Fluorine Abundances in the Globular Cluster M4

The uncertainties in the derived F, C, and Na abundances due to the errors in the stellar parameters can be estimated by establishing the sensitivity of these abundances to changes in the stellar parameters corresponding to their typical errors. We estimate that the uncertainties in the stellar parameters are δT_eff = +100 K, δlog g = +0.25 dex, δ[Fe/H] = +0.1, and δξ = 0.3 km s⁻¹. We used the model atmosphere for the star L4611 (T_eff = 3725 K, log g = 0.30, [Fe/H] = −1.11, and ξ = 1.70 km s⁻¹) as a baseline and changed the parameters by the estimated uncertainties; the variations in the abundances are given in Table 4. The estimated error (Δ) for each element is the square root of the sum in quadrature of the corresponding change in abundance for δT_eff, δlog g, δ[Fe/H], and δξ. The fluorine abundances are most sensitive to the effective temperature, with errors in T_eff accounting for most of the F abundance uncertainties. The sodium abundances are also sensitive, but not as much, to the effective temperature, while the derived carbon abundances show more sensitivity to the microturbulent velocity and, to a lesser degree, to the metallicity of the model atmosphere.

Table 4.  Abundance Sensitivities to Stellar Parameters

Element	δ Teff = +100 K	$\delta \mathrm{log}g$ = +0.25	δ[Fe/H] = +0.1	δξ = +0.3 km s−1	Δ
F	+0.18	+0.00	+0.08	+0.00	±0.20
Na	+0.10	−0.01	+0.01	−0.02	±0.10
C	+0.05	+0.02	+0.06	−0.11	±0.14

Note. Baseline model: T_eff = 3725 K, log g = 0.30, [Fe/H] = −1.11, ξ = 1.70 km s⁻¹.

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As noted previously, the stellar parameters for most of the M4 red giants were taken from Ivans et al. (1999), and due to the sensitivity of the HF line strength to the effective temperature, the derived fluorine abundances are plotted versus T_eff in the left panel of Figure 3; the stars are coded as "CN strong" (filled red circles) and "CN weak" (filled blue circles) according to Ivans et al. (1999). Included in Figure 3 are the results from Smith et al. (2005) as an illustration of the change in the F abundance that results from the change in the HF excitation energy (from χ = 0.48 to 0.227 eV). In both the previous results from Smith et al. (2005) and the updated F abundances presented here, there is a trend of A(F) with T_eff, which is not expected, as low-mass red giants (M ∼ 0.85 M_⊙), such as those in M4, do not deplete F significantly during mixing on the red giant branch (RGB; e.g., stellar models from Lagarde et al. 2012). The right panel of Figure 3 also shows A(F), but here as a function of log g, where A(F) is found to decrease with decreasing log g. In a globular cluster, T_eff and log g are correlated as stars evolve up the RGB to lower values of both T_eff and log g, so the two trends in Figure 3 are consistent. As can be seen in Table 4, the fluorine abundance derived from HF is more sensitive to likely errors in the effective temperature scale when compared to such errors in log g.

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In order to check a possible systematic error in the T_eff scale from Ivans et al. (1999), the Na abundances derived here are plotted against both effective temperature and log g in the left and right panels, respectively, of Figure 4. The points are plotted as in Figure 3, as either CN strong or CN weak, and the large scatter in the Na abundances in M4 is real, with the CN-strong and CN-weak stars segregating as separate sequences, as discussed in Ivans et al. (1999). There is no underlying significant trend of the derived Na abundance with T_eff or surface gravity; a linear fit to the Na abundances versus T_eff finds no significant slope, with a change of only 0.05 dex from a linear fit from 3750 to 4650 K. The sodium abundance is less sensitive to both the effective temperature and surface gravity than the fluorine abundances derived from HF, so a small systematic trend in the Ivans et al. (1999) might still exist to produce a trend of A(F) with T_eff.

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In order to check whether an independent T_eff scale would also produce a significant trend in A(F) with T_eff, a set of effective temperatures were derived for the M4 red giants using the near-IR color (J − K_s) with photometric effective temperature relations from both González Hernández & Bonifacio (2009) and Bessell et al. (1998).

Non-negligible interstellar reddening exists along the line of sight to M4, which must be taken into account in deriving photometric effective temperatures (this is one of the reasons that Ivans et al. 1999 relied on a line-depth ratio T_eff scale). Ivans et al. (1999) mapped the reddening across M4 and found variations around a mean of E(B − V) = 0.32 ± 0.05. Clayton & Mathis (1988) find that E(J − K) = 0.555E(B − V), and we corrected all observed (J − K_s) values for reddening using two methods: in one case the mean value of E(J − K_s) = 0.18 ± 0.03 for M4 was used, while in the other the individual values of reddening, as derived by Ivans et al. (1999, their Table 4), were applied. A comparison of the effective temperatures derived from using individual reddening values for each star with those obtained from an average cluster reddening results in a small mean offset and a scatter of about 60 K (ΔT_eff = −20 ± 61 K, in the sense of derived T_eff values using "individual reddening" minus "mean reddening").

A scatter of ∼60 K is the expected value from a scatter of 0.03 in (J − K_s). Since the offset and scatter within the T_eff values derived from using a mean reddening or using the individual reddening values are small, the photometric effective temperatures derived from the mean reddening to M4 are compared to those from Ivans et al. (1999); the photometric T_eff values from (J − K_s) are cooler than those derived from the line-depth method from Ivans et al. (1999), with the mean ΔT_eff (line depth—(J − K)) = +118 ± 45 K. There is no slope in the ΔT_eff–T_eff points, so adopting this photometric T_eff scale will not remove the trend in A(F) versus T_eff presented in Figure 3. Although adopting the photometric scale for effective temperatures would not remove the trend of A(F) with T_eff, it would systematically lower the absolute fluorine abundances by ∼0.2 dex. This trend is likely due to some other effect, which we investigate below.

As mentioned in the introduction, two other studies have derived fluorine abundances in globular cluster red giants: Yong et al. (2008) for NGC 6712 and de Laverny & Recio-Blanco (2013a) for 47 Tuc. Both of these globular clusters have metallicities that are less metal-poor but not too different from that of M4 (with 47 Tuc having [Fe/H] ∼ −0.75 and NGC 6712 having [Fe/H] ∼ −1.0), and a plot of their fluorine abundances also reveals a trend of A(F) decreasing with decreasing T_eff, having a slope similar to that found by us for M4. Both Yong et al. (2008) and de Laverny & Recio-Blanco (2013a) use their own independent methods of deriving effective temperatures, so it is unlikely that the T_eff trend in all three studies is caused by an incorrect effective temperature scale. We speculate that this trend found in fluorine abundances derived from HF is due to a physical effect related to the spectroscopic analysis of low-metallicity red giants. All globular cluster fluorine abundances show this trend, and the effect caused by the slope with T_eff can be corrected in order to compare relative intercluster abundances.

A physical cause of the A(F)–T_eff trend may be due to the use of 1D static model atmospheres, as discussed by Li et al. (2013) in their analysis of HF in metal-poor field red giants. Li et al. (2013) did test syntheses of HF using convective 3D model atmospheres from the grid of Ludwig et al. (2009) and found significant differences between 1D static and 3D hydrodynamic modeling of the HF (1−0) R9 line. They present corrections for a series of red giant model atmospheres at a metallicity of [m/H] = −2.0 with [α/m] = +0.4, and these corrections follow a trend with T_eff similar to that of the observed globular cluster red giants. The 3D results from Li et al. (2013) suggest that the A(F)–T_eff trends found in the 1D static model atmosphere analyses of globular cluster red giants by Yong et al. (2008), de Laverny & Recio-Blanco (2013a), and this study may result from 3D hydrodynamic effects, which can be removed empirically as a first-order (linear) correction, which is plotted as the straight line in the left panel of Figure 3, and this will be discussed in Section 6.2.2. For reference, the fluorine abundances corrected for the trend with T_eff are presented in the last column of Table 3.

Figure 5 presents the carbon abundances versus bolometric magnitude (M_bol) for the M4 stars in our sample. Overall, the results indicate a trend of decreasing ¹²C abundances with increasing red giant luminosity (a decrease in M_bol implies an increase in luminosity), or lower T_eff values. Such a trend was also observed in previous studies of M4 and other globular clusters (e.g., Langer et al. 1986; Suntzeff & Smith 1991; Bellman et al. 2001; Smith et al. 2005; Kirby et al. 2015). As done previously, we segregate the M4 sample into the CN-strong (carbon-poor nitrogen-rich stars; red circles) and CN-weak (stars with more pristine values of carbon and nitrogen; blue circles) populations. Two sequences are roughly defined given the segregation in carbon abundances of the CN-weak (carbon-"rich") and CN-strong (carbon-poor) stars, and within a sequence we see the effect of internal mixing occurring as the star ascends the RGB. The observed decrease in ¹²C as a low-mass giant ascends the RGB is not surprising, as recent stellar models that include rotational and thermohaline mixing predict such a trend (Lagarde et al. 2012).

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One relevant result from this study is that the derived fluorine abundances are, as expected, significantly lower than those obtained in our previous studies from the literature, which adopted inconsistent values for the excitation potential (χ) and dissociation energy for the analyzed R9 HF transition. The offsets between our derived fluorine abundances for M4 and those from Smith et al. (2005; shown as open circles) and de Laverny & Recio-Blanco (2013a; shown as open triangles) can be seen in Figure 3.

Figure 6 (left panel) shows the comparison between our derived carbon abundances and those determined in different studies in the literature. The comparison between the carbon abundances derived here and those in Smith et al. (2005) shows good agreement (a mean difference of $\langle \delta A({\rm{C}})\rangle =-0.10\pm 0.11$). Smith et al. (2005) determined carbon abundances using the same ¹²C¹⁶O lines at 2.3 μm that we analyze here (Table 2). On the other hand, when compared to ¹²C results obtained from the analysis of low-resolution spectra at 2.2 μm by Suntzeff & Smith (1991), there is a much larger discrepancy: the mean carbon abundance in this study is systematically larger than theirs by $\langle \delta A({\rm{C}})\rangle =0.56\pm 0.28$. Such a difference comes, in part, from inadequate microturbulent velocities adopted in Suntzeff & Smith (1991; see discussion in Smith et al. 2005). When compared to the carbon abundances from the high-resolution optical study by Norris & Da Costa (1995), there is a very small offset in the mean but a larger abundance scatter ($\langle \delta A({\rm{C}})\rangle \,=-0.03\pm 0.25$); the difference with the results from low-resolution spectra (R = λ/Δλ = 600; 1200) from Stanford et al. (2010) shows a larger systematic offset: $\langle \delta A({\rm{C}})\rangle \,=0.33\pm 0.22$.

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Figure 6 (right panel) shows the comparison between our derived sodium abundances and those determined in the literature. For the globular cluster M4, the sodium abundances that we determine are in a good agreement with the results from the high-resolution optical study by Ivans et al. (1999; $\langle \delta A(\mathrm{Na})\rangle =-0.01\pm 0.04$), with results from the infrared study by de Laverny & Recio-Blanco (2013a; $\langle \delta A(\mathrm{Na})\rangle \,=+0.11\pm 0.11$), and with results from MacLean et al. (2018; $\langle \delta A(\mathrm{Na})\rangle =+0.04\pm 0.13$). Our sodium abundances for ω Centauri are in agreement with the optical high-resolution study by Smith et al. (2000), having an average difference of $\langle \delta A(\mathrm{Na})\rangle =0.03\pm 0.06$. Other works in the literature have systematically higher sodium values than ours, presenting differences of $\langle \delta A(\mathrm{Na})\rangle =-0.38\pm 0.18$ for Norris & Da Costa (1995), $\langle \delta A(\mathrm{Na})\rangle =-0.22\pm 0.06$ for Johnson & Pilachowski (2010), $\langle \delta A(\mathrm{Na})\rangle =-0.48\pm 0.26$ for Stanford et al. (2010; R = 600 spectra), and $\langle \delta A(\mathrm{Na})\rangle =-0.27\pm 0.42$ for Stanford et al. (2010; R = 1200 spectra).

Globular clusters are now known to have more than one stellar generation and not to be simple stellar populations (Gratton et al. 2012; Marino 2018). As discussed in the introduction, stars from different generations in a globular cluster show the distinct pattern (not seen in the general field star population) of depletion in the C, O, and Mg abundances corresponding to enhancements in the N, Na, and Al abundances. These abundance variations in globular clusters, or anticorrelations in the abundances of C–N, Na–O, and Mg–Al, are the result of changes in the chemical abundances due to hydrogen burning (proton captures) occurring in the CNO, NeNa, and MgAl cycles.

6.1.1. M4

The left panel of Figure 7 presents the [Na/Fe] versus [O/Fe] abundances for the studied M4 targets. Our results confirm the anticorrelation between O and Na that has been previously found for M4 by Ivans et al. (1999), Smith et al. (2005), Carretta et al. (2009), and Marino et al. (2011). Such an anticorrelation pattern for M4 is consistent with similar results found in the literature for other galactic globular clusters (e.g., Ramírez & Cohen 2002 for M71, Carretta et al. 2004 for 47 Tucanae, Carretta et al. 2009 for 17 globular clusters, and Carretta et al. 2014 for NGC 4833). In fact, the anticorrelation pattern between Na–O abundances is observed in virtually all globular clusters in the Milky Way, and this abundance anticorrelation is inferred as the chemical signature that "tags" a globular cluster population (Carretta et al. 2009; Marino 2018).

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An anticorrelation between the abundances of Na and C for M4 is also obtained in this study, and this is shown in the right panel of Figure 7. The observed anticorrelation between Na and C can be understood as the result of the decrease in the carbon abundances due to the CN cycle (e.g., Sweigart & Mengel 1979; Marino et al. 2016) and the increase in the Na abundances as a result of the NeNa cycle.

6.1.2. ω Centauri

The [O/Fe] and [C/Fe] versus [Na/Fe] abundances for the studied ω Centauri stars are presented in the top and bottom panels of Figure 8, respectively. We also show, for comparison, results from the optical by Smith et al. (2000), and results from the much larger optical study by Marino et al. (2012). Given the complexity in investigating abundance anticorrelations in a globular cluster having an extreme metallicity (iron abundance) spread, such as is observed for ω Centauri (Johnson & Pilachowski 2010), we divide, as in Marino et al. (2012), the stars into the different stellar populations, corresponding to the following metallicity bins (five panels in Figure 8): [Fe/H] <−1.90 dex, −1.90 dex ≤ [Fe/H] < −1.65 dex, −1.65 dex ≤[Fe/H] < −1.50 dex, −1.50 dex ≤ [Fe/H] ≤ −1.05 dex, and [Fe/H] > −1.05 dex.

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We can see from the results shown in the top panels of Figure 8 that the overall pattern of Na–O anticorrelation holds for ω Centauri, or stars richer in sodium tend to have lower oxygen abundances and vice versa. A similar result is also seen for [Na/Fe] versus [C/Fe] (bottom panels). The pattern shown in the different panels might be suggestive of a progression in the anticorrelation slope, which would seem to be progressively displaced toward higher values of [O/Fe] (less clear for carbon) as the metallicity increases, until reaching the most metal-rich population ([Fe/H] > −1.05 dex), which does not show a clear Na–O or C–O anticorrelation pattern, having stars with the highest sodium and oxygen abundances, as well as carbon. The results for the few ω Centauri stars in our study (blue circles), together with those from Smith et al. (2000; green circles), follow the general pattern delineated by the much larger sample by Marino et al. (2012; crosses) for the different ω Centauri populations.

6.2.1. Previous Fluorine Studies in Globular Clusters

6.2.2. Fluorine Abundance in M4 and ω Centauri

As discussed in Section 6.1, our results indicate that the abundances of the elements C, O, and Na are not constant in the globular cluster M4, but rather show anticorrelations between Na–O and Na–C, as would be expected to result from the CNO and Ne–Na hydrogen-burning cycles operating in the first stellar generation in M4, with a second stellar generation forming from gas that was polluted by the first generation.

Our results also indicate that there is an anticorrelation between F and Na in M4 (Figure 9, left panel); the trend is similar to that obtained previously by Smith et al. (2005) and de Laverny & Recio-Blanco (2013a), although the revised absolute [F/Fe] values are lower than previously found in those earlier studies, due to the lower excitation potential of the HF line.

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The Na–F abundance anticorrelation can be understood in a simple way, with a primordial stellar population in M4 having destroyed fluorine in stars that were massive enough to reach interior temperatures high enough for the NeNa cycle to occur, as evidenced by the observed anticorrelation between Na and O in M4. In this simple picture, a fraction of initial ¹⁹F in the primordial cluster material was consumed by (p,γ) and (p,α) reactions, while ²³Na was synthesized by the Ne–Na cycle; this leads to the anticorrelation between A(F) and A(Na), between the primordial (first generation) and second generation of stars. In Section 5.1 the decline in fluorine abundance with decreasing T_eff was discussed as a possible manifestation of inadequacies of 1D modeling of the very temperature-sensitive HF lines, with a fitted straight line shown in the left panel of Figure 3 as an illustration of this trend. Even with the T_eff trend in A(F), it should be noted from Figure 3 that the CN-strong and CN-weak stars segregate on either side of this line, with the CN-strong stars falling systematically below the line and the CN-weak stars falling above the line. Because of this difference in fluorine abundance between the two families of stars, the Na–F anticorrelation from Figure 9 (left panel) is still apparent. The A(F)–T_eff trend from Figure 3 can be removed from the measured F abundances, and these "corrected" F abundances are used in the right panel of Figure 9; in this case, the Na–F anticorrelation becomes smoother and displays less scatter. The result of these tests provides confidence that a real Na–F abundance anticorrelation exists in the two stellar families in M4.

Our results for ω Centauri are less conclusive given the small number of red giants analyzed and the fact that the fluorine results for the ω Centauri sample are, for the most part, upper-limit fluorine abundances. The only ω Centauri star with a measured fluorine abundance is ROA 219 (T_eff = 3900 K, log g = 0.70). This star has a metallicity [Fe/H] = −1.20 and belongs to the intermediate-metallicity population in ω Centauri (−1.50 dex ≤ [Fe/H] ≤ −1.05 dex). Having a metallicity that is very close to that of M4, this star may be compared to the M4 results shown in Figure 9. The fluorine and sodium abundances derived for ROA 219 ([F/Fe] ∼ −0.4, [Na/Fe] ∼ −0.1) put it close to, or just slightly below, the star with the lowest Na abundance in our M4 sample (the latter belongs to the "high fluorine—low sodium" group in M4). Our ω Centauri sample has three other ω Centauri targets in the same metallicity bin, and interestingly, although they all have upper-limit fluorine abundances, they also all have low A(Na) (lower than [Na/Fe] ∼ −0.6), which would make them part of the primordial population. When considering their C and O abundances, their low fluorine abundances appear to be consistent with their loci in the Na–O and Na–C panels in Figure 8 (filled blue symbols), which also would indicate a primordial origin, as their oxygen and carbon abundances are high. Fluorine abundance upper limits are also derived for the two additional ω Centauri stars, ROA 213 and ROA 324; these upper-limit abundances do not provide any additional constraints.

Figure 10 provides a summary view and comparison of derived M4 red giant fluorine and sodium abundances with those arising from a sample of stellar models from both Lagarde et al. (2012) and Smith et al. (2005). This figure plots the Na versus F abundances, with the M4 red giants shown as filled circles and classified as either CN weak (blue), CN strong (red), or CN type unknown (green). These abundances are corrected for the T_eff trend discussed in Section 5.1. Included in Figure 10 are stellar model results presented in Smith et al. (2005) for a 6.5 M_⊙ hot bottom burning (HBB) asymptotic giant branch (AGB) star; this model is of the same type as described in detail in Fenner et al. (2004) and Campbell1 & Lattanzio (2008). The open square at the high-Na and low-F part of the figure is the final yield from this HBB AGB model, while the continuous curve connects this yield to the initial F and Na abundances in the primordial M4 stellar population (high-F and low-Na abundances); the curve connects the initial F and Na abundances in the model with the final HBB AGB abundances via different mixing fractions of the initial and final F and Na abundances. The other model results presented in Figure 10 are from Lagarde et al. (2012) for masses of 4.0 and 6.0 M_⊙ and include models with standard dredge-up (St), along with models that include both rotational and thermohaline mixing (Rot–Th). The abundances are the surface abundances that result from the various mixing episodes that occur as a result of RGB and AGB evolution. In the case of Lagarde et al. (2012), the models are followed to the tip of the AGB and end there at the cessation of He burning, and they do not include the final stripping of the stellar envelope down to the remnant white dwarf core.

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Within the overlap of mixing episodes covered by both the Lagarde et al. (2012) and Smith et al. (2005) models, the comparison is good, with the Lagarde et al. models predicting slightly more F depletion for a given Na enhancement. It is worth noting that the Lagarde et al. (2012) 6.0 M_⊙ model, which includes rotational and thermohaline mixing, produces F along the upper AGB (where it becomes a carbon star), but the model is halted before it undergoes HBB, which would destroy ¹⁹F and synthesize ²³Na and convert ¹²C to ¹⁴N, driving the C/O ratio to less than 1.0 and turning the former carbon star into a luminous S-type AGB star (Wood et al. 1983); it is the lower-mass AGB stars that are net producers of fluorine, as they are not massive enough to undergo HBB. Both sets of models predict a large Na enhancement, with only a small F depletion, until the increase in Na reaches ∼+1 dex before F undergoes significant (>−0.3 dex) depletion. The observed abundances in M4 suggest a somewhat larger depletion of F at a rather modest increase in the Na abundance: the fluorine abundance drops by about 0.2 dex over a +0.5 dex increase in A(Na). Lower-mass stellar models produce less F depletion, so pollution in the early M4 environment from lower-mass stars is not likely. The observed behavior of A(F) as a function of A(Na) and its comparison to models is similar to that found by Fenner et al. (2004) in the globular cluster NGC 6752 for Na and O; Fenner et al. (2004) found that the observed depletion in oxygen was larger at a given Na increase than that predicted by stellar models. In M4 it is not clear what is causing the discrepancy between observations and models for Na and F.