Tracking the Evolution of Lithium in Giants Using Asteroseismology: Super-Li-rich Stars Are Almost Exclusively Young Red-clump Stars

Li abundances were derived by matching the synthetic spectra with the the observed Li line at 6707.78 Å in the medium-resolution LAMOST spectra. We used the 2013 version of the local thermal equilibrium (LTE) radiative transfer code MOOG (Sneden 1973), in combination with the Kurucz ATLAS atmospheric models (Castelli & Kurucz 2003). Atmospheric parameters (T_eff, log g, [Fe/H]) were taken from the Yu et al. (2018) catalog. Our line list, with atomic and molecular data, was compiled using the Linemake code. ⁸ Figure 2 shows a comparison of synthetic spectra with the observed spectra of a few representative stars. The estimated uncertainty in Li abundance is the quadratic sum of uncertainties in Li abundance caused by the estimated uncertainties in atmospheric parameters for each individual star (see Table 1). Li abundances were corrected for non-LTE effects using the Δ_NLTE values provided by Lind et al. (2009).

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We estimated the lower detectability limit in equivalent width (EW) for our data using the Cayrel (1988) formulation for uncertainties in EW for a range of signal-to-noise ratio (S/N) = 55–150. To err on the conservative side, we adopted a lower limit of 3 × δEW = (10.6–28.2) mÅ, which translates to lower limit abundances in the range +0.7 to +1.1 dex, depending on stellar parameters (Figure 2). This criterion resulted in 22 RC stars for which we could reliably derive Li abundances, for 12 of which we have ΔΠ₁ (Table 1).

Of the 59 RC giants in our sample, ΔΠ₁ values for 43 are available in the literature (Mosser et al. 2012a, 2014; Vrard et al. 2016). For the other 16 we derived it ourselves. We downloaded the time series data from the Kepler archive and converted them to the frequency domain using the Lightkurve package ⁹ (Lightkurve Collaboration et al. 2018). Details of our method of ΔΠ₁ estimation are given in Mosser et al. (2014) and Vrard et al. (2016). We were able to derive asymptotic values (Table 1) for 16 RC giants that have sufficient S/N in their power density spectra.

In Figure 3 we display A(Li) versus ΔΠ₁ for the RC stars. We divide the sample into three groups depending on their Li abundance:

• 1.  
  Li-normal (LN): A(Li) < 1.0 dex
• 2.  
  Li-rich (LR): 1.0 < A(Li) < 3.2 dex
• 3.  
  Super-Li-rich (SLR): A(Li) > 3.2 dex

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The A(Li) = 1.0 dex delineation is based on the Kumar et al. (2020) study's distribution on the RC (peaked at +0.7 dex), while the A(Li) = 3.2 dex delineation is based on the interstellar medium value (Knauth et al. 2003). Our key result emerges from Figure 3—the great majority (12/15 = 80%) of the SLR stars have ΔΠ₁ peaked at low values (mean = 257 ± 23 s). We note that two of the three outliers in the SLR group have masses 2σ from the mean mass of our RC sample (∼1.8 M_⊙, where the sample mean mass is 1.2 ± 0.3 M_⊙). Without these three outliers ¹⁰ the average remains the same, at 255 s, but the dispersion is halved (σ = 10 s), as expected from the histogram. In contrast, the Li-normal stars all have higher ΔΠ₁, ranging from 280 s up to ∼330 s. Their mean is 306 ± 14 s, much higher than the SLR group.

The Li-rich stars (Figure 3) show more complex behavior. They have a very broad distribution of ΔΠ₁ values rather than forming a coherent group. We now discuss the implications of the ΔΠ₁–A(Li) observations in relation to stellar evolution.

Low-mass giants (≤2 M_⊙) develop electron-degenerate cores while ascending the RGB. Initiation of an off-center helium flash in the degenerate core terminates the RGB evolution (Schwarzschild & Härm 1962; Demarque & Mengel 1971; Sweigart 1994). The first/main He-flash is very short-lived, lasting about 1000 yr. After the main flash a series of progressively weaker flashes ensues (Figure 4; also see Thomas 1967; Cassisi et al. 2003; Bildsten et al. 2012; Deheuvels & Belkacem 2018), each igniting closer and closer to the center, progressively removing the electron degeneracy in the core. The entire He-flashing phase lasts ∼1.5–2 Myr. Finally the very center of the core becomes convective, marking the start of the RC phase (quiescent core helium burning), which lasts for ∼100 Myr. Throughout this evolution ΔΠ₁ varies predictably, as seen in Figure 4 (also see Bildsten et al. 2012; Constantino et al. 2015; Bossini et al. 2015; Deheuvels & Belkacem 2018). Our new observational data enable us to compare the observed ΔΠ₁ with model predictions.

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We have calculated a series of stellar models using the MESA code (version 12778; Paxton et al. 2011, 2019) that vary in mass ¹¹ (M = 0.9, 1.2, 1.4 M_⊙) and metallicity ([Fe/H] = −0.4, +0.0), to cover the bulk of our observational sample. RGB mass loss was modeled using the Reimers (1975) formula (η = 0.3). We used the standard MESA nuclear network ("basic.net") and standard equation of state (see Paxton et al. 2019 for details), and α_MLT = 2.0. Convective boundary locations were based on the Schwarzschild criterion, extended with exponential overshoot (Herwig et al. 1997). In Figure 4 we show a representative model that matches the mean mass of our sample, 1.2 M_⊙, and is of solar metallicity ¹² (the mean [Fe/H] of our sample is −0.14 ± 0.26 dex). As Bossini et al. (2017) showed, the very early RC ΔΠ₁ evolution is not dependent on mass; however, it has some dependence on metallicity. Comparing the dispersion of [Fe/H] in our sample (0.26 dex) with the models in Figure 3 of Bossini et al. (2017), we expect a variation of ∼5 s in ΔΠ₁. This is approximately the same as our observational error bars (Figure 3). On the other hand, the late RC is particularly sensitive to the treatment of convective boundaries (e.g., Constantino et al. 2015; Bossini et al. 2015). To match the highest ΔΠ₁ values (∼330 s) we adopted an overshoot parameter f_OS = 0.02.

We display the model evolution of ΔΠ₁ versus time in the top panels of Figure 4. Overplotted are the 1σ intervals of ΔΠ₁ for the observations of the SLR and Li-normal groups (see Figure 3). It can be seen that the high values of ΔΠ₁ of the Li-normal stars are only available in the second half of the RC evolution (from ∼40 Myr onward), or for extremely brief periods (∼0.005 Myr) during the early helium flashes, which are unlikely to be observed in such numbers. We thus identify the Li-normal stars as more evolved RC stars.

In contrast, the low ΔΠ₁ values of the SLR stars are only consistent with young RC stars (≲40 Myr in the 1.2 M_⊙ model). Interestingly we find there is very little overlap between the Li-normal and SLR populations. This may indicate a rapid Li-depletion event (but see Section 4.4).

One of the main hypotheses for the Li-enrichment event is that it occurs during the main helium flash (Kumar et al. 2011; Mocák et al. 2011; Silva Aguirre et al. 2014; Kumar et al. 2020; Schwab 2020). Here we explore the possibility that our sample of SLR stars are currently experiencing the CHeF, or are in the following subflashing phases.

In Figure 4 it can be seen that there is some degeneracy in ΔΠ₁ during the early phases of the RC evolution. This makes identifying the exact young RC phase that the SLR stars reside in more difficult.

The vertical portions of the ΔΠ₁ evolution are extremely short-lived, so it is very unlikely to find stars in these phases. Adding the extra dimension of Δν (bottom panel of Figure 4), we see that the Δν values of the model's early subflashes are inconsistent with our sample. This is also true of the main CHeF (not pictured), which has Δν ∼ 0.04 μHz. In addition, the main flash has ΔΠ₁ = 700 s, well outside our observed range. Thus, we can rule out our SLR stars being in the main core helium flash. The third subflash (SF3) has ΔΠ₁ ∼ 300 s, well above the SLR average value of 257 s, so we rule this out also. We checked the variation of ΔΠ₁ during the subflashes in our small set of models and found only small deviations of ∼ ± 5 s in our mass and metallicity range. ¹³ This variation is similar to our uncertainties on ΔΠ₁. Three possibilities remain, defined by the SLR ΔΠ₁ band:

• 1.  
  The first ∼40 Myr of RC evolution, "early RC" (ERC in Figure 4);
• 2.  
  The first ∼0.3 Myr of evolution, which encompasses the "merged" subflash SF5, named "very early RC" (VERC: 1.6–1.9 Myr range in Figure 4);
• 3.  
  The final separated helium subflash, SF4, which has a lifetime of 0.04 Myr and Δν values within the range of our observations.

Large surveys give us statistical information on Li-rich giants that may also help in identifying the exact phase of SLR stars. Using the large samples of Kumar et al. (2020) and Singh et al. (2019) we have calculated the SLR fractions to be 0.3% and 0.5%, respectively. If we hypothesize that all stars go through an SLR phase, then we can estimate timescales of the SLR phase. The RC phase lasts for ∼100 Myr, implying that the SLR phase would last around 0.3–0.5 Myr. The lifetime of SF4 is only 0.04 Myr, so this is inconsistent with the timescale estimated from the surveys. Put another way, we find too many SLR stars for the SF4 scenario, by a factor of ∼10. Further, we estimated the probability of finding even one SF star in our sample and found an expectation of 0.02 stars. Given these various lines of evidence we conclude that our SLR stars are highly unlikely to be in a flashing phase.

To attempt to distinguish between the two remaining phases we turn to our series of models, to quantify the theoretical versus observational dispersion in ΔΠ₁ and Δν. We found that the various stellar tracks covered the whole observed wide range of Δν for the SLR stars. Other uncertain model parameters, such as the convective mixing length α_MLT, would further increase the dispersion in Δν (Constantino et al. 2015; Bossini et al. 2017). Thus, we are unable to distinguish between the VERC and ERC scenarios using Δν.

In contrast, as mentioned above, ΔΠ₁ does not vary much with mass in the early RC, as reported by Bossini et al. (2017). During the VERC phase (not reported by Bossini et al. 2017) we find a small dispersion in our set of models. The variation with mass is ∼ ± 5 s, and with metallicity ∼ ± 10 s, which is comparable to the observed dispersion of the SLR stars (σ = 23 s; or σ = 10 s if outliers are ignored, see Section 3). Thus, within the mass and metallicity variation of our sample, the ERC and VERC phases always present low ΔΠ₁ values, close to what we observe in the SLR stars. This reinforces the finding that these objects are all young, or very young, RC stars.

Unfortunately, due to the Δν and ΔΠ₁ degeneracy we can not distinguish between these two phases. We now briefly discuss the implications of both scenarios.

In the ERC case only a small proportion, ∼1%, of stars would be super-Li-rich. This is a factor of 2–3 higher than the fraction found when taking into account all RC stars, consistent with the SLR stars being only found in the first ∼40% of the RC lifetime. In the VERC case ∼100% of low-mass stars would be SLR. That is, super-Li-richness would be a universal phase of low-mass stars. They would already be super-Li-rich as they start the RC, which would be consistent with the model of Schwab (2020), where the Li enrichment occurs during the main CHeF. A universal SLR phase would also resonate with the finding of Kumar et al. (2020), who report that all low-mass stars appear to go through a Li-enrichment phase, albeit to more moderate abundances—although this difference would be explained by our Li-normal group, which indicates that strong depletion occurs during the RC.

The Li-rich group (Figure 3) is more difficult to interpret, since the ΔΠ₁ distribution is so broad. We speculate that these stars could be in a phase of evolution intermediate to the SLR and Li-normal stars, currently depleting Li on their way to the late RC. This aligns with their ΔΠ₁ distribution being peaked at 290 s, which is between that of the SLR group (257 s) and the Li-normal group (306 s). If the Li-rich stars are currently undergoing Li depletion then it suggests the Li depletion is a slower process. More information is needed to disentangle the evolutionary state(s) of this group.