Lithium Abundances from the LAMOST Medium-resolution Survey Data Release 9

Lithium is a fragile but crucial chemical element in the Universe, and exhibits interesting and complex behaviors. Thanks to the mass of spectroscopic data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) medium-resolution survey (MRS), we can investigate the lithium abundances in a large and diverse sample of stars, which could bring vital help in studying the origin and evolution of lithium. In this work, we use the Li i 6707.8 Å line to derive the lithium abundance through a template-matching method. A catalog of precise lithium abundance is presented for 795,384 spectra corresponding to 455,752 stars from the LAMOST MRS Data Release 9. Comparing our results with those of external high-resolution references, we find good consistency with a typical deviation of σ A(Li) ∼ 0.2 dex. We also analyze the internal errors using stars that have multiple LAMOST MRS observations, which will reach as low as 0.1 dex when the signal-to-noise ratio of the spectra is >20. Besides, our result indicates that a small fraction of giant stars still exhibit a surprisingly high lithium content, and 967 stars are identified as Li-rich giants with A(Li) > 1.5 dex, accounting for ∼2.6% of our samples. If one takes into account the fact that nearly all stars deplete lithium during the main sequence, then the fraction of Li-rich stars may far exceed 2.6%. This new catalog covers a wide range of stellar evolutionary stages from pre-main sequence to giants, and will provide help to the further study of the chemical evolution of lithium.


Introduction
The standard Big Bang nucleosynthesis (SBBN) theory suggests that lithium, the heaviest element formed just after the Big Bang (Wagoner 1973;Yang et al. 1984;Olive et al. 1990;Malaney & Mathews 1993;Mathews et al. 2017;Randich & Magrini 2021), plays a crucial role in unveiling the early stage of the Universe (Coc et al. 2014a).Currently, based on the baryon-to-photon ratio suggested by interpretation of measurements of the microwave background radiation, SBBN predicts robustly a primordial lithium abundance of A(Li) = 2.7 dex (Cyburt et al. 2003(Cyburt et al. , 2008(Cyburt et al. , 2016;;Spergel et al. 2003;Coc et al. 2012Coc et al. , 2014bCoc et al. , 2014c;;Fields et al. 2020).However, the long observation of lithium abundance in the metal-poor halo stars near turnoff contradicts this prediction.In particular, Spite & Spite (1982) found that the metal-poor unevolved stars with T eff > 5500 K exhibit a plateau of lithium abundance, which is independent of effective temperature; it is referred to as the Spite plateau in Deliyannis et al. (1990).Similarly, a plateau is clearly detected by Rebolo et al. (1988), and they suggested that A(Li) is independent of metallicity for metal-poor dwarfs.The primordial lithium abundance exhibited by the Li plateau is around A(Li) ∼2.2 dex, which is more than 3 times lower than the SBBN prediction.
The phenomenon of severe lithium depletion in the Universe is called the cosmological lithium problem.For years, various solutions have been supposed (e.g., Endal & Sofia 1976, 1978, 1981;Pinsonneault et al. 1989Pinsonneault et al. , 1992;;Chaboyer & Demarque 1994;Descouvemont et al. 2004;Kusakabe & Kawasaki 2015;Hou et al. 2017;Kang et al. 2019;Korn 2020;Sasankan et al. 2020).For example, Deliyannis et al. (1990) described how the choice of particular parameters leads to lithium depletion by a factor of 3 in halo dwarfs (as opposed to the factor of 10 predicted by Pinsonneault et al. 1992;Chaboyer & Demarque 1994), long before it was suggested by studies of primordial D and the microwave background that lithium depletion by a factor of 3 would be needed to make SBBN self-consistent at the same baryon-to-photon ratio; also, Pinsonneault et al. (1999) investigated stellar models with rotational mixing and suggested a depletion range of 0.2-0.4dex, which is close to the value needed by SBBN.Additionally, the present lithium abundance is found to be A (Li) = 3.28 dex in meteorites (Lodders et al. 2009), significantly exceeding the solar abundance and the SBBN prediction, which suggests that lithium has undergone some enrichment mechanism, despite being consumed in the interior of stars.
The evolution of lithium in the Milky Way presents a major challenge in modern astrophysics.On the one hand, lithium is easily destroyed by nuclear burning in stellar interiors Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.(Gamow & Landau 1933;Salpeter 1955); on the other hand, observations show that lithium can be produced in some specific evolutionary stages.
At present, growing observational evidence indicates that the thin-and thick-disk stars may have experienced different lithium enrichment paths.Molaro et al. (1997) noted that the metal-poor thick-disk stars exhibit the same lithium abundance as the lithium abundance of the Spite plateau found in halo stars.Guiglion et al. (2016) constructed a homogeneous catalog of lithium abundances for 7300 stars and found that lithium in the thick disk increases slightly with metallicity, while thindisk stars exhibit a steeper increase of lithium enrichment with metallicity.The different lithium enrichment behavior between the thin and thick disks is likely due to two possibilities: different Galactic lithium production between the two groups, and/or different stellar lithium depletion between them; for example, the different distributions in initial angular momentum between the two groups could lead to different lithium depletion (see Pinsonneault et al. 1992 for details).
In young open clusters, lithium content shows a remarkable dependence on effective temperature, T eff (Boesgaard & Tripicco 1986;Soderblom et al. 1993).Hotter stars (T eff > 6800 K), with relatively shallow convective zones, should preserve the primordial lithium within their stellar atmospheres, which have not been fully mixed down to hightemperature interiors; however, they deplete lithium over time even as they spin down (Deliyannis et al. 2019).A different mechanism must be at work, as the lithium depletion and spindown are correlated (see the Yale rotational models, e.g., Endal & Sofia 1976, 1978, 1981;Pinsonneault et al. 1989).Cooler stars (T eff < 5800 K) experience severe lithium depletion, and the standard theory can explain that cooler dwarfs have deeper surface convective zones, which result in a greater lithium depletion (Deliyannis et al. 1990); however, this process only takes place during the pre-main sequence (PMS).It is found that open clusters older than the Pleiades show lithium depletion in G (and cooler) dwarfs, and the depletion continues during the main sequence (MS), resulting in lithium abundances much lower than those seen in the Pleiades.The most likely mechanism is rotational mixing, and evidence suggests that this lithium depletion correlates with spin-down (Pinsonneault et al. 1990), especially as evidenced by the lithium abundance observed in short-period tidally locked binaries (Thorburn et al. 1993;Ryan & Deliyannis 1995).In the medium-temperature range, roughly in the narrow interval between 6500 K and 6850 K, lithium content is rapidly depleted, resulting in what is known as the Li-dip phenomenon, where different kinds of evidence support rotational mixing as its dominant cause (e.g., Boesgaard & Tripicco 1986;Jeffries 1997;Jeffries et al. 2002;Somers & Pinsonneault 2015a, 2015b;Deliyannis et al. 2019).In addition, the Li-dip is no longer as narrow as originally suspected by Boesgaard & Tripicco (1986), but in fact has a considerable structure.More specifically, there is a wall (or the hot or blue side of the Li-dip) of lithium abundances ranging over two dex near 6800-6700 K (Anthony- Twarog et al. 2009;Deliyannis et al. 2019;Twarog et al. 2020;Boesgaard et al. 2022;Sun et al. 2023), then a very deep part near 6700-6600 K (the original Li-dip), after which the lithium abundance increases for stars from 6600 K all the way to 6300 K. Also, there is an Li plateau (6300-5900 K) between the Li-dip and the depletion for T eff < 5800 K.Note that this plateau also depletes over time, as evidenced by SPTLBs (Deliyannis et al. 1994) and comparison of clusters of the same metallicity but different ages (Boesgaard et al. 2022), which might provide a possible connection to the Spite plateau.
According to the standard stellar evolutionary model, surface lithium depletion could occur during the PMS and early MS via nuclear burning at the base of the convective zone (Proffitt & Michaud 1989;Deliyannis et al. 1990;Deliyannis & Demarque 1991).Nearly all dwarfs in which the lithium line can be measured, which includes all A, F, G, K, and M dwarfs, deplete their lithium over time.In particular, the lithium depletion for MS stars in open clusters such as the Hyades and Praesepe is in clear contradiction to standard models (Cummings et al. 2017).The spin-down of MS stars could lead to angular momentum loss, which relates to rotational mixing; the Yale-style and other models based on these or related precepts are considered as factors relevant to this phenomenon (Pinsonneault et al. 1990;Steinhauer & Deliyannis 2004;Deliyannis et al. 2019).Also, observations of beryllium (Be) and boron (B), which can survive to deeper layers, could provide important evidence that rotational mixing depletes lithium in FGK dwarfs (Deliyannis et al. 1998;Boesgaard et al. 2004Boesgaard et al. , 2005Boesgaard et al. , 2020)).Somers & Pinsonneault (2015a) investigated the Li-rotation correlation in the Pleiades, and showed evidence that magnetic fields in rapid rotators can help inflate stellar radii and preserve lithium (Jackson et al. 2018(Jackson et al. , 2019)).
The first dredge-up process, occurring as stars evolve off the MS, can further bring the surface lithium into deeper layers of the convective zone.At this stage, much lithium can be destroyed via nuclear burning; as a result, a widely suggested upper limit is predicted: A(Li) < 1.5 dex for red giant branch (RGB) stars (e.g., Iben 1965Iben , 1967;;Brown et al. 1989;Kumar et al. 2011Kumar et al. , 2018b)).Besides, there are several nonstandard mechanisms suggesting lithium depletion during a star's lifetime, e.g., stellar rotation (Chaboyer et al. 1995;Charbonnel & Talon 2005), magnetic activity (Denissenkov 2010), atomic diffusion (Michaud 1986), and planet engulfment/accretion (Siess & Livio 1999;Delgado Mena et al. 2015;Galarza et al. 2021).Observations found that a small fraction of evolved stars can still retain anomalously high lithium abundance (Wallerstein & Sneden 1982).These stars, known as Li-rich giants, have lithium abundance that significantly exceeds the model prediction, indicating that there are still some unknown processes that noticeably enrich the surface lithium.The definition of an Li-rich giant as one with A(Li) > 1.5 dex assumes that the only lithium depletion mechanism is subgiant dilution by about 1.8 dex (from meteoritic 3.3 to 1.5 dex; Iben 1965Iben , 1967;;Charbonnel & Lagarde 2010).However, when taking the MS lithium depletion into account, the dilution by 1.8 dex will result in abundances lower than 1.5 dex, or possibly much lower (Sills & Deliyannis 2000;Chanamé et al. 2022;Sun et al. 2022).Therefore, assuming Li-rich giants to be only those with A(Li) > 1.5 dex could miss a lot of stars with lower A(Li) that have a greater lithium content than expected from the combination of MS lithium depletion and subgiant dilution, and therefore the fraction of Li-rich stars will be underestimated.
To better understand the complex behavior of lithium in the Universe, a catalog of lithium abundances derived from a homologous and consistent spectroscopic survey is necessary.Over the decades, considerable efforts have been dedicated to obtaining precise lithium abundances, which are essential for unraveling the mechanisms of lithium enrichment and depletion.Spectroscopic surveys, such as the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et al. 2012;Yan et al. 2022a), the Gaia-ESO (Gilmore et al. 2012), the Galactic Archaeology with HERMES (GALAH; Silva et al. 2015;Buder et al. 2018Buder et al. , 2021)), and the AMBRE Project (de Laverny et al. 2013), have provided a vast number of valuable low-and high-resolution stellar spectra, enabling us to deduce lithium contents for a large and diverse sample of stars.For example, Franciosini et al. (2022) measured lithium equivalent widths and abundances of ∼40,000 stars from the Gaia-ESO survey, predominantly distributed in open clusters.Martos et al. (2023) employed high-resolution HARPS spectra and analyzed the impact of metallicities, ages, and planets on lithium abundances for 41 solar analogues.Gao et al. (2021) derived a large sample of lithium abundances for approximately 300,000 LAMOST spectra.Based on the LAMOST low-resolution survey, Zhou et al. (2018) investigated a super Li-rich (A(Li) 3.3 dex, the typical lithium abundance of the interstellar medium, much rarer than Li-rich giants; e.g., de La Reza & da Silva 1995;Balachandran et al. 2000;Kumar & Reddy 2009;Adamów et al. 2015) K giant with a low carbon isotopic ratio and suggested that extra mixing can induce the Cameron-Fowler mechanism, which enhanced lithium in this star.Similarly, Yan et al. (2022b) discovered nine unevolved stars with unusually high lithium abundances (A(Li) > 3.8 dex) from the LAMOST medium-resolution survey, which indicates a different history of lithium enrichment for those unevolved stars.Kowkabany et al. (2022) reported the discovery of a very metal-poor (VMP), ultra-Li-rich giant with A(Li) (3D, NLTE) = 5.62 dex and investigated the possibility of lithium production.Additionally, by combining the LAMOST spectra with asteroseismic measurements from the Kepler mission (Borucki et al. 2010), Yan et al. (2020) presented a study of lithium abundances between the RGB and the red clump (RC) stars, which revealed that the RC stars are more frequently Li-rich rather than traditionally supposed RGB stars.Zhang et al. (2021) further investigated the evolutionary features of lithium for stars evolved from the RGB to the He-burning phase and suggested that the helium flash can be responsible for moderate lithium production.Likewise, Bandyopadhyay et al. (2022) presented a study of the lithium distribution and the kinematics of VMP stars with astrometric parameters from the Gaia mission (Gaia Collaboration et al. 2021) and the highresolution spectra observed from the Hanle Echelle Spectrograph-Galactic Survey of Metal-poor Stars (Kumar et al. 2018a) survey.
In this paper, we present our work in the following structure.Section 2 describes the spectra observed by the LAMOST survey and our sampling strategy.Section 3 introduces the theoretical spectra and the template-matching methodology.In Section 4, we compare our results with the lithium measurements from external surveys.We discuss the deviation and estimate the typical errors in Section 5.In Section 6, the catalog and properties of our lithium abundances are presented.Finally, we briefly summarize our results in Section 7.

Observational Data
The data set used in this work is composed of two parts: the observational spectra from the LAMOST medium-resolution survey (MRS) Data Release (DR) 9 and the reference set consisting of lithium abundances provided by other surveys (GALAH and Gaia-ESO), which is used for validation of our result.

LAMOST MRS Observation
The LAMOST survey uses a large-aperture reflective Schmidt telescope located at the Xinglong Observatory in Hebei province, China.Its focal plane contains 4000 fibers, connected to 16 spectrographs equipped with 32 CCD cameras (4k × 4k).In the year 2017, the spectrographs were upgraded to support two different modes: low resolution (R ∼ 1800) and medium resolution (R ∼ 7500).For the medium-resolution mode, the wavelength range is from 4950 to 5350 Å in the blue band, while the red band covers 6300-6800 Å.
The ninth data release (DR9) of the LAMOST survey includes 8,259,362 medium-resolution and 11,211,028 lowresolution spectra.The large coverage of the stellar samples observed by LAMOST makes it possible to obtain a homogeneous large sample of lithium abundances.

Stellar Parameters
In addition to the vast number of spectra mentioned above, LAMOST DR9 also equips us with stellar parameter measurements through the LAMOST Stellar Parameter Pipeline (LASP; Luo et al. 2015).LASP utilizes an empirical spectral library (ELODIE; Prugniel & Soubiran 2001) and employs a templatematching method to derive the stellar parameters.Furthermore, we crossmatch our data with the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017) DR17.APOGEE is one of the subprojects of the Sloan Digital Sky Survey (Eisenstein et al. 2011), which offers highresolution (R ∼ 22,500) near-infrared spectra with high signalto-noise ratio (S/N > 100) for approximately 650,000 stars.The APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP; García Pérez et al. 2016) fits these observational spectra through comparison to the precomputed grids (Gustafsson et al. 2008) and provides stellar parameter measurements with an assumption of local thermodynamic equilibrium (LTE; Jönsson et al. 2020).

Data Preparation
In order to obtain the synthetic spectra, we generate a series of similar templates of the same stellar parameters (T eff , g log , [Fe/H], and microturbulence velocity ξ) with different lithium abundances, so that the χ 2 minimization can be performed on the targets.To achieve this goal, we first use the stellar parameters provided by LAMOST LRS DR9 for each MRS spectrum.Then we adopt the APOGEE measurements for the common stars to increase the size of our sample.For stars that have both LASP and ASPCAP stellar parameters, we keep the ASPCAP value since that is obtained from high-resolution spectra.Finally, we acquire a sample set of 455,752 individual stars with both stellar parameters and LAMOST MRS spectra.An illustration of the parameter space distribution of our samples is shown in Figure 1.

Methodology
The template-matching method is commonly adopted for determining the stellar parameters in spectral research, which searches for the minimum χ 2 between the observed spectra and the templates.

The Templates
In order to derive the lithium abundance from the LAMOST MRS spectra, we use a grid of synthetic spectra that were computed with the SPECTRUM synthesis code. 6The synthetic spectra are based on the Kurucz stellar atmosphere model (ATLAS9, Castelli & Kurucz 2003) in LTE conditions with the atomic line data for lithium adopted from Shi et al. (2007).
The microturbulence velocity is important in the lithium measurement; in this work, we calculate it separately for different stellar samples using a series of empirical relations (see Gao et al. 2021, for detailed information).The wavelength range of the synthetic spectra is from 6675 Å to 6740 Å in steps of 0.1 Å, and the resolution will be adjusted to match that of the LAMOST medium-resolution spectra.

The Lithium Abundances
Before matching the spectra, we correct the wavelength of the synthetic spectra utilizing a method similar to Li et al. (2021), which calculates the radial velocity based on the crosscorrelation function and successive derivatives.
To measure the lithium abundance, we use the Li I resonance line at 6707.8 Å, which is covered by the red band spectrographs (6300-6800 Å) of the LAMOST MRS.Therefore, only the red band spectra have been preserved for follow-up lithium abundance measurement.First, a grid of synthetic spectra is generated with the same stellar parameters (T eff , g log , and [Fe/H]) as adopted in Section 2.3 with different [Li/Fe] values.More specifically, we adopt an interpolation algorithm to generate synthetic spectra from the templates whose stellar parameters are located at adjacent grid points.For each observed spectrum with specific stellar parameters, we interpolate a series of synthetic spectra with [Li/Fe] varying from −3.0 to 5.1 dex in steps of 0.1 dex.
After obtaining the synthetic spectra with known stellar parameters and [Li/Fe], we use the χ 2 minimization algorithm to find the best-matched spectra.χ 2 is defined as Here, F i is the flux at the ith wavelength point of the synthetic spectrum, and E i is that for the observed one.
Theoretically, E i follows a Poisson distribution, which can also be regarded as the variance s i 2 .Generally, χ 2 describes the deviation between the synthetic spectrum and the observed one.In other words, when the minimum of χ 2 is reached, we obtain the best fit to the observed spectrum.
However, [Li/Fe] of one observed spectrum may fall between two adjacent grid points.Thus, we used a third-order polynomial to fit the χ 2 values, and the final [Li/Fe] is determined by the spectrum corresponding to the lowest χ 2 .Finally, we use A (Li) to indicate the lithium abundance by means of the formula A(Li) = [Li/Fe] + [Fe/H] + A(Li) e .

The Detection Efficiency
Figure 2 shows the four examples of our template-matching result.In each panel, the observed spectrum is marked by a gray curve, while the templates with five different lithium abundances are marked by different colors.The figure clearly shows the decrease in depression of the Li I 6707.8Å line toward higher temperatures, which makes the lithium abundance hard to detect for hot stars with weak Li I lines.
To provide an estimation of an upper limit in this scenario, we measure the depth of the Li I line, the average noise in the wavelength range 6600-6800 Å and the dispersion level of residuals between the observed spectrum and the synthetic spectrum.If the depth of the Li I line is less than those of the latter two, it can be easily drowned out; therefore, only the upper limit can be detected.We visually check the synthetic spectra and provide several empirical upper limits of lithium detection for different types of stars.Specifically, for the majority of FGK stars with T eff above 4500 K, 5500 K, and 6500 K, the upper limits are around 0.0 dex, 1.0 dex, and 2.0 dex, respectively.

Validation
In order to validate the reliability and accuracy of our method, we compare our lithium abundances with those of external measurements.We crossmatch our samples with the GALAH DR3 (Buder et al. 2021)  We first exclude spectra with S/N lower than 20 in order to affirm the reliability.The flag [Li/Fe]  , which provide the upper limits of lithium abundances.Additionally, we use the stellar parameters (T eff , g log , and [Fe/H]) provided by GALAH and Gaia-ESO instead of ours in order to get rid of any errors introduced from different stellar parameters.In this way, we finally selected 4331 and 68 common stars in the GALAH DR3 and the Gaia-ESO DR5, respectively.The distribution of stellar parameters for these stars is presented in Figure 3.
The comparison of our results with those from the common stars observed in the GALAH DR3 and Gaia-ESO DR5 is shown in Figure 4. Overall, good agreement between our results and those from the reference surveys can be found.However, the comparison with GALAH indicates a systematic overestimation of ∼0.1 dex in the lithium abundance derived from our method, while the comparison with the Gaia-ESO demonstrates an overestimation of about 0.2 dex in the same metric.The dispersion of A(Li) measurements is 0.2 dex for the common stars in GALAH, whereas a larger spread of 0.3 dex is found for the Gaia-ESO samples.Additionally, the comparison with the Gaia-ESO shows that stars with lower A(Li) are systematically overestimated, while those with higher A(Li) are slightly underestimated.However, the comparison with GALAH samples shows a rather consistent overestimation for each star.
In order to better understand how spectral quality affects the accuracy of our template-matching measurement, we explore the residuals of A(Li) for varying S/N in Figure 5.The  difference in the lithium abundance is defined as Figure 5 shows that ΔA(Li) is consistent for coverage at all spectral qualities, which suggests that the overestimation actually comes from systematic bias between different methods rather than the difference in spectral qualities.

Error Estimation
In order to evaluate the influences of the observational quality and other stellar parameters on our A(Li) measurements, we conducted a further investigation in this section.Thanks to the multiple observations of the LAMOST survey, we can calculate A(Li) separately for stars with repeated observations, and estimate the error resulting from the S/N of the spectrum.
First, we make comparisons between repeated observations that have similar spectral quality (the difference in S/N should be lower than 20%).Figure 6 exhibits the difference of A(Li) as a function of S/N, which suggests that the measurement precision of A(Li) is greatly influenced by the quality of observed spectra.For spectra with S/N = 20, a typical precision of ∼0.12 dex is found.However, the precision of A (Li) improves as the S/N of the spectra increases, as expected, and the error can be lower than 0.1 dex for spectra with better spectral qualities.
Second, we examine the systematic error that arises from different spectral qualities.For this purpose, we select spectra of repeated observations for the same stars with a significant difference in spectral quality (the difference in S/N should greater than 40). Figure 7 shows the difference of A(Li) derived from spectra of repeated observations as a function of the lower S/N.The distribution of ΔA(Li) is asymmetric, and there is a systematic underestimation for samples with lower resolution, which is significantly reduced when S/N reaches 20, At this point, a typical precision of ΔA(Li) = −0.15dex can be observed.For spectra with higher S/N, the systematic error between repeated observations becomes smaller.Therefore, we emphasize that A(Li) values derived from spectra with S/N > 20 are recommended in order to ensure reliable statistical analysis.

The Catalog of Lithium Abundance
The final catalog consists of 795,384 spectra corresponding to 455,752 unique stars in LAMOST MRS DR9.The definition of important attributes is presented in Table 1.The information on spectral identification includes the designation, the obsid and the source_id, which represents the LAMOST target ID, the LAMOST unique spectra ID, and the Gaia DR3 (Gaia Collaboration et al. 2022) source identifier.max_diff stands for the largest difference of deduced A(Li) between multiple exposures of the same star while std_diff means the standard deviation of these measurements.The flag is a ratio between the depth of the Li I 6707.8Å line and the residual fluctuations, and lim suggests whether the upper limit is reached or not.
Figure 8 illustrates the distribution of A(Li) for these stars.In order to better demonstrate our measurements, we apply more restrictions to our samples.We notice that when we only use the stars with S/N > 20 (the green distribution), the number of stars with A(Li) > 3.6 dex is significantly reduced, which suggests a potential effect of noise on the lithium measurements in low-S/N spectra.Next, we further restrict our sample    following the criteria below, and the result is represented by the blue distribution in Figure 8.
1.The upper limits are excluded.2. For multiple exposures of each spectrum, the maximum difference of A(Li) should be less than 1.5 dex. 3. The dispersion of A(Li) derived from multiple exposures should be less than 0.5 dex.
As can be seen from Figure 2, measurement of A(Li) can be very difficult when the Li I line is weak, which leads to a decrease in detection efficiency.As a result, the number of stars with relatively low A(Li) is significantly reduced.
In addition, both distributions in Figure 8 show two distinct components: one with A(Li) ∼ 2.7 dex, the other one primarily located at ∼1.1 dex.In order to further investigate these components, we present the distributions of lithium with different stellar parameters in Figure 9; similar patterns are found in previous studies (e.g., Buder et al. 2021;Gao et al. 2021).
In the left panel of Figure 9, the T eff -A(Li) relationship is presented, which reveals a decline in lithium abundance as temperature decreases.We can clearly distinguish that the sample is divided into two separate components, first one is around A(Li) ∼ 2.7 dex, which is mainly hot stars that preserved a lot of lithium.The second component consists mainly of cooler stars, which suggests that most of them have experienced significant lithium depletion.
The g log -A(Li) panel shows that the component of A(Li) ∼ 2.7 dex is mainly unevolved stars, near 6000 K, and they have apparently experienced a mild lithium depletion of the order of 0.6 dex compared to the meteoritic value of ∼3.3 dex.The component with lower A(Li) is generally giants; most of them have experienced lithium depletion, while a few of them exhibit comparatively high A(Li) levels-the so-called Li-rich giants.From the literature (Brown et al. 1989;Kumar et al. 2011;Ruchti et al. 2011), the classical definition of Li-rich should be A(Li) > 1.5 dex.Additionally, Lagarde et al. (2010) suggested that after subgiant lithium dilution is complete (after the RGB), stars become cooler than 4800 K. Hence, we use the criteria A(Li) > 1.5 dex, g log < 3.5 dex, and T eff < 4800 K to identify Li-rich giants from the restricted samples discussed above.Following the above definition, we eventually identify 976 Li-rich giants, accounting for ∼2.6% of the sample stars, consistent with fractions in previous studies of 0.5%-2.2%(e.g., Martell & Shetrone 2013;Casey et al. 2016;Kirby et al. 2016;Smiljanic et al. 2018;Gao et al. 2019;Charbonnel et al. 2020;Yan et al. 2020;Martell et al. 2021).This is a far higher fraction than the ∼0.3% found by Kirby et al. (2016) for metalpoor stars.It needs to be pointed out that the A(Li) threshold for which giants should be properly considered as Li-rich depends sensitively on the turnoff T eff that those stars evolved from, and perhaps on their [Fe/H] and other factors, which means that the ratio can greatly depend on the adopted definition of Li-rich giants.Furthermore, we observed 174 giants with lithium abundances exceeding the primordial value of 3.3 dex, which are classified as super Li-rich giants and comprise ∼18% of all our Li-rich giants.The lithium content in these super Li-rich giants is surprisingly high, which makes them valuable samples in further studies.Perhaps most of them undergo a phase of lithium production followed by its destruction, so that only a small fraction of giants are observed to be Li-rich at any given time.Notably, we also discover 335 super Li-rich unevolved candidates that have lithium abundances higher than 3.8 dex, which significantly surpasses the meteoritic value of 3.3 dex.These dwarfs, which have extremely shallow surface convective zones, have extraordinarily high lithium abundance levels that challenge current models.More specifically, mechanisms such as accretion of rocky planetesimals and upward diffusion (for example, radiative acceleration), which could bring lithium to the surface from below and create supermeteoritic values (Richer & Michaud 1993), could possibly explain the unusual enrichment.
The [Fe/H]-A(Li) relationship is also an important indicator of lithium evolution.For that purpose, we trace A(Li) as a function of metallicity in the right panel of Figure 9.We clearly see that dwarfs with −2.4 < [Fe/H] < −1.6 dex show a constant lithium abundance, which is very close to the plateau of the SBBN abundance value.Thus, we visually checked the quality of the fit between the observed and synthetic spectra and find six metal-poor stars that also have a lithium abundance that exceeds the meteoritic abundance value.One of these stars (J1314+3741) has been analyzed by Li et al. (2018) with a high-dispersion spectrum (Noguchi et al. 2002) observed with  the Subaru Telescope to have A(Li) LTE = 3.48 dex, while our A (Li) measurement of J1314+3741 is 3.56 dex using the same stellar parameters from Li et al. (2018).A time variation of the radial velocity is detected for this object, hence the interpretation of its high A(Li) is considered to be the accretion of matter from a highly evolved companion star or an extra mixing caused by merging events with planets or other objects of small mass.Considering that our results have a systematic overestimation of ∼0.1 dex, which is discussed in Section 4, we think this is a consistent result.
It should be emphasized that our catalog is the first time that such a large statistical and homogeneous sample of lithium abundances has been acquired from LAMOST DR9 over a very wide range of stellar parameters.

Conclusion
In this study, we employ a template-matching method to determine the lithium abundance for the LAMOST MRS by fitting the Li I resonance line.We finally derive the lithium abundance of 795,384 spectra for 455,752 stars from the LAMOST MRS DR9.The comparisons between our measurements and high-resolution references such as GALAH and Gaia-ESO show good agreement with a deviation of σA (Li) ∼ 0.2 dex.To evaluate the internal precision of our method, we perform an error analysis based on stars that have multiple observations from LAMOST MRS.The random error of our A(Li) measurement is sensitive to the observational quality; meanwhile, a systematic overestimation was observed for spectra with low S/N.However, for spectra with S/N higher than 20, the internal error becomes smaller, and the typical precision can be better than 0.1 dex for these stars.The catalog of lithium abundance is presented and ∼900 Li-rich giants are found during a provisional analysis of our results.A larger number giants may be Li-rich if lithium depletion during the main sequence is also taken into account.Based on these Li-rich samples, multiple stars with extraordinary lithium enrichment are identified.The chemical and kinematic properties of these results are worth further exploration, and will help to reveal the evolution of lithium.
We supply a LAMOST MRS DR9 catalog with a mass of consistent lithium abundance measurements, and the templatematching method constructed in this work will be applicable to further medium-resolution observations such as the ongoing LAMOST MRS DR10.
Xiang et al. (2015) used a template-matching method to exploit the LAMOST Stellar Parameter Pipeline at Peking University (LSP3) to determine radial velocities and stellar atmospheric parameters for the LAMOST survey.Utilizing the template-matching technique of the LSP3 pipeline, Li et al. (2016) derived the [α/Fe] ratios from the LAMOST lowresolution spectra.Gao et al. (2019) adopted a similar approach to measure [Li/Fe] and search for Li-rich giants from the LAMOST DR7.In this study, we revised the method similar to Gao et al. (2021) for lithium abundance measurement.

Figure 1 .
Figure 1.The distributions of stellar parameters for our samples.
in the GALAH DR3 catalog shows the quality of [Li/Fe] measurement.Objects with flag [Li/Fe] = 0 generally have a more reliable lithium abundance than others.Similarly, [ ] lim Li1 in the Gaia-ESO DR5 shows the Li I measurement type, and we discard objects with =

Figure 2 .
Figure 2. Examples of our fitting results for a cool giant (top left), a cool dwarf (top right), a warm giant (bottom left), and a hot dwarf (bottom right).In each plane, the observed spectrum is plotted the shaded gray region; at the same time, the template spectra are plotted with A(Li) = −1.0(black line), 0.0 (red line), 1.0 (green line), 2.0 (yellow line), and 3.0 (blue line).The stellar parameters and lithium abundances are listed, and the vertical gray dotted lines show the position of the Li I resonance line.

Figure 3 .
Figure 3.The distribution of stellar parameters for common stars from the GALAH DR3 (gray distribution) and the Gaia-ESO DR5 (red dots).

Figure 4 .
Figure 4.The comparison of the lithium abundances derived from our method and those from the GALAH DR3 and the Gaia-ESO DR5.The error bars show the uncertainty.Colors are the same as in Figure 3.

Figure 5 .
Figure 5.The residuals of the lithium abundance as a function of S/N.Colors are the same as in Figure 3.

Figure 6 .
Figure 6.The random errors of A(Li) as a function of S/N.The red dots and error bars are the average values and the standard deviations of each bin.

Figure 7 .
Figure 7.The systematic errors of A(Li) as a function of S/N.The red dots and error bars are the average values and the standard deviations of each bin.

Figure 8 .
Figure 8.The distribution of A(Li) for our result.The whole sample set is plotted in red.Samples with reliable observations are plotted in green.The blue distribution shows the samples that have consistent multiple measurements.The number of stars in each distribution is listed.

Figure 9 .
Figure 9.The behavior of A(Li) as a function of T eff , g log , and [Fe/H].Only stars with S/N > 20 (green distribution in Figure 8) are represented.

Table 1
Description of the Catalog of Lithium Abundance (This table is available in its entirety in machine-readable form.)