# CAPOS: The bulge Cluster APOgee Survey IV
Elemental Abundances of the bulge globular cluster NGC 6558

Danilo González-Díaz,1,2 José G. Fernández-Trincado,1 Sandro Villanova,3 Doug
Geisler,3,4,5 Beatriz Barbuy,6 Dante Minniti,7,8,9 Timothy C. Beers,10
Christian Moni Bidin,1 Francesco Mauro,1 Cesar Muñoz,4,5 Baitian Tang,11 Mario
Soto,12 Antonela Monachesi,4,5 Richard R. Lane,13 and Heinz Frelijj1
1Instituto de Astronomía, Universidad Católica del Norte, Av. Angamos 0610,
Antofagasta, Chile
2Instituto de Física, Universidad de Antioquia, Calle 70 52-21, Medellín,
Colombia
3Departamento de Astronomía, Casilla 160-C, Universidad de Concepción,
Concepción, Chile
4Instituto Multidisciplinario de Investigación y Postgrado, Universidad de La
Serena, Raúl Bitrán 1305, La Serena, Chile
5Departamento de Astronomía, Facultad de Ciencias, Universidad de La Serena.
Av. Juan Cisternas 1200, La Serena, Chile
6Universidade de São Paulo, IAG, Rua do Matão 1226, Cidade Universitária, São
Paulo 05508-900, Brazil
7 Institute of Astrophysics, Facultad de Ciencias Exactas, Universidad Andrés
Bello, Av. Fernández Concha 700, Las Condes, Santiago, Chile
8Vatican Observatory, V00120 Vatican City State, Italy
9Departamento de Fisica, Universidade Federal de Santa Catarina, Trinidade
88040-900, Florianopolis, Brazil
10Department of Physics and Astronomy and JINA Center for the Evolution of the
Elements, University of Notre Dame, Notre Dame, IN 46556 USA
11School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082,
China
12Instituto de Astronomía y Ciencias Planetarias, Universidad de Atacama,
Copayapu 485, Copiapó, Chile
13Centro de Investigación en Astronomía, Universidad Bernardo O’Higgins,
Avenida Viel 1497, Santiago, Chile
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

This study presents the results concerning six red giant stars members of the
globular cluster NGC 6558. Our analysis utilized high-resolution near-infrared
spectra obtained through the CAPOS initiative (the APOgee Survey of Clusters
in the Galactic Bulge), which focuses on surveying clusters within the
Galactic Bulge, as a component of the Apache Point Observatory Galactic
Evolution Experiment II survey (APOGEE-2). We employ the BACCHUS (Brussels
Automatic Code for Characterizing High accUracy Spectra) code to provide line-
by-line elemental-abundances for Fe-peak (Fe, Ni), $\alpha$-(O, Mg, Si, Ca,
Ti), light-(C, N), odd-Z (Al), and the $s$-process element (Ce) for the 4
stars with high signal-to-noise ratios. This is the first reliable measure of
the CNO abundances for NGC 6558. Our analysis yields a mean metallicity for
NGC 6558 of $\langle$[Fe/H]$\rangle$ = $-1.15\pm 0.08$, with no evidence for a
metallicity spread. We find a Solar Ni abundance, $\langle$[Ni/Fe]$\rangle$
$\sim$ $+$0.01, and a moderate enhancement of $\alpha$-elements, ranging
between $+$0.16 to $<+$0.42, and a slight enhancement of the $s$-process
element $\langle$[Ce/Fe]$\rangle$ $\sim$ $+$0.19. We also found low levels of
$\langle$[Al/Fe]$\rangle\sim+0.09$, but with a strong enrichment of nitrogen,
[N/Fe]$>+0.99$, along with a low level of carbon, [C/Fe]$<-0.12$. This
behaviour of Nitrogen-Carbon is a typical chemical signature for the presence
of multiple stellar populations in virtually all GCs; this is the first time
that it is reported in NGC 6558. We also observed a remarkable consistency in
the behaviour of all the chemical species compared to the other CAPOS bulge
GCs of the same metallicity.

###### keywords:

Stars: abundances – Stars: chemically peculiar – Galaxy: globular clusters:
individual: NGC 6558 – Techniques: spectroscopic

††pubyear: 2023††pagerange: CAPOS: The bulge Cluster APOgee Survey IV
Elemental Abundances of the bulge globular cluster NGC 6558–CAPOS: The bulge
Cluster APOgee Survey IV  Elemental Abundances of the bulge globular cluster
NGC 6558

##  1 Introduction

The Milky Way bulge is a centrally concentrated component that has an
associated system of globular clusters (Minniti, 1995). Globular clusters
(GCs) in the central region ($\lesssim$ 3.5 kpc; Barbuy et al., 2018a, b) of
the Galactic Bulge (GB) could contain the oldest stars in the Galaxy. Indeed,
the rapid chemical evolution in the deep potential well of the GB means that
GCs could be potentially older than their halo cousins, which were born and
raised in much less massive satellites (Cescutti, 2008; Barbuy et al., 2018b;
Savino et al., 2020; Geisler et al., 2021). Thus, the bulge GCs are an
excellent fossil to better understand the assembly of the most ancient part of
our Galaxy. They are believed to have developed in situ (Massari et al.,
2019), as opposed to the halo GCs, all or mostly of which originated in
satellite galaxies that later merged with the proto-Milky Way.

NGC 6558 is an important member of these ancient bulge GCs (BGCs). This
cluster presents a post-core collapse structure (Trager et al., 1995), and
lies in a relatively clear region inside the bulge (l = $+$0.20096∘, b =
$-$6.02488∘), with a mean heliocentric distance of
$\sim$7.47${}^{+0.29}_{-0.28}$ kpc (Baumgardt & Vasiliev, 2021a; Moreno et
al., 2022) and a mean Galactocentric distance of $\sim$1.3 kpc. In an early
work, Rich et al. (1998) used $VI$ photometry to identify a strong blue
extended horizontal branch in NGC 6558 with a metallicity estimated to lie in
the range of $-$1.6 <$\langle$[Fe/H]$\rangle$<$-$1.2. Most recently, Cohen et
al. (2021) resolved the cluster main-sequence turnoff using the filters F606W
and F814W from the Hubble Space Telescope (HST), and determined an age of
$\sim$12.3 $\pm$ 1.1 Gyr. For their part, Barbuy et al. (2007, 2018b)
presented for the first time a detailed spectroscopic analysis of five giant
stars in NGC 6558 using high-resolution GIRAFFE optical spectra ($R\sim$
22.000), and four giant stars using very high-resolution FLAMES-UVES spectra
($R\sim$ 45.000). These authors obtained precise abundances of the light
elements C, N, O, the odd-Z elements Na, Al, the $\alpha$-elements Mg, Si, Ca,
Ti, and the heavy elements Y, Ba, La, and Eu. They derived a mean metallicity
of $\langle$[Fe/H]$\rangle$ = $-$1.17 $\pm$ 0.10 for the cluster via UVES
spectra, with strong enhancements of $+$0.40 and $+$0.33 in the
$\alpha$-elements O and Mg, but lower enhancements of $+$0.11 and $+$0.07 in
Si and Ca, respectively. The Odd-Z element Na showed a Solar value, while Al
was slightly enhanced, with $\langle$[Al/Fe]$\rangle$=$+$0.15, suggesting that
these elemental abundances are in good agreement with the typical abundance
behaviour found in other old BGCs such as NGC 6522 (Barbuy et al., 2009, 2014;
Fernández-Trincado et al., 2019b) and HP 1 (Geisler et al., 2021). On the
other hand, the authors also noted a spread in the abundances of Y and Ba,
compatible with expectations from massive spinstars (Chiappini et al., 2011;
Frischknecht et al., 2016), while the $r$-element Eu is highly enhanced, with
$\langle$[Eu/Fe]$\rangle$=$+$0.6, compatible with production by supernovae
type II (SNII) or neutron star mergers (Goriely et al., 2011; Wanajo et al.,
2021). Such high values of Eu are usually found in field halo stars, while
higher enhancements are typically found in some ultra-faint dwarf galaxies
(see, e.g., Ji et al., 2016; Roederer et al., 2016; Hansen et al., 2017;
Simon, 2019; Reichert et al., 2020).

Kinematically, Barbuy et al. (2007, 2018b), obtained precise mean radial
velocities (RVs) for the cluster of $-$197.3$\pm$4.0 km s-1 and
$-$194.45$\pm$2.1 km s-1, respectively. With the close proximity of NGC 6558
to the GB, along with its proper motion, Rossi et al. (2015) and Pérez-
Villegas et al. (2020) found that NGC 6558 is probably an in situ formed GC,
co-rotating with the bar, similar to other GCs they classified. Recent works
like Massari et al. (2019) and Malhan et al. (2022) found similar results
using the proper motions and parallaxes from the Gaia releases available at
that time.

Nowadays, with the high-precision astrometric and photometric data from the
latest release of the ESA Gaia mission (Gaia DR3; Gaia Collaboration et al.,
2022), along with the photometric depth in both the Two-Micron All Sky Survey
(Skrutskie et al., 2006) and the infrared survey VISTA Variables in the Vía
Láctea (VVV, Minniti et al., 2010; Saito et al., 2012), as well as the
accurate chemical elements provided by the seventeenth data release of the
APOGEE-2 survey (Majewski et al., 2017; Abdurro’uf et al., 2022a), there is an
unprecedented opportunity to examine in great detail these ancient GCs toward
the GB, despite their location within very crowded and highly reddened
regions. This is indeed the goal of the CAPOS project (Geisler et al., 2021).

In this paper, we present $H$-band spectroscopy for six members of NGC 6558,
using spectra from the bulge Cluster APOgee Survey (CAPOS, Geisler et al.,
2021), an internal program of the Apache Point Observatory Galactic Evolution
Experimental II survey (APOGEE-2, Majewski et al. 2017) and the Sloan Digital
Sky IV survey (Blanton et al., 2017; Ahumada et al., 2020). These spectra make
it possible to derive detailed elemental abundances for a large number of
giant stars, as well as to achieve RVs with precision better than 1 km s-1.

This paper is organized as follows: Section 2 and 3 present an overview of the
CAPOS data analysed toward the NGC 6558 field, while Section 4 describes the
adopted atmospheric parameters employed to determine the elemental abundances.
The resulting elemental abundances obtained with the BACCHUS code are
described in Section 5. We discuss our results and compare them with previous
literature in Section 6. Our conclusions are presented in Section 7.

Table 1: APOGEE Identifications, Gaia DR3 PMs, Gaia DR3 and VVV magnitudes, radial velocities, spectral signal-to-noise ratio (S/N), and APOGEE-2S programs names of targets toward NGC 6558. APOGEE ID | $\mu_{\alpha}\cos(\delta)$ | $\mu_{\delta}$ | G | BP | RP | J | H | Ks | RV | S/N | APOGEE-2
---|---|---|---|---|---|---|---|---|---|---|---
| (mas yr-1) | (mas yr-1) |  |  |  |  |  |  | (km s-1) | (pixel-1) | programs
High S/N |  |  |  |  |  |  |  |  |  |  |
2M18101354$-$3146216 | $-1.98$ | $-4.04$ | 14.15 | 14.98 | 13.22 | 11.87 | 11.11 | 10.94 |  $-$191.7 | 160 | geisler_19b
AP18102342$-$3146515 | $-1.69$ | $-4.11$ | 14.41 | 15.22 | 13.48 | 12.16 | 11.41 | 11.26 |  $-$193.26 | 130 | geisler_19b
2M18101117$-$3144580 | $-1.70$ | $-4.24$ | 13.90 | 14.53 | 12.80 | 11.60 | 10.81 | 10.61 |  $-$194.13 | 103 | geisler_19b
2M18101768$-$3145246 | $-1.94$ | $-3.94$ | 15.10 | 15.75 | 14.13 | 12.97 | 12.31 | 12.18 |  $-$190.64 | 80 | geisler_19b
Low S/N |  |  |  |  |  |  |  |  |  |  |
2M18102223$-$3145435 | $-1.69$ | $-4.17$ | 15.38 | 16.11 | 14.52 | 13.28 | 12.59 | 12.47 |  $-$193.44 | 46 | geisler_19b
2M18101623$-$3145423 | $-1.77$ | $-4.10$ | 15.98 | 16.30 | 15.18 | 14.51 | 14.13 | 14.03 | $-197.22$ | 10 | kollmeier_17a
Figure 1: Distribution of the stars toward the NGC 6558 field. In all panels,
the six cluster stars are identified with red open symbols. The size of the
symbols is proportional to the signal-to-noise ratio (S/N). The size of the
smaller S/N (red triangle symbol star) was scaled by a factor of 3 in order to
make it visible. Top-left panel: spatial distribution of stars within the
APOGEE-2 survey area. The black symbols refer to the overlapping APOGEE-2S
plug-plates toward NGC 6558, corresponding to three APOGEE-2 programs:
geisler_19b (open circles), kollmeier_17a (open triangles), and apogee (plus
symbols). The cluster tidal radius ( r${}_{\rm t}=$10$\aas@@fstack{\prime}$44
; Harris, 1996, 2010) is marked with a large open black dashed circle. North
is up and east is to the right. Top-right panel: plot of the radial velocity
against metallicity of our member stars with the APOGEE-2S field sources in
the direction of NGC 6558. Both parameters are from the ASPCAP pipeline. The
black box, limited by $\pm$0.15 dex and $\pm$15 km s-1 and centered on [Fe/H]
= $-$1.15 and RV = $-$192.63 km s-1, encloses our potential cluster members
(red open circles), while the final sample of our four members whose
abundances were determined with the BACCHUS code are the open dashed circles
within the zoomed box (see text). Bottom-left panel: proper motion
distribution of the stars within the cluster tidal radius of NGC 6558
extracted from Gaia DR3. The colour-coded bar represents the membership
probabilities. The probability of membership of our six stars is greater than
95%. A circumference with a radius of 0.5 mas yr-1 is shown in the proper
motions diagram. Bottom-right panel: $Ks$ vs. ($BP-Ks$) colour-magnitude
diagram. An isochrone with colour-coded cross-symbol temperatures has been fit
to the most likely cluster members.

##  2 Observations and Data

The second phase of the Apache Point Observatory Galactic Evolution Experiment
(APOGEE-2; Majewski et al., 2017) is a high-resolution ($R\sim 22,500$) near-
infrared (NIR) spectroscopic survey containing observations of $\sim 657,135$
unique stars released as part of the SDSS-IV survey (Blanton et al., 2017),
targeting these objects with selections detailed in Zasowski et al. (2013),
Zasowski et al. (2017), Beaton et al. (2021), and Santana et al. (2021). These
papers additionally provide an extensive explanation of the targeting approach
employed in the APOGEE-2 survey. The spectra were obtained using the
cryogenic, multi-fiber (300) APOGEE spectrograph (Wilson et al., 2019),
mounted on the 2.5m SDSS telescope (Gunn et al., 2006) at Apache Point
Observatory, to observe the Northern Hemisphere (APOGEE-2N), and expanded to
include a second APOGEE spectrograph on the 2.5m Irénée du Pont telescope
(Bowen & Vaughan, 1973) at Las Campanas Observatory to observe the Southern
Hemisphere (APOGEE-2S). Each instrument registers the H-band in wavelengths
between the $15100$ Å and $17000$ Å, utilizing three detectors. There are
small gaps in coverage between them of about 100 Å around $\sim$15800 Å and
$\sim$16400 Å , respectively. Additionally, each fiber provides an on-sky
field of view with an diameter of $\sim$2$\arcsec$ in the Northern instrument
and 1$\aas@@fstack{\prime\prime}$3 in the Southern instrument.

The final version of the APOGEE-2 catalog was published in December 2021 as
part of the 17th data release of the Sloan Digital Sky Survey (DR17;
Abdurro’uf et al., 2022b) and is available publicly online through the SDSS
Science Archive Server and Catalog Archive Server111SDSS DR17 data:
https://www.sdss4.org/dr17/irspec/spectro_data/. The spectra were reduced
following the procedures extensively described in Nidever et al. (2015). For
detailed information, we refer the interested reader to that reference. The
stellar parameters and chemical abundances in APOGEE-2 were derived within the
APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP; García
Pérez et al., 2016). ASPCAP derives stellar-atmospheric parameters, radial
velocities, and as many as 20 individual elemental abundances for each
APOGEE-2 spectrum by comparing each to a multidimensional grid of theoretical
MARCS model atmospheres grid (Zamora et al., 2015), employing a $\chi^{2}$
minimization routine with the code FERRE (Allende Prieto et al., 2006) to
derive the best-fit parameters for each spectrum.

The accuracy and precision of the atmospheric parameters and chemical
abundances are extensively analysed in Holtzman et al. (2018), Jönsson et al.
(2018), and Jönsson et al. (2020), while details regarding the customized
H-band line list are fully described in Shetrone et al. (2015), Hasselquist et
al. (2016), Cunha et al. (2017), and Smith et al. (2021).

##  3 NGC 6558

NGC 6558 was observed as part of the Contributed APOGEE-2S CNTAC222CNTAC:
Chilean Telescope Allocation Committee CN2019B program (P.I: Doug Geisler;
geisler_19b) during July 9–10, 2019, as part of the CAPOS survey (Geisler et
al., 2021).

Fig. 1 shows the spatial distribution of the stars toward the NGC 6558 field
in the APOGEE-2S footprint (top-left panel), together with the six identified
cluster members listed in this work. The main APOGEE-2S plug-plate containing
the NGC 6558 cluster (toward $\alpha_{\mathrm{J2000}}$ $=$ 18h10m18.38s and
$\delta_{\mathrm{J2000}}$ = $-$31d45m48.6s) was centered on (l,b) $\sim$ (0.0,
$-$0.6) degrees, and 15 out of 550 science fibers were located inside the
cluster tidal radius (r${}_{t}=10\aas@@fstack{\prime}44$ ; Harris, 1996, 2010,
dashed circumference in Fig. 1).

CAPOS targets were originally selected on the basis of Gaia DR2 (Gaia
Collaboration et al., 2018) to have proper motions (PMs) within an approximate
radius of $\sim$0.5 mas yr-1 around the nominal PMs of NGC 6558;
$\mu_{\alpha}\cos{}$($\delta$)$=-1.72$ and $\mu_{\delta}=-4.14$ (see, e.g.
Baumgardt & Vasiliev, 2021b). We initially selected these values to estimate
candidate members from the PMs to reduce the potential field star
contamination in both optical and NIR color-magnitude diagrams (CMDs). We re-
examined the PMs from the original sample, but we did not find important
differences between Gaia DR2 (Gaia Collaboration et al., 2018) and Gaia DR3
PMs (Gaia Collaboration et al., 2022) toward NGC 6558. The left-bottom panel
in Fig. 1 shows the updated version of the PMs using Gaia DR3Gaia (Gaia
Collaboration et al., 2022). Besides PMs, the selected stars are distributed
along both the red giant branch (RGB) and the asymptotic giant branch (AGB) of
the cluster, as illustrated in the bottom-right panel of Fig. 1.

Our target stars not only lie inside the tidal radius of the cluster, but also
share similar PMs, follow the same evolutionary track in the optical$+$NIR
CMDs, and share similar radial velocity (RV) and metallicity ([Fe/H], top-
right panel), which confirm that the 5 CAPOS stars (the red open circles) are
very likely cluster members. Both the RV and [Fe/H] were extracted from the
spectra reduced with the ASPCAP pipeline, and these values in the metallicity
were used only for the member selection. In fact, Fernández-Trincado et al.
(2020b) shows that there is usually an offset of $\sim$0.2 dex on average
between the abundances measured with ASPCAP pipeline with respect to the
BACCHUS code in most of the chemical species. The methodology followed to
determine the final values of the abundances is described in detail in
Sections 4 and 5. In this sense, the zoomed black box rectangle in the top-
right panel of the Fig. 1 shows the revised Fe abundances as black dashed open
circles, together with the ASPCAP values (red open circles). The APOGEE-2
designations of the stars, the coordinates, Gaia DR3 and VVV magnitudes, RV,
and S/N are listed in Table 1.

Additionally, we also examined two overlapping APOGEE-2S plug-plates toward
NGC 6558, which contain the APOGEE-2S programs: kollmeier_17a (238 science
fibers) and apogee (332 science fibers). We refer the interested reader to
Santana et al. (2021) for further details on these programs.

From kollmeier_17a, we have identified one star (2M18101623$-$3145423)
satisfying almost all the cluster membership criteria imposed in this work.
However, this star is only recorded in Table 1 together with the APOGEE-2 RV,
Gaia DR3 astrometry, and photometry information because its spectral S/N is
too low ($<10$) to obtain reliable elemental abundances. This star is
positioned along the cluster CMD’s horizontal branch (HB), and is likely
associated with the RR Lyrae population of NGC 6558.

Finally, we imposed a quality cut in the APOGEE-2 spectra using an S/N
threshold $>$ 70 per pixel to ensure the analysis of good-quality spectra and
maximize the precision of the stellar abundances. Thus, elemental abundances
are restricted to the 4 stars with high S/N listed in Table 1.

Table 2: Estimated photometric atmospheric parameters for the NGC 6558 stars with high S/N (see text). APOGEE ID | Teff |  $\log$ g | ${\xi}_{t}$
---|---|---|---
| (K) | (c.g.s) | (km s-1)
2M18101354$-$3146216 | 4319 | 1.3 | 1.61
AP18102342$-$3146515 | 4305 | 1.4 | 1.48
2M18101117$-$3144580 | 4381 | 1.1 | 1.80
2M18101768$-$3145246 | 4729 | 1.8 | 1.61
Figure 2: Example of the quality of the model fit obtained with BACCHUS in this study for selected molecular lines: 12C16O, 12C14N, 16OH, and atomic lines: Mg I, Al I, Si I, Ca I, Ti I, Fe I, Ni I, and Ce II for one target giant in NGC 6558: AP18102342$-$3146515\. The best-fit synthesis and observed spectra are highlighted with red lines and black dots, respectively. Each panel is centered around the selected lines, and the dashed black lines mark the position of the air wavelength lines. Table 3: Elemental abundances of NGC 6558 CAPOS stars. Within parentheses are the re-calibrated abundances for the star in common with Barbuy et al. (2018b) (2M18101768$-$3145246). ID | [C/Fe] | [N/Fe] | [O/Fe] | [Mg/Fe] | [Al/Fe] | [Si/Fe] | [Ca/Fe] | [Ti/Fe] | [Fe/H] | [Ni/Fe] | [Ce/Fe]
---|---|---|---|---|---|---|---|---|---|---|---
2M18101354$-$3146216 |  $-$0.42 |  $+$1.31 |  $+$0.36 |  $+$0.24 |  $+$0.05 |  $+$0.21 |  $+$0.31 |  $+$0.16 |  $-$1.09 |  $-$0.07 | 0.18
AP18102342$-$3146515 |  $-$0.40 |  $+$1.13 |  $+$0.29 |  $+$0.23 |  $+$0.29 |  $+$0.22 |  $+$0.35 |  $+$0.20 |  $-$1.18 |  $-$0.10 | 0.13
2M18101117$-$3144580 |  $-$0.12 |  $+$0.99 |  $+$0.37 |  $+$0.22 |  $-$0.04 |  $+$0.27 |  $+$0.28 |  $+$0.13 |  $-$1.22 |  $+$0.14 | 0.25
2M18101768$-$3145246 | … | … |  $+$0.63 |  $+$0.22 |  $+$0.08 |  $+$0.25 |  $+$0.30 |  $+$0.14 |  $-$1.10 |  $+$0.08 | …
| … | … | ($+$0.62) | ($+$0.40) | ($+$0.05) | ($+$0.19) | ($+$0.16) | ($+$0.16) | ($-$1.10) | … | …
Mean |  $-$0.31 |  $+$1.14 |  $+$0.41 |  $+$0.23 |  $+$0.09 |  $+$0.24 |  $+$0.31 |  $+$0.16 |  $-$1.15 |  $+$0.01 |  $+$0.19

##  4 Atmospheric Parameters

The atmospheric parameters (Teff and $\log g$) were derived using the same
methodology as described in Fernández-Trincado et al. (2022a), that is, the
$Ks$ vs. $BP-Ks$ CMD shown in Fig. 1 (bottom-right panel) was reddening
corrected by using giant stars and adopting the reddening law of Cardelli et
al. (1989) and O’Donnell (1994) and a total-to-selective absorption ratio RV
$=$ 3.1 (see, Barbuy et al., 2018b; Cohen et al., 2021).

We chose the RGB stars located within a 10$\arcmin$ radius from the cluster,
ensuring that their proper motions closely matched those of NGC 6558 within a
margin of 0.5 mas yr-1. Subsequently, following the reddening slope, we
proceeded to determine the separation between these selected stars and a
previously defined reference line, which outlines the RGB. The vertical and
horizontal separation yields the differential absorption A${}_{\rm K_{s}}$ and
reddening E(BP $-$ Ks) values of each individual star, respectively. Our next
step involved the selection of the three closest RGB stars within the field to
calculate the average absorption and reddening values. We then corrected the
Ks magnitude and BP $-$ Ks colour index based on these averages, respectively.
The selection of this number of stars represents an arbitrary decision aimed
at minimizing the impact of photometric random errors while maximizing spatial
resolution to the greatest extent possible. After these corrections the
photometric $T_{\rm eff}$ and $\log$ g were determined by fitting a PARSEC
isochrone (Bressan et al., 2012), chosen to have an age of 12.3 Gyr (Cohen et
al., 2021), and an overall metallicity of [M/H]=$-$0.90 (this work), and
assumed $T_{\mathrm{eff}}$ and $\log$ g to be the effective temperature and
gravity at the point of the isochrones that has the same Ks magnitude as the
star. Finally, microturbulence velocities $\xi_{t}$ were determined using the
relation from Gratton et al. (1996). Table 2 lists the determined photometric
atmospheric parameters, microturbulence velocity, and S/N for the four stars
in our sample for which elemental abundances are provided in this study.

Figure 3: [N/Fe] vs [C/Fe], [Al/Fe] vs [Si/Fe], [Ce/Fe] vs [Al/Fe], [Al/Fe] vs [Mg/Fe], [Si/Fe] vs [Mg/Fe], and [Ce/Fe] vs [N/Fe] diagrams for our NGC 6558 stars (black open star symbols). Open blue squares and circles depict the stars analysed by Barbuy et al. (2007) and Barbuy et al. (2018b) at the same cluster, respectively. Filled symbols represent the star in common with our study. The figure also displays data for the bulge cluster NGC 6522 (open plus symbols, Fernández-Trincado et al., 2019c), as well as the CAPOS clusters Djorg 2, HP 1, NGC 6540, and NGC 6642 (Geisler et al., 2021). Grey dotted lines mark the level of 4$\sigma$ above the Galactic level for [N/Fe] enhanced stars at the metallicity of NGC 6558 (see Fig. 4). Figure 4:  Distribution of [N/Fe] vs. [Fe/H] for the stars in the GCs from Mészáros et al. (2020, grey dots). Symbols and colour codes are the same as in Fig. 3. The dashed black line represents a 4th order polynomial fit at the 4$\sigma$ level, over the usual Galactic values as described in Fernández-Trincado et al. (2022c). Figure 5: Violin plot for the abundances of C, N, O, Mg, Al, Si, Ca, Fe, and Ce of NGC 6558 compared with other CAPOS BGCs. Table 4: Typical abundance uncertainties determined for four stars in our sample. Abundance | $\Delta T_{\mathrm{eff}}$ | $\Delta\log g$ | $\Delta\xi_{t}$ | Mean | ($\Sigma x^{2}$)1/2
---|---|---|---|---|---
| (K) | (dex) | (km s-1) | (dex) | (dex)
|  |  |  |  |
2M18101354$-$3146216 |  |  |
[C/Fe] | 0.08 | 0.07 | 0.02 | 0.07 | 0.13
[N/Fe] | 0.14 | 0.03 | 0.01 | 0.07 | 0.16
[O/Fe] | 0.17 | 0.04 | 0.01 | 0.06 | 0.18
[Mg/Fe] | 0.04 | 0.02 | 0.01 | 0.11 | 0.12
[Al/Fe] | 0.09 | 0.01 | 0.01 | 0.07 | 0.12
[Si/Fe] | 0.01 | 0.04 | 0.02 | 0.05 | 0.07
[Ca/Fe] | 0.03 | 0.04 | 0.01 | 0.05 | 0.07
[Ti/Fe] | 0.12 | 0.01 | 0.00 | 0.07 | 0.14
[Fe/H] | 0.05 | 0.03 | 0.01 | 0.06 | 0.08
[Ni/Fe] | 0.01 | 0.01 | 0.00 | 0.06 | 0.06
AP18102342$-$3146515 |  |  |
[C/Fe] | 0.06 | 0.07 | 0.00 | 0.10 | 0.13
[N/Fe] | 0.15 | 0.07 | 0.00 | 0.07 | 0.18
[O/Fe] | 0.15 | 0.03 | 0.00 | 0.07 | 0.17
[Mg/Fe] | 0.01 | 0.02 | 0.00 | 0.13 | 0.13
[Al/Fe] | 0.04 | 0.01 | 0.00 | 0.08 | 0.09
[Si/Fe] | 0.02 | 0.03 | 0.01 | 0.07 | 0.07
[Ca/Fe] | 0.03 | 0.04 | 0.01 | 0.05 | 0.07
[Ti/Fe] | 0.12 | 0.02 | 0.00 | 0.08 | 0.14
[Fe/H] | 0.03 | 0.03 | 0.00 | 0.07 | 0.08
[Ni/Fe] | 0.05 | 0.06 | 0.00 | 0.05 | 0.09
2M18101117$-$3144580 |  |  |
[C/Fe] | 0.03 | 0.06 | 0.02 | 0.07 | 0.10
[N/Fe] | 0.11 | 0.02 | 0.00 | 0.07 | 0.13
[O/Fe] | 0.19 | 0.02 | 0.01 | 0.06 | 0.19
[Mg/Fe] | 0.03 | 0.01 | 0.00 | 0.11 | 0.12
[Al/Fe] | 0.07 | 0.02 | 0.00 | 0.07 | 0.10
[Si/Fe] | 0.02 | 0.05 | 0.01 | 0.05 | 0.07
[Ca/Fe] | 0.03 | 0.04 | 0.00 | 0.05 | 0.08
[Ti/Fe] | 0.13 | 0.02 | 0.00 | 0.07 | 0.15
[Fe/H] | 0.05 | 0.04 | 0.00 | 0.06 | 0.08
[Ni/Fe] | 0.00 | 0.01 | 0.00 | 0.06 | 0.06
2M18101768$-$3145246 |  |  |
[C/Fe] | … | … | … | … | …
[N/Fe] | … | … | … | … | …
[O/Fe] | 0.17 | 0.07 | 0.01 | 0.06 | 0.19
[Mg/Fe] | 0.01 | 0.05 | 0.01 | 0.11 | 0.12
[Al/Fe] | 0.02 | 0.02 | 0.00 | 0.07 | 0.08
[Si/Fe] | 0.04 | 0.03 | 0.01 | 0.05 | 0.07
[Ca/Fe] | 0.02 | 0.04 | 0.01 | 0.06 | 0.08
[Ti/Fe] | 0.10 | 0.02 | 0.00 | 0.09 | 0.13
[Fe/H] | 0.04 | 0.04 | 0.01 | 0.06 | 0.08
[Ni/Fe] | 0.01 | 0.03 | 0.01 | 0.06 | 0.07

##  5 Elemental Abundances

Elemental abundances were derived from a local thermodynamic equilibrium (LTE)
analysis for the four stars listed in Table 2 using the Brussels Automatic
Code for Characterizing High accuracy Spectra (Masseron et al., 2016), which
relies on the radiative code Turbospectrum (Alvarez & Plez, 1998; Plez, 2012)
and the MARCS model atmosphere grid Gustafsson et al. (2008). With the
atmospheric parameters determined in Section 4, the first step consisted in
determining the metallicity ([Fe/H]) from selected Fe I lines and broadening
parameters.

With the [Fe/H] and main atmospheric parameters fixed, we then computed the
elemental abundance of each chemical species following the same methodology as
described in Fernández-Trincado et al. (2020c), Fernández-Trincado et al.
(2021b), Fernández-Trincado et al. (2021c), and Fernández-Trincado et al.
(2022a), and summarized here for guidance. We performed a synthesis using the
full set of atomic line lists described in Smith et al. (2021), which is used
to fit the local continuum. Subsequently, the cosmic rays and the telluric
lines are removed, and the local S/N is estimated. After that, we follow the
description given in Hawkins et al. (2016). We used four different abundance
determination methods, namely, line-profile fitting, core line-intensity
comparison, global goodness-of-fit estimate, and an equivalent-width
comparison. For each method, we used a set of synthetic spectra of different
abundances to compute the observed abundance. Only the lines with the best fit
of the individual abundances are kept. We chose the $\chi^{2}$ diagnostic for
abundance determination due to its reliability. Nevertheless, we preserved
data from the other diagnostic methods, including the standard deviation
obtained from all four approaches to estimate the uncertainties.

To determine the C, N, and O elemental abundances, a mix of heavily CN-cycled
and $\alpha-$poor MARCS models were used, as well as the same molecular lines
adopted by Smith et al. (2021). The oxygen abundances are first estimated from
the hydroxide molecular lines (16OH). With this abundance known, we derived
the carbon abundances from the carbon monoxide molecular lines (12C16O), and
finally, the nitrogen abundances are obtained from the cyanogen molecular
lines (12C14N). This process is repeated multiple times to eliminate any
dependence on OH, CO, and CN lines.

An illustration of the quality of the model fit obtained in this study is
presented in Fig. 2, where we show the observed (black dotted line) and
synthetic (red line) spectra for the APOGEE-2 region around selected atomic
and molecular lines obtained for our target giant star AP18102342$-$3146515.

Eleven chemical species were investigated for NGC 6558 from the APOGEE-2
spectra, including the Fe-peak (Fe, Ni), $\alpha-$(O, Mg, Si, Ca, Ti), light-
(C, N), odd-Z (Al), and the $s$-process element (Ce). Our study provides a
number of elements in common with optical studies carried out by Barbuy et al.
(2007) and Barbuy et al. (2018b), as well as complementary elements not
previously examined. The resulting abundance derivations are listed in Table
3.

Uncertainties in spectroscopic parameters are listed in Table 4 for our four
cluster stars. The reported uncertainties were obtained by once again
calculating the abundances by varying one by one the mean value of the
effective temperature, surface gravity, and microturbulence velocity by
$\Delta$T${}_{\rm eff}=\pm 100$ K, $\Delta\log$ g $=\pm 0.3$ dex,
$\Delta\xi_{t}=\pm 0.05$ km s-1, respectively. These values represent the
usual uncertainties for the stellar parameters in GCs (see, e.g., Barbuy et
al., 2018b; Fernández-Trincado et al., 2019b). The final uncertainty of each
chemical abundance is the quadratic sum of the individual uncertainties:
$\sigma^{2}_{\rm
total}=\sigma^{2}_{\rm[X/H],T_{eff}}+\sigma^{2}_{\rm[X/H],\log
g}+\sigma^{2}_{\rm[X/H],\xi_{t}}+\sigma^{2}_{\rm mean}$; where
$\sigma^{2}_{\rm mean}$ is the standard deviation of the abundances computed
for each line of a given element. Table 4 also shows the characteristic
uncertainties for each abundance due to variations in the stellar parameters.

We derived a mean spectroscopic metallicity $\langle$[Fe/H]$\rangle$ =
$-1.15\pm 0.08$ for NGC 6558, only 0.02 dex above of the results from Barbuy
et al. (2018b) ($\langle$[Fe/H]$\rangle$ = $-1.17$), who used UVES spectra.
These authors investigated a star in common with our data set, namely, the
star 2M18101768$-$3145246, with [Fe/H] = $-$1.15 computed from both Fe I and
Fe II lines. This value differs by 0.05 dex from ours (see Table 3). Barbuy et
al. (2018b) adopted a Solar iron abundance of $\epsilon$(Fe)⊙ = 7.50 from
Grevesse & Sauval (1998) for computing [X/Fe] abundances, in contrast to our
study, which adopted that from Asplund et al. (2005), $\epsilon$(Fe)⊙= 7.45.
In order to analyse the entire set of data available for NGC 6558, we re-
calibrated the values of those authors to be at the same relative Solar iron
abundances as this work. Re-calibrated values to Asplund’s Solar abundances
for the star in common with Barbuy et al. (2018b) are listed in parentheses in
Table 3. In this way, the star in common now shows the same Fe abundance, and
a mean value for GC NGC 6558 of $\langle$[Fe/H]$\rangle$ = $-$1.12 was
obtained from Barbuy et al. (2018b). This value is in excellent agreement with
our work.

We report for the first time for NGC 6558 abundances in the iron-peak nickel
(Ni) and the $s$-process element cerium (Ce). The former shows an average
abundance essentially Solar $\langle$[Ni/Fe]$\rangle$ = $+$0.01, and even
deficient in two stars, with a clear separation of $\sim$ 0.2 dex, which is
greater than their individual errors. The latter shows an average abundance
slightly super-Solar, $\langle$[Ce/Fe]$\rangle$ = $+$0.19.

We also found strong enrichment for nitrogen, $\langle$[N/Fe]$\rangle$
$\sim+$1.14, well above typical Galactic field star levels (see, e.g.,
Fernández-Trincado et al., 2022c) for the 3 stars for which the spectra
allowed us to measure CNO abundances, as well as carbon-deficient levels of
$\langle$[C/Fe]$\rangle$ = $-$0.31. These high values for N agree with the
average value of $\langle$[N/Fe]$\rangle$ = $+$1.01 reported by Ernandes et
al. (2018), who analysed the same sample of stars as in Barbuy et al. (2018b),
but it strongly disagrees with their average value for carbon,
$\langle$[C/Fe]$\rangle$ = $+$0.23, which is 0.54 dex greater than our
measures when their values are re-calibrated to Asplund et al. (2005).
Although our data use the $H$-band, where molecular lines permit us to achieve
what we believe to be a more accurate determination of C, N, and O together,
both the C and N are affected not only by stellar evolution but also by
multiple populations. We did not obtain reliable measurements for C and N for
our star in common, so a good agreement between the two samples is not
necessarily expected.

The star 2M18101768$-$3145246 exhibits clear differences, about 0.18 dex lower
in our measurement for [Mg/Fe] with respect to Barbuy et al. (2018b), and 0.14
dex higher in [Ca/Fe], which fall outside our error bars, in contrast with the
much smaller differences of only 0.01 and 0.03 dex for [O/Fe] and [Al/Fe]
abundances, respectively, which together with Si and Ti are in agreement
within the error bars.

We found an average enhancement for the $\alpha$-element
$\langle$[O/Fe]$\rangle$ of $+$0.41, and very similar but lower values for the
$\alpha$-elements $\langle$[Mg/Fe]$\rangle$, $\langle$[Si/Fe]$\rangle$, and
$\langle$[Ca/Fe]$\rangle$ of $+$0.23, $+$0.24, and $+$0.31 respectively. The O
and Mg are thought to be produced in the hydrostatic phases of massive stars,
while Si and Ca are formed in a SN type II (Heger et al., 2003; Janka, 2012).
In comparison, Barbuy et al. (2018b) found high $\langle$[O/Fe]$\rangle$ and
$\langle$[Mg/Fe]$\rangle$, but lower $\langle$[Ca/Fe]$\rangle$,
$\langle$[Si/Fe]$\rangle$ and $\langle$[Ti/Fe]$\rangle$.

Table 5: Mean abundances of NGC 6558 compared to selected CAPOS BGCs.  Cluster | [C/Fe] | [N/Fe] | [O/Fe] | [Mg/Fe] | [Al/Fe] | [Si/Fe] | [Ca/Fe] | [Fe/H] | [Ce/Fe]
---|---|---|---|---|---|---|---|---|---
NGC 6558 |  $-$0.31 |  $+$1.14 |  $+$0.41 |  $+$0.23 |  $+$0.09 |  $+$0.24 |  $+$0.31 |  $-$1.15 |  $+$0.19
NGC 6522 |  $-$0.34 |  $+$1.19 |  $+$0.33 |  $+$0.13 |  $+$0.57 |  $+$0.30 | — |  $-$1.04 |  $+$0.16
Djorg 2 |  $-$0.27 |  $+$0.94 |  $+$0.43 |  $+$0.27 |  $+$0.17 |  $+$0.26 |  $+$0.26 |  $-$1.13 |  $+$0.13
HP 1 |  $-$0.37 |  $+$1.11 |  $+$0.36 |  $+$0.17 |  $+$0.27 |  $+$0.25 |  $+$0.22 |  $-$1.19 |  $+$0.11
NGC 6540 |  $-$0.28 |  $+$1.03 |  $+$0.34 |  $+$0.19 |  $+$0.14 |  $+$0.24 |  $+$0.26 |  $-$1.06 |  $+$0.05
NGC 6642 |  $-$0.14 |  $+$0.78 |  $+$0.45 |  $+$0.28 |  $+$0.16 |  $+$0.32 |  $+$0.25 |  $-$1.13 |  $+$0.17

##  6 Discussion

Fig. 3 plots [N/Fe] vs [C/Fe], [Al/Fe] vs [Si/Fe], [Ce/Fe] vs [Al/Fe], [Al/Fe]
vs [Mg/Fe], [Si/Fe] vs [Mg/Fe], and [Ce/Fe] vs [N/Fe] diagrams for the sample
stars, in order to check the expected anti-correlations for N-C and Al-Mg,
correlations for Al-Si and Si-Mg (Carretta et al., 2009; Renzini et al., 2015;
Mészáros et al., 2020), and potential correlations for Ce-Al and Ce-N (see,
e.g., Fernández-Trincado et al., 2021d, 2022b). We also show the re-calibrated
abundances for 2 stars from Barbuy et al. (2007) and 4 stars from Barbuy et
al. (2018b) (open squares and circles, respectively). Our star in common with
Barbuy et al. (2018b) (filled circle) is depicted as a filled star symbol. The
results appear to be consistent with each other, except for one star from
Barbuy et al. (2018b) in the Mg and Si abundances relative to Fe, which shows
an evident shift in the Al-Si, Al-Mg, and Si-Mg diagrams. Despite the
relatively few stars in our sample, anti-correlations for NGC 6558 might be
present in the N-C, but the anti-correlations in Al-Mg, as well as the
correlations in the Al-Si, Si-Mg, and Ce-N diagrams, are not clear. On the
other hand, a weak anti-correlation between Ce and Al could be present, but
the sample is too small to be definitive.

Fig. 3 also displays stars of the GCs NGC 6522, from (Fernández-Trincado et
al., 2019c), as well as the CAPOS clusters Djorg 2, HP 1, NGC 6540, and NGC
6642. These clusters have similar metallicities to NGC 6558
($-$1.2<$\langle$[Fe/H]$\rangle$<$-$1.0), as reported in Geisler et al.
(2021). Abundances derived from Geisler et al. (2021) are from the ASPCAP
system. To avoid any systematic errors and ensure consistency with the
abundances measured with BACCHUS, we applied the same correction in [Fe/H]
determined for NGC 6558 (as indicated by the dashed circles in the zoomed box
of the top-right panel in Fig. 1).

We found that the NGC 6558 stars do not extend over a large range in [Al/Fe],
but instead lie within a confined zone below [Al/Fe]=$+$0.3. This limit has
been used as an easy and graphic marker between the first- and second-
generation stars in GCs (Mészáros et al., 2015, 2020). In spite of that, the
high values in N abundance for the stars of NGC 6558 in Fig. 3, and the low
values in C, are together a good indicator of multiple-population stars. Thus,
using only the Al abundance to distinguish between first- and second-
generation stars may not be enough. Such enhanced N abundances exceed
4$\sigma$ above the typical Galactic level (dotted grey line at
[N/Fe]$\sim+$0.81) at a metallicity of [Fe/H]=$-$1.15), as is shown in
Fernández-Trincado et al. (2022c), and represented as a dashed line in Fig. 4.
This figure presents a 4$\sigma$ fourth-order polynomial fit above the mean
behaviour of the nitrogen for the Galactic stars drawn from the APOGEE
pipeline ASPCAP (Pérez et al., 2016), and corrected to BACCHUS abundances
using the stars belonging to GCs in (Mészáros et al., 2020, grey dots). This
polynomial fit was used by Fernández-Trincado et al. (2022c) to select the
nitrogen-enriched red giant stars distributed across the bulge, metal-poor
disk, and halo of our Galaxy, which exhibit elemental abundances comparable to
those exclusively seen in GCs. These stars are thought to have been likely
formed in the cluster and subsequently lost.

All the BGCs displayed in Fig. 3 exhibit a significant gap of approximately
0.3 dex in nitrogen abundance, with the exception of NGC 6558 and NGC 6522.
The latter two clusters, due to the small sample, only presented stars with
[N/Fe] values over the Galactic levels within this range of metallicities.
When compared to Mészáros et al. (2020, their Fig. 17), this gap is solely
observed in NGC 288, and barely indicated in NGC 5904. This suggests that the
observed effect is likely due to the limited sample size in our clusters.

We could only measure the abundance of the $s$-process element Ce relative to
Fe for three stars, as well as to N. Despite this, [Ce/Fe] shows values that
are slightly overabundant compared to the Sun, but as expected by other BGCs
at the same metallicity, as can be seen in the Ce-Al and Ce-N diagrams.

The remarkable similarities observed in the chemical behaviour between NGC
6558 and the other CAPOS BGCs with the same metallicity can be seen clearly in
Fig. 5 and Table 5. Violin plots displaying the abundance distributions of NGC
6558 in comparison to NGC 6522, Djorg 2, HP 1, NGC 6540, and NGC 6642 are
presented. All the BGC abundance distributions are strongly consistent with
each other. The mean values of [N/Fe] for NGC 6558 and NGC 6522 are slightly
greater than the others, primarily due to the small sample (5 stars for NGC
6522), which include only bona fide second-generation stars. On the other
hand, NGC 6522 exhibits systematically higher Al abundances compared to other
CAPOS clusters with the same metallicity. In fact, according to (Fernández-
Trincado et al., 2019c), this cluster exhibits a significant scatter in
[Al/Fe], with a variation of $\sim$1 dex when considering values from the
literature.

Figs. 3 and 5 show that the [Mg/Fe] abundances for all these bulge clusters,
including NGC 6558, do not exceed the value $\sim+$0.4. This observation is
consistent with the values observed for the APOGEE bulge field stars (see, for
example, Rojas-Arriagada et al., 2020; Geisler et al., 2021). However, they
differ from M 4, M 12, and NGC 288, whose average $\langle$[Mg/Fe]$\rangle$
values are around $\approx+$0.5 (Mészáros et al., 2020). These latter GCs
share similar metallicities to NGC 6558, but they are not associated with the
GB; instead, they are associated with disk formation (M 4 and M 12) or Gaia-
Enceladus (NGC 288, Massari et al., 2019).

##  7 Concluding remarks

We have presented a new high-resolution (R$\sim$22,000) spectral analysis in
the $H$-band for six members of the relatively old, moderately metal-poor BGC
NGC 6558, obtained as part of the CAPOS survey. The memberships are very
likely, due to their spatial distribution, Gaia DR3 proper motions, and our
own RV and metallicity from APOGEE spectra. We found a mean heliocentric RV of
$V_{r}$ = $-$193.4 $\pm$ 0.9 km s-1, where the error is the standard error of
the mean, in good agreement with Barbuy et al. (2018b). Out of the six stars,
four presented spectral S/N greater than 70 per pixel, which allowed us to
determine their abundance ratios [C/Fe], [N/Fe], [O/Fe], [Mg/Fe], [Al/Fe],
[Si/Fe], [Ca/Fe], [Ti/Fe], [Fe/H], [Ni/Fe], and [Ce/Fe] in a reliable way,
through use of the BACCHUS code.

We found a mean metallicity of $\langle$[Fe/H]$\rangle$ = $-1.15$ for NGC
6558, in good agreement with Barbuy et al. (2018b) when their value is scaled
to the same Solar iron abundance as ours. We also found mean values of the
$\alpha$-(O, Mg, Si, Ca, Ti) elements that are slightly enhanced, iron-peak
(Ni) essentially Solar, and the $s$-process element (Ce) slightly overabundant
compared to the Sun. The high enrichment in nitrogen, together with the
depleted carbon, indicates the presence of the multiple-population phenomenon
in this cluster, although the Al values are below the Mészáros et al. (2020)
limit for second-generation stars. This is the first time that the phenomenon
of multiple-populations is observed for this cluster. Such high nitrogen
enrichment for NGC 6558 agrees with the nitrogen abundances for the CAPOS BGCs
at the same metallicities, turning them into potential progenitors of the
nitrogen-enhanced moderately metal-poor field stars identified in the inner
bulge region (e.g., Fernández-Trincado et al., 2016, 2017; Schiavon et al.,
2017; Fernández-Trincado et al., 2019a, 2020a, 2021a, 2022b).

Despite our small statistical sample, we have observed consistent abundance
patterns in all chemical elements studied in this work for all CAPOS BGCs in
the same metallicity range as NGC 6558
($-$1.2<$\langle$[Fe/H]$\rangle$<$-$1.0). However, NGC 6522 stands out due to
its significant spread in [Al/Fe]. These clusters present nitrogen enhancement
and carbon depletion, indicating the presence of multiple populations.
Furthermore, the [Mg/Fe] abundances in these clusters remain within the range
observed for bulge field stars, in contrast to some Galactic GCs outside the
bulge at the same metallicities.

## Acknowledgements

D.G-D and J.G.F-T gratefully acknowledge support from the Joint Committee ESO-
Government of Chile 2021 (ORP 023/2021). J.G.F-T also acknowledges the
financial support provided by Agencia Nacional de Investigación y Desarrollo
de Chile (ANID) under the Proyecto Fondecyt Iniciación 2022 Agreement No.
11220340, and from ANID under the Concurso de Fomento a la Vinculación
Internacional para Instituciones de Investigación Regionales (Modalidad corta
duración) Agreement No. FOVI210020, and from Becas Santander Movilidad
Internacional Profesores 2022, Banco Santander Chile, and from Vicerrectoría
de Investigación y Desarrollo Tecnológico (VRIDT) at Universidad Católica del
Norte (UCN) under resolución No 061/2022-VRIDT-UCN. D.G. gratefully
acknowledges support from the ANID BASAL project ACE210002. D.G. also
acknowledges financial support from the Dirección de Investigación y
Desarrollo de la Universidad de La Serena through the Programa de Incentivo a
la Investigación de Académicos (PIA-DIDULS). S.V. gratefully acknowledges the
support provided by Fondcyt regular n. 1220264. S.V. gratefully acknowledges
support by the ANID BASAL projects ACE210002 and FB210003. D.M. gratefully
acknowledges support by the ANID BASAL projects ACE210002 and FB210003 and by
Fondecyt project No. 1220724. DM Also acknowledges support from CNPq/Brazil
through project 350104/2022-0. T.C.B. acknowledges partial support for this
work from grant PHY 14-30152; Physics Frontier Center/JINA Center for the
Evolution of the Elements (JINA-CEE), and from OISE-1927130: The International
Research Network for Nuclear Astrophysics (IReNA), awarded by the U.S.
National Science Foundation. B.T. gratefully acknowledges support from the
Natural Science Foundation of Guangdong Province under grant No.
2022A1515010732, and the National Natural Science Foundation of China through
grants No. 12233013. BB acknowledges partial financial support from FAPESP,
CNPq and Capes Financial code 001. C.M. thanks the support provided by
FONDECYT Postdoctorado No.3210144. A.M. gratefully acknowledges support by the
ANID BASAL project FB210003, FONDECYT Regular grant 1212046, and funding from
the Max Planck Society through a “PartnerGroup” grant.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High-Performance Computing at the University of Utah. The SDSS
website is www.sdss.org. SDSS-IV is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS Collaboration
including the Brazilian Participation Group, the Carnegie Institution for
Science, Carnegie Mellon University, the Chilean Participation Group, the
French Participation Group, Harvard-Smithsonian Center for Astrophysics,
Instituto de Astrofìsica de Canarias, The Johns Hopkins University, Kavli
Institute for the Physics and Mathematics of the Universe (IPMU) / University
of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für
Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA
Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-
Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatory of China, New Mexico State University, New York University,
University of Notre Dame, Observatório Nacional / MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University.
This work has made use of data from the European Space Agency (ESA) mission
Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular, the institutions
participating in the Gaia Multilateral Agreement.

## Data Availability

All APOGEE DR 17 data upon which this study is based are publicly available
and can be found at https://www.sdss4.org/dr17.

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