# Exploring Simple-Population and Multiple-Population Globular Clusters in the
Outer Galactic Halo using the Hubble Space Telescope

E. P. Lagioia South-Western Institute for Astronomy Research Yunnan
University, Kunming, 650500, P.R. China  A. P. Milone Dipartimento di Fisica e
Astronomia “Galileo Galilei”, Università di Padova, Vicolo dell’Osservatorio
3, 35122, Padova, Italy  Istituto Nazionale di Astrofisica - Osservatorio
Astronomico di Padova, Vicolo dell’Osservatorio, 5, 35122, Padova, Italy  M.
V. Legnardi Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università
di Padova, Vicolo dell’Osservatorio 3, 35122, Padova, Italy  G. Cordoni
Research School of Astronomy and Astrophysics, Australian National University,
Canberra, ACT 2611, Australia  E. Dondoglio Istituto Nazionale di Astrofisica
- Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio, 5, 35122,
Padova, Italy  A. Renzini Istituto Nazionale di Astrofisica - Osservatorio
Astronomico di Padova, Vicolo dell’Osservatorio, 5, 35122, Padova, Italy  M.
Tailo Istituto Nazionale di Astrofisica - Osservatorio Astronomico di Padova,
Vicolo dell’Osservatorio, 5, 35122, Padova, Italy  T. Ziliotto Dipartimento di
Fisica e Astronomia “Galileo Galilei”, Università di Padova, Vicolo
dell’Osservatorio 3, 35122, Padova, Italy  M. Carlos Theoretical Astrophysics,
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20
Uppsala, Sweden  S. Jang Center for Galaxy Evolution Research and Department
of Astronomy, Yonsei University, Seoul 03722, Korea  A. F. Marino Istituto
Nazionale di Astrofisica - Osservatorio Astronomico di Padova, Vicolo
dell’Osservatorio, 5, 35122, Padova, Italy  A. Mohandasan Dipartimento di
Fisica e Astronomia “Galileo Galilei”, Università di Padova, Vicolo
dell’Osservatorio 3, 35122, Padova, Italy  J. Qi South-Western Institute for
Astronomy Research Yunnan University, Kunming, 650500, P.R. China  G. Rangwal
South-Western Institute for Astronomy Research Yunnan University, Kunming,
650500, P.R. China  E. Bortolan  Dipartimento di Fisica e Astronomia “Galileo
Galilei”, Università di Padova, Vicolo dell’Osservatorio 3, 35122, Padova,
Italy  F. Muratore  Dipartimento di Fisica e Astronomia “Galileo Galilei”,
Università di Padova, Vicolo dell’Osservatorio 3, 35122, Padova, Italy

###### Abstract

The pseudo two-color diagram, known as chromosome map (ChM), is a valuable
tool for identifying globular clusters (GCs) that consist of single or
multiple stellar populations (MPs). Recent surveys of Galactic GCs using the
ChM have provided stringent observational constraints on the formation of GCs
and their stellar populations. However, these surveys have primarily focused
on GCs at moderate distances from the Galactic center and composed of MPs.

In this paper, we present the first detailed study of the stellar composition
of four GCs in the outer halo of the Milky Way: Arp 2, Ruprecht 106, Terzan 7,
and Terzan 8. Our analysis is based on high-precision photometry obtained from
images collected with the Hubble Space Telescope in the F275W, F336W, F438W,
F606W, and F814W bands. We find that Ruprecht 106 and Terzan 7 are composed
solely of a single stellar population, whereas Arp 2 and Terzan 8 host both
first- and second-population stars. In these clusters, the second population
comprises about half and one-third of the total number of GC stars,
respectively.

The results from this paper and the literature suggest that the threshold in
the initial GC mass, if present, should be smaller than approximately $10^{5}$
$\mathrm{M}_{\odot}$. The first-population stars of Arp 2 and Terzan 8, along
with the stars of the simple-population GCs Ruprecht 106 and Terzan 7, exhibit
intrinsic ${\rm F275W-F814W}$ color spreads corresponding to [Fe/H] variations
of approximately 0.05 – 0.30 dex. This indicates that star-to-star metallicity
variations are a common feature of star clusters, regardless of the presence
of MPs.

Globular star clusters(656) — Stellar abundances(1577) — Stellar
populations(1622) — Milky Way stellar halo (1060) —Milky Way stellar
halo(1060) — Ultraviolet astronomy(1736)

††facilities: HST(WFC3)††software:

##  1 Introduction

In most Galactic globular clusters (GCs), stars exhibit variations in helium
and light elements (see Kraft, 1994; Bastian & Lardo, 2018; Gratton et al.,
2012; Milone & Marino, 2022, for reviews). In particular, the abundance of C
and N, O and Na, and Mg and Al, show a negative pairwise correlation. Thus,
N-rich stars are depleted in C and O, and enriched in He and Na. In fewer
cases N-rich stars are also Al-rich and depleted in Mg (e.g. Marino et al.,
2008; Carretta et al., 2009).

Old stars rich in C, O and Mg, are also commonly observed in the Galactic-halo
field. It is for this reason that coeval GC stars with similar chemical
composition are thought to be formed during the first star formation burst
that followed the collapse of the giant molecular cloud from which their host
cluster originated. This gives a rationale for calling them first population
or 1P stars.

On the other side, GC members enriched in He, N, Na, and Al are rarely
detected among field stars. The chemical composition of these stars bear the
footprints of hot proton-capture reactions triggered in the CNO, NeNa, and
MgAl chains, which are activated at effective temperatures ($T_{\rm{eff}}$)
$\gtrsim 75$ MK (Denisenkov & Denisenkova, 1989). As a consequence, they are
called second population or 2P stars, because short-lived 1P stars are
regarded as the gas donors from which 2P stars formed. 2P stars can be
therefore identified as a stellar generation subsequent to that of 1P stars
(Cottrell & Da Costa, 1981; D’Antona et al., 1983; Yong et al., 2005;
Denissenkov & Hartwick, 2014), or as 1P stars that incorporated material
processed by massive stars through accretion or binary interaction (de Mink et
al., 2009; Bastian et al., 2013; Krause et al., 2013; Gieles et al., 2018;
Renzini et al., 2022) 2P stars can constitute the main stellar component of
massive GCs with MPs (Martell et al., 2011; Milone et al., 2020; Dondoglio et
al., 2021; Jang et al., 2022) but they are infrequent in the field, so that
halo stars with 2P-like chemistry are thought to be lost from GCs through
tidal interaction with the Galaxy.

Attempting to identify a comprehensive mechanism for the formation of MPs or,
in simpler terms, discerning the nature of the 1P donors, encounters various
observational constraints that are challenging to meet simultaneously (for an
extensive discussion on the various MP formation models and their implications
see Renzini et al., 2015, 2022). Determining the relation between the
properties of the multiple stellar populations (MPs) and the main parameters
of the host cluster, such as the GC mass and the orbit, may provide
constraints to the GC formation. To better refine our understanding of the
formation scenarios, it is also crucial to ascertain whether MPs are a
widespread trait among Galactic GCs or whether only clusters surpassing a
specific mass threshold can sustain the formation of MPs.

Variations in abundance among stars contribute to a corresponding spread in
colors in photometric diagrams obtained from specific filters (e.g. Marino et
al., 2008; Yong & Grundahl, 2008; Milone et al., 2012a; Lee, 2015; Mehta et
al., 2024; Milone & Marino, 2022, and references therein). As an example, the
photometric diagram dubbed chromosome map (ChM) is an efficient and widely
used tool to disentangle 1P and 2P stars along the main sequence (MS), red
giant branch (RGB), and asymptotic giant branch (AGB) of star clusters. The
ChM is a pseudo two-color diagram typically constructed with the pseudo-color
$C_{F275W,F336W,F438W}=(m_{\rm F275W}-m_{\rm F336W})-(m_{\rm F336W}-m_{\rm
F814W})$, mainly sensitive to internal variations in C, N and O; and the color
$m_{\rm F275W}-m_{\rm F814W}$ which improves the identification of stars with
varying helium content (Milone et al., 2015; Marino et al., 2019a; Lagioia et
al., 2018, 2021). Various photometric surveys of Galactic GCs based on ChMs
(Milone et al., 2017; Jang et al., 2022) reveal the ubiquitous presence of MPs
in all investigated clusters. These results support and reinforce similar
conclusions drawn from spectroscopic analyses (Gratton et al., 2004, 2012;
Marino et al., 2019a).

In this context, the identification of simple-population (SP) GCs, namely
clusters with chemically homogeneous stars, casts doubt on the universal
occurrence of MPs, thus challenging the view of MPs as a phenomenon inherent
to the proto-cluster environment. The best prototypes of SP GCs are Ruprecht
106 and Terzan 7. For the first cluster, the spectroscopic analysis of nine
red giant stars by Villanova et al. (2013) revealed homogeneous light-element
abundance. Moreover, the analysis of the cluster HB morphology by Milone et
al. (2014), and the photometry in the F336W, F438W, and F814W bands by Dotter
et al. (2018), suggested that the color distribution of RGB stars was
consistent with that of a single stellar population. Similarly, evidence based
on ground-based $U,B,I$ photometry that the star cluster Terzan 7 contains a
single stellar population has been provided by Lagioia et al. (2019b).

Recently, we have been granted 62 orbits during the cycle 30 of the Hubble
Space Telescope (HST, GO 17075, PI: Lagioia) to investigate for the first time
the ChMs of four outer-halo clusters. The targets include Ruprecht 106 and
Terzan 7, the two aforementioned candidate SP GCs but never been studied
through the ChM, which is mandatory for a conclusive assessment about either
presence or absence of MPs. The other two targets are Arp 2 and Terzan 8.

The choice of our targets was based on the following criteria: galactocentric
distance, metallicity, mass and origin. With respect to the first criterion,
the galactocentric distance of all the targets exceeds 15 kpc (Harris 1996,
2010 update; Baumgardt & Vasiliev 2021).

As for the metallicity, the selected clusters span a wide range of iron
content, ranging from the metal poor cluster Terzan 8 ($\rm{[Fe/H]=-2.27}$
dex; Carretta et al., 2014) to the sub-solar metallicity cluster Terzan 7
($\rm{[Fe/H]=-0.62}$ dex Tautvaišienė et al., 2004). We notice that the
average metallicity values reported in the (Harris, 1996, 2010 update) catalog
span a similar interval, with [Fe/H]$=-2.18$ dex for Terzan 8 and
[Fe/H]$=-0.32$ dex for Terzan 7.

All the targets are relatively small clusters with present-day mass M $\leq
10^{4}$ $\mathrm{M}_{\odot}$, except Terzan 8, which is the most massive GC
with M $\sim 7.5\times 10^{4}$ $\mathrm{M}_{\odot}$ (Baumgardt & Hilker, 2018,
2023 update). Baumgardt and collaborators have also provided an estimate of
the initial mass of the target clusters 111In 2018, Baumgardt & Hilker
provided advanced estimates for the initial masses of the Galactic GCs. Their
determinations face several uncertainties which depend on our limited
understanding of the evolutionary history of the Milky Way, and therefore of
its tidal field. Other uncertainties are related to the knowledge of the
primordial mass segregation in clusters and their early chemo-dynamical
evolution, in particular the amount of mass lost through interaction with the
molecular clouds from which they originated. We notice that the aforementioned
GC mass estimates are obtained by assuming a time-independent Galactic
gravitational potential and no initial mass segregation., ${\rm M_{in}}$, that
for three out of four clusters is smaller (albeit marginally in the case of
Ruprecht 106) than $\sim 1.5\times 10^{5}$ $\mathrm{M}_{\odot}$, a threshold
value proposed by Milone et al. (2020) for the onset of MPs. It is worth
mentioning that according to studies based on the analysis of the CN and CH
indices in low resolution spectra of relatively small and distant globulars,
the initial mass threshold for the onset of MP might be lower than the value
suggested by Milone et al. (2020) and approximately equal to $2\times 10^{4}$
$\mathrm{M}_{\odot}$ (Salinas & Strader, 2015; Tang et al., 2021; Huang et
al., 2024).

Finally, concerning the last criterion, several studies indicate a probable
ex-situ genesis of Arp 2, Terzan 7 and Terzan 8, which are associated to the
Sgr dSph (Law & Majewski, 2010; Bellazzini et al., 2003) and likely still
bound to it (Bellazzini et al., 2020; Shirazi et al., 2023).

The four target clusters represent, therefore, an ideal sample to study to
which extent the environment affect the formation of MPs and to shed new light
on the physical conditions driving the emergence of MPs. Table 1 reports the
main parameters of the four GCs.

The outline of the paper includes Section 2, where we describe the dataset and
the data reduction techniques adopted in our analysis. Then, Section 3
presents the UV-optical-NIR CMDs of the four targets clusters. In Section 4,
we present the first ChMs of our GCs, while in Section 5 we investigate the
metallicity of GC stars. Finally, the summary and the discussion are provided
in Section 6.

Table 1: Main parameters of the four globular clusters analyzed in this work:
cluster ID, galactocentric distance ($\rm R_{GC}$), iron content ([Fe/H]),
reddening (E(B$-$V)), actual mass (M), initial mass (${\rm M_{in}}$), half-
light radius (${\rm r_{hl}}$), escape velocity (${\rm v_{esc}}$), age.

Cluster | ${\rm R_{GC}}$ | [Fe/H] | E(B$-$V) | M | ${\rm M_{in}}$ | ${\rm r_{hl}}$ | ${\rm v_{esc}}$ | Age
---|---|---|---|---|---|---|---|---
| (kpc) | (dex) | (mag) | ($10^{4}$ $\mathrm{M}_{\odot}$) | ($10^{5}$ $\mathrm{M}_{\odot}$) | (arcmin) | (${\rm km\,s^{-1}}$) | (Gyr)
Arp 2 | 21.39 | -1.75 | 0.10 | 3.87 | 0.912 | 1.70 | 4.5 | 13.00
Ruprecht 106 | 18.04 | -1.68 | 0.20 | 3.40 | 1.259 | 1.26 | 5.6 | 11.50
Terzan 7 | 16.85 | -0.32 | 0.07 | 2.23 | 0.525 | 0.90 | 4.6 | 8.00
Terzan 8 | 20.43 | -2.16 | 0.12 | 7.59 | 7.586 | 1.89 | 6.0 | 13.50

Note. — For our analysis, we adopted the average metallicity values from
Harris (1996, 2010 update). The listed reddening values have been also taken
from the same catalog. It is worth noting that Mottini et al. (2008) found
${\rm[Fe/H]=-1.83}$ for Arp 2, while Villanova et al. (2013) obtained
${\rm[Fe/H]=-1.47}$ for Ruprecht 106. Ages are taken from Dotter et al. (2010)
except for Ruprecht 106, for which the age comes from Dotter et al. (2018) .
All other quantities listed in the table are derived from the 2023 updated
version of the catalog of the Fundamental Parameters of Galactic Globular
Clusters available at the following URL:
https://people.smp.uq.edu.au/HolgerBaumgardt/globular/.

##  2 Data analysis

The observation dataset analyzed in this work for Arp 2, Terzan 7, and Terzan
8 consists of images collected by HST with the WFC3 camera in the bands F275W,
F336W, and F438W of the UVIS channel during the cycle 30 (GO 17075; PI:
Lagioia), and of ACS/WFC images in the bands F606W and F814W of ACS/WFC,
already present on the MAST archive 222https://archive.stsci.edu/ before the
execution of the GO-17075 program. For Ruprecht 106, only F275W observations
have been collected during the GO-17075, whereas the F336W and F438W images
are available from the archive. The HST data collected for the GO-17075 and
analyzed in this paper can be found in MAST:
http://dx.doi.org/10.17909/23y6-1r51 (catalog 10.17909/23y6-1r51). Details on
the exposures used in this works are outlined in Table 2.

Table 2: Dataset of HST observations analyzed in this work.  Cluster | Date (DD/MM/YY) | Camera/Channel | Filter | N $\times$ exposure time (s) | Proposal ID (PI Last name)
---|---|---|---|---|---
| March 06–17 2023 | WFC3/UVIS | F275W | $25\times 1325$ | 17075 (Lagioia)
| April 25–26 2023 | WFC3/UVIS | F275W | $2\times 1325$ | 17075 (Lagioia)
| March 12–17 2023 | WFC3/UVIS | F336W | $11\times 795$ | 17075 (Lagioia)
Arp 2 | March 12–17 2023 | WFC3/UVIS | F438W | $11\times 348$ | 17075 (Lagioia)
| May 03 2016 | ACS/WFC | F606W | $45+2\times(554+555)+4\times 556$ | 14235 (Sohn)
| April 22 2006 | ACS/WFC | F606W | $40+5\times 345$ | 10775 (Sarajedini)
| April 22 2006 | ACS/WFC | F814W | $40+5\times 345$ | 10775 (Sarajedini)
| June 29–30 2023 | WFC3/UVIS | F275W | $2\times(1401+1402)$ | 17075 (Lagioia)
| July 07–12 2023 | WFC3/UVIS | F275W | $12\times(1401+1402)$ | 17075 (Lagioia)
| December 10 2016 | WFC3/UVIS | F336W | $2\times 1100$ | 14726 (Dotter)
| March 29 2017 | WFC3/UVIS | F336W | $2\times 1100$ | 14726 (Dotter)
| May 30–31 2017 | WFC3/UVIS | F336W | $2\times 1100$ | 14726 (Dotter)
| September 29 2017 | WFC3/UVIS | F336W | $4\times 1100$ | 14726 (Dotter)
Ruprecht 106 | December 10 2016 | WFC3/UVIS | F438W | $571$ | 14726 (Dotter)
| March 29 2017 | WFC3/UVIS | F438W | $571$ | 14726 (Dotter)
| May 31 2017 | WFC3/UVIS | F438W | $571$ | 14726 (Dotter)
| September 21 2017 | WFC3/UVIS | F438W | $2\times 571$ | 14726 (Dotter)
| July 04 2010 | ACS/WFC | F606W | $55+4\times 550$ | 11586 (Dotter)
| July 12 2016 | ACS/WFC | F606W | $60+841+844+2\times(842+845)$ | 14235 (Sohn)
| July 04 2010 | ACS/WFC | F814W | $60+3\times 585+586$ | 11586 (Dotter)
| March 08–16 2023 | WFC3/UVIS | F275W | $17\times 1325$ | 17075 (Lagioia)
| March 14–15 2023 | WFC3/UVIS | F336W | $3\times 795+837+2\times 838$ | 17075 (Lagioia)
Terzan 7 | March 14 2023 | WFC3/UVIS | F438W | $3\times 348$ | 17075 (Lagioia)
| June 03 2006 | ACS/WFC | F606W | $40+5\times 345$ | 10775 (Sarajedini)
| May 04 2016 | ACS/WFC | F606W | $45+2\times(554+555)+4\times 556$ | 14235 (Sohn)
| June 03 2006 | ACS/WFC | F814W | $40+5\times 345$ | 10775 (Sarajedini)
| March 09–23 2023 | WFC3/UVIS | F275W | $9\times 1325$ | 17075 (Lagioia)
| April 18–30 2023 | WFC3/UVIS | F275W | $15\times 1325$ | 17075 (Lagioia)
| May 01 2023 | WFC3/UVIS | F275W | $1325$ | 17075 (Lagioia)
| March 16 2023 | WFC3/UVIS | F336W | $795$ | 17075 (Lagioia)
| April 24–30 2023 | WFC3/UVIS | F336W | $9\times 795$ | 17075 (Lagioia)
Terzan 8 | May 01 2023 | WFC3/UVIS | F336W | $795$ | 17075 (Lagioia)
| March 16 2023 | WFC3/UVIS | F438W | $348$ | 17075 (Lagioia)
| April 24–30 2023 | WFC3/UVIS | F438W | $9\times 348$ | 17075 (Lagioia)
| May 01 2023 | WFC3/UVIS | F438W | $348$ | 17075 (Lagioia)
| June 03 2006 | ACS/WFC | F606W | $40+5\times 345$ | 10775 (Sarajedini)
| April 28 2016 | ACS/WFC | F606W | $45+2\times(554+555)+4\times 556$ | 14325 (Sohn)
| June 03 2006 | ACS/WFC | F814W | $40+5\times 345$ | 10775 (Sarajedini)

The data reduction has been performed with the software img2xym (Anderson et
al., 2006). The software takes as input the flc images, which are HST
pipeline-calibrated individual exposures corrected for pixel-based charge
transfer efficiency (Anderson & Bedin, 2010). For each analyzed image, a
$5\times 5$ array of perturbed point-spread functions (PSFs) is generated
starting from library empirical PSF models, and improved with spatial-
variation corrections obtained from unsaturated and isolated bright stars.
Saturated stars are also identified and their magnitude is accurately
determined considered flux bleed into adjacent pixels (Anderson et al., 2008;
Gilliland et al., 2010).

Instrumental magnitudes were calibrated to the VEGA-MAG system using the
method of Bedin et al. (2005), incorporating UVIS and WFC encircled energy
distribution and photometric zero points from the STScI website. Geometric
distortion corrections were applied to star positions using the solution
presented by Bellini et al. (2011), and the positions were transformed to the
Gaia DR3 reference system (Gaia Collaboration et al., 2023). Finally, we
selected stars measured with high photometric accuracy, following the
methodology outlined in Milone et al. (2009) which is based on the q-fit, a
quality index provided by the software.

To determine the cluster membership for each target, we took advantage of the
large temporal baseline of our observations and compute proper motions (PMs).
The adopted method is based on the displacement of stars observed at different
epochs with respect to the motion of a sample of reference stars. Since
cluster members have a negligible proper-motion dispersion compared to field
stars, we referred the PMs to a sample of bright, unsaturated cluster stars
that are well fitted by the PSF model. We refer to the papers by Anderson et
al. (2006), Lagioia et al. (2014), and Tailo et al. (2021) and references
therein for details on the procedure.

As shown by Tailo et al. (2021, see their figure 1), who derived the stellar
PMs of stars in the fields of view studied in this paper by using the HST data
available at that time, the field stars and the cluster members are well
separated in the PM diagrams and the residual field contamination is
negligible.

As a final step, we verified that the photometry of each cluster is not
significantly affected by differential reddening. Hence, we corrected the
photometry for the effects of spatial-dependent variation of the photometric
zero point, which are due to small inaccuracies in the PSF models, by applying
the procedure outlined in Milone et al. (2012b).

Overall, the dataset that we collected for analyzing MPs in our four outer-
halo GCs is similar to that adopted in the recent surveys of Galactic GCs
(Piotto et al., 2015; Milone et al., 2017), which are based on similar data in
F275W, F336W, F438W, F606W, and F814W of the WFC3/UVIS and ACS/WFC cameras of
HST. Since we have derived stellar photometry and astrometry using the same
methods and computer programs adopted in previous surveys, we can directly
compare our results with former analyses focused on MPs in GCs, taking
advantage of a sample composed by 62 Galactic GCs.

##  3 The UV-optical-NIR CMDs

The CMDs built with the $m_{\rm F275W}-m_{\rm F814W}$ and $C_{\rm
F275W,F336W,F438W}$ color indices are efficient tools to detect MPs. To this
purpose, we plot in Figure 1 the $m_{\rm F275W}$ versus $m_{\rm F275W}-m_{\rm
F814W}$ CMDs of our four targets, from the most metal-poor (top-left) to the
most metal-rich (bottom-right). In each panel, the error bars on the right
side indicate the typical magnitude and photometric color error at the
corresponding F275W magnitude.

We see that the faint region of each CMD is populated by MS stars reaching
$\sim 1$ to 2 mag below the Turn-Off (TO). We also observed conspicuous
populations of blue stragglers and prominent sequences of MS-MS binary systems
with large mass ratios, which appear on the red side of the MS in each
cluster. The upper CMD region is populated by RGB, Horizontal-Branch (HB)
stars and AGB stars. It is worth noticing the short color distribution of HB
stars in all the target GCs. While theoretical prescriptions imply that young
and metal-rich GCs display short HBs, the same phenomenon observed in
intermediate-metallicity GCs might serve as an indirect indication that there
is negligible to no helium enhancement among the cluster stars, as in the case
of Ruprecht 106 (Milone et al., 2014). Among the analyzed GC, the most metal-
poor targets Arp 2 and Terzan 8 display slightly more extended HBs ($\sim 1.5$
mag).

Figure 1: $m_{\rm F275W}$ versus $m_{\rm F275W}-m_{\rm F814W}$ CMDs of the
four clusters analyzed in this work, arranged by increasing metallicity from
left to right and top to bottom. In each panel, the vertical and horizontal
error bars on the right-hand side represent the typical magnitude and color
errors at different F275W magnitudes.

Figure 2 displays the $m_{\rm F438W}$ versus $C_{\rm F275W,F336W,F438W}$
pseudo-CMDs of our targets, arranged as in Fig. 1. The pseudo-CMDs of the two
GCs in the top row show the largest color spread among the four targets. In
particular, we observe a distinct split along the entire RGB extension in Arp
2, whereas the RGB stars of Terzan 8 with similar magnitudes display a broad
color spread, with indications of bifurcation.

In both the cases, the $C_{\rm F275W,F336W,F438W}$ pseudo-color broadening of
RGB stars is taken as evidence that these clusters harbor MPs. A spurious
effect due to random errors in the pseudo-color is ruled out by the extension
of the color error bars. On the other side, the RGB spread visible in the CMDs
of Ruprecht 106 and Terzan 7 is comparable with the error in color along the
whole RGB extension. This suggests that Arp 2 and Terzan 8 may harbor MPs with
different light-element abundances, while Ruprecht 106 and Terzan 7 may not.

Figure 2: $m_{\rm F438W}$ versus $C_{\rm F275W,F336W,F438W}$ pseudo-CMDs of
the four target clusters, arranged as in Fig 1. In each panel, the error bars
on the right side indicate the typical color and magnitude errors at different
F438W magnitudes.

##  4 The chromosome maps

To further investigate the stellar populations along the RGB of the studied
GCs, we constructed a pseudo color-color diagram called ChM. In this diagram,
stars with different content of light elements such as helium, carbon,
nitrogen, oxygen, and magnesium, occupy specific regions (Milone et al., 2017;
Marino et al., 2019b). As a result, a ChM gives the possibility to tag
distinct stellar populations in a GC with a precision comparable with that
provided by high-resolution spectroscopy (Marino et al., 2019a). In the
subsequent section, we briefly describe the method used to derive the ChMs of
the studied GCs, whereas in section 4.2 we presents the analysis of the ChMs
and results on the fraction of 1P and 2P stars in the target clusters.

###  4.1 Constructing the chromosome maps

A ChM displays along the abscissa and ordinate the indices $\Delta_{\rm
F275W,F814W}$ and $\Delta{C_{\rm F275W,F336W,F438W}}$, respectively. Specific
details on the procedure to derive the ChM have been widely discussed in
various papers of our team (e.g. Milone et al., 2017; Lagioia et al., 2021),
to which we refer the interested reader.

In a nutshell, to derive the ChM abscissa we take advantage of the $m_{\rm
F814W}$ versus $m_{\rm F275W}-m_{\rm F814W}$ CMD, and of the $m_{\rm F814W}$
versus $C_{\rm F275W,F336W,F438W}$ pseudo-CMD to derive the ChM ordinate. In
both these diagrams, we measure the (pseudo-) color displacement of every RGB
star relative to the red boundary of the RGB sequence, and divide it by the
broadening of the RGB sequence. The RGB broadening is defined as the (pseudo-)
color difference between the red and the blue RGB boundaries at the same F814W
star’s magnitude. This result of this process, called verticalization, is a
color ratio that is finally multiplied by a factor called intrinsic RGB width.

To derive the intrinsic RGB width, we first measure the broadening of the RGB,
or observed RGB width, at a reference F814W magnitude set by convention at
$m^{\rm MSTO}-2$ 333The F814W luminosity of the MSTO has been determined by
using the naive estimator method (Silverman, 1986). First, we selected a
magnitude interval in the $m_{F814W}$ versus $m_{F438W}-m_{F814W}$ CMD which
includes MS and sub-giant branch (SGB) stars, and divided it into a given
number of magnitude bins. Then, we computed the median color and magnitude of
the stars in each bin. The whole procedure has been repeated $n$-times, with
$n$ assuming a different value for each cluster ($n$ = 5, 6, 8), keeping the
bin-width unchanged but shifting the starting point of the first bin by an
amount equivalent to 1/$n^{th}$ of the bin-width. For each bin, the resulting
median points have been linearly interpolated across the entire initial
magnitude interval thus obtaining a raw fiducial line, which has been finally
smoothed by boxcar averaging three adjacent points. Finally, the magnitude of
the bluest point of the smoothed fiducial line has been taken as the cluster
MS turn-off luminosity in F814W band. A similar approach has been adopted for
the determination of the RGB boundaries. The blue and red RGB envelopes
correspond, respectively, to the fiducial lines interpolating the $4^{\rm th}$
and $96^{\rm th}$ percentile of the RGB (pseudo-) color distribution in each
bin, across the whole magnitude range covered by the cluster RGB members.
Their relative distance of the distance at two F814W magnitudes above the MSTO
correspond to the observed RGB width..

Then, since the observed RGB width encompasses both the intrinsic RGB width
and the observational error, it is necessary to estimate the contribution of
the latter to the observed RGB width. To do that, we simulated the $m_{\rm
F814W}$ versus $m_{\rm F275W}-m_{\rm F814W}$ and $m_{\rm F814W}$ versus
$C_{\rm F275W,F336W,F438W}$ diagrams for a SP composed of 10,000 stars. The
errors associated to each magnitude of the simulated stars are extracted from
a Gaussian distribution with a dispersion corresponding to the median
magnitude error of the RGB stars. Finally, the intrinsic RGB width in the
color $m_{\rm F275W}-m_{\rm F814W}$ and in the pseudo-color $C_{\rm
F275W,F336W,F438W}$, indicated respectively as $W_{\rm F275W,F814W}$ and
$W_{C\,{\rm F275W,F336W,F438W}}$, have been obtained by subtracting in
quadrature the RGB widths of the simulated CMD from observed RGB width ones.

To evaluate the statistical error affecting our determination of $W_{\rm
F275W,F814W}$ and $W_{C{\rm F275W,F336W,F438W}}$, we applied a bootstrapping
test with replacement 1,000 times to the observed RGB colors and magnitudes.
For each system configuration, we measured the intrinsic RGB width. We
calculated the median value of the 1,000 RGB-width determinations, and the
residuals from the median. We assumed that the $68^{\rm th}$ percentile of the
distribution of the absolute values of the residuals corresponds to the
uncertainty associated to the intrinsic RGB widths $W_{\rm F275W,F814W}$ and
$W_{C{\rm F275W,F336W,F438W}}$. The values of the intrinsic width and the
statistical error for the four targets GCs are reported in Table 3.

The estimate of the RGB width of our target GCs allow us to contextualize
these four clusters within the broader trend of absolute chemical variations
observed in previously studied Galactic GCs (Milone et al., 2017; Lagioia et
al., 2019a). To this purpose, Figure 3 shows the intrinsic $W_{C\,{\rm
F275W,F336W,F438W}}$ as a function of the average iron abundance for the 58
Galactic GCs studied by Milone et al. (2018a, gray dots) and the four outer-
halo GCs studied in this paper (colored symbols). We find that Terzan 8 and
Arp 2 follow the $W_{C\,{\rm F275W,F336W,F438W}}$ \- [Fe/H] correlation of the
bulk of studied GCs. On the other hand, Ruprecht 106 and Terzan 7 are
remarkable exceptions, having RGB width smaller than those of GCs at similar
metallicities. This observation supports the indication from the color
extension in the $m_{\rm F814W}$ versus ${\rm C_{F275W,F336W,F438W}}$ pseudo-
CMD in Fig. 2 that the two latter clusters may not host MPs. In this regard a
definitive conclusion is provided in the next section, where the detailed
stellar composition of the target clusters is explored through the ChM.

Figure 3: RGB width in the pseudo-color $C_{\rm F275W,F336W,F438W}$ as
function of iron abundance. The gray points represent the 58 MW clusters
analyzed in Milone et al. (2018b). The four target clusters studied in this
paper are represented as colored points, as reported in the inset.

###  4.2 Multiple stellar populations in the chromosome map

As mentioned in the beginning of section 4 , the ChM allow us to tag the
different stellar populations in a GC. As an example, in Figure 4 we
illustrate the procedure to select the 1P and 2P stars of the outer-halo GC
Arp 2. In the left panel of the figure, we plot the $\Delta{C_{\rm
F275W,F336W,F438W}}$ versus $\Delta_{\rm F275W,F814W}$ ChM of the RGB members
of the cluster (gray points).

The orange points on the bottom-left corner display the photometric errors of
the ChM. Their elliptical distribution spans few tenths of magnitudes in both
the horizontal and vertical direction, thus indicating that the spread across
the ChM is intrinsic. The choice to artificially plot the error distribution
on the bottom left side, so that its median along the y-axis corresponds to
$\Delta C_{\rm F275W,F336W,F438W}=0$, is instrumental to the illustration of
the procedure for selecting 1P stars and derive their relative fraction.

The study of the ChM of 58 GCs by Milone et al. (2017) has shown that 1P stars
cluster around the origin of the ChM, whereas the 2P defines a sequence that
extends towards larger absolute values of $\Delta{C_{\rm F275W,F336W,F438W}}$
and $\Delta_{\rm F275W,F814W}$ (Milone et al., 2017). For the sake of
representation, we overplot a dot-dashed line on the ChM with a inclination of
$18^{\circ}$ to negative direction of the x-axis. This line represents the
typical inclination of the bulk of 1P stars in the ChM (Milone et al., 2017,
see their Fig. 2) and it has been used to fix the rotation angle of the ChM in
the middle panel. Here, both the ChM and the error distribution have been
rotated counter-clockwise by $18^{\circ}$, so that the dot-dashed line is now
parallel to x-axis. The rotated system, with abscissa and ordinate
$\Delta^{\prime}_{\rm F275W,F814W}$ and $\Delta^{\prime}{C_{\rm
F275W,F336W,F438W}}$, respectively, allows us to identify the candidate 1P and
2P cluster stars and estimate the fraction of 1P stars with respect to the
total number of RGB stars.

To do this, we plot in the right panel the histogram distributions of the
$\Delta^{\prime}C_{\rm F275W,F336W,F438W}$ values (gray-filled histogram) and
of the errors (orange histogram). We see that the ChM histogram shows a
bimodal distribution, with the bottom one associated to the 1P stars, and the
top one to 2P stars. This evidence demonstrates that Arp 2 is not chemically
homogeneous.

Therefore, we calculated the $95^{\rm th}$ percentile of the error
distribution along the y-axis (dotted line in the middle panel). This line
delimits the portion of the ChM histogram that we have used to least-square
fit a first-guess Gaussian to the 1P histogram distribution. Then we performed
a new Gaussian fit but limited to the portion of the histogram with
$\Delta^{\prime}{C_{\rm F275W,F336W,F438W}}$ smaller than twice the dispersion
of the first-guess Gaussian. Finally, we used the red-dashed line,
corresponding to the peak of the best-fit Gaussian function (red curve in the
right panel) shifted by twice the Gaussian dispersion, to identify the groups
of bona-fine 1P and 2P stars. Finally, the ratio between the area of the best-
fit Gaussian and the total area of the ChM histogram has been taken as the
fraction of 1P cluster stars. In the case of Arp 2 we find ${\rm
N_{1P}/N_{TOT}}=0.533\pm 0.052$.

Figure 4: Procedure for the selection of the candidate 1P and 2P stars of Arp
2. _Left panel_ : $\Delta{C_{\rm F275W,F336W,F438W}}$ versus $\Delta_{\rm
F275W,F814W}$ ChM of the cluster RGB stars (gray points). The orange dots
represent the photometric error distribution of the ChM. The dot-dashed line
marks the inclination of 1P stars with respect to the x-axis and has an
inclination of $18^{\circ}$. _Middle panel_ : ChM and error distribution
rotated counter-clockwise by an angle of $18^{\circ}$. In the rotated
reference system $\Delta^{\prime}{C_{\rm F275W,F336W,F438W}}$ versus
$\Delta^{\prime}{\rm F275W,F814W}$, the dot-dashed line is parallel to the
x-axis. The dotted line marks the $95^{\rm th}$ percentile of the photometric
error distribution along the y-axis. _Right panel_ : vertical histogram
distribution of the ChM (gray-filled area) and photometric errors (orange
histogram). The red curve represents the best-fit Gaussian to the region of
the histogram delimited by the dotted line (see text for explanation). The red
dashed line is the vertical coordinate corresponding to twice the dispersion
of the best-fit Gaussian above its peak, and marks the separation between
bona-fide 1P and 2P cluster stars.

We applied the same procedure to build the ChM, select the candidate 1P and 2P
stars and determine the corresponding ${\rm N_{1P}/N_{TOT}}$, in the other
three target clusters.

The ChMs of the four target GCs are shown in Figure 5, where we display on the
bottom-right corner the corresponding photometric error distributions (orange
dots). We note that in the case of Terzan 8, Arp 2, and Ruprecht 106, the
horizontal and vertical extension of their ChM is much larger than that of the
photometric error distribution. However, in Terzan 7, both the horizontal and
vertical spread of the ChM is comparable to those of the photometric error.
These impressions are also confirmed by the density diagrams displayed in the
inset of each panel, where the gray-shaded areas represent the density of the
observed ChM points, and the orange-shaded area refers to the error
distribution.

Similarly to Fig. 4, the red dashed line in the ChM of Terzan 8 and Arp 2
separates bona-fide 1P and 2P stars. As far as Ruprecht 106 and Terzan 7 are
concerned, our procedure results in a homogeneous composition of 1P stars
only.Both Terzan 8 and Arp 2 show a relatively high fraction of 1P stars
compared to most of the studied Galactic GCs. In particular, in Terzan 8 $\sim
71\%$ of the cluster RGB stars belong to the 1P, thus making it one of the
Galactic GCs with the largest fractions of 1P stars. In the case of Arp 2, 1P
stars make up a fraction slightly larger than 50% of the RGB cluster stars.

Given the moderate population of 53 RGB stars in Terzan 7, we conducted Monte
Carlo tests to estimate the probability of detecting zero 2P stars if their
fraction ranges from 1% to 10%. We found that if 2P stars make up 2% of the
total number of stars, the probability of detecting zero 2P stars in a sample
of 53 stars is approximately 68%. Similarly, for Ruprecht 106, which has 109
RGB stars, the fraction of 2P stars that results in a 68% probability of zero
detections is about 1%. Therefore, we considered 0.02 and 0.01 as our estimate
of the uncertainty associated with the fraction of 2P stars in Terzan 7 and
Ruprecht 106.

The fractions of 1P stars, the total number of RGB stars in the ChM of each
target cluster, as well as their maximum radial distance as a function of the
corresponding cluster half-light radius, have been reported in Table 3.

Figure 5: Chromosome maps of the RGB stars in the four target clusters,
arranged as in Fig. 1. In each panel, the orange points display the
corresponding photometric error distribution, while the inset show the density
diagram of the ChM and error distribution. The dashed line in the ChM of
Terzan 8 and Arp 2 delimit the region of the ChM where 1P and 2P candidate
stars lie.

Figure 6 shows the fraction of 1P stars as a function of the logarithm of the
present-day and initial GC mass (left and middle panel, respectively) and the
GC escape velocity (right panel). In addition to the GCs studied in this
paper, the GC sample comprises the Galactic (gray circles) and Magellanic
Cloud star clusters (gray triangles) homogeneously analyzed by using the ChMs
(Milone et al., 2017, 2020; Dondoglio et al., 2021).

Terzan 8 and Arp 2 follow the same trend as the other Galactic GCs, thus
corroborating the evidence of the anti-correlation between the fraction of 1P
stars cluster and both cluster mass and escape velocity. The multiple-
population GC with the smallest initial mass, Arp 2 has ${\rm M_{in}}\lesssim
10^{5}$ $\mathrm{M}_{\odot}$, which is slightly lower than the empirical mass
threshold of $\sim 1.5\times 10^{5}$ $\mathrm{M}_{\odot}$suggested by Milone
et al. (2020) as the limit for the occurrence of MPs. In the same work, Milone
and collaborators have shown that the Large and Small Magellanic Cloud also
host simple-population GCs with initial masses larger than the proposed
threshold.

Figure 6:  Fraction of 1P stars as a function of the logarithm of the GC
present-day mass, initial mass, and escape velocity. The gray symbols refer to
literature determinations of the 1P fractions in Milky Way and Magellanic
Cloud clusters (Milone et al., 2017; Dondoglio et al., 2021), whereas the GCs
studied in this paper are indicated with colored dots, as indicated in the
legend.

Our results represent therefore, the first photometric evidence based on the
distribution of RGB stars in the ChM of the existence of SP clusters, namely
Ruprecht 106 and Terzan 7. At the same time we provide the first photometric
evidence that MPs are present in the GCs Terzan 8 and Arp 2.

##  5 Metallicity variations among first-population stars

A visual inspection of the ChMs of Figure 5 reveals that the 1P stars of all
clusters span a wider $\Delta_{\rm F275W,F814W}$ range than that expected from
the observational uncertainties alone.

In particular, we note that, although Ruprecht 106 does not show any vertical
spread, so no presence of 2P stars, the horizontal extension of its ChM covers
a $\Delta_{\rm F275W,F814W}$ interval of $\sim 0.25$ mag, significantly larger
than that of the photometric errors. Such a phenomenon is even more pronounced
in the case of Terzan 8, where the extension of the 1P candidate stars is
$\sim 0.3$ mag, while in the case of Arp 2 1P and 2P stars seem to span a
comparable interval along the x-axis.

Recent works have shown that the horizontal width of 1P stars in the ChMs is a
widespread phenomenon among Galactic GCs and demonstrated that 1P stars are
not chemically homogeneous (Milone et al., 2015; D’Antona et al., 2016; Milone
et al., 2018b). Papers based on both spectroscopy and photometry have shown
that the $\Delta_{\rm F275W,F814W}$ range of 1P stars is mostly due to
metallicity variations (e.g. Marino et al., 2019a; Legnardi et al., 2022;
Marino et al., 2023).

To quantify the metallicity variations among the 1P stars of the studied
clusters, we followed the method by Legnardi et al. (2022) and Legnardi et al.
(2024). Briefly, we first determined the $\Delta_{\rm F275W,F814W}$ extension
of the 1G sequence as the difference between the 90th and the 10th percentile
of the $\Delta_{\rm F275W,F814W}$ distribution. The intrinsic width, $W^{\rm
1G}_{\rm F275W,F814W}$, was estimated by subtracting the color errors in
quadrature. Assuming that the observed color spread on the ChM solely derives
from metallicity variations, we used the relation between the $m_{\rm
F275W}-m_{\rm F814W}$ color and metallicity by Dotter et al. (2008) to convert
the $W^{\rm 1G}_{\rm F275W,F814W}$ values into [Fe/H] variations. Among the
investigated targets, Terzan 8 exhibits the highest [Fe/H] spread
($\delta$[Fe/H]${}_{\rm 1G}^{\rm MAX}=0.373\pm 0.060$), while Terzan 7
displays the lowest value ($\delta$[Fe/H]${}_{\rm 1G}^{\rm MAX}=0.036\pm
0.010$). Arp 2 and Ruprecht 106 show moderate [Fe/H] variations, with
$\delta$[Fe/H]${}_{\rm 1G}^{\rm MAX}=0.087\pm 0.014$ and $0.120\pm 0.011$,
respectively).

In the left panel of Figure 7 we present the maximum iron variation among 1G
stars plotted against the logarithm of the cluster mass (Baumgardt & Hilker,
2018, 2023 update) and iron abundance (Harris, 1996, 2010 update). The gray
dots represent the 55 Galactic GCs investigated by Legnardi et al. (2022),
whereas the colored symbols indicate the four targets examined in this study.
The SP clusters studied by Legnardi et al. (2024), namely NGC 6791 and NGC
1783, are represented with a square and a triangle, respectively.

Our results corroborate the evidence of a mild correlation between
$\delta$[Fe/H]${}^{\rm 1G}_{\rm MAX}$ and the metallicity, and between
$\delta$[Fe/H]${}^{\rm 1G}_{\rm MAX}$ and mass. Indeed, the
$\delta$[Fe/H]${}_{\rm 1G}^{\rm MAX}$ values obtained for Arp 2, Ruprecht 106,
and Terzan 7 follow the general trend in both the diagrams. Conversely, 1G
stars in Terzan 8 exhibit higher metallicity variations compared to Galactic
GCs with similar mass/metallicity.

Moreover, the evidence of extended 1P sequences in the ChMs of Ruprecht 106
and Terzan 7 shows that the metallicity variations are not peculiar to GCs
with MPs but also characterize SP clusters.

Figure 7:  Maximum iron-abundance variation among 1P stars as a function of the logarithm of present-day GC mass (left) and iron abundance (right). The clusters studied in this paper are plotted with colored points as reported in the legend. The gray points indicate the GCs studied by Legnardi et al. (2022), whereas the simple-population star clusters NGC 6791 and NGC 1783 are represented with a square and a triangle, respectively (Legnardi et al., 2024).  Table 3: Values of the RGB widths, fraction of 1P candidate stars, total number of stars analyzed in the chromosome map, and maximum radial distance from the cluster center ($r_{\rm max}$) as a fraction of the cluster half-light radius ($r_{\rm hl}$).  Cluster | $W_{\rm F275W,F814W}$ | $W_{\rm C_{F275W,F336W,F438W}}$ | $N_{\rm 1P}/N_{\rm TOT}$ | $N_{\rm TOT}$ | $r_{\rm max}/r_{\rm hl}$
---|---|---|---|---|---
| (mag) | (mag) |  |  |
Arp 2 | $0.111\pm 0.096$ | $0.196\pm 0.024$ | $0.533\pm 0.052$ | 96 | 0.98
Ruprecht 106 | $0.125\pm 0.006$ | $0.100\pm 0.020$ | $1.000\pm 0.010$ | 109 | 1.25
Terzan 7 | $0.152\pm 0.051$ | $0.081\pm 0.015$ | $1.000\pm 0.020$ | 53 | 1.66
Terzan 8 | $0.203\pm 0.021$ | $0.188\pm 0.024$ | $0.705\pm 0.044$ | 114 | 0.84

##  6 Summary and conclusions

We used multi-epoch ACS/WFC and UVIS/WFC3 images in F275W, F336W, F438W,
F606W, and F814W from the GO 17075 (PI Lagioia) and from the HST archive to
investigate MPs in the four outer-halo GCs, Arp 2, Ruprecht 106, Terzan 7, and
Terzan 8. We derived high-precision stellar magnitudes, positions, and PMs by
using the methods and the computer programs developed by Jay Anderson (e.g.
Anderson & King, 2000; Anderson et al., 2006). The resulting five-band
photometry is comparable to that of 58 less distant GCs studied in the recent
surveys of MPs (Piotto et al., 2015; Milone et al., 2017), thus providing a
total sample of 62 Galactic GCs homogeneously analyzed. The main results are
summarized in the following.

  1. 1.

We derived the $\Delta_{C\rm F275W,F336W,F438W}$ versus $\Delta_{\rm
F275W,F814W}$ ChM to search for MPs with different light-element abundances.
We find that Arp 2 and Terzan 8 host MPs, whereas Ruprecht 106 and Terzan 7
are SP clusters. This is the first evidence of simple stellar population GCs
based on the ChM, and corroborates previous conclusions based on spectroscopy
of nine stars of Ruprecht 106 (Villanova et al., 2013), photometry in the U,
B, and I bands of RGB stars in both Ruprecht 106 and Terzan 7 (Dotter et al.,
2018; Lagioia et al., 2019a), and the HB morphology of Ruprecht 106 (Milone et
al., 2014).

  2. 2.

It is widely accepted that the $C_{\rm F275W,F336W,F438W}$ pseudo-color width
of the RGB correlates with the average cluster metallicity. In GCs with MPs,
the RGB width mostly depends on the maximum internal variation in the
abundances of certain light elements. This color index is primarily sensitive
to the nitrogen content of the stellar populations and, to a lesser extent, to
variations in helium, carbon, and oxygen (e.g. Milone et al., 2015; Lagioia et
al., 2019a; Jang et al., 2021). In addition to light-element spread, star-to-
star metallicity variations can also contribute to the RGB width (e.g. Marino
et al., 2019b). We find that the observed RGB widths of Arp 2 and Terzan 8
follow the same trend as the bulk of Galactic GCs in the $W_{C\rm
F275W,F336W,F438W}$ versus [Fe/H] diagram. On the contrary, the RGB width of
Ruprecht 106 and Terzan 7 are much smaller than those of GCs with similar
[Fe/H] as expected for clusters with homogeneous abundance of light-elements.

  3. 3.

Previous works have suggested that a mass threshold could govern the
occurrence of MPs in GCs. Based on analysis of the ChMs in 58 Galactic GCs,
Milone et al. (2020) noticed that the MP GCs have masses larger than $\sim
1.5\times 10^{5}$ $\mathrm{M}_{\odot}$. Arp 2 is the Galactic GC with the
smallest initial mass ($\sim 0.9\times 10^{4}$ $\mathrm{M}_{\odot}$) for which
MPs have been detected through the ChMs. The discovery of MPs in this cluster
suggests that the proposed mass threshold, if present, should be smaller than
$\sim 10^{5}$ $\mathrm{M}_{\odot}$. In this context, it is worth noticing that
various SP Magellanic Cloud GCs have initial masses of 1 – 3 $\times 10^{5}$
$\mathrm{M}_{\odot}$, which are larger than those of Arp 2 and Terzan 8. This
fact could indicate that, in addition to cluster mass, the GC formation
environment, affects the occurrence of MPs with metal-poor GCs having a lower
initial-mass threshold for the formation of 2P stars (Krause et al., 2016;
Huang et al., 2024). In this regard, a possible interpretation for the non
occurrence of MPs in some ex-situ GCs is that the formation environment was
not suitable for the formation of different stellar populations. In this
sense, as recently pointed out by Huang et al. (2024), GCs formed in dwarf
galaxies during later starbursts, therefore relatively younger, can be more
metal-rich and less compact, two conditions that disfavor the intra-cluster
retention of gas expelled by rapidly evolved 1P stars, and so the birth of 2P
stars. As a consequence, the GC formation environment would be a discriminant
factors for the onset of MPs (Krause et al., 2016).

An alternative explanation for the lack of MPs is that this phenomenon would
only occur in stars less massive than $\sim 1.6$ $\mathrm{M}_{\odot}$only
(Bastian & Lardo, 2018). In such a case case, the reason why Milone et al.
(2020) we did not detect 2P stars in some Magellanic Cloud star clusters is
that the studies of MPs in these Magellanic Cloud clusters younger than $\sim
2$ Gyr are exclusively based on RGB stars.

  4. 4.

We used the ChM to derive the fractions of 1P stars in Arp 2 and Terzan 8,
which correspond to 53.3$\pm$5.2% and 71.0$\pm$4.4%, respectively. Noticeably,
the Galactic GCs with MPs and large perigalactic radii (${\rm R_{peri}}>3.5$
kpc) studied in the literature tend to have higher fractions of 1P stars
compared to the other Milky Way GCs. This behavior is particularly pronounced
in the clusters studied in the MC, where the fraction of 1P stars is even
higher than in Galactic GCs with large ${\rm R_{peri}}$ (Zennaro et al., 2019;
Milone et al., 2020), thus suggesting that the fraction of 1P stars may depend
on the environment. Intriguingly, while Terzan 8 clearly follows the overall
trend of MW GCs, Arp 2 is a possible outlier and shares similar fractions of
1P stars as some Galactic GCs with similar masses and small ${\rm R_{peri}}$.

  5. 5.

The 1P stars of the multiple-population GCs Arp 2 and Terzan 8 exhibit
intrinsic $m_{\rm F275W}-m_{\rm F814W}$ color spreads, which are indicative of
star-to-star [Fe/H] variations of $\sim 0.1$ and 0.3 dex, respectively. A
recent study of 55 Galactic GCs with MPs by Legnardi et al. (2022) has shown
that the 1P stars of virtually all clusters exhibit inhomogeneous
metallicities, with [Fe/H] abundance variation ranging from less than 0.05 dex
to $\sim 0.3$ dex. Hence, the results on Arp 2 and Terzan 8 corroborate the
evidence that metallicity variations among 1P stars are common features of
GCs.

  6. 6.

We discovered that the stars of the SP GCs Ruprecht 106 and Terzan 7 exhibit
metallicity variations, in close analogy with what is observed in 1P stars of
MP GCs.This fact, together with the findings of star-to-star [Fe/H] variations
in the open cluster NGC 6791 and in the $\sim 1.5$ Gyr old star cluster NGC
1783 (Legnardi et al., 2024), demonstrates that the metallicity variations are
not a peculiarity of multiple-population GCs but are also present in SP GCs,
open clusters, and intermediate-age massive Magellanic-cloud clusters. We
confirm that the maximum iron variation among the 1P stars mildly correlate
with cluster mass and metallicity.

E. P. Lagioia acknowledges support from the ”Science & Technology Champion
Project” (202005AB160002) and from the ”Top Team Project” (202305AT350002),
all funded by the ”Yunnan Revitalization Talent Support Program”. T. Ziliotto
acknowledges funding from the European Union’s Horizon 2020 research and
innovation program under the Marie Skłodowska-Curie Grant Agreement No.
101034319 and from the European Union – Next Generation EU. This work has
received funding from ”PRIN 2022 2022MMEB9W - Understanding the formation of
globular clusters with their multiple stellar generations” (PI Anna F.
Marino), and from INAF Research GTO-Grant Normal RSN2-1.05.12.05.10 - (ref.
Anna F. Marino) of the ”Bando INAF per il Finanziamento della Ricerca
Fondamentale 2022”.

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