Letter | Published:

# The nature of the lithium enrichment in the most Li-rich giant star

## Abstract

About 1% of giant stars1 have anomalously high Li abundances (ALi) in their atmospheres, conflicting directly with the prediction of standard stellar evolution models2. This finding makes the production and evolution of Li in the Universe intriguing, not only in the sense of Big Bang nucleosynthesis3,4 or the interstellar medium5, but also for the evolution of stars. Decades of effort have been put into explaining why such extreme objects exist6,7,8, yet the origins of Li-rich giants are still being debated. Here, we report the discovery of the most Li-rich giant known to date, with a very high ALi of 4.51. This rare phenomenon was observed coincidentally with another short-term event: the star is experiencing its luminosity bump on the red giant branch. Such a high ALi indicates that the star might be at the very beginning of its Li-rich phase, which provides a great opportunity to investigate the origin and evolution of Li in the Galaxy. A detailed nuclear simulation is presented with up-to-date reaction rates to recreate the Li enrichment process in this star. Our results provide tight constraints on both observational and theoretical points of view, suggesting that low-mass giants can internally produce Li to a very high level through 7Be transportation during the red giant phase.

## Main

Lithium is too fragile to survive in deeper layers of a stellar atmosphere due to the high temperature. Thus, the first dredge up (FDU) process can sharply dilute the surface Li abundance (ALi) in red giants. This explains why the first discovery9 of an Li-rich giant evoked great interest in exploring and understanding the Li-rich objects. However, only about 150 Li-rich giants have been found1,10,11,12,13,14 in the past three decades, and ~20 of them were found to be super Li-rich with ALi higher than 3.3. Considering the non-local thermodynamic equilibrium (NLTE) corrections, three stars12,15,16 were found to be at a level of ALi > 4.0. Such rare objects could provide a great opportunity to reveal the nature of the phenomenon of Li richness because high ALi cannot be maintained for a long time due to frequent convection activity. Taking advantage of the powerful ability for spectral collection with the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST), we have obtained a large sample of Li-rich candidates by measuring the equivalent width of the Li i line at λ = 6,707.8 Å. One of our candidates, TYC 429-2097-1, has a super strong ALi line (see Fig. 1a). We then made a follow-up high-resolution observation with the 2.4 m Automated Planet Finder telescope (APF) located at Lick Observatory on 23 June 2015. The spectrum covers a wavelength range of 374–970 nm with a resolution power of ~80,000. The total integration time was 1.5 h and was divided into three single exposures (30 min each) for better subtraction of cosmic rays. The spectrum of TYC 429-2097-1 obtained from APF is presented in Fig. 1b,e, where the spectrum of HD 48381 is also plotted with a vertical shift of +0.3 as a comparison. HD 48381 is a star selected from the Gaia-ESO survey DR2, which has very similar stellar parameters to TYC 429-2097-1.We used the spectroscopic method to derive the stellar parameters (see the Methods for details). We present the final derived parameters of TYC 429-2097-1 and the estimated errors in Table 1. The ALi,NLTE values for 6,707.8, 6,103.6 and 8,126.3 Å are 4.42 ± 0.09, 4.51 ± 0.09 and 4.60 ± 0.08, respectively. The averaged ALi,NLTE = 4.51 ± 0.09. Compared with previous studies, TYC 429-2097-1 has the highest ALi among all Li-rich giants ever discovered (see Fig. 2). The ALi in TYC 429-2097-1 is about 1,000 times higher than the widely used Li-rich ‘standard’ of ALi = 1.5 (lower purple dashed line in Fig. 2), despite it having been suggested that this ‘standard’ is luminosity dependent17. It is also about 15 times higher than meteoritic ALi (upper purple dashed line in Fig. 2), which is thought to be the initial ALi for newly formed young stars.

Although Li-rich giants were reported at various stages, such as red giant branch (RGB) and core helium-burning phases18, the Li-rich phase is likely to be a short-term event. An extremely Li-rich giant (possibly newly enriched) with rigorous investigation on its evolutionary stage would definitely be important. The location of the star was derived by the maximum likelihood method using the observed parameters (in this case, the effective temperature (Teff), surface gravity (log[g]) and [Fe/H] derived from the spectroscopic method) and a grid of evolutionary models computed with the modules for experiments in stellar astrophysics (MESA) code (see the Methods for details). The derived luminosity and mass are log[L/L] = 1.95 and M = 1.43M, respectively. We used the parallax of Gaia DR1 (ref. 19) to test the reliability of the information derived from the maximum likelihood method independently. The luminosity obtained from Gaia data leads to a very similar result of log[LGaia/L] = 2.00. The mass was tested in the sense that if the mass is well determined, the surface gravity from Gaia parallax will show good consistency with the spectroscopic log[g] of 2.25. As expected, the final result is log[gGaia] = 2.23. Thus, we consider that the results derived from the maximum likelihood method are reliable, allowing us to robustly locate this star on the Hertzsprung–Russell diagram, along with the corresponding MESA tracks (see Supplementary Fig. 1). The star is probably occupying the region of the RGB bump—a stage in which the μ-barrier is destroyed and the enhanced extra mixing might be ongoing inside the star. In addition, we also estimated the 12C/13C ratio as it has been suggested that the extra mixing will cause a decrease of 12C/13C to the range of 10–20. We found that the 12C/13C ratio in this star is 12.0 ± 3.0, which is well within the predicted range. All the results obtained above are shown in Table 1.

It has long been suggested that the Li enrichment could be due to contaminations by external sources in the environment, such as engulfment of a substellar component20 (for example, giant planets or brown dwarfs) and accretion from an Li-rich companion or diffuse medium. Yet the contribution from external sources is not infinite, since the contributor itself has a limited amount of Li, typically not higher than 3.3. A simulation on engulfment of a Jovian planet suggested that a typical upper limit for enrichment this way is ~2.2 (ref. 21). Our star has a much higher ALi than any of these values, so it is very unlikely that the overabundant Li comes from the direct contribution of external sources.

In contrast, the internal production of Li is based on the Cameron−Fowler mechanism22. The production of 7Be takes place where the temperature is too high to preserve the newly synthesized 7Li; hence, 7Be must be transported quickly to the cooler region to form Li. This scenario would potentially require the low-mass giants to evolve to the RGB bump, where the mean molecular weight discontinuity (or μ-barrier—a mass gradient caused by the FDU) is erased. Meanwhile, it would need the presence of deep, enhanced extra mixing to increase the depth and efficiency of the convective circulation, which in turn alters the 12C/13C to a lower level than that after the FDU. The observational features on both the evolutionary stage and the 12C/13C ratio of our star coincide with these predictions remarkably well, but the limitation of self-production still remains unknown in the sense that none of the quantitative calculations with a nuclear reaction network has been presented to obtain such a high amount of Li before. To test this speculation, we have built such a simulation with a series of parameters. Using the RGB stellar structure as the input for the extra mixing calculation, with the updated nuclear reaction rates and the asymmetric parameters of the extra mixing model, we found that ALi in the envelope can exceed 4.0 for the processed material when the mass circulation has finished. Our extra mixing calculation with parameters of $$\dot M$$ = 52 × 10−6M yr−1, Δ = 0.15, fd =0.9 and fu = 0.1 yields ALi = 4.506, where $${\dot{M}}$$ is the rate of mass transport, Δ is log[TH] − log[Tp], where TH is the temperature at which the energy released from the hydrogen-burning shell reaches its maximum and Tp is the maximum temperature sampled by the circulating material, and fd and fu are the fractional areas of the ‘pipes’ occupied by the mass flows moving downward and upward, respectively, and their values satisfy fd + fu = 1. This reproduces the observed ALi for TYC 429-2097-1 well. Repeating the same calculation with the alternative set of nuclear reaction rates from the JINA database23 yields a similar ALi of 4.515. In contrast, assuming this star had never experienced any extra mixing, the ALi would be constant at the initial value of ALi = 1.16, because the temperature in the envelope is too low to ignite both the production and destruction reactions of 7Li. The abundances of 3He, 7Li and 7Be as functions of the processing time for the mass circulation are shown in Fig. 3.

During the extra mixing process, 3He is converted to 7Be via the reaction of 3He(4He, γ)7Be, and then 7Be is quickly converted to 7Li via the reaction of 7Be(e, ν)7Li. To achieve such a high level of ALi, abundant 3He is required. The initial surface 3He is computed from the MESA model, which is Y(3He) = 4.038 × 10−4. Figure 3 shows the decrease of 3He as a function of time for extra mixing processing. A total amount of Y(3He)/H ~ 1.477 × 10−4 is burned off during this circulation, and the produced Y(7Li)/H is 3.206 × 10−8. This is because another reaction, 3He(3He, 2p)4He, dominates over the reaction 3He(4He, γ)7Be, thus consuming the majority of 3He. The strong competition from the 3He(3He, 2p)4He reaction prevents more 3He from converting to 7Li. Testing with different sets of extra mixing parameters shows that the maximum of ALi from our network calculation is 5.07. The 3He supply may eventually run out and cannot be renewed by the giant, in which case the surface ALi is likely to decrease, even if the internal conditions remain the same. In contrast, if the internal conditions do change, the surface ALi may also decline due to the destruction by convective activities in stars. Either way, the super Li-rich phase may disappear after a short period of time. In our calculation, the asymmetric mass circulation described by a large ratio of fd/fu is a key factor for achieving super-high Li enrichment. This large fd/fu ratio indicates that the upward flow is moving much faster (since its ‘pipe’ is thinner) than the downward flow, while the mass is conservative in the extra mixing process.

The cause of the extra mixing has not been well understood, and rotationally induced mixing is often attempted. Indeed, TYC 429-2097-1 is a slightly rapid rotator with a projective velocity of 11.3 km s−1, which is about 10 times faster than that of normal giants. The spinning up of an RGB star is either caused by the tidal synchronization effects in a close binary system or the engulfment of a massive planet7,20. We calculated the radial velocities based on the two independent observations through LAMOST and APF (with an interval of ten months), and found no significant radial velocity change at a level of a few kilometres per second, which is the typical uncertainty for radial velocities derived from LAMOST spectra. Thus, it is very unlikely that a star has a stellar companion that is massive and close enough to spin up via tidal synchronization. In contrast, one would expect some associated features that are detectable if a massive planet was engulfed and digested. For example, it was found that there might be a large probability of Li-rich giants exhibiting excess in the infrared flux, yet we found no sign of infrared excess (see Supplementary Fig. 2). In addition, if the matter exchange did happen at a certain time, there should be some fluctuations in the abundance pattern. However, TYC 429-2097-1’s 12C/13C is at a typical level for its stage7, and its α abundance is also quite normal among the giants with similar [Fe/H]. Given all these facts, we speculate that in our case, the enhanced extra mixing might neither be caused by the presence of a massive planet (if there were any) nor a close stellar companion. There are other assumptions often approximated as the internal cause of enhanced extra mixing; that is, thermohaline instabilities and magnetic buoyancy. The thermohaline convection driven by the 3He(3He, 2p)4He reaction, which produces a local depression in the mean molecular weight8, can cause enhanced extra mixing inside the star. The magnetic buoyancy mechanism in the presence of a magnetic dynamo would permit the buoyancy of magnetized material near the hydrogen-burning shell, thus inducing the form of matter circulation in RGB stars24. We speculate that the magnetic buoyancy and thermohaline instabilities might play roles together during the mass circulation, in which the former may lead to very fast upward circulation and the latter drive downward circulation at a much slower speed.

Although the ALi measured in this star is very high, it is still well within the upper limit that the theoretical model could reach. It is also important to note that the RGB bump is not the only stage for inhabitation of Li-rich giants; many Li-rich giants have been reported in various stages in previous studies, including those in the core helium-burning phase, which is very close to the RGB bump region on the Hertzsprung–Russell diagram. Although our data do not support this as the most likely mechanism, if our star occupies this stage, an alternative scenario will be needed for interpreting such a high ALi.

## Methods

### Data reduction

We followed the standard procedure for data reduction with an Interactive Data Language (IDL) package, which was originally designed for the fibre optics Cassegrain échelle spectrograph25. The instrumental response and background scatter light were considered during the reduction, and cosmic rays and bad pixels were removed carefully. The resulting spectrum has a signal-to-noise ratio of ~160 at 6,707.8 Å.

### Deriving the stellar parameters

First, we combined three iron line lists26,27,28 and calibrated 213 lines out of 257 with the solar spectrum29. Then, we eliminated those seriously blended or poorly recognized lines seen from the spectrum of TYC 429-2097-1, as well as the lines that were too strong (>120 mÅ) or too weak (<20 mÅ). Finally, 57 Fe i and 12 Fe ii lines were used as the parameter indicators. Teff was derived from the excitation equilibrium of Fe i lines with an excitation energy (Eexc) greater than 2.0 eV30. The log[g] value was determined by equalizing the two sets of iron abundances obtained from the Fe i and Fe ii lines, respectively. Statistically, the iron abundance derived from each individual Fe i line and the equivalent width from the same Fe i line will be mutually independent if the micro-turbulence velocity (ξt) is correctly set. Using this trick, we can obtain ξt, and then the metallicity ([Fe/H]) can be settled simultaneously if all the mentioned constraints are achieved. All the iron abundances are derived from NLTE analysis with the MARCS atmospheric models31 since it has been suggested that Fe i lines suffer a non-negligible NLTE effect27. The procedure of this approach is much more like an iteration. We started with the results from the LAMOST pipeline as the initial input, and then by calculating MARCS models and adjusting the stellar parameters step by step, we finally ended up with a self-consistent solution. Supplementary Fig. 3 shows the derived iron abundances from individual lines as functions of their equivalent widths (top panel) and Eexc (bottom panel). Based on the experience of our previous work using the similar spectroscopic method, the errors for Teff, log[g], [Fe/H] and ξt are estimated to be ±80 K, ±0.10 dex, ±0.06 dex and ±0.10 km s−1, respectively.

### Determination of the elemental abundances

We used the spectrum synthesis method to derive the abundances of all the species discussed in this paper. The theoretical profiles of the corresponding lines were calculated based on the MARCS model31. An interactive IDL code Spectrum Investigation Utility (SIU) was applied to calculate the synthetic line profiles. The coupled radiative transfer and statistical equilibrium equations for the NLTE calculation were solved based on the accelerated lambda iteration method. We refer readers to Mashonkina et al.27 for a more detailed description of this method27. The resulting departure files were transferred into SIU for NLTE line synthesis. The solar iron abundance of log[εFe] = 7.5 was assumed in our work.

In the abundance analysis of Li, the resonance line at 6,707.8 Å, the subordinate line at 6,103.6 Å and the line at 8,126.3 Å32 were used to derive ALi. Although the line at 8,126.3 Å is blended with two telluric lines, it shows a similar result to those derived from the resonance and subordinate lines. The final ALi was determined by averaging the results from these three lines. Many previous studies note that NLTE corrections are important for strong lines. In general, the NLTE correction for Li is not large for the ‘Li-normal’ stars; however, it will significantly increase for Li-rich objects, especially for the strong resonance line at 6,707.8 Å. In very extreme cases (such as ours), the local thermodynamic equilibrium (LTE) theoretical profile of 6,707.8 Å could be saturated at the core. Therefore, the NLTE effects were taken into consideration in our abundance analysis for Li. For the NLTE analysis, we applied the same atomic model and line data as those presented by Shi et al.33. The carbon abundances were derived from the C i line at 5,086 Å and the C2 line at 5,135 Å34. The nitrogen lines were either blended or too weak in our spectrum, so we turned to the CN band near 8,003.5 Å to estimate the nitrogen abundance by fixing carbon to the value we had just derived. Then, the carbon isotopic ratio was determined by adjusting the contributions from 12C and 13C until we obtained the best fit to the observed CN band profile. The determination of α abundance (Mg, Si and Ca) with NLTE analysis was based on a series of previous studies35,36,37. The final α abundance was obtained by averaging the abundances obtained from those elements. We also derived abundances of several other elements, which are presented in Supplementary Table 1.

The error of the ALi was estimated by changing the stellar parameters (namely, Teff, log[g] and [Fe/H]) within their error ranges and calculating the corresponding variations in abundance. The results of this test are presented in Supplementary Table 2. It is clear that ALi is more sensitive to variation in Teff than log[g] or [Fe/H]. A change of 80 K for Teff results in a variation of ~0.09 dex for ALi. Thus, we adopted the variation caused by the error of the effective temperature as the uncertainty for each Li i line, which was ±0.09, ±0.09 and ±0.08 for the lines of 6,707.8, 6,103.6 and 8,126.3 Å, respectively. The error of the final ALi was obtained by calculating the standard deviation of abundances derived from the three lines. For the other elements, if more than three lines were used for the abundance determination, we calculated their standard deviation and compared it with the error caused by the uncertainties of the stellar parameters. The larger was then adopted as the final error. A few of the species, such as the 12C/13C ratio, were not suitable for the above analysis, so we estimated their errors by giving the upper and lower limit of the best fit to the profile.

### Maximum likelihood method and evolutionary stage

The likelihood function is expressed following Basu et al.38, which is defined as:

$$L = L_{P_{{\mathrm{obs1}}}}{\kern 1pt} L_{P_{{\mathrm{obs2}}}}{\kern 1pt} L_{P_{{\mathrm{obs3}}}} \cdot \; \cdot \; \cdot$$
(1)

where Pobs is the observed parameter (for example, Teff) and

$$L_{P_{{\mathrm{obs}}}} = \frac{1}{{\sqrt {2\pi } \sigma _{P_{{\mathrm{obs}}}}}}{\mathrm{exp}}\left( {\frac{{ - \left( {P_{{\mathrm{obs}}} - P_{{\mathrm{model}}}} \right)^2}}{{2\sigma _{P_{{\mathrm{obs}}}}^2}}} \right)$$
(2)

The normalized probability of each model pi is expressed as

$$p_i = \frac{{L_i}}{{\mathop {\sum}\limits_{i = 1}^{N_{m}} {\kern 1pt} L_i}}$$
(3)

where Li is the likelihood function of the ith model and Nm is the total number of models. The probability was integrated from the boundary constrained by the 3σ error range of the observed parameters. Thus, the maximum value of the integrated probability is 0.5, and the best-fitted parameters are obtained from this probability (ref. 39).

The grid of evolutionary models for calculating the likelihood was generated from MESA40 code. The grid covers a wide range of masses from 0.6–3.0M with a 0.02M interval on mass and a 0.005 interval on metallicity (Z). The evolution tracks were constructed from the pre-main sequence to the asymptotic giant branch (AGB) phase. To generate the grid, the initial parameter setup was mostly as described by Paxton et al.40 except for the solar chemical abundance (Z/X). We adopted (Z/X) = 0.0229 (ref. 41) because the calibrated solar model with this mixture fits the internal structures from helioseismic inversion42 slightly better than the others43. The MESA density–temperature (ρT) tables were based on an updated version of the Rogers and Nayfonov tables44. Ferguson et al.45 extended the opacity for the solar composition to the low-temperature case in 2015, and we adopted their results in our computation. The stellar metallicity was transferred into ‘metal’ abundance Zinit, from which the hydrogen and helium abundances (Xinit and Yinit) were calculated.

To obtain the luminosity and log[gGaia] from the parallax, we first calculated the bolometric magnitude for the absolute V magnitude by Mbol = Vmag + BC + 5 logπ + 5 − AV, where π has the unit arcsecs, BC is the bolometric correction, computed following Alonso et al.46, and AV is estimated using the Galactic extinction map that was presented by Schlafly and Finkbeiner in 201147 (all values needed for the calculation are presented in Supplementary Table 1). We calculated the luminosity using the relation of Mbol − Mbol = $$- 2.5{\kern 1pt} {\mathrm{log}}\left[{\frac{{L_{{\mathrm{Gaia}}}}}{{L_ \odot }}} \right]$$. Finally, log[gGaia] was determined following the fundamental relation log[g] = $${\mathrm{log}}{\kern 1pt}[g_ \odot]$$ + $${\mathrm{log}}\left[{\frac{M}{{M_ \odot }}} \right]$$ + $$4{\kern 1pt} {\mathrm{log}}\left[{\frac{{T_{{\mathrm{eff}}}}}{{T_{{\mathrm{eff}} \odot }}}} \right]$$ + $$0.4\left( {M_{{\mathrm{bol}}} - M_{{\mathrm{bol}} \odot }} \right)$$, where log[g] = 4.44, M = 1.36M, Teff = 5,777 K and Mbol = 4.74 mag. The errors were given by the uncertainty transfer formula assuming that the errors were contributed by the uncertainty of the Gaia parallax.

### Parametric calculation of internal Li enrichment

During the RGB stage of a low-mass star, we introduced the extra mixing or ‘circulation process’ after the hydrogen-burning shell had erased the chemical discontinuity left behind by the FDU, as indicated by the bump of the luminosity function in the RGB. We followed the parameterization of Nollett et al.48 to perform the parametric calculations using $$\dot M$$, Tp, fd and fu as free parameters.

The basic assumptions were as follows. The extra mixing is a process of meridional circulation in the radiative zone of low-mass red giant stars, and the path of mass flow looks like a ‘conveyor belt’. A parcel of material with the initial abundance composition $$Y_i^{\rm{E}}(0)$$ at the base of the convective envelope circulates downward through the radiative zone structure and finally returns to the envelope with newly processed abundance composition $$Y_i^{\rm{P}}$$. The velocity of the sampled material can be expressed as dr/dt = $$\dot M$$/f4πr2ρ, where f is equal to fd (or fu) for the downward (or upward) circulation, and ρ is a function of the radius, r, governed by the stellar structure. The stellar structure, $$\dot M$$ and Δ specify as functions of time the conditions of T and ρ where the material passes through.

The computing code integrates the network of reactions of the hydrogen-burning chain by following the circulation trajectory. All but two of the adopted nuclear reaction rates are from NACRE49, the exceptions being that the updated rate of 7Be(p, γ)8B is from Du et al.50 and the rate of 7Be(e, ν)7Li is from the JINA database. The convective overturn-time of the envelope is set to ~1 yr, which is a good approximation in the sense that the mixing between the processed material and the convective envelope is instantaneous. The abundance changes of the ith nucleus in the envelope during the transport are due to nucleosynthesis and material replacement, and this corresponds to integrating $$\dot Y_i^{\rm{E}}$$ = $$\left( {\dot M{\mathrm{/}}M_{\rm{E}}} \right)\left( {Y_i^{\rm{P}} - Y_i^{\rm{E}}(0)} \right)$$48, where ME is the mass of convective envelope. To obtain the RGB stellar structure, including in particular the initial abundance composition in the envelope and the distributions of temperature and density in the radiative zone, we calculated the stellar evolution model for M = 1.36M using the MESA code. The initial abundance of 7Li in the sample material at the base of the envelope is ~1.024 × 10−11 (ALi = 1.86) when obtained from the present stellar evolutionary model calculation. This may increase to a level of ALi exceeding 4 in the processed material when the mass circulation finishes.

During the downward mass circulation, the abundance of 7Be increases quickly because the construction reaction 3He(4He, γ)7Be wins against the destruction reaction 7Be(p, γ)8B, and the maximum yield of 7Be is around the turning point of the mass circulation, where the temperature reaches the highest value Tp. In contrast, the production change of 7Li behaves rather dramatically during the downward mass circulation due to the complex competition between the production reaction 7Be(e, ν)7Li and the destruction reactions 7Li(p, γ)8Be and 7Li(p, α)4He. The abundance of 7Li drops suddenly at about 200 yr of the processing time as the rates of destruction reactions increase quickly with increasing temperature, and the 7Li abundance stays very low during the downward mass circulation, although it increases slightly after about 230 yr due to a decay of the fast-growing abundant 7Be. In contrast, the abundance of 7Li increases sharply during the upward mass circulation due to the fast decrease in the destruction reaction rates of 7Li as the temperature decreases quickly. The processed abundance $$Y_{{\rm{Li}}}^P$$ finally reaches a super-high-level of ALi = 4.506. The abundance of 7Li in the envelope contains the contributions of the mass circulation and mass replacement processes, and the total processing time can be estimated as $$M_{\rm{E}}{\mathrm{/}}\dot M$$, which is about 2.1 × 104 yr using the average value of the envelope mass for this RGB star.

### Projected rotational velocity

Following the assumption of Bruntt et al.51, the external broadening of the line profile was assumed to be contributed to by the stellar rotation, instrumental broadening and macro-turbulence. The projected rotational velocity (v sin i) was derived using 5 isolated iron lines at 6,151, 6,229, 6,380, 6,703 and 6,810 Å. The instrumental broadening was calculated by fitting the emission lines of the arc lamp with a Gaussian profile. The macro-turbulence velocity was estimated using the relation of Hekker et al.52, which is a function of Teff and log[g]. Then, we calculated a set of the theoretical spectra broadened with different rotational velocities, and v sin i was determined by finding the best fit to the observed iron line profiles.

### Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

This research was supported by the National Key Basic Research Program of China (2014CB845700), National Key Research and Development Project of China (2016YFA0400502) and National Natural Science Foundation of China (under grant numbers 11390371, 11603037, 11473033, 11490560, 11505117, 11573032 and 11605097). The Guoshoujing Telescope (LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. This work is supported by the Astronomical Big Data Joint Research Center, co-founded by the National Astronomical Observatories, Chinese Academy of Sciences and Alibaba Cloud. This research uses data obtained through the Telescope Access Program. The authors acknowledge J. Wicker for proofreading the manuscript. We acknowledge the use of Gaia and WISE data, and of the VizieR catalogue access tool.

## Author information

### Affiliations

1. #### Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China

• Hong-Liang Yan
• , Jian-Rong Shi
• , Yu-Tao Zhou
• , Qi Gao
• , Jun-Bo Zhang
• , Ze-Ming Zhou
• , Hai-Ning Li
•  & Gang Zhao
2. #### School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing, China

• Hong-Liang Yan
• , Jian-Rong Shi
• , Yu-Tao Zhou
• , Qi Gao
• , Ze-Ming Zhou
•  & Gang Zhao
3. #### China Institute of Atomic Energy, Beijing, China

• Yong-Shou Chen
• , Zhi-Hong Li
• , Bing Guo
•  & Wei-Ping Liu

• Er-Tao Li
5. #### College of Physics and Electronics Information, Inner Mongolia University for Nationalities, Tongliao, China

• Suyalatu Zhang
6. #### Department of Astronomy, Beijing Normal University, Beijing, China

• Shao-Lan Bi
•  & Ya-Qian Wu

### Contributions

H.-L.Y., J.-R.S. and G.Z. proposed and designed the study. H.-L.Y. and J.-R.S. led the data analysis, with contributions from Y.-T.Z., Q.G., J.-B.Z. and Z.-M.Z. Y.-S.C., E.-T.L., S.Z., Z.-H.L., B.G. and W.-P.L. performed the nuclear calculations. S.-L.B. and Y.-Q.W. calculated the evolutionary models and tracks. H.-N.L. carried out the observations. All authors discussed the results and contributed to the writing of the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Jian-Rong Shi.

## Supplementary information

1. ### Supplementary Information

Supplementary Figures 1–3, Supplementary Tables 1–2