WIYN Open Cluster Study: The Old Open Cluster, NGC 188, and a Re-evaluation of Lithium-Richness Among Red Giants

We used the IRAF⁴⁴4IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy Inc., under cooperative agreement with the National Science Foundation. task fxcor to measure radial velocities ($V_{RAD}$) for all the spectral lines of each star, fit a Gaussian profile to the $V_{RAD}$ distribution in Fourier space, and then adopted the mean value of the Gaussian profile as the star’s $V_{RAD}$. Using methods described in C17 (for additional details see Cummings Cummings11 2011 and SteinhauerSteinhauer03 2003), comparisons were made to template spectra of radial velocity standards that have v sin i $<$ 5 km s^-1, that were observed with the same instrument and similar resolution (with typical SNR in the hundreds), and that span a wide range of spectral types. We derived $V_{RAD}$ = -59.64 $\pm$ 0.72 km s^-1 for the radial-velocity standard HD 144579 (observed during n1 only), in superb agreement with the value -59.38 $\pm$ 0.015 km s^-1 from Soubiran et al.Soubiran13 (2013). The $V_{RAD}$ for individual stars were measured independently for each night. We found a 0.84 km s^-1 systematic shift of n2 relative to n1. We thus shifted the spectra of n2 by -0.018 Å to match n1 and co-added the shifted spectra from n2 to n1 to get final spectra with a higher signal-to-noise ratio (SNR), on which we ran the fxcor task once again. Table 1 shows our $V_{RAD}$ measurements and errors from the final co-added spectra. Figure 1 shows the $V_{RAD}$ distribution; typical errors for individual stars are 0.5–1.1 km s^-1. A Gaussian fit yields a mean $V_{RAD}$ = -42.89 $\pm$ 0.16 km s^-1 ($\sigma_{\mu}$, $\sigma$ = 0.93 km s^-1), and we initially classified stars within 2 $\sigma$ of the mean $V_{RAD}$ (in the range [-44.75, -41.03] km s^-1) as $V_{RAD}$ probable members. Table 1 also shows our derived rotational velocities (v sin i) and errors calculated from fxcor based on line broadening. Our resolution suggests treating v sin i below $\sim$ 15 km s^-1 as upper limits, so all fxcor-derived values less than 15 km s^-1 are reported in Table 1 as “$<$ 15”.

In their thorough radial-velocity study of NGC 188, Geller et al.Geller08 (2008, G08) took repeated measurements of 1046 stars in the direction of NGC 188, and found 473 probable cluster members. Their average cluster $V_{RAD}$ calculated from single stars in common with our study is $-42.52\pm 0.12$ km s^-1 ($\sigma_{\mu}$). This is within 2.3 $\sigma_{\mu}$ (our $\sigma_{\mu}$) of our value. All of our stars except star 9291 were observed by G08, and the $V_{RAD}$ and membership information from G08 are included in Table 1. Figure 2 shows the difference between our values of $V_{RAD}$ and those of G08 for stars identified as single by G08 (SM = Single Member, SN = Single Nonmember). The mean difference is $\mu_{d}$ = -0.293 $\pm$ 0.135 km s^-1 ($\sigma_{\mu}$). After excluding stars 4294 and 5438, which are outliers that fall beyond $2\sigma$, the mean difference is $\mu_{d}$ = -0.324 $\pm$ 0.073 km s^-1 ($\sigma_{\mu}$). The differences for binary stars are larger, presumably because G08 report the mean binary $V_{RAD}$ derived from numerous individual measurements, whereas ours are instantaneous measurements.

As further checks of membership, especially for stars with $P_{\mu}$ from P03 in the range $10\%\leq P_{\mu}\leq 70\%$, we consider the $V_{RAD}$ in Table 1 and information from Gaia DR2Gaia16 (Gaia Collaboration 2016, 2018) about parallax ($\pi$), $\mu$ in R.A. ($\mu_{\alpha}$) and $\mu$ in dec ($\mu_{\delta}$), shown in the last few columns of Table 1. The stars from Gaia lie within 0.55^∘ of the center of our Hydra configuration and satisfy: $G\ <$ 18 mag, -2.8 mas yr^-1 $<\ \mu_{\alpha}\ <$ -1.8 mas yr^-1, -1.4 mas yr^-1 $<\ \mu_{\delta}\ <$ -0.4 mas yr^-1. Figure 3 shows histograms for $\pi$, $\mu_{\alpha}$, and $\mu_{\delta}$ with Gaussians fit to the obvious cluster. The four stars, 3062, 4408, 6619, and 6719, fall well outside the 2$\sigma$ ranges in $\pi$, $\mu_{\alpha}$, and $\mu_{\delta}$, as illustrated especially clearly in the point vector diagram of Figure 4 for the last two of these criteria (yellow disks), so we label these stars as nonmembers. Star 4565 lies between 2$\sigma$ and 3$\sigma$ away from the mean in $\pi$ but is a clear member based on all other criteria so we label it as a member. Although star 9291 has $\pi$ consistent with membership, its $\mu_{\delta}$ lies between 2$\sigma$ and 3$\sigma$ away from the mean, its $\mu_{\alpha}$ is more than 3$\sigma$ away from the mean, and its (our) $V_{RAD}$ is inconsistent with single star membership, so we label it as a nonmember (5^th yellow disk in Figure 4). We thus label 29 out of 34 stars as members. Regarding membership, we note the following points. Three of our final members had $P_{\mu}$ from P03 in the range $10\%\leq P_{\mu}\leq 70\%$, so including them in our configuration has enhanced our sample. Of the five nonmembers, four have $P_{\mu}$ from P03 in the range $10\%\leq P_{\mu}\leq 70\%$ but one has $P_{\mu}=81\%$. Three of the five nonmembers have $P_{V_{RAD}}=0$ (from G08), but one has $P_{V_{RAD}}=98\%$ (the 5^th star is 9291, not measured by G08). This underscores the desirability of using multiple criteria for delineating membership whenever possible. Figure 5 shows all program stars on the CMD, with members as red disks and nonmembers as green disks. The membership designations from Cantat-Gaudin et al.Cantat18 (2018) based on the Gaia DR2 agree with all of ours except for star 9291, which they list as a member. Our spectrum shows no detectable Li in this star.

Regarding multiplicity, our power spectra from fxcor confirm single-star status for all stars labelled as such by G08, and indicate single-star status for star 9291 (not observed by G08). G08 designate seven of our Hydra stars as binaries, based on radial-velocity variations and orbital solutions. Of these, stars 4524, 4565, 4843, 5048, 5855 (all G08 Binary Members = BM) show double peaks from fxcor analysis of our spectra, confirming binarity. Star 6719, which we classify as a nonmember, does not show more than one peak in the power spectra; perhaps the secondary is faint. Star 4705, a definite binary from G08, also does not show a double/multiple peak; this very interesting star is discussed in detail in Section 6. The only differences between our multiplicity/membership designations and those of G08 are for stars 3062 and 6719 (we designate them as nonmembers); star 9291 was not observed by G08. The last column in Table 1 shows our final multiplicity/membership assignments. Figure 5 shows binaries as downward triangles and nonmembers as green disks. For the rest of the paper, we limit our discussion to the 29 cluster members.

We use the CCD photometry of Hainline et al.Hainline00 (2000, H00, $BVRI$), of Sarajedini et al.Sarajedini99 (1999, S99) ($UBVRI$), and of P03 ($BV$) to derive $T_{\rm{eff}}$. H00 covers a 40’ $\times$ 40’ region of NGC 188 that contains most of our member stars (26 out of 29), and S99 covers a 23’ $\times$ 23’ region that contains 20 out of the 29 members. Since H00 and S99 are on the same photometric scale for all filters to within the errors, we averaged the H00 and S99 $BVRI$ photometry for stars in common, used the H00 or S99 photometry for stars appearing only in one study, and used the S99 U photometry. The P03 photometry has a small offset and slope relative to H00 and S99, so for two stars (4829 and 1141) not observed by either H00 or S99, we adopted the P03 photometry shifted onto the H00 and S99 scale.

To reduce statistical errors and to better sample the spectral energy distributions of our stars, we use all 10 possible color combinations from $UBVRI$ to derive an averaged effective $B-V$ for each star in NGC 188, as follows (advantages of this method are discussed in C17). Using only our stars, we plot each color against $B-V$, fit a polynomial, and then convert that color for each star into an effective $B-V$. We then average the nine transformed $B-V$ and the actual $B-V$ into an overall effective $B-V$ (hereafter simply “$B-V$”). Some stars lack measurements in certain bands, so we use as many existing colors as possible. Table 2 shows the (average) $V$ magnitude, $B-V$, and $\sigma\ (B-V)$ (standard deviation of the 10 $B-V$ colors).

We derive $T_{\rm{eff}}$ by employing the $T_{\rm{eff}}$–($B-V$) relationship for red giant stars from Ramirez & MelendezRamirez05 (2005). To begin with, we assume [Fe/H] = 0.00 dex, which is in the middle of the range of published values (see Section 4.2), and adopt interstellar reddening $E(B-V)$ = 0.09 $\pm$ 0.02 mag from S99. The final (after iteration, see below) $T_{\rm{eff}}$ and $\sigma\ (T_{\rm{eff}})$ (standard deviation based on error propagation from $\sigma\ (B-V)$) are shown in Table 2.

Figure 5, left panel, shows the H00 photometry. A 6.3 Gyr Yale-YonseiDemarque04 (Demarque et al. 2004, hereafter $Y^{2}$) isochrone fits well the MS just below the turnoff, the turnoff, and subgiants just beyond the turnoff, so we use this isochrone to derive surface gravity (log $g$) at the $V$ of the stars. We derive microturbulence ($\xi$) using the relation $\xi\ =\ 1.5-0.13\ \rm{log}\ {\it g}\ km\ s^{-1}$ from Carretta et al.Carretta04 (2004) for red giant stars. Table 2 includes our final (after iteration, see below) values for log $g$ and $\xi$. Fortunately, only a few stars have $\sigma(T_{\rm{eff}})>$ 75 K.

The metallicity of NGC 188 is not only important for our study, but since NGC 188 is a very old open cluster, the metallicity is also of importance to studies of Milky Way formation and evolution. Unfortunately, even recent high resolution spectroscopic studies are discrepant with one another (see discussion below). We aim to shed some light on this issue, using the largest sample of cluster stars to date.

We selected 7 isolated Fe I lines that showed no significant blending out to at least 0.5 Å on either side of the line center in the Arcturus spectrum (R$\sim$150000, Hinkle et al.Hinkle00 2000), and measured the equivalent width of each line for the 29 members of NGC 188. Table 3 shows the wavelength $\lambda$ (Å), Excitation Potential (eV), and log (gf) values of these lines. Figure 6 shows a few examples of the lines that were used. Using the KuruczKurucz92 (1992) model atmosphere grids with [Fe/H] = 0.0 dex, we interpolated to construct model atmospheres matching the $T_{\rm{eff}}$, log $g$, and $\xi$ values for each star. Then, we performed LTE analysis for each Fe I line for each star using the abfind task of MOOGSneden73 (Sneden 1973) to derive A(Fe). We measured the Poisson-based signal-to-noise ratio (SNR) per pixel in a relatively line-free region near the Li 6707.8 Å line (see Table 2).

Figure 7 shows the final (after iteration, see below) A(Fe) derived for each line for each star as a function of the stellar $T_{\rm{eff}}$, log $g$, and $\xi$. We excluded (yellow disks) some entire lines that show dependence on $T_{\rm{eff}}$, log $g$, or $\xi$ ($\lambda$ = 6546.239 Å) and/or excessive scatter ($\lambda$ = 6597.561 Å, 6710.319 Å) and, for the remaining lines, we excluded those from individual stars that show excessive scatter. To derive [Fe/H] we have employed the method of “solar gf-values”, which we also used in Sun et al.Sun20 (2020), calculating [Fe/H] strictly relative to the Sun. In particular, for each line and for each aperture, we derive solar A(Fe) by measuring the same Fe I lines using sky spectra taken from the same configuration. For each line, we then subtracted the solar A(Fe) from the stellar A(Fe), using the solar spectrum from the same fiber as the stellar spectrum to help maximize consistency. For each star, we used the selected lines to calculate an average [Fe/H] in linear (not log) space, weighted linearly (not quadratically) by the 1$\sigma$ error of each line (see also C17). This error is calculated based on the SNR and FWHM of the Fe I line, using the relationship from Deliyannis et al.Deliyannis93a (1993). We also calculated $\sigma$ and $\sigma_{\mu}$ for each star. We show the final (after iteration, see below) results in Table 2 and Figure 8.

For the cluster, we used all the surviving individual Fe I lines to derive a cluster average (again weighted, in linear space) of $[Fe/H]_{188}$ = +0.084 $\pm$ 0.016 dex ($\sigma_{\mu}$, and $\sigma$ = 0.157 dex). This value is very close to the unweighted average $[Fe/H]_{188}$ = +0.087 $\pm$ 0.020 dex ($\sigma_{\mu}$, and $\sigma$ = 0.193 dex). If instead we keep only the 23 SM, we derive a weighted cluster average $[Fe/H]_{188}$ = +0.083 $\pm$ 0.019 dex ($\sigma_{\mu}$, and $\sigma$ = 0.164 dex), and an unweighted cluster average of $[Fe/H]_{188}$ = +0.088 $\pm$ 0.023 dex ($\sigma_{\mu}$, and $\sigma$ = 0.197 dex). Although in principle one might be concerned that the secondary in each BM might contaminate the spectrum sufficiently so as to affect the measured equivalent widths, the above averages are indistinguishable whether they include the BM or not, and Figure 8 also shows that the BM have indistinguishable [Fe/H] compared to SM stars.

These values for the cluster average [Fe/H] are sufficiently different from our assumed value of 0.00 dex for the isochrone that we decided to fine-tune by iterating. Figure 5, right panel, shows that a similar fit can be provided with a 5.35 Gyr isochrone that has [Fe/H] = +0.084 dex, the same $E(B-V)$ = 0.09 mag, and $(m-M)_{V}=11.55$ mag. We now repeated the above analysis of determining log $g$, $\xi$, and abundances, and found new weighted and unweighted averages for [Fe/H]. This process was iterated a few more times until the input and output [Fe/H] converged. Our final weighted average [Fe/H] for the cluster is +0.064 $\pm$ 0.018 dex ($\sigma_{\mu}$, and $\sigma$ = 0.177 dex), very close to the unweighted value of +0.069 $\pm$ 0.019 dex ($\sigma_{\mu}$, and $\sigma$ = 0.186 dex); excluding BM we find again nearly identical results. We stress that Table 2 and Figures 7 and 8 show these final abundances. The trends discussed above in these figures are nearly identical as the original ones.

Unlike the original isochrone (Figure 5, left panel), the iterated younger isochrones (5.35 Gyr, [Fe/H] = +0.084 dex; 5.7 Gyr, [Fe/H] = +0.063 dex, right panel) show a slight kink at the turnoff that does not seem to be present in the data. One way to avoid the kink is to keep the older age of 6.3 Gyr and allow the reddening to vary. A very similar fit as that with the original isochrone, and no kink at the turnoff, can be achieved with [Fe/H] = +0.084 dex, $E(B-V)$ = 0.06 mag and the same distance modulus (left panel). Anticipating a slightly lower final [Fe/H], we use an isochrone with [Fe/H] = +0.05 dex, which also provides a nearly identical fit with $E(B-V)$ = 0.07 mag (left panel), which is at the low end of the error range in reddening. Repeating the analysis now results in an average [Fe/H] for the cluster +0.060 $\pm$ 0.017 dex ($\sigma_{\mu}$, and $\sigma$ = 0.162 dex), weighted, or +0.064 $\pm$ 0.018 dex ($\sigma_{\mu}$, and $\sigma$ = 0.175 dex), unweighted. Encouragingly, this is very close to the final results discussed above, and suggests that systematic errors potentially introduced by these slightly different choices in parameters have little effect on the results.

An independent analysis of the solar spectra using laboratory gf-values gives an average A(Fe)_⊙ = 7.520 $\pm$ 0.015 dex ($\sigma_{\mu}$, $\sigma$ = 0.164 dex), which is in excellent agreement with previous studies (e.g. Lodders et al.Lodders09 2009). Table 4 shows how [Fe/H] depends on $B-V$, $T_{\rm{eff}}$, log $g$, and $\xi$ at three different $T_{\rm{eff}}$ and for the whole cluster.

There have been several high resolution spectroscopic studies during the past decade, but only two before that (summarized in Table 5). The results span the range from Fe/H] = -0.12 to +0.14 dex. Note that the two reduction methods used by Casamiquela et al.Casamiquela17 (2017) on the same data gave results that differed by 0.07 dex. In fact, it seems the high-R studies in Table 5 cluster either near solar or 0.1 dex higher and, taking the stated errors at face value, they do so in a discrepant way. For example, Donor et al.Donor18 (2018) and Jacobson & FrielJacobson13 (2013) are discrepant with Casamiquela et al.Casamiquela17 (2017), Jacobson et al.Jacobson11 (2011), and Randich et al.Randich03 (2003); this is true even when considering only the two more recent studies of Donor et al.Donor18 (2018) and both analyses of Casamiquela et al.Casamiquela17 (2017). Our own result is between the two clustered sets of results. Comparing to the only high-R study with a similar number of stars, namely Jacobson et al.Jacobson11 (2011), for 18 stars in common we find average differences in $T_{\rm{eff}}$, log $g$, and $\xi$ of 11 K, 0.17, and 0.34 km s^-1, respectively, in the sense theirs minus ours. The differences in $T_{\rm{eff}}$ and log $g$ have a negligible effect ($<$ 0.005 dex) on the derived cluster [Fe/H] but adopting the average difference in $\xi$ would decrease our cluster [Fe/H] by 0.073 dex, accounting for the difference in [Fe/H] between our studies of 0.09 $\pm$ 0.04 dex.

We point out that abundances from medium-resolution studies span a similar range in [Fe/H] as from the high resolution studies, though with larger errors and thus there is no issue of discrepant results, see Table 5. Photometrically-derived metallicities span a larger range, and a number of them have been summarized in SunSun21 (2021).

As noted in the Introduction, a particular advantage of studying Li-rich giants in clusters is that clusters provide an invaluable context for the phenomenon by allowing comparison of Li-rich giants to stars of similar mass, composition, age, and evolutionary state, and by supplying a baseline of unevolved stars at the turnoff to constrain the Li evolution of the progenitors of the Li-rich giants. This level of detail can lead to greater insight than may be available in even very large field star samples. As an example, WOCS 7017, a canonically-defined Li-rich giant in NGC 6819 (Anthony-Twarog et al.Anthony13 2013), has been shown to have a substantially lower mass than the other member giants (Carlberg et al.Carlberg15 2015, Handberg et al.Handberg17 2017), suggesting that the origin of its unusual surface A(Li) may be tied to severe mass loss, possibly related to ⁷Be-transport during a particularly severe He-core flash, and implying that some of the surprisingly low giant masses identified in Deepak et al.Deepak20 (2020) may be real. Another example is W2135 in NGC 2243: the unique properties of this star (enhanced Li with binarity and rapid rotation) compared to other member giants are consistent with mass transfer of Li-rich material from a former AGB starAnthony20 (Anthony-Twarog et al. 2020).

The relevant context for NGC 188 goes to the very heart of the canonical definition of “Li-rich” for giants as A(Li) $>$ 1.5 dex. While such a definition may be generically adequate for field stars whose Li evolution during the MS is unknown, i.e. consistent with subgiant dilution by 1.8 dex from a maximum initial A(Li) = 3.3 dex (see the discussion in the Introduction), in a star cluster one can constrain much more precisely what the Li evolution of the progenitors of the Li-rich giants may have been. In the case of NGC 188, A(Li) at the turnoff has been measured at $\sim$ 2.5 dex or slightly lower (Hobbs & PilachowskiHobbs88 1988; Randich et al.Randich03 2003), with a steady decline on the subgiant branch to upper limits of $\sim$ 0.8 dex or slightly lower (Deliyannis et al.Deliyannis22 2022, Figure 13). Among our RGs on the well-delineated first-ascent branch and within the RC (Figure 12), all have upper limits (25 stars) or a detection (1 star) of A(Li) $<$ 0.7 dex (Figure 11). This pattern is similar to what is observed in the 4 Gyr-old M67 Sills00 (Sills & Deliyannis 2000), though the decline isn’t quite as steep. But the similarity to M67 may be quite telling: Li data in M67 subgiants, together with Be data in the same stars, point strongly to the action of rotational mixing as the dominant Li- and Be- depletion mechanism during MS evolution and, together with dilution on the subgiant branch Boesgaard20 (Boesgaard et al. 2020), it is likely the same mechanisms govern the Li depletion in the NGC 188 subgiants. None of the 47 subgiants in NGC 188 deviate from this pattern, i.e. none are found above this A(Li)-$T_{\rm{eff}}$ pattern and thus none have preserved an unusually high amount of Li (Figure 13). This is not surprising since rotational mixing induced by angular momentum loss depletes Li throughout the Li preservation region (the region in the outer layers that remain sufficiently cool to preserve Li), not just at the surface (Pinsonneault et al.Pinsonneault90 1990; Deliyannis & PinsonneaultDeliyannis97 1997). So it is not unreasonable to assume that giants which have evolved further compared to subgiants are also not unusually good preservers of Li, implying that the boundary between Li-rich and not Li-rich may be lower, or even substantially lower, than A(Li) = 1.5 dex for giants in NGC 188, a pattern exhibited by other clusters of slightly younger age (Twarog et al.Twarog20 2020, Anthony-Twarog et al.Anthony20 2020, Anthony-Twarog et al.Anthony21 2021).

To place the evolution of the progenitors of the NGC 188 giants in context, it is important to realize that nearly all low mass dwarfs deplete their surface Li abundance as they evolve during the MS, and that evidence from a variety of angles suggests that rotational mixing induced by angular momentum loss (Endal & SofiaEndal76 1976; Pinsonneault et al.Pinsonneault89 1989, 1990) is the dominant Li-depleting mechanism. We briefly summarize some of that evidence here; for more thorough discussion see C17 and Deliyannis et al.Deliyannis19 (2019). Li, beryllium (Be, this symbol shall refer to the only stable isotope, ⁹Be, in contradistinction to ⁷Be, which shall always be labelled as ⁷Be), and boron (B) survive to progressively greater depths, so their ratios provide especially sensitive and robust probes of physical processes occurring in the outer layers of stars that may vary with depth. The correlated depletion of Li and Be in F dwarfs in the field (Deliyannis et al.Deliyannis98 1998; Boesgaard et al.Boesgaard01 2001) and in six open clustersBoesgaard02 (Boesgaard et al. 2002, 2004) is in excellent agreement with models of rotational mixing (Deliyannis & PinsonneaultDeliyannis93b 1993b, 1997; Charbonnel et al.Charbonnel94 1994), and argues strongly against other mechanisms proposed to explain the Li Dip. Similarly, the correlated depletion of Be and B in F dwarfsBoesgaard98 (Boesgaard et al. 1998, 2005b) also agrees nicely with similar modelsBoesgaard16 (Boesgaard et al. 2016). Furthermore, F dwarfs in young open clusters ($\sim$ 100 Myr) show no correlation between A(Li) and v sin i, but a tight correlation forms as stars age, that becomes steeper with age, at least through the age of the Hyades ($\sim$ 650 Myr); this provides a direct correlation between Li depletion and spindownSteinhauer22 (Steinhauer & Deliyannis 2021). The early formation of the Li Dip also favors rotational mixing since other proposed mechanisms act laterSteinhauer04 (Steinhauer & Deliyannis 2004). But Li depletion due to rotational mixing is not confined to F dwarfs. Contrary to long-held beliefs, late A dwarfs have been discovered to spin down and deplete Li concurrentlyDeliyannis19 (Deliyannis et al. 2019). Short-Period-Tidally-Locked-Binaries (SPTLBs), posited to be at least partly immune to rotational mixing during MS evolution, show higher A(Li) in normal, single late-F, G and K dwarfs, providing evidence of rotationally-induced Li depletion in these stars. This mechanism may be relevant to star 4705 (below), so we expound a bit further. The idea is that binaries observed today with orbital periods less than about 8 d were locked tidally and synchronized during the early pre-MSZahn89 (Zahn & Bouchet 1989) before the stellar interior was sufficiently hot to destroy Li. Therefore, they will not experience the spin-down, mixing, and Li depletion that single stars will experience later on, and thus SPTLBs could preserve their Li better than single stars do, though other possible complications may mean that some SPTLBs do deplete Li (D90, DeliyannisDeliyannis90b 1990b). SPTLBs with higher-than-normal Li are known in the Hyades, the turnoff of the 4-Gyr-old M67, and the field (Soderblom et al.Soderblom90 1990; Thorburn et al.Thorburn93 1993, Deliyannis et al.Deliyannis94 1994, Ryan & DeliyannisRyan95 1995). Other effects traced by Li may also be important for young, rapidly rotating G and K dwarfs that have higher A(Li) than stars rotating more slowly: there is evidence that such stars have inflated radiiJackson16 (Jackson et al. 2016, 2018, 2019), caused by the rapid rotation and the action of magnetic fields (Feiden & ChaboyerFeiden14 2014; Somers & PinsonneaultSomers15 2015). So, uniformly, from late A dwarfs through K dwarfs, rotational mixing is the primary Li depletion mechanism. Subgiants in NGC 188 evolved out of turnoff stars that have A(Li) $\sim$ 2.4 dex, which is depleted nearly a factor of 10 if the initial abundance was similar to meteoritic ($\sim$ 3.3 dex), with rotational mixing the likely cause of the Li depletion. Then, the Li in the entire Li preservation region would also be depleted due to rotational mixing, as evidenced directly by the declining subgiant A(Li).

So what is “Li-rich” in NGC 188? Two of the four stars with detected Li (stars 4705 and 5027) already meet the canonical criterion of A(Li) $>$ 1.5 dex. The A(Li) = 1.17 dex of the yellow giant 4346 is far greater than our upper limits for RGB stars of similar luminosity and, in that sense, this star might be labelled “Li-rich”. However, a great deal depends on how that star has reached this position in the CMD, as discussed below. Figure 12 suggests that star 6353 is a RC star. (A low ¹²C/¹³C ratio could support this suggestion but we are unaware of any C-ratio studies in giants of NGC 188.) Given that the subgiant A(Li) steadily declines to levels below 1 dex as the stars evolve (Figure 13), that our Li upper limits continue to decline with lower $T_{\rm{eff}}$ up the RGB to a level as low as as A(Li) $<$ -1.2 dex, and that star 6353 not only has a higher A(Li) than these RGB progenitor analogs but also higher than four of the five other apparent RC stars, we propose that star 6353 is “Li-rich” even though its A(Li) is “only” 0.60 dex. If the concept of Li-richness identifies stars that have more Li than they could have preserved following MS evolution, then this star qualifies. Rather than simply preserving its MS Li, it is more likely that this star has been enriched in Li, either through internal or external means.

By allowing for the possibility that some field stars with A(Li) $<$ 1.5 dex are Li-rich in this expanded sense, the fraction of Li-rich stars among the various red giant populations is likely to be higher than indicated in the Introduction. In addition to the ongoing cluster analyses by Twarog et al.Twarog20 (2020), Anthony-Twarog et al.Anthony20 (2020), and Anthony-Twarog et al.Anthony21 (2021), support for a more malleable definition of Li-rich has emerged from a number of sources. Based on an extensive sample of GALAH giants, Kumar et al.Kumar20 (2020) find that A(Li) in the RC phase is higher than in the RGB stage and propose that Li production is ubiquitous in low-mass stars. This hypothesis has been discussed in several recent publications. Magrini et al.Magrini21 (2021) derive Li abundances and upper limits for RC and RGB stars which are open cluster members and find that 35% of RC stars have similar or higher A(Li) than the RGB stars. They suggested possible Li production as the explanation but could not confirm that Li production is ubiquitous. By using a larger sample of 1848 field giants, Zhang et al.Zhang21 (2021) find that zero-age sequence, core-helium-burning low mass stars have higher A(Li) than stars above the RGB bump (Thomas Peak) by a value of $\sim$ 0.6 dex, and suggest that the helium flash may produce moderate Li enhancement while super Li-rich stars may require other mechanisms. Chaname et al.Chaname21 (2021) analyzed the GALAH Li field-star data, taking into account the distribution of progenitor masses, and stressed the need to account for population effects when comparing field RC and RGB stars. They find that standard models alone (no rotation, diffusion, magnetic fields, etc.) can account for the moderate A(Li) in RC stars, without the need for a Li production mechanism. They predict that higher mass RC stars should have higher A(Li), and cite some supporting evidence. We stress that, in addition to consideration of the mass-dependence of the progenitor, the MS evolution of the Li abundance prior to entering the subgiant branch must be considered, as we argue in Twarog et al.Twarog20 (2020) and again in this work. For reasons already noted, clusters, rather than field stars, are invaluable in this endeavour.

Some properties of the RG sample in NGC 188 are striking, in particular that 4 of 29 members (14%) are Li-rich. This is a much higher rate than in the field ($<$ 1%) (Casey et al.Casey19 2019; Deepak & ReddyDeepak19 2019), even if we only count the two stars (7%) with A(Li) $>$ 1.5 dex. Assuming that our higher rate isn’t merely an artifact of small number statistics, why would Li-rich stars occur at a higher rate in NGC 188?

It is of interest to compare to the rate of Li-rich stars in other open clusters. In the current discussion, “Li-rich” means A(Li) $>$ 1.5 dex, but “Li-rich-in-context” means A(Li) is less than 1.5 dex but abnormally high A(Li) compared to other relevant cluster stars, as argued here for two of the giants in NGC 188. To minimize the possibility of confusing subgiants still undergoing Li dilution from truly Li-rich giants, we also define “giants” to be those stars on the proper RGB, i.e. brighter than the reddest portion of the subgiant branch. For example, this definition eliminates several subgiants in NGC 2506 that are clearly still undergoing dilution Anthony18 (Anthony-Twarog et al. 2018), star 87 of IC 2714 of Delgado Mena et al.DelgadoMena16 (2016) that has A(Li) = 1.54 dex but a temperature of 5377 K on the subgiant branch, and so on. Table 6 summarizes a number of previous studies. The number of giants indicated corresponds to the number observed and reported in each study that meet the above criterion, except for Andrievsky et al.Andrievsky99 (1999) who report on only one star, a Li-rich giant. We estimate that the cluster may have about 10 giants, so at least 10% are Li-rich. Delgado Mena et al.DelgadoMena16 (2016) observed 67 subgiants/giants in 12 open clusters, but only 32 giants as we defined them above, and found no Li-rich giants but 3 Li-rich-in-context (0% and 9%, respectively). The remaining studies in Table 6 attempted to observe the vast majority of candidate giant members in each cluster. In total, these studies found 2 out of 139 giants to be Li-rich (1.4%), a rate that is somewhat closer to those in the field than that for NGC 188, and also 1 star that was Li-rich-in-context. Thus, 3 out of 139 giants (2.2%) are either Li-rich or Li-rich-in-context. In combining these statistics with the other two studies in Table 6, we note that Delgado Mena et al.DelgadoMena16 (2016) observed 3 giants in NGC 3680, of which two are at the Thomas Peak and 1 is just a bit below. They also observed a few stars in IC 4756 that are too hot to be labeled “giants” by the above criterion. It is possible, perhaps even likely, that these 3 stars were observed by Anthony-Twarog et al.Anthony09 (2009), but we cannot be sure. The two studies find similar A(Li) for stars at that specific phase of evolution which are neither Li-rich nor Li-rich-in-context. We include the 3 stars of Delgado Mena et al.DelgadoMena16 (2016) as distinct from the 9 in Anthony-Twarog et al.Anthony09 (2009), which introduces a risk of slightly underestimating the fraction of Li-rich or Li-rich-in-context stars. Thus, adding together all the stars of Table 6, there are 3 Li-rich stars out of 181 (1.7%), and 7 stars out of 181 (3.9%) that are either Li-rich or Li-rich-in-context. Adding the present statistics from NGC 188, the totals become 5 Li-rich giants out of 210 (2.4%), and 11 stars out of 210 (5.2%) that are either Li-rich or Li-rich-in-context. By comparison, Deepak & ReddyDeepak19 (2019, from the GALAH survey) found only 0.64% of Pop I red giants below $2M_{\odot}$ to be Li-rich while Gao et al.Gao19 (2019) found 1.29% of all giants to be Li-rich. For completeness, Kirby et al.Kirby16 (2016) found only 0.3$\pm$0.1% of globular cluster giants to be Li-rich.

Returning to a point of emphasis in the current analysis, note that the Li-rich giants and giants with measurable Li in other open clusters discussed to date (for example, the ones in Table 6 or in Magrini et al.Magrini21 2021) all come from MS turnoff stars above (more massive than) the Li Dip. By contrast, turnoff stars from NGC 188 come from MS stars below (less massive than) the Li Dip, so the mechanism(s) controlling Li evolution before and on the RGB may be distinctly different in NGC 188, i.e. the statistics and the Li-generating mechanism(s) may change dramatically with lower mass. Compounding the complexity, the giants in M67 and the older super-metal-rich clusters NGC 6253Cummings12 (Cummings et al. 2012) and NGC 6791 Boesgaard15 (Boesgaard et al. 2015) have no detectable Li, but come from MS stars that populate the Li Dip, placing them at a severe Li disadvantage well before leaving the main sequence and substantially lowering the boundary for Li-rich-in-context.

As noted earlier, Figure 12 shows that the majority of NGC 188 stars define a precise RGB. Some stars lie slightly off of this fiducial (orange circles). This is not due to photometric error; the same stars are slightly off in the same way based upon either Gaia photometry or our own extended Stromgren photometry Twarog21 (Twarog et al. 2021). As expected, the RC is slightly to the blue of the RGB for RGB stars of similar luminosity (blue circle). Strikingly, none of the four Li-rich stars lies on the fiducial sequence. One is classified by CMD poisiton as a RC giant, just slightly fainter and redder than the other presumed RC stars. All three of the others are well to the blue of the RGB. We shall refer to these three as “yellow giants” (YG). These unusual CMD positions may be telling us something about the origin of the Li in these stars. Note that while the vast majority of Li-rich field stars are RC stars, only 1 of our 4 Li-rich stars in NGC 188 is a probable RC star. We use the qualifier “probable” to stress again that position in the CMD does not necessarily guarantee knowledge of evolutionary state, as exemplified by star WOCS 7017 in NGC 6819, a RC star fainter than the normal RC and redder than the RGB. In fact, we cannot altogether rule out that this star might be on the RGB; observations of the ¹²C/¹³C could help distinguish between RGB (high ratio) and RC (low ratio). We consider each of the four stars and their possible origins in turn.