11institutetext:  INAF-Osservatorio di Astrofisica e Scienza dello Spazio di
Bologna, Via P. Gobetti 93/3, I-40129 Bologna, Italy

# Discrepancies between spectroscopy and HST photometry in tagging multiple
stellar populations in 22 globular clusters ††thanks: Full Table 3 and Table
A.1 in Appendix A are only available at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc. u-strasbg.fr/viz-
bin/cat/J/A+A/??/??

Eugenio Carretta 11 Angela Bragaglia 11

Multiple populations (MPs) in globular clusters (GCs) are stars distinct by
their abundances of light elements. The MPs can be directly separated by
measuring abundances of C, N, O, Na, Al, Mg with spectroscopy or indirectly
from photometric sequences created by the impact of different chemistry on
band passes of particular filters, such as the HST pseudo-colours in the
ultraviolet. An attempt to link HST pseudo-colours maps (PCMs) and
spectroscopy was done by Marino et al. (2019), using abundances mostly from
our FLAMES survey. However, we uncovered that an incomplete census of stars in
common was used in their population tagging. We correct the situation by
building our own PCMs and matching them with our abundances in 20 GCs, plus
two GCs from other sources, doubling the sample with spectroscopic abundances
available. We found that the pseudo-colour $(mag_{F275W}-2\times
mag_{F336W}+mag_{F438W})$ does not have a monotonic trend with Na abundances,
enhanced by proton-capture reactions in MPs. Moreover, on average about 16% of
stars with spectroscopic Na abundances show a discrepant tagging of MPs with
respect to the HST photometry. Stars with chemistry of second generation (SG)
are mistaken for first generation (FG) objects according to HST photometry and
vice versa. In general, photometric indices tend to overestimate the fraction
of FG stars, in particular in low mass GCs. We offer a simple explanation for
these findings. Finally, we publish all our PCMs, with more than 31,800 stars
in 22 GCs, with star ID and coordinates, for easy check and reproduction, as
it should be in science papers.

###### Key Words.:

Stars: abundances – Stars: atmospheres – Stars: Population II – Galaxy:
globular clusters: general

††offprints: E. Carretta<EMAIL_ADDRESS>
##  1 Introduction

Multiple stellar populations (MPs) in Galactic globular clusters (GCs) are
commonly defined as ensembles of cluster stars that are distinct by their
content in light elements. Striking differences in C and N, as well as in Na
and O content, among GC stars were known and studied since the ’80s (see Smith
1987 and Kraft 1994 for reviews on those studies). Since the seminal paper by
Gratton et al. (2001) on the abundances of unevolved stars in two clusters, it
is crystal clear that presently evolving low mass stars cannot be the
factories of the observed chemical pattern. For production of species like N,
Na, Al (and sometimes Si, Ca, Sc, K) combined to simultaneous depletion of C,
O, Mg, Gratton et al. indicated as responsible the most massive stars, now
extinct, of a stellar population that preceded the one presently observed in
GCs. The polluters among first generation (FG) stars contributed matter
nuclearly processed by proton-capture reactions in H-burning at high
temperature. Different cycles are involved, depending on the temperature
thresholds achievable according to the polluter mass. The processed matter,
coupled with diluting pristine gas, constitutes the necessary mass budget
required to generate the subsequent second generation(s) (SG) with the
observed chemical pattern (see e.g. the extensive reviews by Gratton et al.
2004, 2019 and references therein). In contrast to this widely accepted
scenario, there is no consensus on a variety of issues regarding MPs, starting
from no less than the nature of the polluters required to provide the raw
material to be recycled into subsequent stellar generations or populations
with modified composition. This mainly stems from the difficulties found to
match (quantitatively, and sometimes qualitatively) theoretical models to the
observed pattern of correlations and anti-correlations among light element
abundances in GC stars (see e.g. Bastian and Lardo 2018). Thus, none of the
many candidates proposed for FG polluters (e.g. intermediate mass asymptotic
giant branch, AGB, stars: Cottrell and Da Costa 1981, Ventura et al. 2001;
massive, fast rotating stars: Decressin et al. 2007; massive binaries: de Mink
et al. 2009; super-massive stars: Denissenkov and Hartwick 2014) seems to
provide a fully satisfactory answer so far.

To gain more insight on MPs, it is useful to to study and compare the
properties of distinct populations. The bedrock to this approach is to
identify them with precision. In turn, the ratio first to second generations
is a key parameter to effectively constrain models to reconstruct the
formation and early evolution of GCs. As an example, the extensive database of
[O/Na] values spanned by different stellar populations in GCs allowed to
define the main property of MPs in GCs, i.e. that the relevance of the MP
phenomenon is strictly correlated to the mass of the GC (Carretta 2006,
figures 12 and 13; Carretta et al. 2010a), a fact later confirmed also by
photometric means (e.g. Milone et al. 2017).

At the same time, the homogeneous tagging of stellar populations with
primordial and altered chemical composition in a large set of GCs allowed to
draw attention to the so called mass budget problem. Since the chemical
composition of the polluted component must be inherited from only a part (the
most massive) of an early stellar generation, the population ratio has a
significant impact on every scenario devised to explain the formation of GCs,
since it provide strong constraints to the initial GC mass. The proportion of
FG and SG (about 30:70) stars derived from homogeneous spectroscopy and the
Na-O anti-correlation implies that initially GCs could have been much more
massive than today and that most of their FG low mass stars were lost at early
times in the GC lifetime (e.g. Prantzos and Charbonnel 2006, Decressin et al.
2007, Carretta et al. 2010a, D’Ercole et al. 2010, Vesperini et al. 2010,
2013).

It is then of paramount relevance to correctly identify among GC stars those
maintaining the original composition, identical to that of field stars of
similar metallicity for all practical purposes, and those belonging to the
next generation born in the cluster.

The main method to tackle this issue is to directly measure the abundances of
light elements with spectroscopy. Spectra, preferentially at high resolution
for accurate abundances of atomic species, but even at low resolution for
molecular features, allow to directly separate stars with FG and SG chemical
composition. Since different species are destroyed or produced at different
temperatures, a complete survey of light element abundances is actually a
tomography performed on the temperature distribution, hence on the involved
mass range, of the putative polluters.

Indirect measures are possible with photometry, exploiting filters with
bandpasses that cover wavelength ranges affected by change in flux due to the
effect of molecular bands, whose strength is modified by reactions enhancing N
at the espense of depleting C and O. Hence, usually only UV/blue filters,
encompassing the regions where OH, NH, and CN molecular features are located,
are particularly efficient in this specific task. Several photometric systems
have been used to this purpose (see e.g. Calamida et al. 2007, Sbordone et al.
2011, Carretta et al. 2011a, Lee et al. 2009, Massari et al. 2016 for $ubvy$
Strömgren filters; Monelli et al. 2013 for the Johnson UBVI bands; Johnson et
al. 2023 for the Sloan $ugri$ system; Piotto et al. 2015 and Milone et al.
2017 for the combinations using ultraviolet HST filters).

Suitable combinations of magnitudes in these filters result in pseudo-colours
able to separate photometric sequences mostly populated by stars of different
composition. The method uses appropriate normalizations suitable to clearly
enhance the separation of populations with different abundance of light
elements, in particular C, N, and sometimes O.

Some photometric systems seem more suitable than others to provide accurate
population tagging of stars in GCs (see e.g. Lee 2019, 2023), but recently the
approach that uses UV/blue/optical HST photometry has drawn much attention,
due to the large sample of GCs observed (57) and to the exploitation of more
absorbtion molecular bands in some suitable filters: OH in F275W, NH in F336W,
CN and CH in F438W, again NH in F343N (the last was employed by Larsen et al.
2014 to study GCs in the Fornax dwarf spheroidal galaxy).

The largest difference is obtained using a pseudo-colour derived by
subtracting from the F275W magnitude (sensitive to the abundance of O, which
is depleted in proton-capture reaction) two times the F336W magnitude
(sensitive to N, which is enhanced) and finally adding the magnitude in F438W
(whose bandpass includes region of CH, another species depleted). Other,
redder filters such as F814W are not particularly sensitive to the MP
atmospheric composition, not including useful regions of molecular bands, but
in combination with filters at much bluer wavelengths (e.g. F275W) are very
sensitive to variations in the star effective temperature. In the assumption
that the changes in light elements are accompanied by small differences in the
He content, colours like $mag_{F275W}-mag_{F814W}$, combining UV and optical
bands, may provide some indications about He.

A few words on notation. For clarity and conciseness we will adopt the
simplifications illustrated in Table 1.

Figure 1: The upper panels show the CMDs for NGC 104, $col$ versus
$mag_{F814W}$ and $col3$ versus $mag_{F814W}$. The red and blue lines are the
fiducials used. Lower left panels: rectified RGBs in the normalized $col$ and
$col3$. Lower right panel: resulting PCM, where FG stars are those located
below approximately 0.1 in $\Delta col3$ and SG stars above. Table 1: Notation
adopted in the present paper $col=mag_{F275W}-mag_{F814W}$
---
$col3=(mag_{F275W}-mag_{F336W})-(mag_{F336W}-mag_{F438W})$
$\Delta col=W_{col}((col-xr)/(xr-xb))$
$\Delta col3=W_{col3}((col3-yr)/(yr-yb))$ (see Section 2)
$W_{col}$ and $W_{col3}$ = widths of the RGB in $col$ and $col3$
PCM = pseudo-colour map = $\Delta col$ in abscissa and $\Delta col3$ in
ordinate

The quantity $col3$ is called a pseudo-colour because it is actually the
difference of two true colours. Formally, $col$ is an actual colour, but
similarly to the previous quantity it is used in a differential manner, as
observed distances from a blue and a red ridge line in suitable colour-
magnitude diagrams (CMDs), for normalization purposes (see below, Section 2).
The resulting combination is called a pseudo-colour map, PCM in the following.
On these maps, giant stars are generally located in two groups that are
distinct along the ordinate by different values of $\Delta col3$.

Simulations with synthetic spectra hint that this behaviour can be mainly
attributed to variations in the N abundance (see e.g. Milone et al. 2017).
Often the two groups are rather well separated, but in some cases they seem to
form almost a continuous sequence, with no clear evidence for separation.
Interestingly, this does not seem clearly related to the cluster metallicity,
affecting the detectability of bi-metal molecular features like CN, as metal
poor GCs may show a neat separation (such as, e.g. NGC 4833) while more metal-
rich GCs (like NGC 6205) do not.

An attempt to link the photometric classification of MPs to the spectroscopic
direct method was made by Marino et al. (2019), mostly using abundances from
our extensive high resolution FLAMES survey in GCs (Carretta et al. 2009a).
However, we uncovered that a largely incomplete census of stars with
abundances from spectroscopy was identified and used by Marino et al. (2019)
to test the agreement of population tagging with the HST photometry.

We correct the situation in the present paper, using a full cross-matching of
stars in common between the HST photometry and spectroscopy for 22 GCs among
those used in Marino et al. (2019). For each analysed GC, Table 2 shows the
number of stars with spectroscopic abundances individuated on the pseudo-
colour maps of Marino et al. (2019) in the second column, and how many of them
have [Fe/H] and [Na/Fe] ratios (third and fourth columns). In column 5 we
report the number of stars we actually counted on the figures of the
Na-$\Delta col3$ relations shown by Marino et al. Column 6, 7, and 8 show how
many stars with spectroscopic abundance we were able to match and use in the
present work, while the references to the sources of abundance analysis are
given in the last column. From this Table is evident that Marino et al. (2019)
neglected a large number of stars available in both the photometric and
spectroscopic datasets.

Table 2: Number of stars identified from spectroscopy in each GC GC | PCM | Fe | Na | Na-$\Delta$col3 | Fe | Na | Na-$\Delta$col3 | ref.spectroscopy
---|---|---|---|---|---|---|---|---
| M19 | M19 | M19 | M19 | us | us | us |
NGC 104 | 10 | 10 | 10 | 10 | 17 | 17 | 17 | Carretta et al. (2009a)
NGC 288 | 18 | 18 | 18 | 18 | 25 | 24 | 24 | Carretta et al. (2009a)
NGC 362 | 9 | 9 | 9 | 9 | 15 | 15 | 15 | Carretta et al. (2013)
NGC 1851 | 10 | 10 | 10 | 10 | 26 | 26 | 26 | Carretta et al. (2011b)
NGC 2808 | 39 | 39 | 39 | 38 | 50 | 50 | 50 | Carretta (2015)
NGC 3201 | 22 | 22 | 22 | 22 | 28 | 28 | 28 | Carretta et al. (2009a)
NGC 4590 | 19 | 22 | 17 | 17 | 30 | 23 | 23 | Carretta et al. (2009a)
NGC 4833 | 14 | 14 | 11 | 11 | 18 | 14 | 14 | Carretta et al. (2014)
NGC 5904 | 10 | 10 | 10 | 10 | 16 | 16 | 16 | Carretta et al. (2009a)
NGC 6093 | 9 | 9 | 8 | 8 | 31 | 29 | 29 | Carretta et al. (2015)
NGC 6121 | 11 | 11 | 11 | 11 | 27 | 27 | 27 | Marino et al. (2008)
NGC 6205 | 23 | 23 | 23 | 23 | 26 | 26 | 26 | Johnson & Pilachowski (2012)
NGC 6254 | 21 | 21 | 18 | 18 | 32 | 25 | 25 | Carretta et al. (2009a,b)
NGC 6388 |  |  |  |  | 35 | 35 | 35 | Carretta & Bragaglia (2023)
NGC 6397 | 19 | 19 | 13 | 13 | 28 | 18 | 18 | Carretta et al. (2009a,b)
NGC 6535 | 13 | 13 | 11 | 11 | 19 | 16 | 16 | Bragaglia et al. (2017)
NGC 6715 | 18 | 18 | 18 | 18 | 34 | 34 | 34 | Carretta et al. (2010b)
NGC 6752 | 22 | 22 | 20 | 20 | 27 | 25 | 25 | Carretta et al. (2007,2009b)
NGC 6809 | 11 | 11 | 7 | 7 | 27 | 21 | 21 | Carretta et al. (2009a)
NGC 6838 | 14 | 14 | 14 | 14 | 23 | 23 | 23 | Carretta et al. (2009a,b)
NGC 7078 | 12 | 12 | 8 | 8 | 28 | 21 | 21 | Carretta et al. (2009a)
NGC 7099 | 17 | 17 | 7 | 7 | 27 | 16 | 16 | Carretta et al. (2009a,b)

In this work we will focus on Na as a favoured indicator, very well suited for
tagging different stellar populations in GCs. Produced in the NeNa chain, it
is tightly linked to the O depletion (providing the enhancement of N) in the
Na-O anti-correlation, which is a feature found in almost every GC studied to
date and such a key feature to be assumed as a true definition of genuine GCs
(Carretta et al. 2010a). Sodium is not directly related to photometric
sequences, but is a good proxy for chemical alterations due to the MP
phenomenon, maybe even better than O. Proton-capture reactions do enhance this
species in SG stars with respect to the plateau imprinted by supernova
nucleosynthesis, so that the abundance of Na is easier to be derived than that
of other species depleted in the same nuclear processing, such as O, for
instance. Furthermore, [Na/Fe] ratios can be reliably derived even in metal-
poor GCs using the strong doublet at 5682-56-22 Å, securing homogeneous
abundances for the vast majority of GCs, down to the lowest metallicity
objects.

Our analysis is organized in the paper as follows. In Section 2 we describe
the data and the construction of the PCM. In Section 3 we show our first
results on the comparison between the spectroscopic and photometric
classification of MPs. These results are discussed in Section 4, where the
population ratios obtained from different methods are tested against a sample
of unpolluted, FG-like field stars. Our present work is summarised in Section
5.

##  2 The database of pseudo-colour maps (PCMs)

The only data published in Marino et al. (2019) are average abundances of
elements from literature, largely from our FLAMES survey (Carretta et al.
2006, Carretta et al. 2010a and references therein). In particular, most Na
abundances are from our analysis of GIRAFFE spectra in 15 GCs (Carretta et al.
2009a, see also Table 2). Unfortunately, no PCM has ever be made public by
that collaboration, despite what pledged in Piotto et al. (2015) and Marino et
al. (2019). Although a PCM is sometimes used by other groups in literature,
the only public PCM we are aware of is the one of NGC 362 published by Vargas
et al. (2022). We were then forced to construct our own PCM starting from
scratch, exploiting the photometric catalogues of HST photometry in GCs by
Nardiello et al. (2018), following the procedure illustrated e.g. in Milone et
al. (2017) and Dalessandro et al. (2019).

From the dataset of our FLAMES survey we selected 19 GCs with HST photometric
catalogues in Nardiello et al. (2018) as target GCs. To this sample we added 2
GCs with abundance analysis for a large number of stars from other sources
(see Table 2), for consistency and safety checks. To this set we added NGC
6388, whose large spectroscopic sample of 185 stars, studied in Carretta and
Bragaglia (2023), was not available in 2019. For the 20 GCs in our survey, we
used results from Carretta et al. (2009a), and other original papers of the
series, adding data from Carretta et al. (2009b) for stars with only UVES
spectra available.

The photometric information (coordinates, magnitudes, and quality flags of
stars) comes from the HUGS database, that is the Large Legacy Treasury Program
HST UV Globular Cluster Survey (Piotto et al. 2015, Nardiello et al. 2018).

Figure 2: Comparison of photometric parameters for the group of stars in all
GCs with spectroscopy found in Marino et al. (2019; blue crosses) and those
added only in the present work (red crosses), as a function of the magnitudes
in F814W. The parameters quality and sharpness are from the catalogues of
Nardiello et al. (2018) used to construct the PCMs.  Figure 3: Distribution of
the membership parameter from Nardiello et al. (2018) for stars only used by
Marino et al. (2019: blue line) and only added in the present work (red line).
Upper panel: histogram of the membership parameters. Lower panel: cumulative
distribution.

###  2.1 Building a PCM

The procedure we followed is described here for one GC (NGC 104) and results
for all clusters are presented in Appendix A. We downloaded the relevant files
from the HST MAST archive111https://archive.stsci.edu/prepds/hugs/, choosing
meth01, the more suitable for bright stars such as the RGB ones we are dealing
with. We selected stars in the RGB region using topcat (Taylor 2005) and drew
the blue and red fiducials for it. The lines were computed in magnitude bins
(using $mag_{F814W}$) starting about 1.5 mag brighter than the main sequence
turn-off, taking the 4th and 96th percentiles in colour ($col$ and $col3$, see
Table 1 for the definition) of the stars in each bin; some manual adjustments
were made where too few stars were present, for instance above the HB level in
most clusters. We then used a polynomial interpolation to produce finer and
smoother fiducial lines. An example of the procedure followed by us is
illustrated in Fig. 1, where we show these fiducials in the upper panels, on
the colour-magnitude diagrams (CMDs) $col$ versus $mag_{F814W}$ on the left
and $col3$ versus $mag_{F814W}$ on the right.

No cut in photometric error was applied, as errors are tiny for bright stars
(less or much less than 0.01 mag). Similar considerations are valid for other
parameters such as sharpness or goodness of the PSF fits (quality),see Fig. 2.
For each of the selected star we then computed the distance from the blue and
red fiducials using eqs. 1 and 2 in Milone et al. (2017, see also Table 1). To
achieve the highest homogeneity possible, we adopted their widths of the RGB
in $col$ and in $col3$ (see Milone et al. 2017 for details and their Table 2
for the values).

The corresponding $\Delta col$ and $\Delta col3$ versus magF814W (i.e. the
verticalized RGBs) are shown in the lower left panels of Fig. 1. Finally, the
lower right panel of the figure shows the resulting PCM, where there is a
separation of stars into two main groups, the one at lower $\Delta col3$
values representing the FG stars and the one at higher $\Delta col3$ values
indicating the SG component (see Milone et al. 2017).

In Appendix A we provide the same steps of the procedure for the remaining
GCs. We will publish at the CDS Strasbourg the whole set of PCM for the entire
sample of more than 31,800 giants in 22 GCs used in the present work, with the
format $\Delta col$, $\Delta col3$, RA, Dec, ID, where ID is a 8-digit
identifier from Nardiello et al. (2018), unique for each star in a given GC.

###  2.2 Cross matching with the spectroscopic database

As the next step, we cross-matched the spectroscopic samples and the PCMs
derived from HST photometry (see above) using topcat (Taylor 2005) for each
GC, retaining only stars in common (see Table 2 for the number of matches
compared to the matches used in Marino et al. 2019). Beside simple matches of
coordinates we used the precaution of looking at the differences between the
$mag_{F606W}$ and the ground-based V magnitudes adopted in the individual
papers. Large differences indicate a probable mis-identification with a star
within the separation range adopted for the match (1 arcsec), but usually much
fainter than the spectroscopic target. In such cases, we inspected the
possible different candidate matches, choosing the one possibly slightly more
distant from the spectroscopic target, but within about 0.3-0.5 mag from its V
magnitude, to allow for differences between the Johnson and the F606W HST
filter.

No data or star identifications were published in Marino et al. (2019).
However, from the figures shown in that paper, and knowing the Na, O
abundances from the published papers, we were able to identify all stars used
in Marino et al. in their comparison with spectroscopic results with good
confidence. A few problematic cases are reported and discussed in Appendix B.

In Table 3 we list the stars with both spectroscopy and HST photometry
available in each of the 22 GCs of the present work. The star ID is from
Nardiello et al. (2018) and it is unique within a given GC. Using this ID and
the corresponding RA and Dec coordinates, it is easy to retrieve the stars
from spectroscopic papers. The classification in MPs for each star (pop=1 for
FG and pop=2 for SG stars) follows the spectroscopic criterion based on Na
(see below). Flag=F indicate the stars found and used by Marino et al. (2019),
identified through the position in their figures. The flag=M is used for
additional stars in common between HST catalogues by Nardiello et al. (2018)
and the papers of abundance analysis listed in Table 2, found by us and
instead missing in Marino et al. Here we show only the excerpt of Table 3
concerning NGC 104. The complete Table is available at the CDS.

Table 3: Stars with Na abundances retrieved in HST photometric catalogues (The complete Table is available at CDS) GC | starID | [Na/Fe] | pop. | flag
---|---|---|---|---
104 | R0018794 | 0.375 | 1 | F
104 | R0008856 | 0.101 | 1 | F
104 | R0014514 | 0.388 | 1 | F
104 | R0008669 | 0.626 | 2 | F
104 | R0010831 | 0.435 | 2 | F
104 | R0018788 | 0.417 | 2 | F
104 | R0022191 | 0.504 | 2 | F
104 | R0006211 | 0.731 | 2 | F
104 | R0015269 | 0.691 | 2 | F
104 | R0021007 | 0.674 | 2 | F
104 | R0009274 | 0.686 | 2 | M
104 | R0011193 | 0.528 | 2 | M
104 | R0016453 | 0.514 | 2 | M
104 | R0018702 | 0.540 | 2 | M
104 | R0023714 | 0.619 | 2 | M
104 | R0024168 | 0.519 | 2 | M
104 | R0024181 | 0.574 | 2 | M
Figure 4: Examples of the saturation effect in the $col3,F814W$ plot for three
GCs in our sample. Filled black circles are stars with spectroscopy available
used by Marino et al. (2019). These stars lie also outside the vertical
distribution of the RGB, so we extended the fiducial lines to bracket also
these objects. Figure 5: Relations $\Delta col3$-[Na/Fe] for NGC 104, NGC 288,
NGC 362, NGC 1851, NGC 2808, and NGC 3201. For each GC, in the left panel the
green and magenta symbols are FG and SG stars, respectively, as classified
from HST photometry (through the PCMs). The red triangles represent stars in
the so-called red-RGB region. In the right panel, for each GC black circled
symbols are stars in common between photometry and spectroscopy, yet neglected
in Marino et al. Here, FG and SG stars (cyan and red, respectively) are
separated according to the spectroscopic Na abundances (see text). Figure 6:
As in Fig. 5, but for NGC 4590, NGC 4833, NGC 5904, NGC 6093, NGC 6121, NGC
6205, NGC 6254, and NGC 6397 Figure 7: As in Fig. 5, but for NGC 6535, NGC
6715, NGC 6752, NGC 6809, NGC 6838, NGC7078, NGC 7099, and NGC 6388. For the
last GC only the relation from our data in the present paper is available.

As clear from Table 2, there are many more stars with spectroscopic abundances
than those used by Marino et al. (2019), even on the limited field of view
sampled by HST observations. We were able to identify in the 22 GCs of the
present sample 298 stars used by Marino et al., all of them with a
spectroscopic Na abundance222This number is slightly different from the total
of the fifth column of Table 2 due to some problematic stars, see Appendix B.
To this set we were able to add 291 stars (231 with Na), doubling the dataset
of objects with both HST photometry and spectroscopy available. In the
following, the stars used in the present work in addition to those adopted by
Marino et al. are indicated in all the plots as bordered in black.

It is not clear why Marino et al. (2019) neglected a large number of stars in
each GC. To understand whether we selected stars differently from Marino et
al. (2019) we checked the distribution of a few parameters on photometric
quality and membership taken from the catalogues of Nardiello et al. (2018),
used to construct the PCMs. In this exercise, we consider as if they were
different samples the stars with flag=F and those with flag=M.

In Fig. 2 we compare the photometric parameters sharpness and quality, as
given by Nardiello et al. (2018), as a function of the magF814W. Blue crosses
are for the limited sample of stars with spectroscopic abundances used in
Marino et al (2019). Red crosses indicate stars added in the present work. The
two samples occupy essentially the same region.

The membership is compared in Fig. 3. The median value for the membership is
the same for both groups, and a Kolmogorov-Smirnov test (bottom panel) returns
a probability that does not allow to reject the null hypothesis that the two
sample are extracted from the same parent population. We further note that
Marino et al. (2019) claimed that only stars that according to their proper
motion are cluster members were included in their study. However, we uncovered
that about 30 stars ($\sim 11\%$ of their adopted stars with spectroscopy) are
listed in the catalogues by Nardiello et al. (2018) with mem=-1, meaning that
the membership from proper motions is not available. A similar fraction
($11\%$) is found among the stars added in the present work, increasing to
about to $13\%$ when considering only stars with a Na abundance. Anyway, all
stars with spectroscopy are cluster members according to their radial
velocities and metallicities, which is probably a more robust criterion with
respect to proper motions in particular within the crowded central regions of
the GCs. Hence we consider members all the stars flagged either F or M,
disregarding the statement by Marino et al. (2019).

###  2.3 How to deal with very bright stars

A number of stars with spectroscopic abundances are flagged with ’99’ in the
catalogues by Nardiello et al. (2018), indicating that the stars in question
are saturated in one or more frames. A posteriori, this is expected, since
high S/N spectra are required to obtain accurate abundances at high
resolution, and usually only the brightest stars are observed in GCs.
Nevertheless, many of these bright stars were used by Marino et al. (2019),
meaning that even these stars have a correspondence on their PCMs. Other
bright stars were identified and added in the present paper.

Using the stars identified by Marino et al. (2019) we were able to place them
on the PCM and in various diagrams, in particular the magF814w vs $col3$
diagram. The brightest stars follow a sharp turn to the left in the magF814w
vs $col3$ diagram, so conservatively we in primis truncated the RGB fiducial
lines there when deriving the PCMs (see Fig. 1). However, when we counter-
identified the stars observed spectroscopically, we saw that in half of the
GCs, many were close to this limit or exceeded it, even in the sample of stars
used by Marino et al. (2019).

For those clusters (NGC 362, NGC 2808, NGC 4833, NGC 6093, NGC 6205, NGC 6388,
NGC 6715, NGC 6809, NGC 6838, NGC 7078, and NGC 7099) we then extended the
fiducial lines by eye to follow the RGB stars distribution. While not
explicitly described in Milone et al. (2017) or Marino et al. (2019), this
permitted to place the stars in reasonable positions in the PCMs. An example
of this is shown in Fig. 4 for NGC 2808, NGC 6205, and NGC 6715. Stars of the
spectroscopic sample used in Marino et al. (2019) are over-plotted as larger
filled symbols. Several stars in the saturated region are considered in the
work of Marino et al. so that they likely used the same procedure, extending
the fiducial lines up to this region.

###  2.4 A few words on the impact of reddening

As a general rule, we did not apply correction for reddening, since this would
move all stars in the same way while the essence of PCMs is working with
differences with respect to fiducial sequences.

However, we checked that disregarding the differential reddening present in a
few GCs has no significant impact. We used NGC 3201, a cluster well known to
be affected by differential reddening, and we applied a random variation of
$\pm$0.03 in the average E(B-V) for each star. This amount is compatible with
the range of differential reddening recently found by Cadelano et al. (2024)
over the limited HST field of view centered on this GC (about 0.06 mag peak-
to-peak).

After this random addition, we repeated the complete procedure to build the
new PCM of NGC 3201. The resulting PCM features resulted a little less
compact, but perfectly able to separate FG from SG stars on its basis. This is
enough for the goal of our paper, waiting for the publication of the precise,
differential reddening-corrected PCMs by the Legacy Program group.

##  3 Spectroscopic and photometric classification of MPs

We have now at our disposal the newly derived PCMs, the stars with both
photometry and spectroscopy available used by Marino et al., as well as the
new additions (sometime very numerous) presented in the present paper. This
means that we have a large database of 22 GCs where it is possible to compare
the classification of MPs based on the HST photometry (indirect way) with that
based on high resolution spectroscopy (direct way).

The comparison is shown in the next Sections.

###  3.1 The Na-$\Delta col3$ relations

As a first step to understand the agreements or possible discrepancies in the
classification of MPs with spectroscopy and photometry, we proceeded to
scrutinize the Na-$\Delta col3$ relations as a main diagnostic tool.

In the pair of panels for each GC in Fig. 5, on the left we reproduce the
relations exactly as given in Marino et al. (2019; their figures 9 and 15).
The first six GCs in our sample, NGC 104, NGC 288, NGC 362, NGC 1851, NGC
2808, and NGC 3201, are plotted in Fig. 5 In Fig. 6 and Fig. 7 we show the
other GCs in our sample.

The green and magenta colours are adopted for FG and SG stars, respectively,
having Na (and Fe) abundances from spectroscopy. Red triangles in NGC 362, NGC
1851, and NGC 6715 indicate stars located on the so called red-RGB sequence,
defined as an additional SG sequence above and to the red of the main SG
distribution by Milone et al. (2017).

In the left panels of each pair, the stars have both HST photometry and high
resolution spectroscopy, but the assignment to different populations was made
in Marino et al. (2019) on a purely photometric basis, i.e. stars belong to
the FG or the SG group if they are located in the lower or upper “blob” on the
PCM, regardless of their actual chemical composition.

To add also stars missing in Marino et al. we had no choice but to use our own
PCMs, in order to associate a [Na/Fe] value to a given $\Delta col3$ value.
The resulting relations are plotted in the right panels of each pair of the
above figures. We used the same scale as in the left panels. However, for NGC
2808 and NGC 6121 the scale of abscissa is different, to include all matches
with our PCMs. Black bordered symbols indicated stars ignored by Marino et al.
(2019) even if they have both photometric and spectroscopic data. The cyan and
red colours mark FG and SG stars, respectively. However, now the populations
are assigned on a pure spectroscopic criterion.

According to the definition given in Carretta et al. (2009a), we selected
stars in the FG (i.e. the primordial P component) with O, Na contents similar
to field stars of the same metallicity. Stars are assigned to this component
if their [Na/Fe] ratios lie in the range within [Na/Fe]min and [Na/Fe]${}_{\rm
min}+0.3$ dex, where [Na/Fe]min is given by the lower envelope of the Na
abundance observed in each GC. This criterion ensures that all the FG stars,
with normal composition of halo stars, are included, since 0.3 dex is about
4$\sigma$([Na/Fe]), where $\sigma$([Na/Fe]) is the typical internal error on
[Na/Fe] in our FLAMES survey. For consistency, we applied the same criterion
also to the samples in NGC 6121 and NGC 6205, taken from other sources, but
with similar internal errors on Na.

This selection offers a very homogeneous approach for all GCs in the sample,
and it is based on Na abundances, that are well measurable even in the most
metal-poor GCs, and are involved in the Na-O anti-correlation, a prominent
feature of MPs in GCs. Its extension is found to be well correlated to the
global GC mass (Carretta et al. 2010a, their fig. 15) which is one of the main
driver of the MPs phenomenon, as inferred in a number of studies (Carretta
2006, Carretta et al. 2009a,b, Carretta et al. 2010a, Pancino et al. 2017,
Milone et al. 2017, Mészáros et al. 2020). Moreover, the choice of the minimum
Na content in GCs of different metallicity allows to follow the pattern of
field halo stars derived from the plain Galactic chemical evolution. The
soundness of the above criterion is proven by the good match between the FG
fraction and the floor of unpolluted field stars over the whole metallicity
range spanned by Galactic GCs (see Carretta 2016 and Section 4 in the present
paper).

The relations shown by Marino et al. generally present a clean separation
between FG and SG stars, with a sort of monotonic progression of Na abundances
increasing as the $\Delta col3$ values increase. Often there is a even a gap
separating the two populations in this plane. This is simply a reflection of
the adopted photometric criterion. On the PCM, the density thickening of stars
corresponding to FG and SG stars shows only a slight superposition along the
$\Delta col3$ coordinate, and this explains the aspect of these relations.
According to Figure 27 in Marino et al. (2019), the spread along the $\Delta
col3$ ordinate in the PCM is measuring essentially the variation in [N/Fe]. In
proton-capture reactions in H-burning at high temperature both N and Na are
enhanced (see e.g. Langer et al. 1993), in the ON cycle and NaNa chain,
respectively, explaining the observed correlation.

Nonetheless, already at a glance the photometric classification of MPs shows
several inconsistencies, visible in the Na-$\Delta col3$ relations by Marino
et al. (2019). Some FG stars (e.g. in NGC 6397, NGC 6752, NGC 6838) have large
Na abundances that are different from the low values typical of the primordial
population. On the contrary, some SG stars show low Na abundances, consistent
with the normal, unpolluted stellar population in GCs. A few objects are at
the border between FG and SG stars, but in other cases (e.g. NGC 6093, NGC
6205, and NGC 6715) their Na abundance is clearly discrepant with respect to
their photometric classification. Finally, we note that in some very metal-
poor GCs (e.g. NGC 4590, NGC 7078) FG and SG stars are totally confused, and
both classes share the same range of Na abundances.

The monotonic progression in the Na-$\Delta col3$ trend weakens when the
tagging is done using the spectroscopic criterion, as in the right panels of
each pair in Figures from 5 to 7. Despite a smooth increase of Na along the
Na-O anti-correlation, often we do not observe a clean, almost one to one
correspondence. Instead, to a given $\Delta col3$ value corresponds a large
range of Na abundances, reaching even 0.7-1 dex in some cases.

Finally, in Fig. 7 we show our result for NGC 6388. Marino et al. (2019) did
not consider this GC, so there is no relation Na-$\Delta col3$ from their
work. We exploited the large spectroscopic sample recently assembled in
Carretta and Bragaglia (2023) and the relation is shown in the last panel of
Fig. 7 using the usual spectroscopic tagging, as in previous figures.

We conclude our analysis by noting that in NGC 2808 we see a FG star on the
PCM of Marino et al. (2019) which then disappears in their Na-$\Delta col3$
relation even if all the matches for NGC 2808 have a Na abundance. It was then
impossible for us to identify this star. On the contrary, a few stars with
spectroscopy used by Marino et al. (2019) in some GCs should not appear on the
PCM, because they do not have all the required magnitudes in the catalogues by
Nardiello et al. (2018). These and a few other peculiar stars are discussed in
Appendix B.

Figure 8: Stars with spectroscopy on the PCMs of NGC 0104, NGC 288, NGC 362,
and NGC 1851. In the left panels the photometric classification of MPs is
adopted and in the middle panels the population assignment is based on
spectroscopy. Our PCMs are indicated with small grey dots. In the right
panels, stars considered mismatches in classification are superimposed to the
Na-O anti-correlation (as filled symbols). Solid lines in each GC indicate the
limit [Na/Fe]${}_{\rm min}+0.3$ dex (with a range $\pm 0.07$ dex, dashed
lines) used to separate FG and SG stars. The colour coding is as in Fig. 5.
Figure 9: As in Fig. 8 for NGC 2808, NGC 3201, NGC 4590, and NGC 4833. Figure
10: As in Fig. 8 for NGC 5904, NGC 6093, NGC 6121, and NGC 6205. Figure 11: As
in Fig. 8 for NGC 6254, NGC 6397, NGC 6535, and NGC 6715. Figure 12: As in
Fig. 8 for NGC 6752, NGC 6809, NGC 6838, and NGC 7078. Figure 13: As in Fig. 8
for NGC 7099 and NGC 6388.

###  3.2 Population classification on the PCMs

The enlarged sample of stars with spectroscopic abundances and our new PCMs
available for the cross-identification of stars allow us to check in detail
the agreement or differences arising from the classification of MPs using
photometry or spectroscopy.

The comparison is shown for the first four GCs in Fig. 8. Figures from Fig. 9
to Fig. 13 are for the remainder of GCs. On the left panels we reproduce the
position on the PCMs of the stars with spectroscopic abundances used by Marino
et al. (2019). Again, green and magenta colours are employed according to
their photometric classification, disregarding direct measures of the chemical
composition of stars. Adopting this classification, the FG stars generally
have values of $\Delta col3$ lower than those of SG stars, likely due to a
lower N abundances in their chemical composition. However, this general rule
presents a few exceptions in about a third of the sample of GCs (e.g. NGC
2808, NGC 6093, NGC 6205, NGC 6254, NGC 6397, NGC 7078). In these cases, FG
and SG stars are found at the same level in $\Delta col3$.

In the central panels we plot the stars with spectroscopic abundances,
superimposed to our PCMs (small grey dots). The colour code for stars is the
same as in Fig. 5 and follows the same assignment to MPs based on the [Na/Fe]
abundance ratio as described in Section 3.1 and visualised in the panels on
the right side for each GC. A solid line illustrates the criterion
[Na/Fe]${}_{\rm min}+0.3$ dex used to separate FG stars (cyan open circles)
from SG stars (red open circles). Dashed lines indicate the range $\pm 0.07$
dex around the separation, corresponding to the typical internal error on
[Na/Fe] in abundance analyses from high resolution spectra (e.g. Carretta et
al. 2009a).

The spectroscopic classification of MPs is made ignoring a priori where the
stars are located on the PCM, being based only on their Na content. This
second approach immediately reveals a number of mismatches, with respect to
the population division of MPs based on photometry and, ultimately, on the
effect of N abundances. Some stars belonging to the SG according to their
enhanced Na are found on the PCM in the lower group that should be populated
by unpolluted stars with the normal composition of halo stars of similar
metallicity.

Vice versa, FG stars, that should display only the abundance pattern imprinted
by supernovae nucleosynthesis, are found well inside the upper group on the
PCMs, the one populated by giants with high or very high N abundances.

The observed mismatches in classification fall in two categories. We call
major mismatches those whose Na abundance is unambiguously distant from the
dividing line of FG and SG stars (the separation of P and I components in the
scheme defined in Carretta et al. 2009a). We define minor mismatches those
whose Na abundance lies within $\pm 0.07$ dex from the separation. In
principle, this second class of misclassifications could be due to the star to
star errors associated to the Na abundances. However, we note that the adopted
criterion for the selection of FG stars ([Na/Fe]${}_{\rm min}+0.3$ dex)
already includes a generous range of more than 4 times this internal error, so
that it is unlikely that some FG stars are missing. Moreover, the internal
error in Na is by definition a random one, so we expect that FG stars near the
separation are shifted upward or SG stars are pushed downward simply from the
associated error with the same probability, so that statistically the neat
effect is roughly unchanged.

On the other hand, a similar effect is present even in the photometric
division of MPs, where a separation line between the two groups on the PCM is
adopted with the same slope for all GCs, regardless of e.g. crowding,
metallicity or global GC mass333This assumption clashes with the knowledge
that the Na-O anti-correlation, albeit being universal among GCs, is different
in extent and shape from cluster to cluster.. For the photometry of bright
giants in GCs the associated errors in magnitudes are usually tiny, however
the resulting observational error on $\Delta col3$ (estimated from Fig. 2 of
Milone et al. 2017 or Fig. 2 of Marino et al. 2019) amounts on average to
about 0.05 mag. The meaning is that a similar drifting effect is likely to
impact also the photometric fraction of MPs in GCs. Actually, in several GCs
there are a few stars that it is impossible to flag as discrepancies or
agreements between photometry and spectroscopy simply because it is unclear
their belonging to one or the other of the two groups in the PCM, falling
equally far from both groups. To conclude, there could be a grey zone in both
methods where observational uncertainties may slightly blur the adopted
criteria for population tagging. The majority of stars is nevertheless clearly
distinct in both the photometric and spectroscopic approaches, allowing an
useful comparison of their merits and drawbacks.

The mismatches in classification identified in the present sample of GCs are
indicated on the Na-O anti-correlation (Fig. 8 to Fig. 13) as filled symbols,
coloured red or cyan according to their status of SG or FG stars following the
Na criterion. We list in Table 4 all stars whose classification differs
between the HST photometry and the high resolution spectroscopy. Using the
information reported in this Table it is possible to situate each star on both
our PCMs and on the Na-O anti-correlation. In Table 4 we list the value of
[Na/Fe]${}_{\rm min}+0.3$ dex and all the mismatches we found for each GC,
with star ID, $\Delta col$ and $\Delta col3$, the photometric classification
based on PCMs, the [Na/Fe] and [O/Fe] ratios. Finally, a flag is used to label
major mismatches with respect to the photometric population (capital YES). The
lower case flag yes warns that the mismatch is a minor one.

Our enlarged sample in 22 GCs adds up 529 stars with both a Na abundance and a
pair of coordinates on the PCM. We found 75 mismatches in the population
tagging on the whole, i.e. a fraction of $14\pm 2\%$ (Poissonian error). Among
these, 53 are major mismatches and only 22 minor mismatches, in the sense
explained above. We are confident that even using the limit in Na as a strict
condition is justified, and in the following we consider both categories
together, except for noting if some results are affected by a particular
prevalence by one of the types.

##  4 Discussion and conclusions

We quantify all the observed mismatches in the sample of GCs in Table 5 where
we counted both occurrences, i.e. SG stars from spectroscopy mimicking FG
stars (according to HST photometry) and FG stars (according to their Na
abundance) posing as SG stars on the PCMs. In Table 5 we report in parenthesis
the fraction of these events in each GC, computed over the total number of
stars with abundance of Na found in that GC. On average, over 20 GCs, the
fraction of inconsistencies between the two methods of tagging is about
$16\%$, ranging from a minimum of $\sim 4\%$ (NGC 1851, NGC 2808, NGC 6121) to
a rather impressive maximum of about $33\%$ of stars in NGC 6809 and NGC 7078.
The result does not depend much on the category of mismatch, being the average
fraction about $14.5\%$ if we limit to the major mismatches.

Despite the small numbers involved, the results summarized in Table 5 are
informative. At first glance it is possible to infer that the largest number
of discrepancies between spectroscopy and HST photometry occurs among the most
metal-poor GCs.

This impression is visually confirmed in the left panel of Fig. 14 where the
fraction of mismatches in the classification of MPs is plotted as a function
of the metallicity of GCs. The [Fe/H] values are from our homogeneous
metallicity scale based on high-resolution UVES spectra (Carretta et al.
2009c), with the exception of NGC 6205, taken from Johnson and Pilachowski
(2012).

There is a clear anti-correlation between the fraction of cases with a
discrepant tagging of MPs and the cluster metallicity. Admittedly, the
Poissonian errors associated to the fractions are rather large (about 8% on
average), due to the limited number of cross-identifications between ground-
based spectroscopy and the small field of view of HST observations, centered
on the GC centres. However, the relation appears to be statistically
significant. A linear regression returns a high value of the Pearson
correlation coefficient with a significant two-tail probability that the
relation is not due to a chance effect. Both values are indicated in Fig. 14,
where the solid line indicates the regression. This Figure visualizes that the
fraction of stars misclassified on the PCMs, according to their Na abundance,
is generally low in metal-rich or moderately metal-rich GCs but it raises
significantly among metal-poor GCs.

In the right panel of Fig. 14 the fraction is computed using only the major
mismatches. We must duly note that the three most metal-rich GCs disappear, as
also the statistical significance of the relation. Nevertheless, the trend
still exists.

The increase in the number of discrepancies observed in more metal-poor GCs is
compatible with the reduced response of RGB colours to the strength of the
molecular bands, in particular the NH and CN features driving the behaviour of
the $\Delta col3$ coordinate on the PCM. The metallicity dependence of the
band strength for bi-metal molecules varies quadratically with the metal
abundance, so that the tagging with the photometric classification is expected
to be more fraught with uncertainties when the metallicity is decreasing (see
e.g. the discussion in Lee 2023 about the increasing confusion in population
tagging in some photometric systems for more metal poor GCs).

In general, however, the relevant number of mismatches found between
photometry and spectroscopy is a bit surprising. The N abundance is the main
source of the gross differences between FG and SG stars on the PCM, as this
element directly affects the fluxes in the bands used to build the pseudo-
colours and the resulting maps. The Na abundances do not directly affect the
HST fluxes, but the correlation between this species and $\Delta col3$ is a
clear proxy of a correlation between Na and N.

A progressive enhancement of N along the RGB is expected in the normal
evolution of low mass stars, following the first dredge-up and another mixing
episode after the luminosity bump level on the RGB (e.g. Charbonnel 1994;
Gratton et al. 2000). However, the almost constant values of $\Delta col3$ as
a function of luminosity along the RGB (lower left panels in the Figures of
Appendix A) excludes that the observed pattern on the PCMs is related to any
mixing episode. On the contrary, the variations in N must be intrinsic to the
chemical composition of the whole star (Cohen et al. 2002) originated by the
incomplete CN and ON burning at the same temperature where the NeNa cycle is
active.

As a consequence, the failure of PCMs to correctly locate stars according to
their Na abundance in a non negligible number of cases is at first glance a
puzzle. The solution to this apparent riddle is that we uncovered the modern
manifestation of the decoupling between N and heavier atomic species such as
Na, well known since the first studies on MPs (Smith et al. 2013, Smith 2015).
Extensive works by Graeme Smith and collaborators unveiled that there is often
a decoupling between the N abundances derived from molecular bands on one hand
and the abundances of heavier elements such as O and Na on the other. This
occurrence may be indicative of a complex enrichment by polluters with a range
of masses and formation times within each GC.

Accurate comparison of C, N and O, Na abundances in GC stars is neither easy
nor immediate, since these elements are usually measured with different
techniques, mostly low resolution spectroscopy for the former pair and high
resolution spectroscopy for the second one. The comparison shown in Fig.15
represents a typical case.

The CN index S(3839) for giants in NGC 5904 (Smith et al. 2013) measuring the
$\lambda 3883$ CN band strength is compared to Na abundances for RGB stars in
common from Carretta et al. (2009a,b). To compensate at first order for
different effective temperature of RGB stars, the residuals with respect to
the baseline defined by CN-weak stars as a function of magnitude, $\Delta
S(3839)$, are used. The dashed horizontal line separates CN-weak and CN-strong
stars, according to Smith et al. (2013). This level was labelled “phot”
because the criterion dividing FG, CN-weak stars from SG, CN-strong stars is
basically the same tracing mainly the N abundance derived by the incidence of
molecular bands on photometric fluxes. The vertical line along the Na axis is
labelled “spectr” because the division is made using the criterion defined in
Section 3.1 for the tagging of MPs based on Na abundances.

In Fig. 15 the same evidence as given by the analysis of PCMs from HST
photometry is reproduced. There is clearly a decoupling between the abundances
of the lighter and the heavier proton-capture elements, superimposed to a
global trend, with SG stars being more enhanced in CN and Na than FG, N-poor,
Na-poor (and C-rich) stars. Even when N abundances are estimated from low
resolution spectroscopy, there are a few mismatches between the two
classifications. A number of stars assigned to the FG according to their CN
index have Na abundances as high as those classified as SG stars by both
criteria. Conversely, in the pool of objects in common one CN-strong star has
[Na/Fe] compatible with the primordial level in NGC 5904. The effect is
striking because 23Na is produced through the destruction of 22Ne already at
25 MK, whereas O achieve simultaneously a depletion. However, at the above
temperatures the CN isotopes have already reached their equilibrium value
(Prantzos et al. 2017)

In Fig. 16 the example of NGC 5904 is extended to four other GCs using a
variety of different indicators for CN both from photometric systems or low
resolution spectroscopy in NGC 104, NGC 6205, NGC 6121, and NGC 6752. The
separation between CN-strong and CN-weak stars are from the original papers.
The first three GCs seem to show the same “pathology” of NGC 5904, with a
discrepant classification of FG and SG stars in a few cases. In all
occurrences CN-strong stars are found with low levels of Na.

Our definition of second generation(s) is based on the abundance variations of
Na that distinguish stars with composition altered by proton-capture reactions
in GCs from their unpolluted counterparts, e.g. in the halo field. The
comparison shown in Fig. 15 and Fig. 16 seems to point out that classification
schemes based on CN indices, either photometric or spectroscopic, tend to
overestimate the fraction of FG stars. This result is well confirmed by the
statistics of mismatches in Table 4. The vast majority of discrepancies
($73\pm 10\%$) consists in stars erroneously classified as FG on the PCMs,
whereas the contrary is true only for a minor fraction of the cases ($27\pm
7\%$).

The impact of this unbalanced discrepancy on the population ratios of MPs in
GCs is visualised in Fig. 17, where we plot the difference $\Delta FG$ in the
unpolluted FG component as given by HST photometry (N1/Ntot, Milone et al.
2017) and as derived from the Na criterion (primordial P fraction, Carretta et
al. 2010a and references in Tab. 2).

Figure 14: Relation between the fraction of mismatches in population tagging
and the cluster metallicity. On the left panel all the mismatches in Table 5
are counted, and the solid line is a linear fit to the data (Pearson
correlation coefficient and the two-tail probability are labelled in the
panel). In the left panel fractions are computed using only major mismatches.
Figure 15: Comparison of CN (Smith et al. 2013) and Na (Carretta et al.
2009a,b) indicators of MP tagging in NGC 5904 for stars in common between the
two studies. The horizontal dashed line separates CN-strong (top) and CN-weak
(bottom) stars, whereas blue and red filled circles represent FG and SG stars,
respectively, as tagged by our spectroscopic criterion based on Na abundances
(see Section 3.1). Figure 16: The same as in Fig.15 for four more GCs. Upper
left panel: 47 Tuc, with CN index from Smith (2015) and O,Na from Cordero et
al. (2014). Upper right panel: M 13, with CN index from Smith & Briley (2006)
and O,Na from Johnson & Pilachowski (2012). Lower left panel: M 4, with CN
index from Smith & Briley (2005) and O,Na from Marino et al. (2008). Lower
right panel: NGC 6752, with CN index from Smith (2007) and O,Na from Carretta
et al. (2007). Figure 17: Differences $\Delta FG$ in the fraction of FG stars
from HST photometry through the PCMs and from the Na criterion as a function
of the fraction of mismatches found in the present paper. A linear fit, with
Pearson correlation coefficient and probability is also plotted. Figure 18:
Sodium distribution in the three GCs ouliers in Fig. 17 compared to the sample
of field stars homogenized in Carretta (2013, triangles). Red, blue, and green
filled circles are the P, I, and E components according to Carretta et al.
(2009a). The red line reproduce the fraction of FG stars according to Milone
et al. (2017) from PCMs (see text). From left to right the panels are for NGC
288, NGC 2808, and NGC 6838. Figure 19: Differences $\Delta FG$ as a function
of the total absolute magnitude of the 22 GCs in this study.

As the fraction of mis-classification increases, the photometric method via
PCMs increasingly overestimates the fraction of FG stars compared to the
spectroscopic approach, and the trend is so regular that a simple linear
regression results statistically significant (the Pearson correlation
coefficient and the two-tail probability are reported in Fig. 17).

For the three major outliers in Fig. 17, NGC 288, NGC 2808, and NGC 6838, we
compare the spectroscopic and photometric tagging of MPs in Fig. 18, using the
sample of field stars assembled in Carretta (2013) as reference. This sample
is homogenized to match as much as possible the abundance analysis of GC
stars, so that the FG component in GCs individuated by Na only must be
compatible with the floor of unpolluted field stars. In Fig. 18, red, blue,
and green filled circles are used for the P, I, and E components defined in
Carretta et al. (2009a). In particular, the primordial, FG groups in each GC
seems to be a fair match for the field counterpart (empty grey triangles).
Filled black triangles indicate stars that seem to deviate from the bulk of
distribution at a given metallicity. As discussed in Carretta (2013), they are
composed by a sequence of stars whose origin is attributed to accretion. The
horizontal red line in all the panels of Fig. 18 represents the level required
by the estimates in Milone et al. (2017) to reproduce in the spectroscopic
sample the fraction of FG stars derived from the PCMs.

For the cases of NGC 288 (left panel) and NGC 6838 (right panel) the concept
of primordial population according to the N-based selection from HST would
include a consistent fraction of stars whose Na abundances clearly exceed the
level imprinted in field stars by SNe nucleosynthesis only. We remind that
several studies found than only a mere $2-3\%$ of halo stars shows a chemical
composition typical of SG stars in GCs (e.g. Carretta et al. 2010a, Martell et
al. 2011, Koch et al. 2019). On the contrary, in NGC 2808 (middle panel of
Fig. 18) the HST classification would leave out an important number of FG
stars with composition identical to that of unpolluted field stars, in order
to reproduce the low fraction (about $23\%$) quoted in Milone et al. (2017).
We must note that the unusually low FG fraction for NGC 2808 appears to be at
odds with most of the determination from both spectroscopy and photometry (see
Table 9 in Carretta 2015).

How much CN-based evaluations may overestimate the FG fraction with respect to
the GC global characteristics can be evaluated from Fig. 19 where we show the
difference $\Delta FG$ as a function of the total absolute magnitude for the
22 GCs in the present study.

The total luminosity is a proxy of the present day mass of GCs, but the trend
exists and it is equally statistically significant when using the initial
masses of GCs as listed in the database by H.
Baumgardt444https://people.smp.uq.edu.au/HolgerBaumgardt/globular/parameter.html.
Our previous studies based on the Na-O anti-correlation detected a fraction of
the primordial P component essentially constant in GCs (about 30% of stars),
so the trend observed above is hardly surprising, since Milone et al. (2017)
found from their PCM estimates a trend for N1/Ntot to increase in the lower
mass GCs.

To conclude, the N-based methods of population tagging for MPs tend to
overestimate the fraction of FG stars, and this tendency seems to be more
frequent in more metal-poor and less massive GCs. As a consequence, the
fraction of SG stars in these GCs is underestimated. For the high mass GCs,
like e.g. NGC 2808, this trend could even be reversed, although data are still
too sparse for a firmer conclusion.

The scenario is furthermore made more complex by the need to dilute the matter
processed in proton-capture reactions (in polluters whose exact nature is
still unknown) with pristine gas in GCs (whose abundance can be only guessed
at).

Table 4: List of mismatches between the photometric and spectroscopic classification of MPs GC | [Na/Fe]min | star ID | $\Delta col$ | $\Delta col3$ | class. | [Na/Fe] | [O/Fe] | mismatch
---|---|---|---|---|---|---|---|---
| +0.3 dex |  |  |  | PCM |  |  |
0104 | 0.40 | R0018794 | -0.2206 | 0.2659 | SG | 0.375 | 0.409 | yes
0288 | 0.15 | R0000592 | -0.2020 | 0.1232 | FG | 0.198 | 0.040 | YES
0288 |  | R0000061 | -0.0535 | 0.0978 | FG | 0.182 | 0.097 | yes
0288 |  | R0000498 | -0.0508 | 0.0589 | FG | 0.370 | -0.023 | YES
0288 |  | R0001469 | -0.0341 | 0.0491 | FG | 0.191 | 0.377 | yes
0288 |  | R0000355 | -0.0268 | 0.0059 | FG | 0.172 | 0.426 | yes
0288 |  | R0001265 | -0.0346 | -0.0306 | FG | 0.247 | 0.302 | YES
0362 | -0.03 | R0005128 | -0.0875 | 0.1806 | SG | -0.055 |  | yes
0362 |  | R0000917 | -0.0371 | 0.0196 | FG | 0.072 | 0.342 | YES
0362 |  | R0001008 | -0.0290 | 0.0013 | FG | 0.050 | 0.239 | yes
1851 | 0.00 | R0016222 | -0.0964 | 0.0359 | FG | 0.133 | 0.282 | YES
2808 | 0.18 | R0009902 | -0.2594 | 0.2921 | SG | 0.127 | 0.335 | yes
2808 |  | R0033840 | -0.2369 | 0.2102 | SG | 0.170 |  | yes
3201 | 0.00 | R0002194 | -0.2427 | 0.0767 | FG | 0.057 | -0.086 | YES
3201 |  | R0003189 | -0.0151 | -0.0062 | FG | 0.135 |  | YES
3201 |  | R0003013 | 0.0098 | -0.0187 | FG | 0.016 | 0.191 | YES
3201 |  | R0000409 | 0.0670 | -0.0208 | FG | 0.001 | 0.373 | yes
4590 | 0.25 | R0000498 | -0.0535 | 0.0288 | FG | 0.260 |  | yes
4590 |  | R0000791 | -0.0441 | 0.0156 | FG | 0.368 | 0.299 | YES
4590 |  | R0000383 | -0.0389 | 0.0579 | SG | 0.080 |  | YES
4590 |  | R0000899 | -0.0371 | 0.0826 | SG | 0.111 |  | YES
4590 |  | R0000317 | -0.0613 | 0.0917 | SG | 0.199 | 0.040 | YES
4590 |  | R0001167 | -0.0489 | 0.1196 | SG | 0.193 |  | yes
4833 | 0.29 | R0003717 | -0.0282 | 0.0634 | FG | 0.597 | 0.382 | YES
4833 |  | R0001553 | -0.0399 | 0.0452 | FG | 0.293 | 0.273 | YES
5904 | 0.10 | R0012503 | -0.0041 | 0.1754 | SG | 0.098 | 0.494 | yes
6093 | 0.25 | R0002835 | -0.0953 | 0.0413 | FG | 0.393 | 0.200 | YES
6093 |  | R0000925 | -0.0187 | 0.0858 | FG | 0.695 | 0.415 | YES
6093 |  | R0004803 | -0.0803 | 0.0944 | FG | 0.478 | 0.127 | YES
6121 | 0.25 | R0000553 | -0.0483 | 0.1091 | SG | 0.20 | 0.48 | YES
6121 |  | R0001582 | -0.0461 | 0.1149 | SG | 0.11 | 0.51 | YES
6121 |  | R0001355 | -0.0775 | 0.1195 | SG | 0.23 | 0.40 | YES
6121 |  | R0001022 | -0.0755 | 0.1276 | SG | 0.25 | 0.38 | YES
6205 | 0.00 | R0003306 | 0.0104 | 0.1905 | SG | -0.14 | 0.09 | YES
6205 |  | R0014192 | -0.0910 | 0.0283 | FG | 0.45 | 0.12 | YES
6205 |  | R0015663 | -0.0087 | 0.0272 | FG | 0.08 | 0.25 | YES
6205 |  | R0011115 | -0.0106 | 0.0434 | FG | 0.04 | 0.36 | yes
6205 |  | R0003505 | 0.0015 | 0.0460 | FG | 0.22 | 0.30 | YES
6205 |  | R0014143 | -0.0647 | 0.0207 | FG | 0.09 | 0.34 | YES
6254 | 0.02 | R0004141 | -0.2074 | 0.0550 | FG | 0.182 | 0.309 | YES
6254 |  | R0002170 | -0.1166 | 0.0188 | FG | 0.073 |  | yes
6254 |  | R0001688 | -0.0438 | -0.0130 | FG | 0.097 |  | YES
6254 |  | R0004487 | 0.0082 | 0.0372 | FG | 0.178 | 0.473 | YES
6254 |  | R0003806 | -0.0795 | 0.0623 | FG | 0.076 | 0.304 | YES
6254 |  | R0001328 | -0.0419 | 0.0223 | FG | 0.181 | 0.529 | YES
6388 | 0.20 | R0018623 | 0.0059 | 0.7061 | FG | 0.111 | -0.149 | YES
6388 |  | R0023149 | -0.4395 | 0.3905 | FG | 0.093 | 0.089 | YES
6388 |  | R0011104 | -0.2750 | 0.3736 | FG | 0.134 | 0.353 | YES
6388 |  | R0022136 | -0.2303 | 0.1892 | FG | -0.014 | 0.010 | YES
6397 | 0.10 | R0001425 | -0.0466 | 0.0587 | SG | -0.134 |  | YES
6397 |  | R0000935 | -0.0220 | 0.0228 | FG | 0.118 |  | yes
6752 | 0.20 | R0003195 | -0.0350 | 0.1662 | SG | 0.120 | 0.695 | YES
6752 |  | R0004277 | -0.0182 | -0.0065 | FG | 0.365 | 0.523 | YES
6752 |  | R0007736 | 0.0217 | 0.0129 | FG | 0.648 |  | YES
6752 |  | R0005094 | -0.0363 | 0.0540 | FG | 0.338 | 0.183 | YES
6809 | 0.05 | R0001112 | -0.0518 | 0.0655 | FG | 0.613 | 0.212 | YES
6809 |  | R0001928 | -0.0210 | 0.0604 | FG | 0.875 | 0.082 | YES
6809 |  | R0000880 | -0.0169 | 0.0617 | FG | 0.413 | 0.081 | YES
6809 |  | R0000087 | -0.0041 | 0.0620 | FG | 0.539 | 0.280 | YES
6809 |  | R0001035 | -0.0171 | 0.0444 | FG | 0.364 | 0.235 | YES
6809 |  | R0002430 | -0.0051 | 0.0251 | FG | 0.210 | 0.410 | YES
6809 |  | R0002134 | -0.0012 | 0.0027 | FG | 0.260 | 0.429 | YES
Table 4: continue GC | [Na/Fe]min | star ID | $\Delta col$ | $\Delta col3$ | class. | [Na/Fe] | [O/Fe] | mismatch
---|---|---|---|---|---|---|---|---
| +0.3 dex |  |  |  | PCM |  |  |
6838 | 0.30 | R0001028 | -0.1492 | 0.2445 | SG | 0.226 | 0.325 | yes
6838 |  | R0000100 | -0.0825 | 0.0189 | FG | 0.373 | 0.418 | yes
6838 |  | R0000419 | -0.0600 | 0.0171 | FG | 0.316 | 0.350 | yes
6838 |  | R0001862 | -0.0125 | 0.0158 | FG | 0.436 | 0.424 | yes
7078 | 0.22 | R0000861 | -0.1049 | 0.1551 | SG | 0.166 |  | yes
7078 |  | R0000106 | -0.1521 | 0.1501 | SG | 0.188 |  | yes
7078 |  | R0008536 | -0.2064 | 0.0433 | FG | 0.440 | 0.242 | YES
7078 |  | R0001894 | -0.0725 | 0.0425 | FG | 0.643 |  | YES
7078 |  | R0007957 | -0.0646 | 0.0328 | FG | 0.293 | 0.262 | YES
7078 |  | R0002778 | -0.0900 | 0.0217 | FG | 0.375 |  | YES
7078 |  | R0006154 | -0.0065 | 0.0057 | FG | 0.266 |  | yes
7099 | 0.22 | R0002313 | -0.0831 | 0.1309 | SG | 0.099 | 0.506 | YES
7099 |  | R0003697 | -0.0196 | 0.0007 | FG | 0.461 | 0.710 | YES
Table 5: Number of mismatches between the photometric and spectroscopic classification of MPs GC | mismatch | GC | mismatch
---|---|---|---
NGC 104 | 1 (6%) | NGC 6205 | 6 (23%)
NGC 288 | 6 (25%) | NGC 6254 | 6 (24%)
NGC 362 | 3 (20%) | NGC 6388 | 4 (11%)
NGC 1851 | 1 (4%) | NGC 6397 | 2 (11%)
NGC 2808 | 2 (4%) | NGC 6535 | 0
NGC 3201 | 4 (14%) | NGC 6715 | 0
NGC 4590 | 6 (26%) | NGC 6752 | 4 (16%)
NGC 4833 | 2 (14%) | NGC 6809 | 7 (33%)
NGC 5904 | 1 (6%) | NGC 6838 | 4 (17%)
NGC 6093 | 3 (10%) | NGC 7078 | 7 (33%)
NGC 6121 | 4 (15%) | NGC 7099 | 2 (13%)

##  5 Summary

We addressed the issue of population tagging of MPs in GCs through different
methods. To this purpose we compared indicators based on HST photometry and
direct probes of MPs such as the Na abundance from high resolution
spectroscopy.

Due to the lack of published data, we newly derived pseudo-colour maps (PCMs)
for 22 GCs with photometric catalogues from Nardiello et al. (2018). To check
how photometric indicators perform in the population tagging, the photometry
was then matched with stars having Na abundances mostly from our very
homogeneous FLAMES survey. With respect to a similar attempt by Marino et al.
(2019) we retrieved all the stars they used with both HST photometry and high
resolution spectroscopy available and added a new sample of matches, doubling
the database of cross identifications between photometry and spectroscopy.

Our conclusions can be summarised as follows:

  * 1)

Our analysis shows that PCMs perform a coarsely correct ranking in populations
for the bulk of stars in GCs, based essentially on the pseudo-colour $col3$
sensitive basically to N abundances through the effect of NH and CN molecular
bands on fluxes in proper bandpasses.

  * 2)

When the classification from PCM is compared to the direct individuation of
MPs from spectroscopic abundances, there are a number of mismatches or mis-
classifications, in particular when Na is used as privileged species to
disentangle FG and SG stars. Stars populating the SG region are found with low
Na abundances whereas stars belonging to the PCM region of FG stars have Na
abundances at the level of stars with content of light elements clearly
altered by proton-capture reactions responsible for the MPs phenomenon. The
latter group constitutes the majority of the observed mis-classifications.

  * 3)

On average, we found that about $16\%$ of stars with spectroscopic abundances
are erroneously classified in PCMs. The fraction of mismatches increases in
metal-poor GCs, suggesting that the weakening of molecular features may play a
role in the mis-classification.

  * 4)

Hence, the estimates of the fraction of FG stars are different when using
different indicators. Those based on NH or CN (hence the majority from
UV/optical photometry) are usually higher than those from pure spectroscopic
abundances from heavier elements. The comparison with the unpolluted floor as
given by halo field stars shows that photometric tagging tends to overestimate
the FG fraction.

  * 5)

The difference in estimates seems to vary from cluster to cluster, according
to the cluster total mass. The overestimate of the FG fraction seems to be
quantitatively more severe and pronounced in more metal-poor and less massive
GCs.

To conclude, what we found in the present work is the modern form assumed by
the well known decoupling observed in abundances of N and Na among the MPs in
GCs. We confirm the early extensive studies by Smith and collaborators: the
phenomenon as seen by CN, and O, Na is the same, namely the multiple stellar
populations in GCs, but different aspects are likely sampled by the lighter
and the heavier proton-capture elements.

The PCMs seem to follow rather well only the outcome of the C-N cycle at
moderate or low temperatures ($T>10$ MK for C$\rightarrow$N processing). When
going to higher temperature regimes, where both the O-N cycle and the Ne-Na
chain are at work ($T>40$ MK), there are mistakes in the classification and
usually stars with Na abundances high enough to be located in the SG region
along the Na-O anti-correlation are mistaken for FG stars.

This finding represents a strong caveat for all the issues concerning the
correct population ratios in MPs, like e.g. the mass budget problem, since the
FG fraction is the pool from which some massive polluters provide the
nuclearly processed matter to be used, together with pristine gas, for the
assembly of the stellar population with altered chemical composition. Despite
some decades of observations from both photometry and spectroscopy gained for
GC stars, the whole issue of MPs seems to be even now still far to be solved.

Finally, we note that all the conclusions in the present work have been
possible only thanks to publicly available data.

###### Acknowledgements.

This research has made large use of the SIMBAD database (in particular
Vizier), operated at CDS, Strasbourg, France, of the NASA’s Astrophysical Data
System, and TOPCAT.

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##  Appendix A Pseudo-colour maps of all the GCs in the sample

In this Appendix we present in detail the results of the procedure illustrated
in Section 2 for the remaining of the GCs in the sample not shown in Fig. 1.

In Figures from Fig. 20 to Fig. 40 in the upper panels are shown the CMDs
$col$ versus $mag_{F814W}$ and $col3$ versus $mag_{F814W}$. The red and blue
lines are the fiducials used to normalise the pseudo-colours. In the lower
left panels we show the rectified RGBs in the normalized $col$ and $col3$.
Finally, in the lower right panel we present the resulting PCM.

Table A.1 lists all the PCMs derived in the present work. Star IDs are from
the catalogues of Nardiello et al. (2018) and are unique for each star within
a given GC. Here we only show an excerpt of this Table as a guidance. The
whole Table is available only in electronic form at CDS.

Table 6: Pseudo-colour maps (PCMs) for all 22 GCs in the sample. The complete Table is only available at the CDS. $\Delta col$ | $\Delta col3$ | RA | Dec | star ID | GC
---|---|---|---|---|---
-0.2109 | 0.2258 | 6.076004 | -72.107040 | R0000586 | 104
-0.2055 | 0.1613 | 6.066042 | -72.106667 | R0000641 | 104
-0.1938 | 0.1755 | 6.067145 | -72.105949 | R0000766 | 104
-0.1637 | 0.2712 | 6.058540 | -72.105705 | R0000811 | 104
-0.1816 | 0.1747 | 6.047574 | -72.105133 | R0000910 | 104
-0.1608 | 0.1571 | 6.023707 | -72.105064 | R0000917 | 104
-0.0847 | -0.0300 | 6.026685 | -72.105034 | R0000929 | 104
-0.2605 | 0.2699 | 6.018813 | -72.104927 | R0000951 | 104
-0.1281 | 0.2678 | 6.043403 | -72.104774 | R0000984 | 104
-0.1612 | 0.0519 | 6.047808 | -72.104568 | R0001028 | 104
-0.1510 | 0.1516 | 6.048434 | -72.104340 | R0001067 | 104
-0.2553 | 0.2338 | 6.004899 | -72.104340 | R0001070 | 104
0.0521 | 0.4089 | 6.028763 | -72.104332 | R0001073 | 104
-0.0756 | 0.0280 | 6.068101 | -72.104294 | R0001076 | 104
-0.1837 | 0.2275 | 6.032630 | -72.104263 | R0001086 | 104
-0.2091 | 0.1949 | 6.039308 | -72.104240 | R0001089 | 104
-0.1940 | 0.2577 | 6.034832 | -72.104095 | R0001113 | 104
-0.2905 | 0.2657 | 6.023297 | -72.104034 | R0001122 | 104
-0.3772 | 0.3225 | 6.030381 | -72.104034 | R0001126 | 104
-0.2396 | 0.2103 | 6.076389 | -72.103943 | R0001137 | 104
Figure 20: As in Fig. 1 but for the globular cluster NGC 288

Figure 21: As in Fig. 1 but for the globular cluster NGC 362

Figure 22: As in Fig. 1 but for the globular cluster NGC 1851

Figure 23: As in Fig. 1 but for the globular cluster NGC 2808

Figure 24: As in Fig. 1 but for the globular cluster NGC 3201

Figure 25: As in Fig. 1 but for the globular cluster NGC 4590

Figure 26: As in Fig. 1 but for the globular cluster NGC 4833

Figure 27: As in Fig. 1 but for the globular cluster NGC 5904

Figure 28: As in Fig. 1 but for the globular cluster NGC 6093

Figure 29: As in Fig. 1 but for the globular cluster NGC 6121

Figure 30: As in Fig. 1 but for the globular cluster NGC 6205

Figure 31: As in Fig. 1 but for the globular cluster NGC 6254

Figure 32: As in Fig. 1 but for the globular cluster NGC 6388

Figure 33: As in Fig. 1 but for the globular cluster NGC 6397

Figure 34: As in Fig. 1 but for the globular cluster NGC 6535

Figure 35: As in Fig. 1 but for the globular cluster NGC 6715

Figure 36: As in Fig. 1 but for the globular cluster NGC 6752

Figure 37: As in Fig. 1 but for the globular cluster NGC 6809

Figure 38: As in Fig. 1 but for the globular cluster NGC 6838

Figure 39: As in Fig. 1 but for the globular cluster NGC 7078

Figure 40: As in Fig. 1 but for the globular cluster NGC 7099

##  Appendix B Notes on particular stars in a few GCs

In a few plots some stars apparently are either missing with respect to the
numbers given in Table 2 or are in an odd position on the PCMs. In the
following we highlight possible problems related to the identification of
stars with spectroscopic abundances from the figures in Marino et al. (2019)
and we note about particular stars on the PCMs. Flag F indicates stars found
and used by Marino et al. (2019) and flag M indicates additional stars found
only by us (see Section 2.2).

#### NGC 104

Star R0009274 could be a star on the AGB, according to its position in the CMD
magF275W, (magF275W-mag${}_{F814W})$ (although not judging from other CMDs).

#### NGC 362

Stars R0000796 and R0009389 (both found also in Marino et al. 2019) could be
among the so called red-RGB stars, according to the magF336W,
(magF336W-mag${}_{F814W})$ CMD. To these, we add star R0009282, neglected by
Marino et al., as a possible red-RGB star.

#### NGC 1851

Two stars neglected in Marino et al. (2019, star R0000480 and star R0015479)
are located in the region attributed to red-RGB stars, the same of star
R0015322, used by Marino et al.

#### NGC 2808

There is a star in the PCM by Marino et al. (2019) located at about $\Delta
col,\Delta col3=(-0.416,0.175)$ and classified as FG star (figure 1 in Marino
et al.). We note that this is the object making the sequence of FG stars in
NGC 2808 so extended. However, we were unable to find a star located at this
value of $\Delta col3$ in their figure 9, even if all the matches in this GC
have a Na abundance. For unknown reasons, this star, plotted on their PCM as
having spectroscopic abundances, was then dropped in the Na-$\Delta col3$
relation. Several stars in this GC, both found and neglected in Marino et al.
(e.g. stars R0033484, R0027893, R0016679, R0009902) seem to lie in the
saturation region. Stars R0005798 (flag=F) and star R0021965 (flag=M) are
outside the RGB in the magF336W, (magF336W-mag${}_{F814W})$, but not in the
magF275W, (magF275W-mag${}_{F814W})$.

#### NGC 6121

On the Na-$\Delta col3$ relation derived by us, three stars with flag=M
(R0000373, R0000417, and R0000781; [Na/Fe]=0.05, 0.41, and 0.43) are
superimposed to stars R0000301, R0000863, and R0000749 ([Na/Fe]=0.06, 0.38,
and 0.40), flag=F, respectively. Star R0001022 ([Na/Fe]=0.25) is superimposed
to star R0001728 ([Na/Fe]=0.24), both with flag=F. Judging by its position on
the PCM, star R0000101 (flag=F) could be a mis-identification of ours. Both
the superpositions and the possible mis-identification are mostly due to the
abundances in Marino et al. (2008) being provided with only 2 significant
decimal figures, so that many stars result with the same or very similar Na
and are difficult to assign only on the base of the figures in Marino et al.
(2019).

#### NGC 6205

In this GC we identified three stars from the figures in Marino et al. (2019)
that do not have the complete set of colours to make them appear on the PCM
(based on the photometry by Nardiello et al. 2018), even if they are likely
matches according to the coordinates. Star R0001523 (L-666, [Na/Fe]=0.12 in
Johnson and Pilachowski 2012) does not have magF336W. Star R0012534 (L-261,
[Na/Fe]=0.06 in Johnson and Pilachowski) does not have magF336W. Star R0002021
( L-324, [Na/Fe]=0.27 in Johnson and Pilachowski) does not have magF438W. It
is unlikely that we mis-identified all three: e.g. among the stars matched in
coordinates between Nardiello et al. and Johnson and Pilachowski there is no
star having [Na/Fe]=0.12, such as star L-666=R0001523. When considering both
coordinates and Na abundances we have no explanation on why these objects are
located on the PCM used in Marino et al. (2019). Finally, star R0001319
(L-370, [Na/Fe]=0.27), with flag=F is superimposed to star R0003036 (L=296,
[Na/Fe]=0.28), with flag=M.

#### NGC 6254

Star R0001704 ([Na/Fe]=-0.137, flag=F) is superimposed to star R0001056
([Na/Fe]=-0.128, flag=M).

#### NGC 6715

Star R257062 ([Na/Fe]=0.587) found by Marino et al. (2019) should not be on a
PCM, having no magF814W. Perhaps this is a mis-identification in Marino et
al., confused for another star.

#### NGC 6752

Analogously, star R010792, found in Marino et al. (2019) should not be in a
PCM, having no magF336W. From the Na-O anti-correlation shown in Figure 8 of
Marino et al. this object is unambiguously identified as star NGC 6752-21694
in Carretta et al. (2009a), with ([O/Fe], [Na/Fe]=0.091, 0.318), yet we were
not able to put it on our PCM for the lack of all required magnitudes. It is
unclear how this star can appear among those with both HST photometry and Na
abundances in Marino et al. (2019).