Holocene reconstructions of solar activity from cosmogenic isotopes (carbon-14 in tree rings and beryllium-10 in ice cores) show variations on timescales from centuries to millennia, but it remains unresolved whether these very-long-period signals are of solar origin or are imprinted by terrestrial processes — the geomagnetic field, the climate system, or archive-specific effects. The sharpest test case is the ~2300-year Hallstatt cycle (a quasi-periodicity named after the Hallstatt archaeological period, prominent in both cosmogenic and climate records): Svalgaard (2018, arXiv:1810.11952) found no significant Hallstatt power in the combined nine-millennia sunspot series (the Wu et al. 2018 reconstruction extended with his multimessenger data) and noted it is unclear whether any very-long-period variation in the cosmogenic record is solar, while the Hallstatt band appears prominently in climate records. Later literature is openly contradictory: a joint 14C–10Be analysis (Usoskin et al. 2016) attributed the ~2400-year component to the Sun, whereas amplitude-modulation modeling (Dergachev & Vasiliev 2019) and a hemispherically resolved cosmic-ray inversion (Nilsson et al. 2024, Nature Geoscience) attribute millennial-and-longer variations, explicitly including the Hallstatt cycle, to the geomagnetic field. The attribution question therefore remains open: the published solar-versus-geomagnetic attributions conflict, no solar multi-millennial cycle has been established, and the robustness confounders (model-dependent absolute calibration and reconstruction breakdown at very low solar activity) remain unresolved.

Background

Cosmogenic radionuclides are the only quantitative proxy for solar activity before telescopic sunspot observations. Galactic cosmic rays entering the atmosphere produce radioactive isotopes — carbon-14 (recorded in tree rings) and beryllium-10 (recorded in polar ice cores); their production rates fall when the Sun's heliospheric magnetic shielding strengthens. The cosmic-ray spectrum at the top of the atmosphere is conventionally summarized by the heliospheric modulation potential, a model-dependent energy parameter. Because the modulation potential is not directly observable on long timescales, reconstructions convert it to the sunspot number (the standard index of solar activity, counted since 1610 and now issued as version 2 by the SILSO center, the Sunspot Index and Long-term Solar Observations world data center) through models of the Sun's open magnetic flux (field lines carried by the solar wind out into interplanetary space rather than closing back to the solar surface); this conversion chain has freely chosen physical assumptions (open-flux prescriptions, solar-wind structure, and the local interstellar cosmic-ray spectrum, whose model dependence is quantified by Herbst et al. 2017). Wu et al. (2018) built the current reference reconstruction — a consistent multi-proxy decadal sunspot series back to 6755 BC from both 14C and 10Be archives. Svalgaard (2018) extended it to the present with independent 'messengers' (the sunspot Group Number, a historical index counting sunspot groups rather than individual spots; the range of the diurnal variation of the geomagnetic field; and the interdiurnal variation of the geomagnetic ring current, the electric current circling Earth at several Earth radii), reconciled the scales, and examined its periodicities.

Problem Statement

Determine the physical origin of the longest-period (multi-century to multi-millennial) variations in Holocene cosmogenic-isotope records of solar activity: decide whether any of this variance — most sharply the ~2300-year Hallstatt band (the Hallstatt cycle, a quasi-periodicity named after the Hallstatt archaeological period) — is genuinely solar magnetic variability, or whether it is produced by geomagnetic-field variations, climate-system or archive effects, and reconstruction methodology. This single attribution objective, posed by Svalgaard (2018) as 'it is not clear if the very long-period variations are of solar origin' together with the non-detection of the Hallstatt cycle in the reconstructed sunspot spectrum, is resolved by jointly addressing the following scientific questions: (a) reconcile the contradictory published attributions — solar origin via common 14C–10Be secondary components (Usoskin et al. 2016) versus geomagnetic origin via dipole-moment modulation (Dergachev & Vasiliev 2019) and hemispherically resolved production modeling (Nilsson et al. 2024); (b) establish whether any statistically robust solar multi-millennial cycle exists, given that only about four Hallstatt periods fit in the nine-millennia record; (c) establish how sensitive the attribution is to the confounders the source flagged: the model-dependent absolute calibration of the modulation-potential-to-sunspot-number conversion (including the factor-of-1.667-versus-2.0 scaling dispute between Wu et al. 2018 and Svalgaard 2018) and the breakdown of reconstruction assumptions in very-low-activity regimes (evidenced by unphysical slightly negative reconstructed decadal values around 1450 AD, where the usual assumption of a spherically symmetric solar wind may fail); and (d) explain why Hallstatt-band variability appears in climate records while lacking significant power in the reconstructed solar series — i.e., whether that climate signal can be solar at all.

References

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