Large ¹⁴C excursion in 5480 BC indicates an abnormal sun in the mid-Holocene

We used a bristlecone pine specimen from the White Mountains (California) for annual ¹⁴C measurements. Further information about the wood is provided in Fig. S2. We prepared the cellulose samples by standard chemical cleaning methods at the Accelerator Mass Spectrometry (AMS) laboratory at the University of Arizona, and measured ¹⁴C contents at three different AMS laboratories [University of Arizona, Nagoya University, and Swiss Federal Institute of Technology (ETH)] to cross-validate our results and ascertain any laboratory offset between different AMS systems.

Fig. 1, Upper, shows ¹⁴C results of three replicated series from our measurements. Because the three series are consistent with each other, we can immediately conclude that there are no laboratory offsets between the different AMS measurements. Because the values for the same year all agree well (Table S1), we combined the three series shown in Fig. 1, Upper. Fig. 1, Lower, shows a comparison between the combined data and the IntCal13 (3). The combined data are almost consistent with the IntCal13 and original data of the IntCal13.

From our measurements, it becomes clear that the marked increase in the IntCal13 data (5490−5460 BC) shows a very large change in annual resolution. The increase occurred from 5481 BC to 5473 BC (or 5485−5471 BC: min−max values), and the increase rates are 17.0‰/8 y (or 26.2‰/14 y), respectively. Although a variation of this event (hereafter called the 5480 BC event) is different from the previously identified events like the AD 775 event, the total increase in ¹⁴C contents of the event is larger than that of the AD 775 event (∼15‰). We show a comparison between the 5480 BC event and the AD 775 event in Fig. S3.

Previous studies classified the peak around 5460 BC as a grand solar minimum, using the IntCal data (16–18). Grand solar minima are defined as the periods when the solar activity is at a very low level, i.e., it is defined as the group sunspot number becoming less than 15 during at least two consecutive decades, according to Usoskin et al. (18). In a grand solar minimum, the ¹⁴C content increases largely due to a reduction of the solar modulation parameter Φ. It is estimated that Φ was ∼160 MV during the Maunder Minimum, while the present-day value varies between 400 MV and 1,000 MV (19).

We compared the annual 5480 BC event with other grand solar minima, that is the Maunder, the Spörer, the Oort, the AD seventh century, and the fourth century BC grand solar minima, where we have annual resolution ¹⁴C data (5, 20–22). Fig. 2 shows a comparison between our combined datasets and other grand solar minima (more details on the grand solar minima are provided in Table S2). On average, the increase rate of the other five grand solar minima is about 0.3‰/y. Against the normal grand solar minima, the increase rate of the 5480 BC event is 2‰/y. Although the total ¹⁴C increment of the 5480 BC event is almost equal to the other minima (∼20‰), the 5480 BC event increases much faster than the others. Therefore, we expect that the origin of the 5480 BC event is apparently different from the other normal grand solar minima.

To explain a rapid and large ¹⁴C increase, a dramatic decrease of the solar magnetism, or extreme SPEs, is necessary. Apart from these causes, changes in the geomagnetic field can also affect the GCR flux to Earth. However, it is generally considered that the geomagnetic field does not change significantly over several centuries (4). Over ∼3,000 y from ca. 6000 BC to 3000 BC, the geomagnetic dipole field was ∼0.9 times smaller than today’s field, and had an almost constant value (23). We do not consider the consequence of the geomagnetic effect here. Also, a change of the oceanic carbon cycle and reservoir age would affect ¹⁴C; however, ocean circulation events cannot explain ¹⁴C variations on a decadal scale, because these normally require up to 200 y, as shown in a study of the Younger Dryas event by Singarayer et al. (24). Whereas another galactic event, e.g., GCR flux increases for ∼10 y followed by a tail (a few decades), may explain the 5480 BC event, we do not know of any such event. Therefore, we hypothesize that plausible causes of this 5480 BC event are (i) special state of the grand solar minimum, (ii) successive extreme SPEs over ∼20 y, or (iii) a combination of some extreme SPEs and a normal grand solar minimum (or solar magnetic activities).

First, we consider the case of a special state of the grand solar minimum. We calculated a production rate for our measured periods using a four-box carbon cycle model (Fig. S4) with the assumption that the starting point (5484 BC) was at steady-state preindustrial value 1.8 atoms per square centimeter per second (14). Further information about the production rate is provided in SI Text, Production Rate and Error Estimation. Fig. 3 shows the result of this calculated ¹⁴C production rate in comparison with the Δ¹⁴C data.

According to several studies, if the solar modulation parameter becomes zero, the ¹⁴C production rate can increase to ∼3 atoms per square centimeter per second (19, 25, 26). Averages of the production data for the periods of 5476–5471 BC (6 y) and 5482–5471 BC (10 y) are 2.9 and 2.6 atoms per square centimeter per second, respectively. Then, the production rate during the increase period is comparable to the zero level of the solar modulation parameter. It may be difficult to explain these data only by the solar magnetic variation, because a phenomenon where the modulation parameter becomes almost zero for ∼10 y is unknown, including sun-like stars; however, we cannot fully exclude a very weak sun.

The structure of the 5480 BC event indicates a rapid increase in ¹⁴C after 5470 BC followed by a gradual plateau-like increase for the next 15 y and then a gradual decay. Although the initial increase in ¹⁴C for this event is different from the behavior in a normal grand solar minima, the time scale of the plateau and the following decay is consistent with the Maunder Minimum (here we have assumed the Maunder Minimum is a standard variation of a grand solar minimum; Fig. S6). Therefore, if our event is explained only by a grand solar minimum, this means the solar activity rapidly decreased to an extremely low level, and then the solar activity became gradually higher, in a similar way to other grand solar minima.

Second, we consider the cases of successive SPEs and the combination of SPEs and solar magnetic activity. Although it is, in principle, possible that the variation is explained only by solar energetic particles over the whole period, it is less likely that the plateau and the following decay can be explained by only SPEs.

Because it is difficult to divide ¹⁴C variations into the contribution by solar magnetic activities and that by SPEs, we suggest the following two scenarios: (i) several SPEs occurred during the early normal grand solar minimum, or (ii) several SPEs occurred, and then the solar magnetic activity became gradually higher. Here, we assume SPEs only occurred in the increasing period 5481–5468 BC. Knowing that a ¹⁴C production rate during the Maunder Minimum varies between 2.1 atoms per square centimeter per second and 2.6 atoms per square centimeter per second (19), we can accept that a production rate for the low solar magnetic activity during the increasing ¹⁴C period is an average of upper values, 2.35 atoms per square centimeter per second. In contrast, we note that the average production rate of ¹⁴C during normal solar magnetic activity is 1.8 atoms per square centimeter per second. Based on these hypotheses, a total ¹⁴C production by SPEs above 2.35 and 1.8 atoms per square centimeter per second during the increase can be shown to be 6.0 ± 2.4 and 10.5 ± 3.0 atoms per square centimeter per second, respectively. The total production rate of the AD 775 event has been estimated to be 3.9 atoms per square centimeter per second to 6.9 atoms per square centimeter per second (8, 10, 11, 14). Then, it is possible that the total production by SPEs of the event is comparable to or larger than the AD 775 event.

From direct measurements of the sun, we know solar flares tend to occur during a solar maximum, e.g., the number of SPEs increases in solar maximum periods (27). Also, the two annual ¹⁴C events (AD 774–775 and AD 993–994) occurred in higher solar activity periods, or at least did not occur during grand solar minimum periods (7). Thus, scenario i (several SPEs occurred in the grand solar minimum) seems less plausible; however, the viability of one scenario over another is currently limited by our poor understanding of the mechanism for occurrence of extreme SPEs.

In the observation of solar-type stars by the Kepler telescope, stars where several superflares occurred over several years were detected (28). Such observations of solar-type stars may support an extreme SPE origin of the 5480 BC event. Further investigations of the ¹⁴C record, or of other radionuclides such as annual ¹⁰Be data in ice cores, may turn up similar events, which would help to further discussion of the cause of this event.

In any case, the ¹⁴C variation of the 5480 BC event indicates an unprecedented anomaly in solar activity compared to other periods.

There are few examples of an extremely rapid increase rate of ¹⁴C, except in the two annual cosmic ray events at AD 774–775 and AD 993–994. However, some data in the beginning of the Dalton minimum show also a large increase rate, as can be seem in the annual ¹⁴C dataset of Stuiver et al. (5), i.e., 9.2‰ increase from AD 1796 to AD 1800 and 7.6‰ increase from AD 1808 to AD 1810 (increase rates for these periods are comparable to that of the 5480 BC event). We have also measured this interval using a Japanese cedar sample. However, we did not observe such a rapid increase in the cedar record. Fig. S1 shows a comparison of annual ¹⁴C datasets [our result, Stuiver et al. (5), and McCormac et al. (33)] during the beginning of the Dalton Minimum.

We calculated the production rate using the four-box model, which is based on Miyake et al. (6) and Usoskin et al. (8) (Fig. S4), and the 11-box model (10). We assumed the start point as a steady state (1.8 atoms per square centimeter per second), and calculated the ¹⁴C input (production rate Q). Fig. S5 shows a comparison of the production rate of two box models.

To estimate errors of the production rate, we generated 1,000 error series E(t) as where i = 1–1,000, Δ¹⁴C(t) is the series of original Δ¹⁴C time series, Δ¹⁴C_error(t) is the error series of the original Δ¹⁴C time series, and R(t) is the normal distributed random number series. We converted each E_i(t) series to a production rate series using the four-box model, and calculated an SD for each age t which is an error of the production rate.

We thank the staff of the Arizona Accelerator Mass Spectrometry (AMS) Laboratory and ETH AMS Laboratory for their technical assistance. We also thank Dr. H. Tajima and Dr. W. Beck for commenting on our manuscript. F.M. is supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (Grants 26887019 and 16H06005), JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, under Grant G2602, and Toyoaki Scholarship Foundation.