A rapid cosmic-ray increase in BC 3372–3371 from ancient buried tree rings in China

Cosmic rays interact with the Earth’s atmosphere to produce 14C, which can be absorbed by trees. Therefore, rapid increases of 14C in tree rings can be used to probe previous cosmic-ray events. By this method, three 14C rapidly increasing events have been found. Plausible causes of these events include large solar proton events, supernovae, or short gamma-ray bursts. However, due to the lack of measurements of 14C by year, the occurrence frequency of such 14C rapidly increasing events is poorly known. In addition, rapid increases may be hidden in the IntCal13 data with five-year resolution. Here we report the result of 14C measurements using an ancient buried tree during the period between bc 3388 and 3358. We found a rapid increase of about 9‰ in the 14C content from bc 3372 to bc 3371. We suggest that this event could originate from a large solar proton event.

mosphere. Through the global carbon cycle, some of 14 CO 2 produced in the atmosphere can be retained in annual tree rings 1-3 . Therefore, 14 C concentrations in annual tree rings indicate the intensity of cosmic rays. The flux of cosmic rays reaching the earth is modulated by time variations of geomagnetic and heliomagnetic fields. The international radiocarbon calibration curve IntCal13 contains tree ring records of 14 C data with a typical 5-year resolution extending to 13,900 years before the present 4 . The IntCal13 curve shows variations due to solar and geomagnetic activities on a decadal to millennial time scale. However, there are only a few annual 14 C data measured from tree rings. So some rapid 14 C increases caused by cosmic-ray events may be hidden in the IntCal13.
Interestingly, a large amount of cosmic rays can be generated on a short time scale by highenergy phenomena, such as supernovae (SNe) 5 and large solar proton events (SPEs) [6][7][8] . Meanwhile, the energy deposited in γ-rays of SNe 1 and short gamma-ray bursts (GRBs) 9 can also cause a rapid 14 C increase. Accordingly, rapid increases of 14 C content in tree rings are valuable tools to explore high-energy phenomena occurred in ancient times. three reported events are unlikely caused by SNe 11,14,15 . The other possible explanations of the three events are short GRBs 14,16 or large SPEs 6,8,11,12 . The 10 Be measurements in ice cores from Antarctica, Greenland and Arctic also show a spike around AD 775 17, 18 , which indicates that a large SPE is the most likely explanation. But whether short GRBs could generate substantial increase in 10 Be remains unclear 14,16 . Meanwhile, the local event rate of short GRBs is much smaller than the rate of 14 C increase events. Other attempts have been made to search for rapid 14 C increases. For example, the 14 C content has been measured in bristlecone pine tree-ring samples in BC 2479-2455, BC 4055-4031, BC 4465-4441, and BC 4689-4681 19 . But no large 14 C increases during these periods are found. It is possible that there were other rapid 14 C increases in the past, undetected due to the lack of annual 14 C measurements. In order to find more rapid increases in 14 C data at annual resolution, we select the periods during which the 14 C value increases significantly in the IntCal13 data. There are two intervals where the increase rate is greater than 0.6‰ per year between BC 3380 and 3370. It is possible that larger annual changes hide in the averaged five-year data.
Here, we report the measurement of 14 C content for an ancient buried tree in China during the period BC 3388-3358 to search 14 C increase events, and find a rapid increase from BC 3372 to BC 3371. Considering the occurrence rate of the rapid 14 C increase events, the 14 C event could originate from a large SPE.

Results
Wood sample. We use a Chinese wingnut (Pterocarya stenoptera) tree, which was found in the city of Yichang, Hubei Province (30 • 31 ′ N, 111 • 35 ′ E), China. The sample of Chinese wingnut is housed in the Yichang museum. The tree is shown in Supplementary Figure 1. This type of wood was formed in the following way. Living trees were buried in river bed or low-lying place by an earthquake, floods or debris flows. Then, after thousands of years of carbonization process, this type of wood would be formed. The carbonization process is the early stage of the coalification process 20 , which can be taken as the slow hydrothermal carbonization process 21 , and the annual rings are preserved. The buried wood was first introduced to the West by Ernest Henry Wilson in 1913 22 . It is regarded as priceless raw material for carving. It also has substantial artistic and scientific research values, such as revealing forest information, for studying paleoclimate, and speculating on natural disasters.
Unlike very aging trees, the ancient buried woods are relatively common in nature. The period of buried woods spans a long era back. On the other hand, unlike coal, the buried woods still contain the structure of the trees. Therefore, the ancient buried woods are good samples of the carbon abundance research on past epochs up to tens of thousand years ago, as well as on other plant archaeology. For example, the use of the sample may extend the data of IntCal13.
The tree was dated with tree-ring records using standard dendrochronology. We use the master chronology of tree ring widths from California 23 . The program dpLR is used to perform the dendrochronology 24 . We find that the correlation value with the master is 0.525. The possible age error of the wood sample is about 2 years. Considering the age error of 14 C dating is about 20 years, the age from dendrochronology is consistent with that from 14 C dating. We separated annual rings carefully using a knife. The cellulose samples are prepared by standard chemical cleaning methods. The tree rings are measured using the Accelerator Mass Spectrometry (AMS) method at the Beta Analytic radiocarbon dating laboratory 25 . In order to cross check our results, we also measured another sheet of wood from the same tree (as a different sample) at the Institute of Accelerator Analysis laboratory (IAA) 26 .
Measurement data. In general, AMS measures the fraction of modern carbon F , δ 13 C and ∆ 14 C. The definitions of these values can be found in Stuiver & Polach (1977) 27 . First we measure the 14 C content between BC 3388 and 3358 every five years. Then the yearly measurements of 14 C content from BC 3379 to 3365 are performed, because the 14 C increase rate is greater than 0.6‰ per year in this period. Figure ( Table 1 and Table 2). So the measurement results are reproducible. We find an increase of 14 C content of about 9.4‰ from BC 3372 to BC 3371. After the increase, a gradual decrease over several years due to the carbon cycle is observed. The significance of this increase with respect to the measurement errors is 5.2σ. The profile of this 14 C event shows a rapid increase within about 1 year followed by a decay due to the carbon cycle, which is similar to the AD 774-775 event. In order to estimate 14 C production required for this event, we use the four-box carbon cycle model to fit the ∆ 14 C data. The four reservoirs are troposphere, stratosphere, biosphere, and surface ocean water 28  Therefore, the intensity of this event is about 0.6 times as large as the AD 774-775 event. In order to compare our results with IntCal13 4 , we average the annual data to obtain a series with 5-year resolution. The result is shown in Figure 2. Considering the measurement errors, the two sets of data are consistent with each other. We also compare our data with the original tree-ring data 29,30 of IntCal13 in Figure 3. Interestingly, our measured results well agree with the original data of IntCal13.

Discussion
The rapid 14 C increase around BC 3372 must be caused by cosmic high-energy phenomena.
The solar cycle cannot produce this large increase. There are several plausible origins for this event.
GRBs are the most powerful electromagnetic explosions in the Universe 31, 32 . According to their duration T , they can be divided into long (T ≥2 s) and short (T <2 s) GRBs. Because the intensity of this event is less than that of AD 774-775 event, the energy of a typical short GRB located at a few kpc can provide necessary energy 14 for this event. The previous three 14 C events may not be caused by short GRBs 17 . So if a short GRB causes this event, it implies that one short GRB explodes in our galaxy about 5,000 years. But the local rate of short GRBs pointed to the Earth is ∼ 10 −5 yr −1 7, 15 . So the short GRB hypothesis is largely ruled out.
Supernovae are also powerful explosions with high-energy emissions. For a supernova, the 14 C increase is attributed to both high-energy photons and cosmic rays, but only the high-energy photons would be abrupt. Previous work has shown that a rapid 14 C increase of 6‰ occurred three years after the SN 1006 explosion 1 . However, this result is challenged by a recent study 33 . The 14 C increase event reported in this paper occurred about 5,300 years ago, at a time from which there is no human historical record. Based on the above calculation, the gamma-ray energy required for this event in the atmosphere is about 10 24 erg. The typical total energy of a supernova is 10 51 erg. If a fraction of its total energy, η γ ≃ 1%, radiates in gamma-rays, then the supernova must be closer than 326 pc. From the Chandra Catalog of Galactic Supernova Remnants (http://hea-www.cfa.harvard.edu/ChandraSNR/snrcat gal.html), we find five supernova remnants with distances closer than 400 pc. The possible ages for these five supernova remnants are: t = 391 kyr for G006.4+04.9 34 , t = 4.4 × 10 9 yr for G014.7+09.1 35 , t = 3.1 × 10 6 yr for G047.3-03.8 36 , t = 340 kyr for Geminga 37 , and t = 2, 000 − 13, 000 yr for G266.2-1.2 (Vela Jr.) 38 . Indeed, nearby SNe are rare within the last 300 kyr 39 . Interestingly, the Vela Jr. 40 locates at hundreds of parsecs and its age is 2, 000 − 13, 000 years 38 . From this point of view, a supernova origin of the BC 3372-3371 event appears to be plausible. Unfortunately, η γ is much smaller than 1% 41 , so a supernova origin for this event becomes highly implausible.
The most probable origin is a large SPE. Usually, SPEs are associated with solar flares and coronal mass ejections 42 . Due to the uncertainty of the SPE energy spectrum, the estimated fluence of SPE caused the AD 774-775 event varies by as much as two orders of magnitude 8,43 . Based on more realistic models, Usoskin et al. (2013) found that the AD 774-775 event could be explained by a large SPE, which was about 50 times larger than the SPE in AD 1956 8  we assume the energy of an SPE is comparable to that of an X-ray flare, the occurrence frequency of large SPEs is consistent with the frequency of superflares on solar-type stars 48 .
In conclusion, we find a rapid increase about 9‰ of 14 C content in buried tree rings from BC 3372 to 3371. Whether this event is worldwide is unknown. Therefore, measuring the 14