Annual radiocarbon measurements from tree rings dating from 1 to 970 CE reveal four periods when solar activity remained unusually low, while analysis of the same record shows two distinct patterns in how the Sun’s roughly 11-year cycle weakened and recovered during those quiet intervals.
Reconstructing solar activity from tree rings
Every year, trees record changes in the amount of radiocarbon, or carbon-14, in the atmosphere. This isotope is produced when cosmic rays interact with atoms in the upper atmosphere. The Sun’s magnetic activity affects how many of those cosmic rays reach Earth, so changes in atmospheric carbon-14 can preserve a record of past solar activity.
The researchers assembled eight annual carbon-14 datasets covering 1 to 970 CE. Five were newly measured for this study, while three had been published previously. Together, the measurements filled a major gap between earlier high-resolution records covering the first millennium BCE and the second millennium CE.
The five new datasets contain 852 of the 961 years in the combined record. Of those, 827 individual tree rings were measured at the Curt-Engelhorn-Center Archaeometry in Mannheim, Germany, while 25 years from 1 to 25 CE were measured at the Centre for Isotope Research at the University of Groningen.
The new measurements had an average analytical uncertainty of 1.72 parts per thousand. Independent measurements of identical tree rings at the two laboratories showed excellent agreement.
Most of the new measurements fall within two standard deviations of the Northern Hemisphere IntCal20 radiocarbon reference record. But the researchers found notable differences in several periods, including offsets between their annual measurements and the lower-resolution IntCal20 record during 1 to 40 CE and 820 to 840 CE.
From 560 CE onward, most of the new measurements were also lower than IntCal20. The differences were particularly noticeable between 560 and 720 CE and between 820 and 970 CE.
These differences matter because atmospheric carbon-14 is used to reconstruct past solar activity. The researchers therefore used their annual measurements to build a more detailed record of how strongly the Sun’s magnetic field modulated incoming cosmic rays.
Four periods of unusually low solar activity
The researchers reconstructed a quantity called the solar modulation parameter, or Φ. It describes how strongly the Sun’s magnetic activity shields Earth from galactic cosmic rays.
A sustained low value of Φ can indicate a Grand Solar Minimum, a period lasting decades or longer when solar activity is unusually weak.
The researchers used three criteria to identify candidate Grand Solar Minima from their carbon-14 record. The record had to show an overall increase in carbon-14 of more than 10 parts per thousand, Φ had to fall below 400 MeV, and the low-activity interval had to last more than 40 years.
Four periods met all three criteria.
The first occurred from 105 to 150 CE. Carbon-14 rose by 11.76 parts per thousand during this interval, which lasted about 45 years according to the study’s definition.
The second extended from 200 to 280 CE. The carbon-14 increase reached 17.49 parts per thousand, and the reconstructed minimum lasted about 80 years.
A third occurred from 400 to 450 CE. Carbon-14 increased by 13.45 parts per thousand, with a duration of about 40 years.
The fourth and strongest sustained candidate extended from 640 to 730 CE. Carbon-14 rose by 19.93 parts per thousand, and the reconstructed minimum lasted about 90 years.
The researchers note that the 640–730 CE minimum had previously been measured by another study, which called it the Horrebow Minimum. The new record indicates that the minimum began slightly before the period covered by that earlier measurement.
The researchers also identified another possible low-activity interval from 885 to 908 CE. Carbon-14 rose by about 10 parts per thousand and Φ fell well below 400 MeV. But the feature was too short-lived to meet the study’s criteria for a Grand Solar Minimum. Additional data would be needed to determine whether it represents an extremely short solar minimum.
The 11-year solar cycle changed during the minima
Finding periods of low solar activity was only part of the study. The researchers also wanted to determine what happened to the Sun’s approximately 11-year Schwabe cycle during those intervals.
The cycle is not perfectly fixed at 11 years. Direct observations show that individual cycles can vary in length, roughly from eight to 14 years.
Extracting this changing signal from carbon-14 records is difficult because the record contains other variations as well. The researchers therefore used a data-driven technique called empirical mode decomposition, or EMD, to separate the record into different oscillating components.
They found a component dominated by an approximately 11-year cycle. Statistical tests indicated that the extracted signals were significant, although the researchers caution that the extracted component is not a direct reconstruction of the sunspot cycle.
The analysis showed that the 11-year signal became weak or nearly disappeared during the four candidate Grand Solar Minima.
More importantly, the researchers found two different patterns in how the cycle changed.
During the two shorter minima, from 105 to 150 CE and 400 to 450 CE, the cycle’s amplitude weakened and then recovered in a relatively symmetric pattern. Its amplitude fell from around 0.5 parts per thousand before rising above 1 part per thousand again. Possible changes in cycle length also occurred, although the researchers caution that those changes could partly result from a known limitation of EMD called mode mixing.
The two longer minima showed a different pattern.
During the 200–280 CE and 640–730 CE intervals, the cycle began with a reduced amplitude of around 0.5 parts per thousand. It then recovered to more than 1 part per thousand in the middle of the minimum before weakening again toward the end.
The cycle length also changed in a characteristic way. It initially increased from about 10 years to about 13 years before shortening again toward roughly 10 years.
The researchers say this pattern resembles the behavior seen during the Maunder Minimum, a much later period of very low solar activity. Their analysis of data from the last millennium also found similar patterns in four Maunder-type Grand Solar Minima.
However, one feature seen before the Maunder Minimum was not present in the new first-millennium record. Earlier research had reported a gradual lengthening of the Schwabe cycle to as much as 16 years across three cycles before the Maunder Minimum. The longest cycle preceding each of the four minima in the new record did not exceed 13 years.
Possible explanations for the different cycle patterns
The researchers discuss possible solar-dynamo mechanisms that could produce the two patterns.
For longer, Maunder-type minima, one proposed model involves a diffusion-dominated solar dynamo. In that framework, the magnetic field becomes weaker because the poloidal component dissipates more readily. The cycle period can also become longer because it is governed more strongly by a diffusive timescale.
The researchers say this framework may help explain the behavior of the two longer minima identified in their record.
The shorter minima showed a more symmetric weakening and recovery of both cycle amplitude and period. The researchers point to earlier modeling of open solar flux and beryllium-10 as one possible explanation. That work found that when solar activity is low, open solar flux becomes more sensitive to the inclination of the heliospheric current sheet rather than to changes in sunspot number.
The study does not establish that these mechanisms caused the observed patterns. Instead, they are discussed as possible explanations for the different behavior recorded in the carbon-14 data.
The record also contains possible evidence of particle events
The annual measurements provided another opportunity. Sudden increases in carbon-14 can preserve evidence of unusually energetic particle events.
The best-known examples are called Miyake Events. Six single-year carbon-14 increases exceeding 10 parts per thousand have been confirmed in tree-ring records from around the world. These events are widely believed to represent extreme solar energetic particle events, although their exact origin has not been established.
Researchers have also looked for smaller increases of roughly 4 to 10 parts per thousand. These intermediate events are harder to identify because natural carbon-14 variability can obscure them.
To search for such events, the researchers developed a Bayesian method that estimated the probability and size of additional carbon-14 production for every year in their datasets. They used five-year moving windows and calculated the probability that additional production exceeded several thresholds.
The method initially identified nine years of interest: 14, 325, 508, 553, 598, 605, 675, 893 and 954 CE.
Further analysis eliminated several of these candidates.
The 325 CE increase was removed because it appeared in only one of two overlapping datasets, while the other showed a gradual increase over six years. The increases around 508, 598 and 893 CE were also within twice the measurement uncertainty and were therefore considered less likely to represent particle events.
The 603 CE feature was excluded because carbon-14 increased steadily by about 2.73 parts per thousand per year for three consecutive years, rather than showing the rapid pattern expected for the type of event being sought.
That left four candidate events around 14, 553, 675 and 954 CE.
Four candidate particle events need more evidence
The four remaining candidates showed abrupt carbon-14 increases followed by two to three years of elevated values. The researchers say these patterns could represent medium-sized Miyake Events.
The evidence is not sufficient to confirm them.
The researchers emphasize that additional tree-ring samples are needed to test the candidates. They also note that the candidate around 14–15 CE has some unusual behavior. Carbon-14 fell back to its previous level in the following year but then rose again by more than 6 parts per thousand in 16 CE. This weakens the case for a single event, although the longer-term record still shows a clear discontinuity.
The 954 CE candidate also requires further verification. An earlier annual dataset showed only a 2.3 parts per thousand increase between 955 and 956 CE, but the researchers retained the candidate because the measurement uncertainties were large enough that the increase remained worthy of further investigation.
The study therefore treats the four events as candidates rather than confirmed particle events.
A more detailed record of the first millennium
The study combines annual carbon-14 measurements, carbon-cycle modeling and several statistical techniques to reconstruct solar activity between 1 and 970 CE.
The resulting record identifies four candidate Grand Solar Minima. It also shows that the approximately 11-year solar cycle became weak or nearly absent during those intervals and indicates two different patterns of weakening and recovery. Shorter minima showed a more symmetric reduction and recovery, while the longer minima showed a cycle that weakened, recovered during the middle of the minimum and weakened again.
The same annual record also points to four possible intermediate-sized particle events around 14, 553, 675 and 954 CE, although these require confirmation with additional datasets.
The researchers say future work should expand high-resolution carbon-14 measurements across different geographic regions and tree species. They also recommend combining these records with other archives, including ice cores and beryllium-10 records, to test whether suspected events occurred globally and to improve reconstructions of past solar activity.
The study was published in Communications Earth & Environment.
