11institutetext:  Centro de Astronomía (CITEVA), Universidad de Antofagasta,
Av. Angamos 601, Antofagasta, Chile 22institutetext: Instituto de Astronomía y
Ciencias Planetarias, Universidad de Atacama, Copayapu 485, Copiapó, Chile
33institutetext: Departamento de Astronomía, Casilla 160-C, Universidad de
Concepción, Concepción, Chile 44institutetext: Departamento de Astronomía,
Universidad de La Serena, 1700000 La Serena, Chile 55institutetext: Instituto
de Investigación Multidisciplinario en Ciencia y Tecnología, Universidad de La
Serena. Benavente 980, La Serena, Chile 66institutetext: Universidade de São
Paulo, IAG, Rua do Matão 1226, Cidade Universitária, São Paulo 05508-900,
Brazil 77institutetext: Depto. de Cs. Físicas, Facultad de Ciencias Exactas,
Universidad Andrés Bello, Av. Fernández Concha 700, Las Condes, Santiago,
Chile 88institutetext: Vatican Observatory, V00120 Vatican City State, Italy
99institutetext: Department of Physics and JINA Center for the Evolution of
the Elements, University of Notre Dame, Notre Dame, IN 46556, USA
1010institutetext: Instituto de Astronomía, Universidad Católica del Norte,
Av. Angamos 0610, Antofagasta, Chile 1111institutetext: Instituto de
Astronomía, Universidad Nacional Autónoma de México, Apdo. Postal 106, 22800
Ensenada, B.C., México 1212institutetext: Instituto de Astronomía, Universidad
Nacional Autónoma de México, Apdo. Postal 70264, México D.F., 04510, México
1313institutetext: Millennium Institute of Astrophysics , Nuncio Monseñor
Sotero Sanz 100, Of. 104, Providencia, Santiago, Chile 1414institutetext:
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA

# CAPOS: the bulge Cluster APOgee Survey
II. The Intriguing ”Sequoia” Globular Cluster FSR 1758

María Romero-Colmenares To whom correspondence should be addressed, Email:
María Romero-Colmenares<EMAIL_ADDRESS>and/or
maria.romero21@alumnos.uda.cl)1122 José G. Fernández-Trincado in .cc to: José
G. Fernández-Trincado<EMAIL_ADDRESS>and/or jfernandezt87@gmail.com)22
Doug Geisler 334455 Stefano O. Souza 66 Sandro Villanova 33 Penélope Longa-
Peña 11 Dante Minniti 7788 Timothy C. Beers 99 Cristian Moni Bidin 1010
Angeles Pérez-Villegas 1111 Edmundo Moreno 1212 Elisa R. Garro 77 Ian Baeza 33
Lady Henao 33 Beatriz Barbuy 66 Javier Alonso-García 11 13 13 Roger E. Cohen
1414 Richard R. Lane 22 Cesar Muñoz 4455

(Received …; Accepted …)

We present results from a study of fifteen red giant members of the
intermediate-metallicity globular cluster (GC) FSR 1758 using high-resolution
near-infrared spectra collected with the Apache Point Observatory Galactic
Evolution Experiment II survey (APOGEE-2), obtained as part of CAPOS (the
bulge Cluster APOgee Survey). Since its very recent discovery as a massive GC
in the bulge region, evoking the name Sequoia, this has been an intriguing
object with a highly debated origin, and initially led to the suggestion of a
purported progenitor dwarf galaxy of the same name. In this work, we use new
spectroscopic and astrometric data to provide additional clues to the nature
of FSR 1758. Our study confirms the GC nature of FSR 1758, and as such we
report for the first time the existence of the characteristic N-C anti-
correlation and Al-N correlation, revealing the existence of the multiple-
population phenomenon, similar to that observed in virtually all GCs.
Furthermore, the presence of a population with strongly enriched aluminium
makes it unlikely FSR 1758 is the remnant nucleus of a dwarf galaxy, as Al-
enhanced stars are uncommon in dwarf galaxies. We find that FSR 1758 is
slightly more metal rich than previously reported in the literature, with a
mean metallicity [Fe/H] between $-1.43$ to $-1.36$ (depending on the adopted
atmospheric parameters), and with a scatter within observational error, again
pointing to its GC nature. Overall, the $\alpha$-enrichment ($\gtrsim+0.3$
dex), Fe-peak (Fe, Ni), light- (C, N), and odd-Z (Al) elements follow the
trend of intermediate-metallicity GCs. Isochrone fitting in the Gaia bands
yields an estimated age of $\sim 11.6$ Gyr. We use the exquisite kinematic
data, including our CAPOS radial velocities and Gaia eDR3 proper motions, to
constrain the N-body density profile of FSR 1758, and found that it is as
massive ($\sim$2.9$\pm 0.6\times 10^{5}$ M⊙) as NGC 6752. We confirm a
retrograde and eccentric orbit for FSR 1758. A new examination of its
dynamical properties with the GravPot16 model favors an association with the
Gaia-Enceladus-Sausage accretion event. Thus, paradoxically, the cluster that
gave rise to the name of the Sequoia dwarf galaxy does not appear to belong to
this specific merging event.

###### Key Words.:

Stars: abundances – Stars: chemically peculiar – Galaxy: globular clusters:
individual: FSR 1758 – Techniques: spectroscopic

##  1 Introduction

Table 1: Photometric, kinematic, and astrometric properties of fifteen likely members of FSR 1758. APOGEE-ID | $\alpha$ | $\delta$ | J | H | Ks | $(G_{BP}-G_{RP})_{0}$ | $G_{0}$ | RV | $\mu_{\alpha}\cos{}(\delta)$ | $\mu_{\delta}$
---|---|---|---|---|---|---|---|---|---|---
| hh:mm:ss | dd:mm:ss |  |  |  |  |  | km s-1 | mas yr-1 | mas yr-1
S/N $>$ 60 |  |  |  |  |  |  |  |  |  |
2M17314970$-$3956247 | 17:31:49.71 |  $-$39:56:24.8 | 10.60 | 9.57 | 9.31 | 2.51 | 13.61 | 220.9 |  $-$2.994$\pm$ 0.028 | 2.511$\pm$0.019
2M17305424$-$3950496 | 17:30:54.24 |  $-$39:50:49.6 | 11.13 | 10.19 | 9.93 | 2.42 | 14.04 | 227.7 |  $-$3.005$\pm$ 0.027 | 2.489$\pm$0.021
2M17310731$-$3953523 | 17:31:07.32 |  $-$39:53:52.4 | 11.74 | 10.82 | 10.58 | 2.35 | 14.69 | 224.5 |  $-$2.863$\pm$ 0.035 | 2.526$\pm$0.023
2M17310187$-$3950066 | 17:31:01.88 |  $-$39:50:06.7 | 12.07 | 11.19 | 10.91 | 2.36 | 14.97 | 228.6 |  $-$2.895$\pm$ 0.039 | 2.477$\pm$0.029
2M17314263$-$3947053 | 17:31:42.64 |  $-$39:47:05.4 | 12.18 | 11.35 | 11.16 | 2.24 | 14.91 | 220.7 |  $-$2.983$\pm$ 0.039 | 2.529$\pm$0.030
2M17312661$-$3951342 | 17:31:26.62 |  $-$39:51:34.3 | 12.20 | 11.48 | 11.24 | 2.31 | 15.29 | 226.3 |  $-$2.769$\pm$ 0.040 | 2.584$\pm$0.028
2M17310738$-$3952298 | 17:31:07.39 |  $-$39:52:29.9 | 12.50 | 11.65 | 11.35 | 2.24 | 15.20 | 228.2 |  $-$2.850$\pm$ 0.048 | 2.405$\pm$0.033
2M17311707$-$3950382 | 17:31:17.07 |  $-$39:50:38.2 | 12.73 | 11.91 | 11.70 | 2.20 | 15.54 | 226.4 |  $-$2.863$\pm$ 0.049 | 2.392$\pm$0.034
2M17313165$-$3949120 | 17:31:31.65 |  $-$39:49:12.1 | 12.85 | 12.11 | 11.92 | 2.03 | 15.43 | 220.2 |  $-$2.863$\pm$ 0.050 | 2.690$\pm$0.035
2M17311230$-$3949493 | 17:31:12.31 |  $-$39:49:49.4 | 11.90 | 11.06 | 10.75 | 2.29 | 14.91 | 223.4 |  $-$2.619$\pm$ 0.038 | 2.713$\pm$0.026
2M17310618$-$3943037 | 17:31:06.18 |  $-$39:43:03.8 | 13.25 | 12.48 | 12.23 | 2.14 | 15.92 | 225.0 |  $-$2.777$\pm$ 0.053 | 2.526$\pm$0.041
S/N $<$ 60 |  |  |  |  |  |  |  |  |  |
2M17304430$-$3952504 | 17:30:44.31 |  $-$39:52:50.5 | 12.62 | 11.86 | 11.67 | 2.11 | 15.27 | 225.5 |  $-$2.729$\pm$ 0.041 | 2.573$\pm$0.029
2M17310004$-$3954546 | 17:31:00.04 |  $-$39:54:54.7 | 13.21 | 12.43 | 12.24 | 1.96 | 15.64 | 225.7 |  $-$2.774$\pm$ 0.055 | 2.506$\pm$0.041
2M17312078$-$3948416 | 17:31:20.79 |  $-$39:48:41.7 | 13.16 | 12.35 | 12.20 | 2.00 | 15.74 | 225.9 |  $-$2.836$\pm$ 0.057 | 2.529$\pm$0.043
2M17305633$-$3953349 | 17:30:56.34 |  $-$39:53:35.0 | 13.09 | 12.39 | 12.16 | 2.08 | 15.78 | 222.2 |  $-$2.832$\pm$ 0.050 | 2.367$\pm$0.038

The bulge of the Milky Way (MW) is populated by a large collection
($\gtrsim$40) of ancient globular clusters (GCs) within $\sim$3.5 kpc of the
Galactic center (for a detailed description, see a review by Bica et al.,
2016; Barbuy et al., 2018; Pérez-Villegas et al., 2020), which serves as the
‘fossil record’ of its evolutionary history (Recio-Blanco et al., 2017;
Minniti et al., 2018a; Kundu et al., 2019, 2021; Fernández-Trincado et al.,
2019a, b, 2020a, 2020c, 2020e, 2021a, 2020b, 2021b; Minniti et al., 2021,
Minniti2021a).

However, until very recently only a very small number of them have been
studied with sufficient detail, including uncovering the multiple-population
phenomenon (Côté, 1999; Minniti, 1995; Mészáros et al., 2020; Fernández-
Trincado et al., 2019c, 2020f, 2021a, 2021c; Geisler et al., 2021, and
references therein). Due to the high and variable extinction produced by the
large amount of dust present in the Galactic plane,which highly hampers
optical observations, most of these GCs have remained barely explored.

More recently, with the aid of near-infrared (NIR) photometric and high-
resolution spectroscopic instruments, capable of penetrating the obscuring
dust, several modern surveys have allowed us to overcome these limitations and
begin to explore and scientifically exploit these fascinating objects. The
Vista Variables in the Via Lactea survey (VVV: Minniti et al., 2010; Saito et
al., 2012; Alonso-García et al., 2018), and its eXtension (VVVX: Minniti et
al., 2018b) is a key large-scale NIR photometric survey of the bulge and the
surrounding disk.

In addition to providing deep NIR photometry for all known bulge GCs, VVV/VVVX
has revealed that the GC census toward the Galactic bulge is incomplete, and
more than 100 new low-luminosity GC candidates have been discovered in the
bulge area (Minniti et al., 2017a, b, c, 2018c; Ryu & Lee, 2018; Bica et al.,
2018; Contreras Ramos et al., 2018; Camargo, 2018; Camargo & Minniti, 2019;
Minniti et al., 2019; Gran et al., 2019; Palma et al., 2019; Minniti et al.,
2020; Garro et al., 2021), and toward the Sagittarius dwarf galaxy (see, e.g.,
Minniti et al., 2021).

Complementarily, large spectroscopic surveys such as the Apache Point
Observatory Galactic Evolution Experiment (APOGEE; Majewski et al., 2017)
reveal detailed information about the chemical properties of obscured GCs for
a number of species with a variety of nucleosynthetic origins with high
precision ($<$0.05 dex). Fortunately, APOGEE has helped fill in the missing
link of bulge GC abundances and velocities. However, despite the large number
of SDSS-IV bulge fields, the Survey only observed a handful of bulge GCs.
Masseron et al. (2019), Mészáros et al. (2020) and Mészáros et al. (2021)
present the first homogeneous study of the SDSS-IV sample of 44 GCs, of which
only 2 are bona fide Main Bulge GCs according to Massari et al. (2019) and
have a large enough sample of well-observed members and low enough reddening
for their study. This is ¡4% of the total number of bulge GCs known, a
disconcertingly low value. In order to take full advantage of the wealth of
astrophysical detail these key objects can provide, as complete a sample as
possible is essential.

Figure 1: Properties of our FSR 1758 targets. Panel (a): Spatial position.
Colour-coded symbols represent the SNR of stars with APOGEE spectra whose
sizes are proportional to their G mag. Open black squares and grey triangles
are stars analyzed in Simpson (2019) and Villanova et al. (2019),
respectively. Field stars are black crosses. A circle with 15′ radius is
overplotted. Panel (b): The proper motion density distribution of stars
located within 15′from the cluster center, with color contours refering to the
Kernel Density Estimation of this sample. FSR 1758 is clearly distinguishable
from the field population. The inner plot on the top-right shows a zoom-in of
the cluster, with concentric ellipses showing the 1, 2, and 3$\sigma$ levels
of our best fit proper motions of FSR 1758 based on Gaia EDR3 data, whose mean
values are highlighted. Symbols are the same as in panel (a). Panel (c):
Colour-magnitude diagram corrected by differential reddening and extinction-
corrected in the Gaia bands of our sample and stars within 15 ′. Our targets
all lie along the red giant branch. Panel (d): Radial velocity versus
metallicity of our members compared to field stars. The [Fe/H] of our targets
have been determined with BACCHUS and photometric atmospheric parameters (see
Table 2), while the [Fe/H] of field stars are from the ASPCAP pipeline. The
red box limited by $\pm 0.15$ dex and $\pm 10$ km s-1 and centered on
[Fe/H]$=-1.36$ and RV $=225.73$ km s-1 encloses our potential cluster members.
Figure 2: Differences in atmospheric parameters and elemental abundances
produced by two runs adopting different effective temperatures (Teff) and
surface gravities ($\log$ g): photometric versus spectroscopic values as
listed in Table 2. The vertical axis refer to the $\Delta$ of every
atmospheric parameter and chemical specie ([X/Fe]) analyzed in this work. The
horizontal axis refer to the T${}_{\rm eff}^{photometry}$. The hexagonal
symbols are color-coded by the S/N. The average and standard deviation around
the mean of the differences is listed in each panel, and are marked by a black
line and gray shadow.

Figure 3: Elemental abundances. [X/Fe] and [Fe/H] abundance density estimation
(violin representation) of FSR 1758 (black) compared to Galactic GCs at
similar metallicity from Mészáros et al. (2020). Panels (a) and (b) show our
determinations by adopting photometric atmospheric parameters from photometry
and spectroscopy (see Table 2), respectively. Each violin representation
indicates with vertical lines the median and limits of the distribution.
(c)–(f): [Al/Fe] – [Mg/Fe], [N/Fe] – [C/Fe], [Al/Fe]–[Si/Fe], and
[Al/Fe]–[N/Fe] distributions for GCs from Mészáros et al. (2020) at similar
metallicity. The black dotted line at [Al/Fe] $=+0.3$ denotes the generalized
separation of first- and second-generation stars as envisioned by Mészáros et
al. (2020). FSR 1758 stars shown ‘star’ symbols refers to our determinations
with adopted photometry parameters, while the blue lines show the
corresponding position of [X/Fe] determined from spectroscopic paramters. The
typical internal error bars are also shown.

Hence the CAPOS project, the bulge Cluster APOgee Survey (Geisler et al.
2021). The primary goal of CAPOS is to obtain detailed abundances and
kinematics for as complete a sample as possible of bona fide members in bulge
GCs, using the unique advantages of APOGEE in order to complement the small
sample observed by SDSS-IV.

One of the CAPOS targets is FSR 1758. It was originally catalogued as a
diffuse open cluster by Froebrich et al. (2007) and Kharchenko et al. (2013).
Recently, Cantat-Gaudin et al. (2018) and Barbá et al. (2019) re-discovered
this object using a combination of data from the DECam Plane Survey (DECaPS;
Schlafly et al., 2018) and the VVVX survey, complemented with Gaia DR2 (see
Gaia Collaboration et al., 2018a). The latter study revealed that the cluster
motion is very different from nearby field stars.

Presumably located on the far side of the Galactic bulge region from the Sun
at $\sim$11.5$\pm$1.0 kpc (Barbá et al., 2019), FSR 1758 is as large (with a
tidal radius $\sim$150 pc) as $\omega$ Cen and NGC 2419, with possibly some
signatures of extra-tidal features. The GC lies in a region strongly affected
by the large foreground reddening, with E(B$-$V)$>0.7$ mags (this work), even
larger than the value previously estimated, E(B$-$V)$\sim$0.37, in Barbá et
al. (2019). In their re-discovery paper, Barbá et al. (2019) posited that FSR
1758 could be the central part of a defunct dwarf galaxy, based on a possible
halo of common proper motion stars in the surrounding regions of the cluster,
or instead an unusually large GC.

However, a subsequent spectroscopic study in the optical (Villanova et al.,
2019) revealed that FSR 1758 displays no significant intrinsic metallicity
spread ($\sim$0.08 dex, within the observational errors) and also only a small
velocity dispersion ($<5$ km s-1). In addition, it also possesses a Na-O anti-
correlation similar to those seen in other GCs at similar metallicity.
Moreover, it is now believed that the putative extratidal stars found by Barbá
et al. (2019) were simply outliers in the surrounding field star proper motion
distribution and likely not associated with the GC. All of this evidence
supports the genuine GC nature of FSR 1758, and not the hypothesis that this
is the remnant nucleus of a dwarf galaxy. However, the dynamical properties of
FSR 1758 reveal that it is not a cluster that originated in the inner Galaxy,
and on the contrary is a halo intruder which circulates throughout the bulge
in a highly eccentric, radial, and retrograde orbital configuration (see,
e.g., Simpson, 2019; Villanova et al., 2019; Yeh et al., 2020).

Regarding its origin, several different scenarios have been proposed for FSR
1758. Simpson (2019), based on its retrograde orbit, claimed that it could be
an accreted halo GC; Villanova et al. (2019) argued that it is a genuine MW GC
based on the above evidence; and Yeh et al. (2020) also supports the idea that
it is likely a halo GC formed inside the MW, as the highly eccentric and
retrograde orbital configuration are not uncommon among in situ halo GCs
(Massari et al., 2019). On the other hand, Myeong et al. (2019) suggested that
it belongs to the remnant debris of an early accretion event in the Milky Way,
likely associated with a massive dwarf galaxy, similar to accretion events
suggested for other GCs (see, e.g., Myeong et al., 2019; Kruijssen et al.,
2019). Myeong et al. (2019) coined the name Sequoia for the putative
progenitor dwarf, based on the description of FSR 1758 as a ”Sequoia in the
garden” given in the title of the paper by Barbá et al. (2019). Subsequent
work (Massari et al., 2019; Koppelman et al., 2019; Fernández-Trincado et al.,
2019a, 2020a) have shown that indeed such an event occurred, with clear
kinematic and chemical evolution signatures, and the name Sequoia has stuck
for the progenitor. What is not clear, and one of the issues we will address
here, is whether or not this eponymous GC is indeed a member of the Sequoia
dwarf. We in fact show that it was likely not a member.

In this work, we take advantage of data from the CAPOS survey (Geisler et al.,
2021) to examine, for the first time in the H-band, the chemical and kinematic
properties of FSR 1758, clarifying the characteristics of this interesting
object in the dense inner regions of the MW, in particular its origin. This
paper represents the second in the series on CAPOS data. In Section 2, we
describe the data. In Section 3, the potential cluster members are presented.
In Section 4, we describe the adoption of the atmospheric parameters. In
Section 5, the elemental-abundance determinations are highlighted. In Section
6, we present our estimation of the age of the cluster by adopting a Bayesian
approach, while in Section 7, we provide a mass estimation of FSR 1758 based
in the available kinematic data. In Section 8, the origin of FSR 1758 is
examined from a dynamical point of view. Summary and concluding remarks are
presented in Section 9.

##  2 Data and sample

The Apache Point Observatory Galactic Evolution Experiment II survey
(APOGEE-2; Majewski et al., 2017) is one of the internal programs of the Sloan
Digital Sky Survey-IV (Blanton et al., 2017; Ahumada et al., 2020) developed
to provide precise radial velocities (RV $<$1 km s-1) and detailed chemical
abundances for an unprecedented large sample of giant stars, aiming to unveil
the dynamical structure and chemical history of the entire MW galaxy.

The APOGEE-2 instruments (capable of observing up to 300 objects
simultaneously) are high-resolution ($R\sim 22,500$), near-infrared (NIR)
spectrographs (Wilson et al., 2019) observing all the components of the MW
(halo, disc, and bulge) from the Northern Hemisphere on the 2.5m telescope at
Apache Point Observatory (APO, APOGEE-2N; Gunn et al., 2006) and the Southern
Hemisphere on the Irénée du Pont 2.5m telescope (Bowen & Vaughan, 1973) at Las
Campanas Observatory (LCO, APOGEE-2S). Each instrument records most of the
H-band (1.51$\mu$m – 1.69$\mu$m) on three detectors, with coverage gaps
between $\sim$1.58–1.59$\mu$m and $\sim$1.64–1.65$\mu$m, and with each fiber
subtending a $\sim$2” diameter on-sky field of view in the northern instrument
and 1.3” in the southern.

DR 17 is the final release of APOGEE-2 data from SDSS-III/SDSS-IV. We used our
access to the internal version of DR 17, as the public version is not yet
available. It includes all APOGEE data, including data taken at APO through
November 2020 and at LCO through January 2021. The dual APOGEE-2 instruments
have observed more than $650,000$ stars throughout the MW, targeting these
objects with selections detailed in Zasowski et al. (2017), Santana et al.
(2021) and Beaton et al. (2021). These papers also give a detailed overview of
the targeting strategy of the APOGEE-2 survey. Spectra are reduced as
described in Nidever et al. (2015), and analyzed using the APOGEE Stellar
Parameters and Chemical Abundance Pipeline (ASPCAP; García Pérez et al.,
2016), and the libraries of synthetic spectra described in Zamora et al.
(2015). The accuracy and precision of the atmospheric parameters and chemical
abundances are extensively analyzed in Holtzman et al. (2018), Jönsson et al.
(2018), and Jönsson et al. (2020), while details regarding the customised
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 FSR 1758

The GC FSR 1758 was observed as part of the Contributed APOGEE-2S
CNTAC111Chilean National Telescope Allocation Committee CN2019A$-$98 program
(P.I: Doug Geisler) during July 9–10, 2019 as part of the CAPOS survey
(Geisler et al., 2021).

###  3.1 Proper motion selection

The APOGEE-2S plug-plate containing the FSR 1758 cluster was centered on
($l$,$b$) $\sim$ (350, $-3.0$), and 21 of 264 science fibers were located
inside a radius of $\leq 15$′from the cluster center, as shown in Figure 1(a).
Targets were selected on the basis of Gaia DR2 (Gaia Collaboration et al.,
2018a) proper motions within a radius of $\sim$0.7 mas yr-1 around the nominal
PMs of FSR 1758 computed by Villanova et al. (2019) from Gaia
DR2:$\mu_{\alpha}\cos(\delta)=-2.79\pm 0.01$ mas yr-1 and
$\mu_{\delta}=2.60\pm 0.01$ mas yr-1. However, here we re-examine these values
taking advantage of the improved data from Gaia EDR3 (Gaia Collaboration et
al., 2021). Thus, Figure 1(b) shows an updated version of the PMs using Gaia
EDR3, which shows that only 15 out of the 21 originally observed “cluster”
stars share PMs similar to the nominal PMs of FSR 1758, making them likely
cluster members.

As in Villanova et al. (2019), we furthermore took potential cluster members
within 15 ′ with Gaia EDR3 information, and having a Renormalised Unit Weight
Error, RUWE $\leq 1.4$ (Lindegren et al., 2018), in order to ensure that the
selected stars were astrometrically well-behaved. Cluster members were also
selected within an approximate radius of 1.0 mas yr-1 as an initial guess for
proper motion members in order to remove field contamination from the colour-
magnitude diagram (CMD). We fit one to ten Gaussians to the distribution of
$\mu_{\alpha}\cos(\delta)$ and $\mu_{\delta}$ with a Gaussian Mixture Model
(GMM), and measured the Akaike Information Criterion (AIC) (Akaike, 1974) and
the Bayesian Information Criterion (BIC) (Schwarz, 1978). Using these
criteria, we then apply a GMM with only one Gaussian as this number minimized
both the AIC and BIC, indicating it was the best fit. The two PM components of
FSR 1758 in Gaia EDR3 are found to have $\mu_{\alpha}\cos(\delta)=-2.85\pm
0.05$ mas yr-1 and $\mu_{\delta}=2.47\pm 0.05$ mas yr-1–as indicated by black
dashed lines in Figure 1(b), which are similar to the previously estimated
value from Villanova et al. (2019), and in excellent agreement with the
nominal values reported in Vasiliev & Baumgardt (2021),
$\mu_{\alpha}\cos(\delta)=-2.880\pm 0.026$ mas yr-1 and $\mu_{\delta}=2.519\pm
0.025$ mas yr-1.

Aside from PMs, stars in our sample are positioned close to the tip of the red
giant branch (RGB), as shown in the Gaia EDR3 CMD in Figure 1(c). All selected
stars had 2MASS H-band brighter than 12.5. This was required in order to
achieve a nominal minimal signal-to-noise, S/N $\gtrsim$60 pixel-1, in one
plug-plate visit ($\sim$ 1 hour). Although more visits were originally
planned, in the end, given weather and time allocation and airmass
constraints, only 1 visit was indeed obtained. Eleven out of the fifteen
observed stars reached S/N$>60$ pixel-1, while the remaining spectra have
lower S/N, ranging from 33 to 51. In the following, we use all stars to
provide reliable and precise ($<1$ km s-1) radial velocities for cluster
member confirmation, but limit ourselves to the 11 higher S/N stars for the
abundance analysis, which are highlighted in Figure 1(d).

###  3.2 Photometric selection

The CMD presented in Figure 1(c) was differential 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 $R_{V}=3.1$. For
this purpose, we selected all RGB stars within a radius of 15 ′ from the
cluster center and that have proper motions compatible with that of FSR 1758
within 1 mas yr-1. First, we draw a ridge line along the RGB, and for each of
the selected RGB stars we calculated its distance from this line along the
reddening vector. The vertical projection of this distance gives the
differencial ${A_{G}}$ absorption at the position of the star, while the
horizontal projection gives the differential ${E(G_{BP}-G_{RP})}$ reddening at
the position of the star. After this first step, for each star of the field we
selected the three nearest RGB stars, calculated the mean differential ${\rm
A_{G}}$ absorption and the mean differential ${E(G_{BP}-G_{RP})}$ reddening,
and finally subtracted these mean values from its ${G_{BP}-G_{RP}}$ colour and
${G}$ magnitude. We underline the fact that the number of reference stars used
for the reddening correction is a compromise between having a correction
affected as little as possible by photometric random error and the highest
possible spatial resolution.

###  3.3 Spectroscopic selection

Figure 1(d) reveals the BACCHUS [Fe/H] abundance ratios versus the radial
velocity of our eleven potential cluster members compared to field stars with
ASPCAP/APOGEE-2 [Fe/H] determinations, which have been shifted by $+$ 0.11 dex
in order to minimize the systematic differences between ASPCAP/APOGEE-2 and
BACCHUS, as highlighted in Appendix D in Fernández-Trincado et al. (2020d).
First, we note that all of our targets have very similar velocities which are
extreme compared to the field star distribution. This again points to the very
strong likelihood of cluster membership for all of our targets. We find a mean
RV from 15 APOGEE-2 stars of $+$224.9$\pm$ 0.7 km s-1, which is in good
agreement with Simpson (2019), $RV=+227\pm 1$ km s-1, and Villanova et al.
(2019), $RV=+226.8\pm 1.6$. Other apparent sources inside this box are
fore-/background stars with properties do not compatible with the cluster.

The red box highlighted in Figure 1(d) encloses the cluster members within
$\pm 0.15$ dex and $\pm 10$ km s-1 from the nominal mean [Fe/H]$=-1.36$ dex
and RV$=+225.73$ km s-1 of FSR 1758, as determined in this work (see Section
7). Note that one of our stars, 2M17314263$-$3947053, exhibits an [Fe/H] of
$-1.61$, which is $\gtrsim$ 3$\sigma$ more metal poor than the mean
metallicity of the other members. For this particular case, the low-
metallicity effect could be attributed to variability signature in this star
(see, e.g., Muñoz et al., 2018, for instance), but its confirmation is beyond
the scope this work. However, given the similarity of this star in RV and PM
to the kinematics/astrometry of the other stars, we consider that this is
indeed a member with an outlying metallicity value.

Table 1 lists the 2MASS photometry, the differential reddening corrected Gaia
photometry, and the main astrometric and kinematic properties of the observed
FSR 1758 stars.

##  4 Atmospheric parameters

###  4.1 The BACCHUS code

Since the method of deriving stellar parameters and elemental abundances is
identical to that as described in Fernández-Trincado et al. (2019b) and
Fernández-Trincado et al. (2019a), here we provide only a short overview of
it. We adopted the uncalibrated Teff and $\log$ g, and as a first guess the
uncalibrated overall metallicity, as computed by the ASPCAP pipeline.
Secondly, we made a careful inspection of each spectrum with the BACCHUS code
to re-derive the metallicity, broadening parameters, and chemical abundances,
based on a simple line-by-line approach. The abundance determination uses the
BACCHUS code, which relies on the radiative transfer code Turbospectrum
(Alvarez & Plez, 1998; Plez, 2012) and the MARCS model atmosphere grid
(Gustafsson et al., 2008). The abundance of each chemical species is computed
as follows: (a) A synthesis is performed, using the full set of atomic and
molecular line lists described in Shetrone et al. (2015), Hasselquist et al.
(2016), Cunha et al. (2017), and Smith et al. (2021). This set of lists is
internally labeled as linelist.20170418 based on the date of creation in the
format YYYYMMDD. This is used to find the local continuum level via a linear
fit; (b) Cosmic rays and telluric line rejections are performed; (c) The local
S/N is estimated; (d) A series of flux points contributing to a given
absorption line is automatically selected; and (e) Abundances are then derived
by comparing the observed spectrum with a set of convolved synthetic spectra
characterized by different abundances. Then, four different abundance
determination methods are used: (1) line-profile fitting; (2) core line-
intensity comparison; (3) global goodness-of-fit estimate; and (4) equivalent-
width comparison. Each diagnostic yields validation flags. Based on these
flags, a decision tree then rejects or accepts each estimate, keeping the
best-fit abundance. Here, we adopted the $\chi^{2}$ diagnostic as the
abundance because it is the most robust. However, we store the information
from the other diagnostics, including the standard deviation between all four
methods.

As described in Fernández-Trincado et al. (2019b), 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., 2013), and employed to determine the C, N, and O
abundances. In addition, we have adopted the C, N, and O abundances that
satisfy the fitting of all molecular lines consistently. We first derive 16O
abundances from 16OH lines, then derive 12C from 12C16O lines, and 14N from
12C14N lines; the CNO abundances are derived several times initeratively to
minimize the OH, CO, and CN dependences. The resulting elemental abundances
are provided in the next section.

###  4.2 Photometric and Spectroscopic Parameters

We also applied a simple approach of fixing Teff and $\log$ g to values
determined independently of spectroscopy. In order to get Teff and $\log$ g
from photmetry, we compared the differential reddening corrected $G_{0}$ vs.
($G_{BP}-G_{RP}$)0 CMD of Fig. 1 with isochrones obtained from the PARSEC
database (Bressan et al., 2012). We used a preferred (see Section 6) age of
11.6 Gyrs and a global metallicity calculated taking both [Fe/H] and
$\alpha$-enhancement according to the equation of Salaris et al. (1993).
[Fe/H] and $\alpha$-enhancement were obtained from the BACCHUS measurements.
We got the best fit to the RGB using a distance of $\sim$8.6 kpc and an
absorption AV=2.5. After that, we projected horizontally the position of each
star until it intersected the isochrone and assumed Teff and $\log$ g to be
the temperature and gravity of the point of the isochrones that have the same
G magnitude of the star. We underline the fact that for highly reddened
objects like FSR 1758 the absorption correction depends on the spectral energy
distribution of the star, i.e. on its temperature. For this reason we applied
a temperature-dependent absortion correction to the isochrone. Without this
trick, it is not possbile to obtain a proper fit of the RGB, expecially of the
upper and cooler part. The adopted stellar parameters are listed in Table 2.

In Figure 2, we compare the sensitivity to the derived atmospheric parameters,
depending on the species and line in question. When the spectroscopic and
photometry-based atmospheric parameters were adopted, we found discrepancies
in the effective temperature of the order of $\sim 18$ – $360$ K, and surface
gravity differences between $\gtrsim 0.09$ – $0.5$ dex. The larger
uncertainties are found mostly for stars in our sample with a lower S/N
spectrum, and particularly for hotter ($\gtrsim 4500$ K) stars. This issue
does not strongly affect the derived [X/Fe] abundance ratios, but some
chemical species such as carbon, nitrogen, oxygen, and titanium are more
sensitive to these discrepancies in the lower S/N regime. It is important to
note that these discrepancies do not have a large impact on our conclusions.

Table 2: BACCHUS elemental abundances of the observed stars. The median and mean abundances, and 1$\sigma$ error are shown for the whole sample. BACCHUS results by adopting photometric and spectroscopic atmospheric parameters are presented in the 30 first lines of the table, which are compared to ASPCAP DR17 and literature results at the end of the table. All the listed elemental abundances have been scaled to the Solar reference from Asplund et al. (2005). APOGEE-ID | S/N | [M/H] |  Teff |  $\log$ g | $\xi_{t}$ | [C/Fe] | [N/Fe] | [O/Fe] | [Mg/Fe] | [Al/Fe] | [Si/Fe] | [Ca/Fe] | [Ti/Fe] | [Fe/H] | [Ni/Fe]
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  pixel-1 |  | K | cgs |  km s-1 |  |  |  |  |  |  |  |  |  |
Photometry |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2M17314970$-$3956247 | 250 | $-1.31$ | 4159 | 0.53 | 2.69 |  $-$0.59 |  $+$1.36 |  $+$0.51 |  $+$0.15 |  $+$0.54 |  $+$0.25 |  $+$0.34 |  $+$0.34 |  $-$1.32 |  $+$0.02
2M17305424$-$3950496 | 172 | $-1.34$ | 4300 | 0.80 | 2.07 | … |  $+$1.28 |  $+$0.33 |  $+$0.40 |  $+$0.16 |  $+$0.35 |  $+$0.22 |  $+$0.22 |  $-$1.38 |  $+$0.03
2M17310731$-$3953523 | 126 | $-1.39$ | 4506 | 1.18 | 1.71 |  $-$0.33 |  $+$0.96 |  $+$0.77 |  $+$0.46 |  $+$0.20 |  $+$0.32 |  $+$0.31 |  $+$0.45 |  $-$1.22 |  $+$0.01
2M17310187$-$3950066 | 118 | $-1.38$ | 4588 | 1.33 | 1.90 |  $-$0.43 |  $+$1.22 |  $+$0.64 |  $+$0.53 |  $+$0.35 |  $+$0.30 |  $+$0.26 |  $+$0.36 |  $-$1.29 |  $+$0.01
2M17314263$-$3947053 | 110 | $-1.70$ | 4571 | 1.29 | 1.35 |  $-$0.20 |  $+$0.67 |  $+$0.56 |  $+$0.33 |  $-$0.02 |  $+$0.44 |  $+$0.45 |  $-$0.11 |  $-$1.61 |  $-$0.09
2M17312661$-$3951342 | 93 | $-1.41$ | 4675 | 1.49 | 1.79 |  $-$0.19 | … |  $+$0.78 |  $+$0.42 |  $+$0.01 |  $+$0.31 |  $+$0.41 |  $+$0.46 |  $-$1.26 |  $+$0.06
2M17310738$-$3952298 | 82 | $-1.31$ | 4653 | 1.45 | 1.68 |  $-$0.80 |  $+$1.61 |  $+$0.46 |  $+$0.45 |  $+$0.85 |  $+$0.33 |  $+$0.31 |  $+$0.39 |  $-$1.35 |  $+$0.04
2M17311707$-$3950382 | 75 | $-1.34$ | 4742 | 1.62 | 1.81 |  $-$0.12 |  $+$1.10 |  $+$0.68 |  $+$0.50 |  $+$0.25 |  $+$0.29 |  $+$0.36 |  $+$0.42 |  $-$1.29 |  $+$0.19
2M17313165$-$3949120 | 71 | $-1.43$ | 4715 | 1.57 | 1.47 |  $-$0.68 | … | … |  $+$0.20 |  $+$0.41 |  $+$0.43 |  $+$0.27 |  $+$0.28 |  $-$1.45 |  $+$0.13
2M17311230$-$3949493 | 69 | $-1.58$ | 4572 | 1.30 | 1.64 | … |  $+$0.75 |  $+$0.68 |  $+$0.21 |  $-$0.02 |  $+$0.25 |  $+$0.30 |  $+$0.68 |  $-$1.44 |  $+$0.12
2M17310618$-$3943037 | 61 | $-1.54$ | 4839 | 1.81 | 1.61 |  $-$0.00 |  $+$1.04 |  $+$0.80 |  $+$0.40 |  $-$0.02 |  $+$0.30 |  $+$0.39 |  $+$0.25 |  $-$1.35 |  $-$0.04
Median | … | … | … | … | … | $-0.33$ |  $+$1.11 |  $+$0.66 |  $+$0.40 |  $+$0.20 |  $+$0.32 |  $+$0.31 |  $+$0.36 | $-1.35$ |  $+$0.03
pink Mean | … | … | … | … | … |  $-$0.38 |  $+$1.12 |  $+$0.63 |  $+$0.37 |  $+$0.25 |  $+$0.33 |  $+$0.33 |  $+$0.34 |  $-$1.36 |  $+$0.04
$1\sigma$ | … | … | … | … | … | 0.26 | 0.26 | 0.15 | 0.13 | 0.24 | 0.05 | 0.07 | 0.11 | 0.08 | 0.07
Spectroscopy |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
2M17314970$-$3956247 | 250 |  $-$1.31 | 4047 | 0.79 | 2.66 |  $-$0.42 |  $+$1.11 |  $+$0.25 |  $+$0.11 |  $+$0.39 |  $+$0.35 |  $+$0.22 |  $+$0.20 |  $-$1.33 |  $+$0.04
2M17305424$-$3950496 | 172 |  $-$1.34 | 4281 | 1.03 | 1.92 | … |  $+$1.15 |  $+$0.27 |  $+$0.33 |  $+$0.14 |  $+$0.42 |  $+$0.17 |  $+$0.26 |  $-$1.36 |  $+$0.06
2M17310731$-$3953523 | 126 |  $-$1.39 | 4190 | 1.01 | 1.69 |  $-$0.21 |  $+$0.57 |  $+$0.31 |  $+$0.31 |  $+$0.08 |  $+$0.44 |  $+$0.19 |  $+$0.19 |  $-$1.35 |  $+$0.07
2M17310187$-$3950066 | 118 |  $-$1.38 | 4320 | 1.23 | 1.72 |  $-$0.33 |  $+$0.96 |  $+$0.29 |  $+$0.42 |  $+$0.29 |  $+$0.43 |  $+$0.19 |  $+$0.06 |  $-$1.39 |  $+$0.10
2M17314263$-$3947053 | 110 |  $-$1.70 | 4398 | 0.81 | 1.63 |  $-$0.04 |  $+$0.47 |  $+$0.41 |  $+$0.25 |  $-$0.02 |  $+$0.45 |  $+$0.49 |  $-$0.14 |  $-$1.73 |  $-$0.16
2M17312661$-$3951342 | 93 |  $-$1.41 | 4322 | 1.22 | 1.58 |  $-$0.13 | … |  $+$0.32 |  $+$0.29 |  $-$0.09 |  $+$0.44 |  $+$0.36 |  $+$0.22 |  $-$1.41 |  $+$0.13
2M17310738$-$3952298 | 82 |  $-$1.31 | 4609 | 1.56 | 1.62 |  $-$0.62 |  $+$1.43 |  $+$0.32 |  $+$0.33 |  $+$0.79 |  $+$0.38 |  $+$0.27 |  $+$0.38 |  $-$1.36 |  $+$0.12
2M17311707$-$3950382 | 75 |  $-$1.34 | 4522 | 1.52 | 1.83 |  $-$0.07 |  $+$0.96 |  $+$0.48 |  $+$0.36 |  $+$0.25 |  $+$0.40 |  $+$0.33 |  $+$0.39 |  $-$1.38 |  $+$0.19
2M17313165$-$3949120 | 71 |  $-$1.43 | 4740 | 1.29 | 1.47 |  $+$0.21 | … | … |  $+$0.21 |  $+$0.41 |  $+$0.44 |  $+$0.23 |  $+$0.30 |  $-$1.43 |  $+$0.13
2M17311230$-$3949493 | 69 |  $-$1.58 | 4289 | 1.15 | 0.85 | … |  $+$0.62 |  $+$0.20 |  $+$0.31 |  $-$0.13 |  $+$0.37 |  $+$0.20 |  $-$0.05 |  $-$1.50 |  $+$0.10
2M17310618$-$3943037 | 61 |  $-$1.54 | 4476 | 1.32 | 1.49 |  $-$0.13 |  $+$0.77 |  $+$0.34 |  $+$0.33 |  $-$0.08 |  $+$0.36 |  $+$0.37 |  $+$0.05 |  $-$1.52 |  $-$0.06
Median | … | … | … | … | … | $-0.13$ |  $+$0.96 |  $+$0.32 |  $+$0.31 |  $+$0.14 |  $+$0.42 |  $+$0.23 |  $+$0.20 | $-1.39$ |  $+$0.10
pink Mean | … | … | … | … | … |  $-$0.19 | $+$0.89 |  $+$0.32 |  $+$0.29 |  $+$0.18 |  $+$0.41 |  $+$0.27 |  $+$0.17 |  $-$1.43 |  $+$0.07
$1\sigma$ | … | … | … | … | … | 0.17 | 0.28 | 0.06 | 0.05 | 0.24 | 0.04 | 0.09 | 0.16 | 0.08 | 0.07
ASPCAP DR17 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Median | … | … | … | … | … | $-0.41$ |  $+$0.89 |  $+$0.35 |  $+$0.34 |  $+$0.21 |  $+$0.27 |  $+$0.29 |  $+$0.02 | $-1.38$ | $-0.02$
pink Mean | … | … | … | … | … |  $-$0.41 |  $+$0.71 |  $+$0.31 |  $+$0.29 |  $+$0.18 |  $+$0.27 |  $+$0.27 |  $-$0.01 |  $-$1.43 |  $-$0.01
$1\sigma$ | … | … | … | … | … | $0.12$ | 0.34 | 0.11 | 0.07 | 0.29 | 0.04 | 0.05 | 0.15 | 0.09 | 0.05
Villanova et al. (2019) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Median | … | … | … | … | … | … | … |  $+$0.37 |  $+$0.67 |  $+$0.44 | … |  $+$0.37 |  $+$0.33 |  $-$1.49 |  $-$0.10
pink Mean | … | … | … | … | … | … | … |  $+$0.32 |  $+$0.67 |  $+$0.43 | … |  $+$0.35 |  $+$0.31 |  $-$1.53 |  $-$0.11
$1\sigma$ | … | … | … | … | … | … | … | 0.08 | 0.09 | 0.13 | … | 0.08 | 0.06 | 0.06 | 0.05

##  5 Elemental abundances

We limit our discussion to [X/Fe] and [Fe/H] abundance ratios obtained from a
line-by-line inspection of the APOGEE-2 spectra with the BACCHUS pipeline
(Masseron et al., 2016) – independent of ASPCAP, in order to reduce a number
of problems produced by the blind ASPCAP processing in lower-metallicity
cluster stars (see, e.g., Masseron et al., 2019; Mészáros et al., 2020).

Ten chemical species were investigated from the APOGEE-2 spectra, including
the Fe-peak (Fe, Ni), $\alpha$\- (O, Mg, Si, Ca, Ti), light- (C, N), and odd-Z
(Al) elements. Our study provides complementary information on elements not
accessible from Villanova et al. (2019), therefore C, N, and Si are reported
for the first time. The BACCHUS elemental abundances are listed in Table 2
highlighting the mean value of each chemical specie in FSR 1758 from different
methods. Internal errors were derived using sensitivities of the abundances to
variations in the adopted atmospheric parameters, and the internal
uncertainties in each parameter as estimated in Fernández-Trincado et al.
(2020a).

This study now places our chemical understanding of FSR 1758 alongside that of
other well-studied intermediate-metallicity GCs. Overall, the results for FSR
1758 are in agreement with other GCs of similar metallicity for all species,
as shown in Figure 3(a).

###  5.1 The iron-peak elements: Fe, and Ni

We found a mean metallicity [Fe/H] $=-1.36$ and [Fe/H] $=-1.43$ depending on
the adopted atmospheric parameters. This difference in [Fe/H] is smaller that
the internal 1$\sigma$ deviation, 0.08 dex, as listed in Table 2. Furthermore,
the results listed in Table 2 reveal there is no significant metallicity
spread, which confirms that FSR 1758 is consistent with other GCs at similar
metallicity, as seen in Figure 3(a). However, it is important to note that our
mean metallicity is on average $\sim 0.10$–$0.17$ dex higher than the mean
metallicity ([Fe/H]$=-1.53$) determined from optical spectra (Villanova et
al., 2019), and $\sim$0.07 higher than ASPCAP DR17 determination when compared
to our determinations by adopting photometric parameters. These differences
are highlighted in Table 2.

The nature of this discrepancy could be attributed to several different
factors. Unfortunately, there are no common stars between these studies.
However, we list some possible causes. Different reference solar abundances or
atmospheric models could be responsible. Another possible source of systematic
differences could be the result of NLTE and/or 3D effects, which are currently
not modeled when fitting the APOGEE spectra (see, e.g., Masseron et al., 2019;
Mészáros et al., 2020).

As far as the other iron-peak element we studied, nickel (Ni) is on average
slightly over-solar ([Ni/Fe]$=$ $+0.04$ – $+0.07$) with a relatively small
star-to-star [Ni/Fe] spread, $<$0.07 dex. We find a $\langle$[Ni/Fe]$\rangle$
slightly higher ($\gtrsim 0.15$ dex) than [Ni/Fe] abundance ratios determined
in Villanova et al. (2019). The measured [Ni/Fe] abundance ratio in FSR 1758
is at a similar level to that observed in extragalactic environments at
similar metallicity as seen in Figure 4.

Figure 4: Kernel Density Estimation (KDE) models of [X/Fe] versus [Fe/H] for
star in extragalactic environments, taken from the compilation of stars from
Gaia Collaboration et al. (2018b) with ASPCAP DR17 determinations. The black
symbols show our BACCHUS elemental abundances determined from spectroscopic
(dot symbol) and photometric (triangle symbol) atmospheric parameters.

###  5.2 The odd-Z elements: Al

We find median values for [Al/Fe] compatible with other Galactic GCs at
similar metallicity, as shown in Figure 3(b). The sample has an observed star-
to-star spread in [Al/Fe] of $\gtrsim+0.8$ dex, which greatly exceeds the
observational uncertainties. There is at most a weak Al-Mg anti-correlation,
possibly showing the signs of a moderate Mg-Al cycle in FSR 1758, common to
most intermediate to metal-poor GCs in the Galaxy (Masseron et al., 2019;
Mészáros et al., 2020, 2021). Inspection of the [Si/Fe] ratio as a function of
[Al/Fe] for the few stars with reliable Si measurements, as shown in Figure
3(d), reveal that there is not a statistically significant correlation between
Al and Si, as will be expected from the Mg-Al cycle, as Al-rich stars also
present enrichment in Si (see, e.g., Yong et al., 2005; Carretta et al.,
2009). Thus, the observed Si-Al trend in Figure 3(d) explains the apparent
weak Al-Mg anti-correlation seen in Figure 3(a).

Figure 3(b:e) reveals that, by adopting the rough limit of [Al/Fe]$=+0.3$ to
separate the so-called first- and second-generation stars, as suggested in
Mészáros et al. (2020, 2021), there are two apparent groups of stars in FSR
1758. One of these groups, dominated by first-generation stars, exhibits low
Al and (slight) Mg enrichment with intermediate N enrichment ([N/Fe]$\lesssim$
1); while the second group, dominated by second-generation stars, shows high
Al and N enrichment simultaneous with depleted C. Therefore, we conclude that
FSR 1758 does indeed host multiple populations common to virtually all GCs,
and that in addition to the Na-O anti-correlation identified in Villanova et
al. (2019), we also identified the signatures of N-C anti-correlation typical
of GCs at similar metallicity. In particular, the presence of a population
enriched in [Al/Fe] ($>+0.5$) in FSR 1758 rules out the possible scenario of
FSR 1758 being the nucleus of an accreted dwarf galaxy, since large enrichment
in Al has not been observed in dwarf galaxy stellar populations (see, e.g.,
Shetrone et al., 2003; Hasselquist et al., 2017, 2019).

Figure 5: Age estimation of FSR 1758. Left panel: The best isochrone fit in
the Gaia bands CMD using DSED models for likely cluster members within 10
arcmin, where the red and brown lines show the most probable solutions, and
the shadowed regions indicate the solutions within $1\sigma$. Right panel: The
posterior distributions of the indicated quantities.

###  5.3 The light-elements: C and N

Figures 3(c) and (e) reveal a clear N-C anti-correlation, Al-N correlation,
and a large N spread ($>+0.9$ dex). We conclude that the intra-GC abundance
variations reported in Figures 3(c) and (e) are indicative of the presence of
multiple populations in FSR 1758. It is the first time that the presence of a
spread in C and N has been established in FSR 1758.

###  5.4 The $\alpha$-elements: O, Mg, Si, Ca and Ti

Figure 3(a) shows that the $\alpha$ elements in FSR 1758 follow the same trend
as other GCs at similar metallicity, again confirming the genuine GC nature of
FSR 1758, as originally suggested by Villanova et al. (2019). However, as can
be appreciated in Figure 4, the [Ca/Fe] abundance ratio appears to be at the
same level as that seen in extragalatic environments.

Finally, Figure 4 reveals that all the chemical species (except [Ni/Fe] and
[Ca/Fe]) in our sample depart from the typical level of extragalactic
environments, making FSR 1758 unlikely associated with the nucleus of a dwarf
galaxy as previously hipothetised in (Barbá et al., 2019). We conclude that
the measured elemental abundance ratios and anti-correlation/correlation
features support the genuine GC nature of FSR 1758.

##  6 Age

We estimate the age of FSR 1758 through isochrone fitting. To accomplish this,
we employ the SIRIUS code (Souza et al., 2020), which applies a Bayesian
statistical inference based on the Markov Chain Monte Carlo method. For the
isochrone fitting in the RGB region, we adopt the Darthmouth Stellar
Evolutionary Database (DSED: Dotter et al., 2008) with an $\alpha$-enhancement
of $+0.4$ and canonical helium models of Zero-Age Horizontal Branch (ZAHB)
from the Bag of Stellar Tracks and Isochrones (BaSTI: Pietrinferni et al.,
2006).

Since we do not have the entire CMD available, in particular the turn-off
region, we imposed Gaussian distribution priors for the metallicity of
[Fe/H]$\sim-1.36$ (see Section 5), based on the mean determination from this
work, and by assuming an error of $\sim$0.05 dex. Metallicity plays a key role
in the morphology of stellar evolutionary models, mainly in temperature
(color). Lower metalicities tend to higher temperatures (blue region, see fig.
2 in Souza et al. (2020)). Since the evolutionary stage available in our case
is restricted to RGB, we imposed a Gaussian prior in metallicity to limit the
permitted values.

Figure 5 presents the best isochrone fitting of the Gaia EDR3 CMD. Our fit
provides a reasonable solution both in the overplotted isochrone (left panel)
and the posterior distributions of the corner plot (right panel). As the best
determination to represent the distributions, we adopted the median as the
most probable value and the uncertainties calculated from 16th and 84th
percentiles. A close inspection of the Gaia EDR3 CMD reveals that a lower
heliocentric distance of $\sim$8.84${}^{+2.16}_{-2.05}$ kpc better fits the
horizontal and RGB simultaneously, with evident large uncertainties likely due
to false-positive members located in the red side of the CMD, yielding an age
estimate of $\sim 11.6^{+1.25}_{-1.31}$ Gyr for FSR 1758. Suggesting that FSR
1758 is about $\sim$11.6 Gyr old. Clearly, deeper photometry, especially
reaching below the MS turnoff, is required to best estimate the age.

The $1\sigma$ region (the shaded stripes in Figure 5) is mostly affected by
the uncertainties on the distance (vertical) and on the age (horizontal),
given our well-determined metallicity. It is relevant to mention that in the
RGB region of the CMD, an age variation could be seen as a colour displacement
(see Figure 2 of Souza et al., 2020). Also, we want to highlight that our
probable solutions within $1\sigma$ fit well the central part of the CMD,
reinforcing that the age estimation could be a reasonable determination for
FSR 1758.

It is also important to note that our detailed analysis yields an estimated
reddening of E(B-V)$>0.77$, which is 0.4 mag larger than previously estimated
by Barbá et al. (2019), E(B-V)$\sim 0.37$. A close inspection of this field
show that FSR 1758 is very near to the GCs Tonantzintla 2 (Ton 2; Bica et al.,
1996), and NGC 6380 (Ortolani et al., 1998), where the extinction have been
found to be as large as E(B$-$V)$\sim$ 1.17 – 1.24 (see, e.g., Bica et al.,
1996; Ortolani et al., 1998). This discrepancy could be due to the fact that
in Barbá et al. (2019) the 2MASS photometry was employed, which is less
sensitive to extinction. Thus, our Bayesian estimation of E(B-V) reveals that
FSR 1758 lies in a region with higher reddening, E(B$-$V¿0.76), than derived
by Barbá et al. (2019), which may in fact have been erroneous on the distance
estimation of FSR 1758. This value also appears to be overestimated in Barbá
et al. (2019), as confirmed in Figure 5, which shows that a closer distance to
FSR 1758 better fits the primary sequences (horizontal branch and RGB) of the
cluster.

It is also important to mention, that our estimate distance (8.84 kpc) is in
excellent agreement with the mean parallaxes reported by Vasiliev & Baumgardt
(2021), 0.119 $\pm$0.011 mas (296 stars), 8.40 kpc. It is important to note
that independent methods seem to converge reasonably.

##  7 Mass

The precise APOGEE-2 RV information of our 15 sample stars were combined with
other existing RV measurements of FSR 1758 members. In particular, Villanova
et al. (2019) provided $RV$ determinations for nine additional cluster members
from optical high-resolution MIKE spectra, while Simpson (2019) reported RVs
for two additional cluster stars with Gaia radial velocities. This yields a
unique collection of 26 likely members of FSR 1758 with RV information. With
this large sample in hand, we report a mean radial velocity of FSR 1758 of
$+225.73\pm 0.69$ km s-1 with a velocity dispersion of 3.51$\pm$0.49 km s-1,
which is in good agreement with the mean and dispersion reported by Villanova
et al. (2019), $+226.8\pm 1.6$ km s-1 and $4.9\pm 1.2$ km s-1.

With this relatively large sample of stars with RV information, we match the
line-of-sight dispersion profiles to the updated version of N-body simulations
(private communication with H. Baumgardt) of FSR 1758 from Baumgardt & Hilker
(2018); Baumgardt et al. (2019), as shown in Figure 6, and thus determine the
most likely mass of the cluster from kinematic constraints.

We adopted two radial bins (with bin centers of 2′and 8′), chosen to ensure
that at least twelve stars were in each bin; resulting in the two points shown
in 6. We find $\sigma_{0}\sim 4.3\pm 0.5$ km s-1. This yields a present-day
estimated mass of $\sim 2.9\pm 0.6\times$105 M⊙, which suggests that FSR 1758
is as massive as NGC 6752 ($\sim 2.32\pm 0.003\times 10^{5}$ M⊙) (Baumgardt &
Hilker, 2018; Baumgardt et al., 2019).

Figure 6: Line-of-sight velocity dispersion versus radius for our target
cluster stars from APOGEE-2 plus Villanova et al. (2019) and Simpson (2019)
data set (blue dots). The error bars are refered as $\sigma_{RV}/\sqrt{2\times
N}$. The prediction of the best-fitting updated (private communication) N-body
model from (Baumgardt & Hilker, 2018) and Baumgardt et al. (2019) is shown as
a solid-grey line, and the light-grey shaded region indicates the 1$\sigma$
uncertainty from the fit.

##  8 Orbital parameters of FSR 1758

The orbit of FSR 1758 has been extensively discussed in Villanova et al.
(2019), Simpson (2019), and Yeh et al. (2020), using different Galactic
models. In general, the orbital solutions determined in those studies are
consistent, concluding that FSR 1758 is on a highly eccentric and retrograde
orbit, with apo-Galacticon $<$20 kpc and with inner incursions close to the
bulge region.

###  8.1 The Galactic model

Here, we re-visit the orbit of FSR 1758 by adopting the new state-of-the art
orbital integration model GravPot16222https://gravpot.utinam.cnrs.fr with a
”boxy/peanut” bar structure in the bulge region along with other composite
stellar components (Fernández-Trincado et al., 2020e), which best fit the
known structural and dynamical parameters of our Galaxy, to the best of our
knowledge. It is important to note that Villanova et al. (2019) employed the
GravPot16 model from the web service (https://gravpot.utinam.cnrs.fr) with a
simple ”prolate” bar structure.

The structural parameters of our bar model (mass, present-day orientation and
pattern speed) are 1.1$\times$1010 M⊙ (Fernández-Trincado et al., 2020e), 20∘
(Rodriguez-Fernandez & Combes, 2008; Fernández-Trincado et al., 2020e), and 41
km s-1 kpc (Sanders et al., 2019), respectively, consistent with observational
estimates. The bar scale lengths are $x_{0}=$1.46 kpc, $y_{0}=$ 0.49 kpc, and
$z_{0}=$0.39 kpc, and the middle region ends at the effective semimajor axis
of the bar $Rc=3.28$ kpc , whose density profile is exactly the same as in
Robin et al. (2012).

For reference, the Galactic convention adopted by this work is: $X-$axis
oriented toward $l=$ 0∘ and $b=$ 0∘, $Y-$axis is oriented toward $l$ = 90∘ and
$b=$0∘, and the disc rotates toward $l=$ 90∘; the velocity is also oriented in
these directions. Following this convention, the Sun’s orbital velocity
vectors are [U⊙,V⊙,W⊙] = [$11.1$, $12.24$, 7.25] km s-1 (Brunthaler et al.,
2011). The model has been rescaled to the Sun’s galactocentric distance, 8.3
kpc, and the local rotation velocity of $244.5$ km s-1 (Sofue, 2015).

###  8.2 Orbital Elements

For the computation of Galactic orbits, we have employed a simple Monte Carlo
approach and the Runge-Kutta algorithm of seventh to eight order, elaborated
by Fehlberg (1968). As input parameters we adopted the following observables:
(1) RV $=$ 225.73 km s-1 (see Section 7); absolute proper motions
$\mu_{\alpha}\cos(\delta)=-2.85$ mas yr-1 and $\mu_{\delta}=2.47$ mas yr-1
(see Section 3); and a range of heliocentric distances from $8.84$ kpc (as
estimated from our isochrone fits in Section 6) and $11.5\pm 1$ kpc from Barbá
et al. (2019). The uncertainties in the input data (e.g. $\alpha$, $\delta$,
distance, proper motions and RV errors) were randomly propagated as 1$\sigma$
variation in a Gaussian Monte Carlo resampling. Thus, we ran ten thousand
orbits, computed backwards in time during 3 Gyr. The median value of the
orbital elements were found for these 10,000 realizations, with uncertainty
ranges given by the 16th and 84th percentile. The resulting orbital elements
are listed in Table 3. It is important to note that we list the minimal and
maximum value of the z-component of the angular momentum in the inertial
frame, since this quantity is not conserved in a model with non-axiymmetric
structures like GravPot16. In the case of FSR 1758, Lz,min and Lz,max are
close to each other within the uncertainties, thus confirming the genuine
retrograde nature of FSR 1758, as shown on the top-right panel in Figure 7.

Overall, our orbital study based on a different Galactic model configuration
than previous studies confirms that FSR 1758 lies in an radial, eccentric, and
retrograde halo-like orbit, which circulates across the ”bulge /bar” region
with relatively high vertical excursions from the Galactic plane, —Z—${}_{\rm
max}\lesssim$ 8 kpc, depending on the adopted heliocentric distance as listed
in Table 3.

As noted above, there are several studies of FSR 1758 that have attempted to
unveil its origin. For instance, Barbá et al. (2019), Myeong et al. (2019),
and Massari et al. (2019) proposed that it is likely part of the Sequoia dwarf
galaxy, while Simpson (2019) suggested that FSR 1758 is an intruder from the
halo into the inner Galaxy. More recent work by Villanova et al. (2019) and
Yeh et al. (2020) suggest that the chemical enrichment, high eccentricity, and
retrograde orbital configuration of FSR 1758 is not uncommon among other halo
GCs, thus favoring a possible in situ origin.

To alleviate this tension, we examine the orbital properties of FSR 1758
within the GravPot16$+$”boxy/peanut”-bar computational environment. Figures 7
and Figure 8 provide an ”Orbital Energy” map that identifies the main
structures of GCs with an accreted and in situ origin, respectively. This
diagram provides one of the best dynamical representations of the conserved
motion quantities in a non-axisymmetric MW model. These include the plot of
the characteristic orbital energy, (Emax\+ Emin)/2, versus the orbital Jacobi
constant (EJ), as envisioned by Moreno et al. (2015), with Emax, Emin the
maximum and minimum energies per unit mass along each orbit, and computed with
respect to the Galactic inertial frame, while EJ has a constant value in the
non-inertial reference frame where the bar is at rest.

###  8.3 Comparison of the orbital elements of FSR 1758 to other globular
clusters

We computed the above quantities for the recent compilation of GCs listed in
Vasiliev & Baumgardt (2021), adopting the same Monte Carlo approach as
described above. Further, we adopted the same GC classification as presented
in Massari et al. (2019) to identify the main structures in our maps, and
computed the Kernel Density Estimation (KDE) models for each of the GCs groups
belonging to the Main-Disc, Main-Bulge, High-Energy, Low-Energy, Sequoia,
Gaia-Enceladus-Sausage, Helmi Stream, and Saggitarius population. The
resulting KDE models and the their corresponding structure are presented in
Figures 7 and 8. This complementary analysis provides us with important
insight into the origin of FSR 1758.

Figures 7 and 8 reveal that FSR 1758 lies in the area of this diagram mostly
dominated by populations with retrograde orbits. In this diagram, FSR 1758 is
located on the boundary of four main structures, the Gaia-Enceladus-Sausage,
Helmi Stream, and Sequoia accretion event, and the structure dominated by
High-Energy GCs. However, a close inspection of other orbital elements (the
orbital eccentricity, the vertical excursions above the Galactic plane,
$Z_{max}$, and the apo-/peri-galactic distance), as presented in Figures 7 and
8, reveal some significant differences. Figure 8 shows that the orbital
elements of the FSR 1758 barely overlap the tail of the distribution of the
High-Energy structure, which is mostly dominated by highly eccentric and
radial orbits with extremely large vertical excursions above the Galactic
plane, making less probable that FSR 1758 belongs to this structure.

Figure 7 shows that the Sagittarius structure is dominated by GCs in highly
eccentric and radial orbits with $Z_{max}\gtrsim 10$ kpc, barely overlapped by
the orbit of FSR 1758 and far away in the “Orbital Energy” map. The same
figure reveals that, depending on the adopted heliocentric distance, FSR 1758
departs relatively far away in the “Orbital Energy” map from the Sequoia
structure, and is beyond the tail in the eccentricity–$Z_{plane}$, and barely
overlapping the tail of other orbital elements. In other words, GCs in the
Sequoia structure are dominated by mostly highly eccentric orbits with large
vertical excursions from the Galactic plane ($\gtrsim 20$ kpc), and also
reaching large apogalactocentric distances ($>30$ kpc), making FSR 1758 a low-
probability candidate for association with the Sequoia accretion event. This
is also supported by the very old age estimate provided in Section 6.

In addition, Figure 7 reveals that the Gaia-Enceladus-Sausage structure is
more confined to the Galactic plane ($<20$ kpc), with apogalactocentric
distances within $<30$ kpc and eccentricities as low as $e\gtrsim 0.55$).
Thus, FSR 1758 exhibits orbital properties overlapping fairly well to all the
orbital elements of the Gaia-Enceladus-Sausage structure. Therefore, our
analysis favors a possible link of FSR 1758 with the Gaia-Enceladus-Sausage
accretion event rather than to the Sequoia structure or any possible in situ
origin. We conclude that it is possible that FSR 1758 has likely been
dynamically ejected into the inner halo of the MW from the Gaia-Enceladus-
Sausage dwarf galaxy.

Table 3: Main orbital properties of FSR 1758 $d_{\odot}=$ 8.84 kpc (This work) |
---|---
Perigalacticon | 1.53$\pm$0.72 kpc
Apogalacticon | 7.11$\pm$ 1.24 kpc
eccentricity | 0.64$\pm$0.10 kpc
—Z—max | 2.71$\pm$0.82 kpc
Lz,min | 0.51$\pm$0.26 $\times{}10^{3}$ km s-1 kpc
Lz,max | 0.62$\pm$0.17 $\times{}10^{3}$ km s-1 kpc
EJ |  $-$1.76$\pm$0.22 $\times{}10^{5}$ km2 s2
Emin |  $-$2.09$\pm$0.16 $\times{}10^{5}$ km2 s2
Emax |  $-$1.88$\pm$0.10$\times{}10^{5}$ km2 s2
$d_{\odot}=$11.5 kpc (Barbá et al., 2019) |
Perigalacticon | 3.45$\pm$0.6 kpc
Apogalacticon | 14.2$\pm$ 4.7 kpc
eccentricity | 0.61$\pm$0.04 kpc
—Z—max | 8.1$\pm$3.2 kpc
Lz,min | 0.12$\pm$0.03 $\times{}10^{3}$ km s-1 kpc
Lz,max | 0.13$\pm$0.03 $\times{}10^{3}$ km s-1 kpc
EJ |  $-$1.04$\pm$0.28 $\times{}10^{5}$ km2 s2
Emin |  $-$1.59$\pm$0.18 $\times{}10^{5}$ km2 s2
Emax |  $-$1.56$\pm$0.14 $\times{}10^{5}$ km2 s2
Figure 7: Kernel Density Estimation (KDE) models of the characteristic orbital
energy ((Emax \+ Emin)/2), the orbital Jacobi energy (EJ), orbital pericenter
and apocenter, orbital eccentricity, maximum vertical height above the
Galactic plane for GCs with an accreted origin (e.g., Massari et al., 2019).
FSR 1758 is highlighted with black dot symbols, by considering a heliocentric
distance of 8.84 kpc (large symbol), and 11.5 kpc (small symbol) The top-right
panel show the minimal and maximum value of the z-component of the angular
momentum in the inertial frame, and indicates the regions dominated by
prograde and retrograde orbits, and those dominated by orbits that change
their sense of motion from prograde to retrograde (P-R). Figure 8: Same as
Figure 7, but now considering GCs with an in situ origin (Massari et al.,
2019).

##  9 Summary and concluding remarks

We have performed the first high-resolution (R$\sim$22,000) spectral analysis
in the H-band of the intriguing GC FSR 1758, which was recently discovered
toward the bulge region. We used APOGEE data from the CAPOS survey of fifteen
RGB stars which are all very likely members. We also provided a dynamical
study of the cluster by adopting the state-of-the-art GravPot16 Galactic model
with a ”boxy/peanut” bar structure, and employing newly revised estimation of
its parameters, inlcuding PMs, RV and distance.

We found a mean metallicity of [Fe/H]$=-1.36$ and [Fe/H]$=-1.43$, by adopting
photometric and spectroscopic atmospheric parameters for FSR 1758,
respectively. This value is somewhat more metal rich than previously reported
(see, e.g., Barbá et al., 2019; Villanova et al., 2019), with no evidence for
an intrinsic metallicity spread. The mean radial velocity of the cluster,
determined from a large sample (26 stars), was found to be $+225.73\pm 0.69$
km s-1 with a velocity dispersion of 3.51 km s-1, and the mean PMs in Gaia
EDR3 are found to be $\mu_{\alpha}\cos(\delta)=-2.85\pm 0.05$ mas yr-1 and
$\mu_{\delta}=2.47\pm 0.05$ mas yr-1. These values are in good agreement with
the literature within the uncertainties.

We derived detailed abundances for 10 species, several of which were not
studied previously. Thus, C, N, and Si abundances are reported for the first
time. We found evidence for a C-N anti-correlation and N-Al correlation of the
sample analyzed. These signatures of multiple populations support the findings
from the Na-O anti-correlation found by Villanova et al. (2019) that this GC
displays this phenomenon. All of the evidence, including multiple populations,
no metallicity spread, relatively high metallicity and small velocity
dispersion, clearly indicate that FSR 1758 is a bonafide GC, and not the
remnant nucleus of a dwarf galaxy, as originally speculated by Barbá et al.
(2019). Note that the suspected tidal tails they noted are now known to be
simply outliers in the field star PM distribution. However, this object
remains as an outlier in the size vs. Galactocentric distance plot, being very
large for a GC so near the center, undoubtedly stemming from the fact that its
orbit only brings it this close on occasion.

The SIRIUS code is applied to provide a self-consistent age of FSR 1758 by
using a statistical isochrone fitting to the Gaia band system. We find that
FSR 1758 is as old as 11.6${}^{+1.25}_{-1.31}$ Gyr.

Additionally, the new dataset was combined with other existing RV
measurements, allowing a better constraint on the predictions of the N-body
line-of-sight velocity dispersion of FSR 1758. This yields an estimated mass
of $\sim$2.9$\pm$0.6 $\times$ 105 M⊙, which make FSR 1758 as massive as NGC
6752. We also confirm the prevalence of a small velocity dispersion ($3.51\pm
0.49$ km s-1), which is typical for a GC.

The orbital properties of FSR 1758, combined with its chemical properties and
old age estimation, leads to the conclusion that FSR 1758 matches well with
the physical properties seen in a good fraction of GCs associated with the
Gaia-Enceladus-Sausage accretion event, rather than those associated with the
Sequoia event. We favor the association of FSR 1758 with the Gaia-Enceladus-
Sausage accretion event, which is also consistent with the age-metallicity
relation provided by Massari et al. (2019). Thus, the ”Sequoia” GC is not in
fact a member of the dwarf galaxy progenitor whose name it inspired (Myeong et
al., 2019; Koppelman et al., 2019).

###### Acknowledgements.

The author is grateful for the enlightening feedback from the anonymous
referee. We warmly thank Holger Baumgardt for providing his more recent
numerical N-body modeling of the line-of-sight velocity dispersion of FSR
1758. M. I. R.-C. was supported by VRIIP, UA through ”Concurso de Asistentes
de Investigación” funded by ”Ministerio de Educación Chile” No. ANT1855 and
ANT1856 projects and gratefully acknowledges support from the Graduate School
of the Universidad de Antofagasta for their support with ”Beca de Excelencia”
(Scholarship of Excellence). D.G. gratefully acknowledges support from the
Chilean Centro de Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL
grant AFB-170002. 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). D.G. and
D.M. gratefully acknowledge support from the Chilean Centro de Excelencia en
Astrofísica y Tecnologías Afines (CATA) BASAL grant AFB-170002. D.M. is also
supported by Fondecyt 1170121. T.C.B. acknowledges partial support from grant
PHY 14-30152, Physics Frontier Center/JINA Center for the Evolution of the
Elements (JINA-CEE), awarded by the US National Science Foundation. SOS
acknowledges the FAPESP PhD fellowship 2018/22044-3. SOS and APV acknowledge
the DGAPA-PAPIIT grant IG100319. BB acknowledges grants from FAPESP, CNPq and
CAPES - Financial code 001. J.A.-G. acknowledges support from Fondecyt Regular
1201490 and from ANID – Millennium Science Initiative Program – ICN12_009
awarded to the Millennium Institute of Astrophysics MAS. L.H. gratefully
acknowledges support provided by National Agency for Research and Development
(ANID)/CONICYT-PFCHA/DOCTORADO NACIONAL/2017-21171231.
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.
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
web site 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.

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