🔭 astrophysics

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

This study presents the first detailed reconstruction of annual sunspot numbers for the period 1–969 CE using radiocarbon data and physics-based modeling, revealing 91 solar cycles with a mean length of 10.6 years and identifying key events like the 774 CE extreme solar event and the 650–730 CE Grand solar minimum.

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

Published 2026-04-22

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CC BY 4.0

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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Sun's Secret Diary: Decoding a Thousand Years of Sunspots

Imagine the Sun not as a constant, blazing ball of fire, but as a living, breathing heart that beats in a rhythm. Sometimes it beats strong and fast; other times, it slows down to a whisper. Scientists call these "sunspots" (dark patches on the Sun's surface) the heartbeat of our star. We've been able to watch this heartbeat directly with telescopes since 1610, but what about before that? What was the Sun doing during the Roman Empire, the Dark Ages, or the time of the Vikings?

This paper is like a time-traveling detective story. The authors, led by Ilya Usoskin, have managed to reconstruct the Sun's "heartbeat" for the entire first millennium (years 1 to 969 CE) using a clever trick involving ancient trees and cosmic radiation.

Here is the story of how they did it, explained simply:

1. The Cosmic Detective Work: Reading Tree Rings

Since we can't look back in time with a telescope, we have to look for clues left behind. The authors used radiocarbon (Carbon-14) found in ancient European oak trees.

Think of the Earth's atmosphere as a giant shield. When the Sun is very active, it pushes away cosmic rays (particles from deep space), so fewer Carbon-14 atoms are created. When the Sun is quiet, the shield drops, and more Carbon-14 rains down on Earth. Trees absorb this Carbon-14 as they grow.

The Analogy: Imagine the tree rings are a tape recorder. Every year, the tree records how much "cosmic rain" fell. By measuring the Carbon-14 in these rings, the scientists can hear the Sun's "voice" from 2,000 years ago.

2. The "Glitch" in the Recording

There was a problem. In the year 774 CE, something massive happened. The Sun threw a massive solar storm (an "Extreme Solar Particle Event") that was so strong it looked like a glitch in the tape recorder. It created a huge spike in Carbon-14 that wasn't caused by the Sun's normal cycle, but by a single, violent explosion.

The Fix: The scientists had to use a digital "eraser" to remove this glitch from their data. If they hadn't, they would have thought the Sun went completely silent (or even negative!) right after the storm, which doesn't make sense physically.

3. The Math Magic: Turning Clues into Numbers

Once they cleaned the data, they used a complex computer simulation (a "physics-based method") to translate the Carbon-14 levels into Sunspot Numbers.

The Process:
1. Tree Data: How much Carbon-14 is in the wood?
2. Earth's Shield: They corrected for the strength of Earth's magnetic field (which also blocks cosmic rays) at that time.
3. The Sun's Magnetism: They calculated how much magnetic energy the Sun was holding.
4. The Result: Finally, they converted that energy into a number representing how many sunspots the Sun likely had that year.

They ran this calculation 10,000 times (like rolling dice thousands of times) to account for errors and uncertainties, giving them a very reliable average.

4. What Did They Find?

The results were fascinating. They reconstructed 91 solar cycles over 970 years. Here are the big takeaways:

The "Horrebow Minimum" (650–730 CE): The Sun went into a deep sleep for about 80 years. This was a "Grand Minimum," similar to the famous "Maunder Minimum" in the 1600s when the Sun barely had any sunspots. During this time, the Sun was very quiet.
The Rhythm: On average, the Sun's cycle was 10.6 years long. However, it wasn't a perfect metronome. Some cycles were short (8 years), and some were long (15 years). It's like a drummer who usually keeps a steady beat but occasionally speeds up or slows down.
The 774 CE Monster: They confirmed that the massive solar storm of 774 CE was the strongest one in the last 10,000 years. It was a "once-in-a-millennium" event.
No Grand Maxima: Unlike the 20th century, where the Sun was very active, this period didn't have any "Grand Maxima" (periods of extreme, record-breaking activity). The Sun was generally calmer.

5. Why Does This Matter?

You might ask, "Why do we care about sunspots from 1,000 years ago?"

Testing the Theory: Scientists have theories about how the Sun generates its magnetic field (called the "Solar Dynamo"). To prove these theories right, they need a lot of data. Before this, we only had about 25 cycles of direct telescope data. Now, with this new study plus previous ones, we have nearly 300 cycles of data. It's like going from having a few puzzle pieces to having almost the whole picture.
Predicting the Future: By understanding how the Sun behaves over long periods, we can better predict how it might affect our technology (like satellites and power grids) in the future.
The "Clock" Question: Scientists have debated whether the Sun's cycles are like a perfect clock (predictable) or a series of random pulses. This new data suggests it's a bit of both: there's a rhythm, but it's flexible and sometimes gets confused.

The Bottom Line

This paper fills a massive gap in our history books. It connects the dots between the ancient past and the modern era, showing us that the Sun has been a dynamic, sometimes sleepy, and occasionally explosive neighbor for the last 2,000 years. By listening to the "tape recording" in ancient oak trees, we've finally heard the Sun's heartbeat from the first millennium, giving us a much clearer picture of our star's personality.

1. Problem Statement

Direct observations of solar activity (sunspots) only date back to 1610 CE, covering approximately 25 well-resolved cycles. This limited dataset restricts the statistical understanding of solar dynamo theory, particularly regarding:

The nature of Grand Minima (periods of very low activity, e.g., Maunder Minimum) and Grand Maxima.
The validity of empirical rules like Waldmeier's relation (linking cycle strength to rise time).
Whether solar cycles operate as a phase-locked clock or independent dynamo pulses.

Previous reconstructions using cosmogenic isotopes ( $^{14}$ C and $^{10}$ Be) could resolve long-term trends but lacked the temporal resolution to identify individual Schwabe cycles (approx. 11-year cycles) for the first millennium CE (1 – 969 CE). While recent high-precision datasets filled gaps for the first millennium BCE and the second millennium CE, a critical "millennium-long gap" remained for the period 1–969 CE.

2. Methodology

The authors reconstructed annual sunspot numbers (SN) for 1–969 CE using a physics-based, multi-step inversion method driven by high-resolution radiocarbon ( $\Delta^{14}$ C) data.

Data Sources:

Primary Input: Annual $\Delta^{14}$ C measurements from European oak trees (Wang et al., 2026) with $\sim$ 1.6‰ precision.
Geomagnetic Correction: Six recent archeo/paleomagnetic models (Virtual Dipole Moment, VDM) were used to correct for geomagnetic shielding variations.
Event Correction: The dataset was detrended to remove the signature of the extreme solar particle event (ESPE) of 774 CE, which otherwise distorts the solar activity signal.

Reconstruction Pipeline (MCMC Approach):
The authors employed a Markov Chain Monte Carlo (MCMC) method with 10,000 ensemble realizations to propagate uncertainties through four sequential steps:

$\Delta^{14}$ C to Production Rate ( $Q$ ): Using a multi-box carbon cycle model to convert measured concentrations into $^{14}$ C production rates.
Geomagnetic Correction ( $Q^*$ ): Adjusting production rates to a standard geomagnetic field strength (VDM = $7.75 \times 10^{22}$ A m $^2$ ) using calibration curves.
Open Solar Flux ( $F_o$ ): Converting $Q^*$ into the Open Solar Magnetic Flux using a heliospheric cosmic-ray modulation model.
Sunspot Number (SN): Inverting an empirical model of solar magnetic field evolution to derive annual sunspot numbers (ISN v.2 definition).

Uncertainty Quantification:
The MCMC approach allowed for the isolation of error sources:

Radiocarbon measurement errors (dominant source, $\sim$ 20–70 SN units).
Geomagnetic model uncertainties (modest, $\sim$ 10–20 SN units due to stable VDM).
Model conversion uncertainties (stable at $\sim$ 15 SN units).

3. Key Contributions

Bridging the Gap: This work provides the first detailed, annual-resolution reconstruction of solar activity for the first millennium CE, connecting the previously reconstructed periods of the first millennium BCE and the second millennium CE.
Cycle Identification: Identification of 91 individual solar cycles within the 970-year period.
Quality Flagging: Introduction of a rigorous quality flag ( $q=0$ to $5$) to categorize cycles based on resolution and definition, distinguishing between well-defined, reasonably defined, and poorly defined cycles.
Event Handling: Explicit correction and analysis of the 774 CE ESPE, demonstrating its impact on reconstructed cycle quality.

4. Key Results

Solar Cycle Statistics:
- Total Cycles: 91 identified.
- Quality Distribution: 26 well-defined ( $q \ge 4$ ), 24 reasonably defined ( $q=3$ ), 30 poorly defined ( $q=1-2$ ), and 10 undefined/guessed.
- Cycle Length: The mean cycle length is 10.6 years. Individual cycles range from 8 to 15 years (9–13 years for well-defined cycles), consistent with direct observations and other proxy reconstructions.
Activity Levels:
- Grand Minimum: A distinct Grand Minimum, termed the Horrebow Minimum, occurred between 650 – 730 CE, comparable in depth to the Maunder Minimum.
- Grand Maximum: No periods of sustained high activity (SN > 200) were found, unlike the late 20th century.
- Weak Activity: Several shorter low-activity episodes were identified (c. 120, 250, 430, and 900 CE).
Periodicity Analysis:
- Wavelet analysis confirms the dominance of the 11-year Schwabe cycle.
- No statistically significant periodicities were found for longer cycles (e.g., Suess/de Vries $\sim$ 200 years, Gleissberg $\sim$ 70–140 years) within this specific dataset.
Empirical Relations: The existence of Waldmeier's relation remains inconclusive due to uncertainties in the reconstructed cycle shapes and amplitudes.
Uncertainty: The reconstruction is uncertain for SN < 50. For strong cycles, uncertainty reaches $\sim$ 1/3 of the SN value.

5. Significance

Solar Dynamo Constraints: The dataset significantly expands the statistical sample of solar cycles from ~25 (direct) to ~280 (reconstructed across three millennia). This provides vital constraints for testing solar dynamo models and understanding the stochastic nature of the solar cycle.
Irradiance Modeling: The reconstruction offers improved boundary conditions for models of total solar irradiance on millennial timescales, crucial for climate modeling.
Future Work: The authors note that while this fills the gap, a fully consistent, composite 3-millennium reconstruction based on a unified multi-proxy record is still pending to eliminate potential boundary distortions between the separate millennium-long studies.

In summary, this paper successfully utilizes high-precision radiocarbon data to reconstruct the first millennium of solar activity, revealing a period dominated by moderate activity with a significant Grand Minimum, while highlighting the limitations and uncertainties inherent in proxy-based cycle reconstruction.