secchi. I. Sunspot
(Ermolli+, 2023)
J/other/FrASS/9.1019751 : Sunspot on 1904-2017 (Jha+, 2022)
J/A+A/698/A182 : 1000-year sunspot series (Usoskin+, 2025)
Byte-by-byte Description of file: q1000ce.dat
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Bytes Format Units Label Explanations
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1- 3 I3 -- Year Year CE
5- 9 F5.3 1/cm2/s Q Annual value of 14C production rate (Q)
11- 15 F5.3 1/cm2/s e_Q 1-sigma uncertainty of Q
17- 21 F5.3 1/cm2/s Smoothed (22-yr SSA) 14C production rate
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Byte-by-byte Description of file: qa1000ce.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 3 I3 --- Year Year CE
5- 9 F5.3 1/cm2/s Q* Annual value of 14C production rate
reduced to the present-day conditions (Q*)
11- 15 F5.3 1/cm2/s e_Q* 1-sigma uncertainty of Q*
17- 21 F5.3 1/cm2/s <Q*> Smoothed (22-yr SSA) 14C production rate
reduced to the present-day conditions
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Byte-by-byte Description of file: fo1000ce.dat
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Bytes Format Units Label Explanations
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1- 3 I3 --- Year Year CE
5- 9 F5.2 10+14Wb Fo Annual value of the reconstructed
open solar flux (OSF)
11- 14 F4.2 10+14Wb e_Fo 1-sigma uncertainty of Fo
16- 19 F4.2 10+14Wb <Fo> Smoothed open solar flux value
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Byte-by-byte Description of file: sn1000ce.dat
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Bytes Format Units Label Explanations
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1- 3 I3 --- Year* Year CE
5- 9 F5.1 --- SN Annual value of the reconstructed
sunspot number (SN)
11- 15 F5.1 --- e_SN 1-sigma uncertainty of SN
17- 21 F5.1 --- * Smoothed sunspot number value
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Byte-by-byte Description of file: cycles.dat
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Bytes Format Units Label Explanations
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1- 2 I2 --- N Internal cycle number
4- 6 I3 --- Ymin Year of solar cycle minimum
8- 10 I3 --- Ymax ?=- Year of solar cycle maximum
(--- = undefined)
12- 14 I3 --- Cycle-averaged sunspot number
16- 17 I2 --- e_ 1-sigma uncertainty of
19- 20 I2 yr T ?=- Solar cycle length (min-to-min)
22 I1 --- q [0/5] Quality flag
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Acknowledgements:
Ilya Usoskin, ilya.usoskin[at]oulu.fi
License: CC-BY-4.0
(End) Patricia Vannier [CDS] 19-Mar-2026