© The Authors 2025

1 Introduction

Among the many unsolved issues concerning multiple stellar populations (MPs) in globular clusters (GCs), one of the most surprising and recent is the possible existence of a metallicity spread in first generation (FG) stars. These stars are recognised as the original population that formed during the primary burst of star formation at the beginning of the lifetime of a GC. Polluters within this first generation provided the processed matter through proton-capture reactions in H burning at a high temperature. The mixing of this processed matter with pristine gas explains the composition of the polluted stars of the second generation (SG), as well as the correlation and anti-correlation of light elements that bear clear traces of proton-capture reactions (He, C, N, O, Mg, and Al, sometimes K, Ca, and Sc; see e.g. the extensive reviews by Gratton et al. 2004; Gratton et al. 2012; Gratton et al. 2019; Bastian & Lardo 2018).

The recent claim regarding iron spreads among FG stars is surprising in light of the fact that most of the candidate polluters proposed to enrich the pristine proto-cluster environment with processed ejecta are not able to produce metallicity variations. Asymptotic giant branch (AGB) stars (Ventura et al. 2001), fast rotating massive stars (Decressin et al. 2007), interacting massive binaries (de Mink et al. 2009), and supermassive stars (Denissenkov & Hartwick 2014) might reproduce the relationship between light elements, although with some quantitative problems.

To alter the cluster content of iron (and heavier elements), supernova (SN) nucleosynthesis must necessarily be involved. Furthermore, all the above candidates are massive stellar objects, which implies short evolving times and a time range for their action restricted to a maximum of a few tens of millions of years for the slowest evolving among them (AGB stars). However, the near homogeneity of heavy elements in the majority of GCs (better than 12% or less than 0.05 dex, Carretta et al. 2009) implies that ejecta from SNe should not be retained in GCs and contribute to secondary star formation.

A few GCs in the Milky Way are known to host intracluster metallicity variations. The amount of star to star differences in [Fe/H]¹ varies. On the one hand, GCs such as NGC 1851 show a spread barely larger than the observational errors (Carretta et al. 2011). At the other extreme, the most massive GC in the galaxy, NGC 5139 (ω Cen), shows clear evidence of star to star variations for all elements (see e.g. Gratton et al. 2004; Johnson & Pilachowski 2010). The possibility that this GC was the nucleus of a dissolved nucleated dwarf galaxy has been speculated upon in many studies (e.g. Zinnecker et al. 1988; Freeman 1993). The second most massive Galactic GC, M 54, may also be the nucleus of another dwarf, Sagittarius. Analogies and differences between these two massive GCs can be attributed to a common dynamical evolution observed at different stages (Carretta et al. 2010). To explain the few iron-complex GCs, peculiar dynamical conditions for their formation in dwarf galaxy satellites (Bekki & Tsujimoto 2016) and the mechanisms of inhomogeneous chemical evolution following cloud-cloud collisions (e.g. Tsujimoto & Shigeyama 2003) have been proposed.

Nevertheless, in most GCs the level of metallicity variations rarely exceeds the typical internal errors of precise abundance analysis, that is, about 0.05 dex. However, recently the issue of metallicity spreads in FG stars for these objects that are generally found to be very homogeneous in iron on the basis of spectroscopic analysis is debated.

Milone et al. (2017) used Hubble Space Telescope photometry with appropriate filters to sample the spectral regions where molecular features of CNO elements are preferentially located, and they arranged the stars in 57 GCs on a pseudo-colour map (PCM). On the PCMs, the stars are mostly located in two regions, which correspond to the groups of stars that have a primordial composition and chemistry that was altered by protoncapture processes, hereafter RG1 and RG2, respectively (see the simplified notation in Table 1, borrowed from Carretta & Bragaglia 2024).

Milone and collaborators estimated that RG1 in the PCMs was too extended with respect to the observational errors obtained via Monte Carlo simulations. Since the horizontal coordinate Δcol is related to shifts in the effective temperatures of stars, sampled by a colour with a long baseline in wavelength, the authors claim that star to star variations in metallicity or in the He content could explain the extended RG1 sequence. Since FG stars are by definition objects where the He mass fraction, Y, has been untouched since Big Bang nucleosynthesis, the consequent inference is that variations among them should be attributed to the spread in [Fe/H] (see also Legnardi et al. 2022).

From a differential high-resolution abundance analysis of five FG stars in NGC 2808, Lardo et al. (2023) found a correlation between abundances and the position along RG1, with a lower amount of Si, Ca, Ti II, and Ni for stars with more negative values of Δcol, in agreement with the above inference from photometry. For [Fe/H], they derived a range equal to 0.25 ± 0.06 dex. This result conflicts with the analysis of a large sample of stars in NGC 2808 by Carretta et al. (2006), who set a limit of ≲0.05 dex on the maximum iron spread in this GC, a result later confirmed by Carretta (2015). Moreover, Carretta et al. (2006) found that the average iron abundance in NGC 2808 increased, going from stars with a primordial composition to stars that were increasingly enriched with products from protoncapture reactions. Since He is the main outcome of the required H-burning, this was in qualitative agreement with an increased strength of the metallic lines due to the increase in He content (Böhm-Vitense 1979). Unfortunately, the statistical significance of this result was not very high, due to the attached observational errors. On the other hand, even if the correlations are clear in Lardo et al. (2023), none have a high statistical significance due to the very limited number of stars.

To delve more into the existence of metallicity spreads in FG stars, we tested the above inference by comparing the abundance analyses of FG stars in two GCs, namely NGC 3201 (Marino et al. 2019: M19) and NGC 104 (47 Tuc; Marino et al. 2023, hereinafter M23). The idea was simple. If the metallicity spread is an intrinsic property of FG stars in GCs, we should see similar patterns standing out in both GCs under scrutiny, regardless of their difference in global metallicity ([Fe/H] = − 0.768 dex for 47 Tuc and [Fe/H] = −1.512 dex for NGC 3201, Carretta et al. 2009). We had the advantage that both analyses were performed by the same group, with the same instrument and very similar (if not identical) techniques for analysing the abundances obtained from high-resolution spectra. We aim to demonstrate whether the findings are consistent and depict a coherent scenario, or whether there are discrepancies that weaken the conclusion about the metallicity spread in FG stars.

In this paper, we first state the implications of a claimed metallicity spread when the internal observational errors are of the same magnitude (Section 2). Then we compare trends in the derived metallicities in the two GCs with parameters and Δcol values, to ascertain how and how well the variations in effective temperatures, T_eff, are matched by a shift in metallicity along the PCM (Section 3). A discussion and final considerations on the observed trend in the two GCs under scrutiny are given in Section 4.

2 Intrinsic spreads with an internal error of 0.1 dex in [Fe/H]

The data compared in the present paper are the abundances of 18 FG stars in NGC 3201 and 23 FG stars in 47 Tuc derived by M19 and M23, respectively, using high-resolution spectra from the FLAMES-UVES (Ultraviolet and Visual Echelle Spectrograph) instrument on the ESO-VLT UT2 telescope. In both cases, the stellar parameters (T_eff, log g,[A/H], and v_t) were derived using a fully spectroscopic analysis.

Complete PCMs from Milone et al. (2017) are not available because they were never published. However, the Δcol and Δcol3 values for the FG stars analysed are given in M19 and M23, which allows us to evaluate the displacements of stars along the RG1.

Excluding three binary candidates, M19 found a small metallicity range of ∼0.10 dex among the other 15 FG giants in NGC 3201. The same amount of variation was also found in the sample of FG stars in 47 Tuc (M23), where two candidate binaries were left in the sample. However, both abundance analyses came with an attached internal error of 0.10 dex in metallicity (M19 and M23). The same amount found for errors and the claimed spread of [Fe/H] raises doubts over the existence of the spread.

The concept is visualized in Fig. 1. In the upper panels, we plot the sample of FG stars in 47 Tuc (upper-left panel) and in NGC 3201 (upper-right panel) where the giants are colour-coded according to the metallicities derived in M19 and M23. In the lower panels, we plot the same stars, but this time assigning the same colour to all stars within ±0.1 dex from the average [Fe/H] value of the GCs. The result is that there seems to be no clear relation between Δcol and the metallicity spread. Apart from very few outliers, the majority of the stars share a common metallicity within the associated internal error of 0.1 dex.

Another feature that is immediately evident is that the RG1 sequence in NGC 3201 is about 0.15 mag more extended than that in 47 Tuc. Since the observational error (estimated from the figures in Milone et al. 2017) is about 0.05 mag in Δcol, this is a 3σ difference. However, for both GCs the derived metallicity spread is the same, namely 0.1 dex.

A more quantitative estimate of the intrinsic spread in the presence of a given internal error is obtained by the approach suggested in Mucciarelli et al. (2012). The method searches within a grid of the ([Fe/H], σ) space, where σ is the intrinsic spread, the couple of parameters that maximise a maximum likelihood function. This function was defined accounting for the number of stars in the sample and the associated error. By employing this approach for the datasets of FG stars in the two GCs by Marino et al. (2019, 2023), we found null intrinsic spreads, that is, σ = 0.00 ± 0.031 dex and σ = 0.00 ± 0.032 dex for 47 Tuc and NGC 3201, respectively, when an internal error of 0.1 dex was considered.

Fig. 1 Pseudo-colour maps of 47 Tuc (upper left panel) and NGC 3201 (upper right panel) from the only published data in M23 and M19, respectively. Stars are colour-coded according to their metallicity. In the lower panels, aqua is used for all stars that have [Fe/H] values within ±0.10 dex (the internal error associated with the metallicity) of the average metallicity of FG stars in each cluster, whereas those that lie outside this range are marked in black.

3 Comparison of abundance analyses in 47 Tuc and NGC 3201

The location of stars along RG1 should be a direct consequence of the position of stars on the colour-magnitude diagram (CMD). In the plane m_F814W versus col, more metal-poor stars lie on the blue side of the RGB, whereas more metal-rich stars populate the red side. This is a general property of stellar models (e.g. Salaris et al. 2002). For a given absolute brightness, the RGB colour (i.e. the stellar T_eff) is strongly affected by the value of metallicity. Even when differences in colour from red and fiducial lines are combined in a PCM, stars with a lower metallicity should be found at bluer values of Δcol along RG1. In short, this is the basis of the claims for a metallicity spread among FG stars (M19; Lardo et al. 2023; M23).

In Fig. 2, we show the metallicity derived for FG stars in 47 Tuc (left panel, from M23) and in NGC 3201 (right panel, from M19) as a function of the effective temperature of stars. In 47 Tuc, cooler stars are found to be more metal-poor than stars with higher temperatures. This trend is opposite to the expectations from the colour-metallicity dependence of RGB models, and hence it is likely to be a spurious occurrence due to the abundance analysis.

To test the statistical significance of this trend, we computed a linear regression between [Fe/H] and T_eff. In the left panel of Fig. 2, we list the Pearson's correlation coefficient and the twotail probability that tests the null hypothesis that the observed values come from a population in which the true correlation is zero. We obtained a probability p = 0.036 (23 stars), and hence the observed correlation results are real and have a high statistical significance.

Interestingly, the same group, with the same methodology, obtained the opposite trend for FG stars in NGC 3201. From the data of M19, shown in the right panel of Fig. 2, there seems to be a gradient, with cooler stars showing slightly higher metallicities. However, the two-tail probability for the correlation is p = 0.204 (18 stars), so formally the correlation does not have a high statistical significance and it is likely to be only apparent, probably driven only by the most metal-poor star, which is indicated as a candidate binary star in M19.

The treatment of candidate binary stars is another source of discrepancy between the analyses of M23 and M19. In NGC 3201, the three probable binaries are all confined to the RG1 region at the most negative values, and are excluded by M19 from the correlations. Instead, in 47 Tuc the two stars that are probable binary (according to their large rms values in radial velocity) span the whole range of Δcol values and are considered in the analysis and ensuing correlations. Accordingly, we removed the three binary stars in NGC 3201 from consideration and kept the two stars in 47 Tuc. In Fig. 2 (right panel), the Pearson's coefficient and the two-tail probability refer to 15 stars, without the candidate binaries.

We examined the remote possibility that cooler stars in 47 Tuc were fortuitously clustered at a low metallicity, with all the metal-rich stars in the sample having higher temperatures. To demonstrate whether this is the case, we show Fig. 3 in which the metallicities derived by M23 are plotted as a function of the V magnitudes of stars, tabulated in M23. Formally the observed trend (in which brighter stars have lower [Fe/H] values) does not have a high statistical significance, however it reflects the trend shown in Fig. 2. There is no astrophysical process able to generate such a trend among RGB stars, so the implication is that this must be a spurious trend, due to some problems in the spectroscopic analysis and the derived atmospheric parameters. In NGC 3201 as well, the gradient of metallicities as a function of the V magnitude reflects the trend observed in Fig. 2, although its statistical significance is not high, in particular when the candidate binaries are neglected.

We can check the claim concerning the relation between displacement in Δcol along RG1 and metallicity through the link with the effective temperature, which on the RGB is strongly mediated by the metal abundance. In Fig. 4 (left panel), we plot the sample of FG stars in 47 Tuc with the values tabulated in M23. The run of Δcol as a function of T_eff is clearly flat and there is no dependency on the temperature of the stars. Hence, there is no evidence of a variation in the metallicity when moving along this coordinate on the PCM locus that is populated by FG stars.

For NGC 3201 (right panel of Fig. 4), there is a hint of a trend, with stars at lower values in Δcol being slightly warmer and therefore supposedly more metal-poor, as claimed.

Nevertheless, the relation shown is not of high statistical significance formally, in particular when the binaries are excluded, as was done in M19.

In a forthcoming paper (Carretta & Bragaglia, in prep.) we explore the precise lengths of the RG1 regions in a sample of 20 GCs extensively. In Fig. 5, we show a direct comparison of the extent of RG1 in the two GCs under scrutiny in the present paper.

The extension of each RG1 locus is represented by ellipses enclosing the FG stars selected in the col3 versus m_F814W plane in Fig. 5. This figure allows us to confirm the result based on the much sparser published data (Δcol values for 23 stars in 47 Tuc and 18 stars in NGC 3201 from M23 and M19, respectively). The length of RG1 in Δcol is about 0.3 mag for 47 Tuc and 0.5 mag in NGC 3201. Yet the claim by M23 and M19 is that the same metallicity variation (∼ 0.1 dex) is apparently detected in both GCs.

Fig. 2 Relations between Teff and the (derived) metallicity [Fe/H] in FG stars of 47 Tuc (left panel, red points) and NGC 3201 (right panel, blue points) from M23 and M19, respectively. In each panel we list the Pearson's coefficient for the linear regression and the two-tail probability that the true correlation is zero. Circular black points indicate candidate binary stars (here and in the following figures). Error bars indicate typical errors taken from M19 and M23.

Fig. 3 Metallicity of FG stars in 47 Tuc (left panel) and in NGC 3201 (right panel) as a function of the apparent V magnitude, from M23 and M19, respectively.

4 Final considerations and summary

In this paper, we addressed the issue of possible metallicity variations among FG stars. These stars are the outcome of the primary star formation phase in GCs and are not supposed to be polluted by matter processed by proton-capture reactions in H burning at high temperatures. To test the claim that the different extent of the RG1 in the PCM is related to the metallicity spread, we compared the abundance analysis of FG stars in 47 Tuc and NGC 3201, performed by the same research group, with an identical methodology, that is, a fully spectroscopic derivation of atmospheric parameters and metallicity [Fe/H] based on high-resolution UVES spectra.

In 47 Tuc we uncovered clear trends of the metallicity as a function of T_eff and luminosity among the 23 FG stars, with cooler (and brighter) stars being more metal-poor than warmer (and fainter) giants along the RGB. These gradients are unambiguous, cannot be explained by any known astrophysical mechanism, and are probably attributed to some problems in the abundance analysis.

These problems have consequences for the conclusion drawn from the abundance analysis of FG stars in 47 Tuc. From a comparison of the abundance spread (or lack thereof) in FG and SG stars, M23 advanced a scenario in which FG stars were born in an inhomogeneous medium during the first phase of the star formation, whereas the next generation formed in a more centrally concentrated way in regions where a cooling flow was able to more efficiently mix the gas used to produce the polluted population.

However, this scenario is weakened by the spurious trend with the effective temperature that has been uncovered for iron. The inhomogeneities in other species could be simply a reflection of this trend. A countercheck is offered by Fig. 6, where we plot the α elements Mg, Si, Ca, Ti I, and Ti II as a function of the T_eff for all 23 FG stars in 47 Tuc from M23. In the panels in the left column, the abundance ratios [X/Fe] are shown. The Pearson's correlation coefficient and the two-tail probability of the linear regression are reported in each panel. All elements except Ti II show a correlation with T_eff with a high statistical significance. However, when we exclude the contribution of iron and we simply plot the absolute abundance (in number density) of each species (panels in the right column), the run is compatible with a constant level or, at least, absence of any correlation with statistical significance. Furthermore, while the ratio [Ti/Fe] II was flat with T_eff, the run of log ε(Ti II) shows a noticeable trend that almost has a statistical significance.

Therefore, it is quite difficult to envisage a coherent scenario of a primordial proto-cluster medium where iron is not well mixed, but other products of SN nucleosynthesis, such as the α elements, are homogeneous to such an extent as not to show any significant variation with T_eff, as implied in Fig. 6. Evidence that SG stars generally formed in a denser and probably more well-mixed medium does exist. The lower binary fraction among SG stars strongly suggests that the environments where unpolluted and polluted stars formed had different conditions. The high efficiency of infant mortality in binary systems among SG stars explains the observed difference in binary fractions well (D'Orazi et al. 2010; Lucatello et al. 2015). On the other hand, data shown in Fig. 6 do not seem adequate enough to confirm such a scenario.

The situation is less uncertain for NGC 3201. With the notable exceptions of Mg, Cu, and Pr, no species in NGC 3201 show a trend with T_eff (in either the abundance ratio with iron or the absolute elemental abundance), which has a statistical significance². The absence of spurious trends derives from the nearly constant values in Fig. 2 in which candidate binaries are excluded.

In both GCs, there seems to be no compelling evidence for a variation in T_eff for the FG samples as a function of the Δcol coordinate. Since the T_eff of giants on the RGB is a strong function of the metallicity of stars, overall these findings cast some doubts on the claim that there is a metallicity spread among FG stars, or at least weakens its relevance.

On the other hand, we confirm that in both GCs, the absolute chemical abundances for most of the species analysed present a trend in which chemical abundances are higher in FG stars with Δcol near zero, and lower when Δcol has increasingly negative values (see Fig. 7 for an example of the trends with Δcol of the α elements in 47 Tuc and NGC 3201). The few exceptions are for Al, Sc, Co, Y, Zr, and Pr in NGC 3201 and for Zn, Y, Ba, and La in 47 Tuc. This could be surprising, since col and Δcol should not be influenced by the abundances of these elements (with the possible exception of oxygen). The variation, essentially due to temperature, should only be related to changes in helium or metallicity. Considering the lack of significant variations in T_eff with Δcol, it is not clear how different abundances can be associated with different positions along the horizontal coordinate in the PCMs.

Finally, we stress that both analyses (identical as far as their methodology is concerned) compared in the present paper derive the same metallicity spread in GCs with clearly different extensions of the RG1 region of FG stars and global metallicity [Fe/H], despite the fact that the abundance analysis of 47 Tuc produces spurious trends that are incompatible with stellar physics. The problem of the possible existence of metallicity spreads among FG stars in multiple populations of GCs still seems to remain an open issue at the moment.

Fig. 4 Coordinate Δcol along the RG1 in the PCM of 47 Tuc as a function of the effective temperature of stars from M23 (left panel). Right panel: same for NGC 3201 from M19. Typical error bars from M19, M23, and M17 are indicated.

Fig. 5 Plots of col3 versus mF814W and PCM for 47 Tuc (two left panels), and for NGC 3201 (two right panels), taken from Carretta & Bragaglia (2024). In all panels, FG stars are plotted in red. Ellipses enclosing FG stars in the PCMs show the extension of RG1 in the two GCs.

Fig. 6 Abundances of α elements as a function of Teff in 23 FG stars of 47 Tuc from M23. Left column: abundance ratios [el/Fe]. Right column: absolute number density abundances. In each panel, we report the Pearson's correlation coefficient and the two tails probability of the linear regression with Teff.

Fig. 7 Absolute number density abundances of α elements in FG stars of 47 Tuc (left panels, from M23) and of NGC 3201 (right panels, from M19) as a function of the displacement Δcol on the RG1 region of the PCMs.

Acknowledgements

We thank the anonymous referee for their fair and constructive comments. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France (DOI: 10.26093/cds/vizier). The original description of the VizieR service was published in 2000, A&AS 143, 23. Use of the NASA’s Astrophysical Data System, and TOPCAT (Taylor 2005) are also acknowledged.

References

All Tables

All Figures

Fig. 1 Pseudo-colour maps of 47 Tuc (upper left panel) and NGC 3201 (upper right panel) from the only published data in M23 and M19, respectively. Stars are colour-coded according to their metallicity. In the lower panels, aqua is used for all stars that have [Fe/H] values within ±0.10 dex (the internal error associated with the metallicity) of the average metallicity of FG stars in each cluster, whereas those that lie outside this range are marked in black.

In the text

Fig. 2 Relations between Teff and the (derived) metallicity [Fe/H] in FG stars of 47 Tuc (left panel, red points) and NGC 3201 (right panel, blue points) from M23 and M19, respectively. In each panel we list the Pearson's coefficient for the linear regression and the two-tail probability that the true correlation is zero. Circular black points indicate candidate binary stars (here and in the following figures). Error bars indicate typical errors taken from M19 and M23.

In the text

	Fig. 3 Metallicity of FG stars in 47 Tuc (left panel) and in NGC 3201 (right panel) as a function of the apparent V magnitude, from M23 and M19, respectively.
In the text

	Fig. 4 Coordinate Δcol along the RG1 in the PCM of 47 Tuc as a function of the effective temperature of stars from M23 (left panel). Right panel: same for NGC 3201 from M19. Typical error bars from M19, M23, and M17 are indicated.
In the text

	Fig. 5 Plots of col3 versus mF814W and PCM for 47 Tuc (two left panels), and for NGC 3201 (two right panels), taken from Carretta & Bragaglia (2024). In all panels, FG stars are plotted in red. Ellipses enclosing FG stars in the PCMs show the extension of RG1 in the two GCs.
In the text

	Fig. 6 Abundances of α elements as a function of Teff in 23 FG stars of 47 Tuc from M23. Left column: abundance ratios [el/Fe]. Right column: absolute number density abundances. In each panel, we report the Pearson's correlation coefficient and the two tails probability of the linear regression with Teff.
In the text

	Fig. 7 Absolute number density abundances of α elements in FG stars of 47 Tuc (left panels, from M23) and of NGC 3201 (right panels, from M19) as a function of the displacement Δcol on the RG1 region of the PCMs.
In the text