Lithium abundances in giants as a function of stellar mass: An evidence for He-flash as the source of Li enhancement in low mass giants

It is well understood that stars on the red giant branch (RGB) undergo convective mixing or the first dredge-up, which alters photospheric abundances of several elements like helium, carbon, nitrogen, and lithium. Of those, Li is the most affected element. The surface Li abundance, A(Li), drops to $\sim$ 95% of their main-sequence value ²⁰. The discovery of the first Li-rich giant (LRG) ⁴¹ four decades ago challenged the general understanding of Li evolution. Since then, numerous works ³, ²², ²⁵, ¹⁴, ⁶ established that a small fraction ($\sim$ 1 %) of giants exhibit high levels of Li abundances compared to standard model predictions of A(Li) = 1.5 - 1.8 dex depending on mass. In many cases, the enhancement surpasses the primordial A(Li) $\simeq$ 2.7 dex, and in a few cases, A(Li) is more than the present interstellar medium value of $\sim$ 3.2 dex which is tagged as super lithium-rich (SLR) stars. The existence of such stars transcends the standard evolutionary theories implying some ancillary mechanism behind the production and preservation of Li in LRGs. Various theories were proposed to explain the mechanism and site of Li production in giants which include in-situ production and external origin ², ¹⁰, ¹¹, ¹⁵, ⁵.

While the Li origin debate was underway, a large observational study by ²² hypothesized that Li enhancement might be associated with the red clump (RC) stars with a helium-burning core. Lithium synthesized in the interior by a process known as Cameron-Fowler mechanism ⁴ might have mixed up with the outer layers by non-canonical processes during the Helium flash - a runaway nuclear burning at the RGB tip in low-mass stars ($\leq$ 2 M_⊙). Now hundreds of LRGs exist in the literature primarily due to large systematic studies ¹⁴, ³³, ⁶, ⁴⁴, ²⁶ based on large spectroscopic surveys such as LAMOST and GALAH and the space-based data sets of Gaia astrometry and time-resolved photometry from Kepler and TESS. Also, these studies concluded that most LRGs belong to the He-core burning RC phase. The study by Kumar et al. ²¹ demonstrated that Li enhancement is ubiquitous among core He-burning low-mass RC giants, and Li gets only depleted in giants ascending the RGB implying He-flash at the RGB tip is the most likely cause for Li enhancement among RC giants. Further, ³⁴, using Li abundances and asteroseismic parameters, showed that most of the SLR giants are very young RCs compared to Li-normal RC giants implying Li enhancement in SLRs occurred very recently. A recent observational study by Sneden et al. ³⁵ showed that the Li-rich giants are more likely to have a strong chromospheric He line at 10830 Å  opening a new avenue to probe Li-rich origin. These observational results are yet to be supported by theoretical modeling. One of the physical mechanisms proposed for Li enhancement is extra mixing due to the excitation of internal gravity waves by turbulent convection caused by He-flash and the associated large luminosity ³¹.

There are still questions related to high Li origin in giants. Is the He-flash a universal production mechanism for Li? Does Li enhancement occur only in Low mass giants, or are there massive ($>$ 2 M_⊙) Li-rich giants as well? Till now, surveys focused mostly on low-mass RC giants at the cooler end of the horizontal branch (HB). It would be interesting to map LRGs over a range of masses to understand the origin of Li enhancement. This is because if He-flash is the sole mechanism for high Li in giants, one wouldn’t expect LRGs among high-mass giants as He-flash is expected to occur only in low mass ($\leq$ 2 M_⊙) giants. Recently, the two observational studies ²⁶, ⁴⁶ showed the presence of LRGs across mass and evolutionary phases implying Li enhancement in giants could be from multiple sites. However, both studies suffer from ambiguity in determining giants’ evolutionary phase due to a lack of direct measurement of asteroseismic parameters.

Here, we assembled one of the largest data sets of 1240 giants for which direct measurements of asteroseismic parameters and LAMOST medium-resolution spectra are available. The maximum initial mass of a star (M_HeF) to experience He-flash ranges from 1.8 - 2.2 M_⊙ depending on its metallicity ¹². In this study, we probed Li abundance patterns as a function of mass among RC giants. In particular, among the “secondary RC stars” using a cut-off mass M_HeF $>$ 2 M_⊙.

It is challenging to unambiguously identify giants’ evolutionary phase, particularly the He-core burning RC giants from those ascending the RGB solely by their location in the $T_{\rm eff}-L$ diagram (HRD). It is because the luminosity bump and upper RGB overlap with the red clump regions. It is essential to have an independent way of knowing stars’ evolutionary phases, either as RC or RGB giants. The Kepler space mission data provides high-quality and high-cadence time-resolved photometry required for asteroseismic analysis. RC and RGB giants show characteristic oscillation properties enabling one to separate RC giants from those on RGB ¹.

We adopted a sample of 16,094 giants from the catalogue by Yu et al. ⁴⁵, who compiled giants for which oscillations were detected. It contains only stars with log $g$ $\geq$ 1.5 or log ($L/L_{\odot}$) $\leq$ 2.24 dex i.e., only RC and RGB giants. The catalogue excluded stars with the frequency of maximum oscillation power, $\nu_{\rm max}$ $<$ 5 $\mu$Hz and $\nu_{\rm max}$ $\geq$ 275 $\mu$Hz. The lower value culls out super giants, and the higher limit excludes dwarfs and sub-giants. This sample is shown in the HRD (Fig. 1) with the entire Kepler data as background. The sample’s luminosity values are estimated using stellar parallax, and values of apparent magnitude are taken from the Gaia DR3 catalogue. One could notice giants in the well-defined RC region in the HRD. Yu et al. ⁴⁵ provided asteroseismic parameters ($\nu_{\rm max}$, $\Delta\nu_{\rm max})$ and stellar parameters (mass, radius, log $g$, $[Fe/H]$) for the entire sample based on homogeneous asteroseismic analysis.

Our main focus in this study is to understand the distribution of Li among giants as a function of mass. For this, we cross-matched the Yu et al. ⁴⁵ sample with the LAMOST medium resolution spectroscopic survey DR7 catalogue ²⁴. We found 1240 giants common between the two catalogues. All the giants have reasonably good spectra with Signal-to-Noise (SNR) $\geq$ 30. Most of the spectra (88 $\%$) have S/N $>$ 50. For the classification of giants as RC or RGB we turned to literature because Yu et al. ⁴⁵ catalogue did not provide mixed mode period spacing ($\rm\Delta P$) values. Their classification is based on $\nu_{\rm max}$ and $\Delta\nu$ ( see their Fig 7). We have not adopted this method as there may be a possibility of contamination of RCs with RGB or vice versa, particularly at lower $\Delta\nu$ ($<$ 10 $\mu$Hz). To minimize contamination, we adopted directly measured values of $\rm\Delta\Pi_{1}$ from the literature ⁴⁰, ³³. We found $\Delta\Pi_{1}$ values for 584 giants. For the remaining 656 giants, the $\rm\Delta P$ values are calculated in this study using Kepler light curves (see appendix A). The 1240 giants will be our working sample for this study, and the sample is shown in the asteroseismic diagram of $\rm\Delta P$ vs $\Delta\nu$ along with the sample of RC and RGBs classified by ⁴⁰ as background. Going by the convention, we classified giants with $\Delta P$(or $\Delta\Pi_{1}$) $\geq$ 150 s as RC giants and giants with $\rm\Delta P$(or $\Delta\Pi_{1}$) $<$ 150 s as RGB giants. The $\rm\Delta P$ demarcation divides the sample into 777 RC giants and 463 RGB giants. Small contamination can’t be ruled out as there is a small overlap of RC and RGB space in the $\rm\Delta P$ - $\Delta\nu$ diagram, particularly at  $\Delta\nu\approx 5\ \mu Hz$. However, as the sample in Fig. 1 suggests, the RC sample with $\rm\Delta P$ $\geq$ 150 s may be least contaminated with RGB sample as the RC sample cut-off at $\rm\Delta P$ is $\approx$ 3-$\sigma$ away from the mean trend of RGB in the plot.

Our primary goal in this study is to understand Li abundances among RC giants with a range of stellar masses.

Abundances of Li as a function of stellar mass for the entire sample are shown in Fig. 3. The transition mass M_HeF = 2 M_⊙ divides the giants into two groups: a) pRCs ($\leq$ 2 M_⊙), which develop degeneracy at the core while evolving on RGB, and b) sRCs ($>$ 2 M_⊙), which develop sufficient core temperatures to burn He at the core in convective conditions while evolving on RGB, meaning no He-flash in high-mass giants. In the case of low-mass giants, at the RGB tip, ignition of He near the central core results in a thermal runaway with He-flashes generating massive energy. Note, the adopted 2 M_⊙ demarcation is an approximate average value predicted by various studies with a range of 1.8 to 2.2 M_⊙ ¹², ¹⁸. The vertical region in Fig. 3 indicates a possible range of masses that could separate pRC and sRC stars. (See Appendix B). Though predictions suggest He-flash generates a huge amount of energy only a part of it goes into lifting the H-burning shell upwards and hence causes a sudden drop in luminosity. The bulk of the energy goes into removing the central degeneracy. Post-He-flash, stars settle at the RC with He-burning at the core in convective conditions.

The key result from Fig. 3 is that none of the sRC giants ($>$ 2 M_⊙) shows A(Li) values more than that expected from the first dredge-up. The mean errors in A(Li) = 0.19 dex and mass = 0.14 M_⊙ are indicated by an error cross in Fig. 3. We have drawn a horizontal line at A(Li) = 1.8 dex, the expected maximum first dredge-up value for a star of mass 1.5 M_⊙ ²⁰. We found similar maximum A(Li) values for high mass giants by computing models using Modules for Experiments in Stellar Astrophysics (MESA), an open-source 1 D stellar evolution code ²⁸, ²⁹, based on the study by Schwab ³¹. Models are constructed for solar metallicity, as most of our giants are close to [Fe/H] = 0.0. Post first dredge-up, however, the models of high-mass giants show further depletion of Li as giants evolve to the sRC phase though at a much slower rate than their low-mass pRC counterparts which undergo extra-mixing during stars’ luminosity bump evolution ¹³.

The computed models for sRC giants yield A(Li) values between $\approx$ 0.7 - 1.6 dex, depending on mass (see Fig. 4). The expected A(Li) values agree well with the observed values of sRC giants. However, three sRC giants show A(Li) values slightly higher, by $\sim$ 0.1-0.3 dex than the maximum model predictions of A(Li) = 1.6 dex. Given the uncertainties in the observed values of about 0.2 dex, the slightly higher values of Li in these giants may not be attributed to fresh enhancement but to their evolution. Also, High-mass giants begin burning He at the center well before they settle in the RC phase which means some of these giants still can have slightly higher Li abundance than those settled at RC (see Fig. 4).

Importantly, unlike pRCs, none of the 109 sRCs in our sample are super Li-rich ( A(Li) = 3.2 dex). Slightly higher A(Li) (after taking into account estimated $\approx$ 0.2 dex measurement uncertainty) for a couple of sRC giants is most probably due to insufficient mixing rather than enhancement. The observed range of A(Li) values among sRC giants is probably due to varying levels of depletion and, of course, the initial values of Li with which stars might have evolved off the main sequence. Further, one could notice from the data in Fig. 3 and the models in Fig. 4 that the range of A(Li) among sRC giants is relatively smaller compared to pRC giants. It is known that low-mass giants undergo severe depletion of Li due to 1st dredge-up and extra-mixing near the luminosity bump. The high mass giants neither have sufficient time for Li depletion, as they evolve faster nor do they have extra-mixing at luminosity bump. As shown in Fig. 4, the 1 M_⊙ model suffers significant Li depletion both during 1st dredge-up and luminosity bump evolution. The lack of LRGs among sRCs provides another clue that He-flash is the key source of Li-enrichment among pRCs.

Previous attempts by Deepak & Reddy ¹⁴, Deepak & Lambert ¹³ to understand Li distribution as a function of mass could not resolve the issue either due to small sample size or unreliable mass determinations using stellar evolutionary tracks. Most mass tracks overlap in RC region in HRD making it challenging to derive masses solely based on evolutionary tracks. Our study overcame these shortcomings by assembling a large sample common among Kepler and LAMOST catalogues. The studies by Martell et al. ²⁶, Zhou et al. ⁴⁶, however, suggest LRGs are a diverse population found among sRCs, pRCs and also among RGB giants. The main differences between theirs and our study are; the primary sample source and the method used to classify giants as RCs and RGBs. Our sample is sourced from Yu et al. ⁴⁵ catalogue of Kepler giants with oscillations identified. All giants in our study have direct measurement of $\nu_{\rm max}$, a key asteroseismic parameter for evolutionary phase determination and also have $\rm\Delta P$ values measured directly from asteroseismic data. On the other hand, the primary source of the sample for the ²⁶ study is GALAH, and hence most of their sample giants do not have asteroseismic data. They identified giants as RCs and RGBs using stellar parameters which are proven to be ineffective for obvious reasons as RC and upper RGB regions overlap in the HRD. The study by ⁴⁶ also shows a few SLRs among sRCs. Their sample is primarily drawn from the LAMOST survey similar to ours but the classification of RCs and RGBs is based on neural networks. Unfortunately, there are no common giants between ²⁶ and ours. ⁴⁶ didn’t publish their sample set. The other difference between ours and Martell et al. ²⁶ is their lower mass cut-off of 1.7 M${\odot}$. However, this does not make difference to the results shown in Fig. 3. Among the many LRGs, only two are close to the adopted M_HeF = 2 M_⊙, an upper limit for the He-flash phenomenon which is possibly due to metallicity effect (see Appendix B). It may be possible that giants might have lost 0.2 M_⊙ to 0.3 M_⊙ as they evolved to the RC phase (see Chanamé et al. ⁹). This suggests that stars with an initial mass of about $\leq$ 2.2 M_⊙ undergo He-flash implying only RC giants with a current mass of about 2 M_⊙ or less show Li enrichment.

We have used a large sample of RGB and RC stars with evolutionary phases classified using the asteroseismic diagram of $\rm\Delta P$ - $\Delta\nu$ based on direct measurements of Kepler light curves. For the entire sample of 1240 giants (777 RCs and 463 RGBs), we derived Li abundances using spectral synthesis. We found no evidence of Li-enrichment among sRCs. The observations conform with the theoretical A(Li) predictions for sRC giants of M $>$ 2 M_⊙. We found all pRC giants, including three SLRGs and 11 giants with A(Li) $>$ 1.8 dex, whose A(Li) values are much higher than that expected from models and their counterparts on upper RGB. Also, we found no giant on RGB with Li abundance more than the upper limit of A(Li) = 1.8 dex expected from models for low-mass giants within the uncertainties. The lack of Li-rich giants among sRC stars is another clue that the He-flash, which only occurs in low-mass giants, is the potential site for Li-enrichment among low-mass giants. This result further strengthens the growing evidence that Li-enrichment occurs during He-flash. However, the transport process and mixing mechanism are yet to be explored. It would be worthwhile to combine carbon isotopic ratios ($\mathstrut{}^{12}C$/$\mathstrut{}^{13}C$) with lithium studies to understand mixing mechanisms.

This work has used data from the Yu et al. ⁴⁵ catalogue available at http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/ApJS/236/42. All spectra were taken from LAMOST public data release 7, operated and managed by National Astronomical Observatories, Chinese Academy of Sciences. We are grateful to the team of Stellar Classification Program (SCP) for the Kepler Mission. We acknowledge utilization of MESA models assembled by Josiah Schwab. Schwab’s input and output files are publicly available on Zenodo at doi: 10.5281/zenodo.3960434 (catalog 10.5281/zenodo.3960434).