J/A+A/708/A333ivo://CDS.VizieR/J/A+A/708/A333CDSUsoskin I.Solanki S.K.Krivova N.A.Chatzistergos T.2026-04-21T09:40:31Z2026-04-21T10:40:03ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frthe-sunSolar 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}^14^C 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}^14^C was performed using a physics-based method which involves several steps: using the modern carbon-cycle box model, the ^14^C 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.2026A&A...708A.333Uhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/708/A333CatalogResearchIsServedByTAP VizieR generic servicerelated-toVI/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)J/ApJS/269/53 : Solar observations by Angelo Secchi. I. SunspotJ/other/FrASS/9.1019751 : Sunspot on 1904-2017 (Jha+, 2022)J/A+A/698/A182 : 1000-year sunspot series (Usoskin+, 2025)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/708/A333https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/708/A333http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/708/A333https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/708/A333https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/708/A333http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/708/A333GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapdefaultJ/A+A/708/A333/q1000ceAnnual reconstructions of the ^14^C production raterecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintYearYear CEtimeintQAnnual value of ^14^C production rate (Q)cm**-2.s**-1stat.fit.paramfloate_Q1-sigma uncertainty of Qcm**-2.s**-1stat.errorfloat<Q>Smoothed (22-yr SSA) ^14^C production ratecm**-2.s**-1stat.fit.paramfloatJ/A+A/708/A333/qa1000ceAnnual reconstructions of the ^14^C production rate reduced to the present-day conditions (Fig. 1b)recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintYearYear CEtimeintQ*Annual value of ^14^C production rate reduced to the present-day conditions (Q*)cm**-2.s**-1stat.fit.paramfloate_Q*1-sigma uncertainty of Q*cm**-2.s**-1stat.errorfloat<Q*>Smoothed (22-yr SSA) ^14^C production rate reduced to the present-day conditionscm**-2.s**-1stat.fit.paramfloatJ/A+A/708/A333/fo1000ceAnnual reconstructions of the open solar flux (Fig. 1c)recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintYearYear CEtimeintFoAnnual value of the reconstructed open solar flux (OSF)1e+14Wbphot.flux.density;em.optfloate_Fo1-sigma uncertainty of Fo1e+14Wbstat.errorfloat<Fo>Smoothed open solar flux value1e+14Wbphot.flux.density;em.optfloatJ/A+A/708/A333/sn1000ceAnnual reconstructions of the sunspot number (Fig. 1d)recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintYear*Year CEtime.epochintSNAnnual value of the reconstructed sunspot number (SN)meta.numberfloate_SN1-sigma uncertainty of SNstat.errorfloat<SN>*Smoothed sunspot number valuemeta.numberfloatJ/A+A/708/A333/cyclesCycles (Table A1)recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintNInternal cycle numbermeta.idintYminYear of solar cycle minimumtime.epochintYmax? Year of solar cycle maximum (--- = undefined)time.epochintnullable<SN>Cycle-averaged sunspot numbermeta.numberinte_<SN>1-sigma uncertainty of <SN>stat.errorintT? Solar cycle length (min-to-min)yrtime.intervalintnullableq[0/5] Quality flagmeta.code.qualint