11institutetext:  Institut Utinam, CNRS UMR 6213, Université Bourgogne-
Franche-Comté, OSU THETA Franche-Comté, Observatoire de Besançon,
BP 1615, 25010 Besançon Cedex, France 22institutetext: Instituto de Astronomía
y Ciencias Planetarias, Universidad de Atacama, Copayapu 485, Copiapó, Chile
33institutetext: Department of Physics and JINA Center for the Evolution of
the Elements, University of Notre Dame, Notre Dame, IN 46556, USA
44institutetext: Depto. de Cs. Físicas, Facultad de Ciencias Exactas,
Universidad Andrés Bello, Av. Fernández Concha 700, Las Condes, Santiago,
Chile 55institutetext: Vatican Observatory, V00120 Vatican City State, Italy
66institutetext: Instituto de Astronomía, Universidad Nacional Autónoma de
México, A.P. 70-264, 04510, Ciudad de México, Mexico 77institutetext: NSF’s
National Optical-Infrared Astronomy Research Laboratory, Tucson, AZ 85719, USA
88institutetext: Korea Astronomy and Space Science Institute, 776 Daedeokdae-
ro, Yuseong-gu, Daejeon 34055, Republic of Korea 99institutetext: Departamento
de Astronomí a, Casilla 160-C, Universidad de Concepción, Concepción, Chile
1010institutetext: Departamento de Astronomía, Universidad de La Serena,
1700000 La Serena, Chile 1111institutetext: Instituto de Investigación
Multidisciplinario en Ciencia y Tecnología, Universidad de La Serena.
Benavente 980, La Serena, Chile 1212institutetext: Universidade de São Paulo,
IAG, Rua do Matão 1226, Cidade Universitária, São Paulo 05508-900, Brazil
1313institutetext: Instituto de Astronomía, Universidad Nacional Autónoma de
México, Apdo. Postal 106, 22800 Ensenada, B.C., México 1414institutetext:
Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482
Potsdam, Germany 1515institutetext: Laboratório Interinstitucional de
e-Astronomia - LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ -
20921-400, Brazil 1616institutetext: School of Physics and Astronomy, Sun Yat-
sen University, Zhuhai 519082, China 1717institutetext: Centro de Astronomía
(CITEVA), Universidad de Antofagasta, Av. Angamos 601, Antofagasta, Chile
1818institutetext: Millennium Institute of Astrophysics, Santiago, Chile
1919institutetext: Instituto Interdisciplinario de Ciencias Básicas (ICB),
CONICET-UNCUYO, Padre J. Contreras 1300, M5502JMA, Mendoza, Argentina
2020institutetext: Consejo Nacional de Investigaciones Científicas y Técnicas
(CONICET), Godoy Cruz 2290, C1425FQB, Buenos Aires, Argentina
2121institutetext: Universidad Nacional de Córdoba, Observatorio Astronómico
de Córdoba, Laprida 854, 5000 Córdoba, Argentina 2222institutetext: Consejo
Nacional de Investigaciones Científicas y Técnicas (CONICET), Godoy Cruz 2290,
Ciudad Autónoma de Buenos Aires, Argentina 2323institutetext: Universidade
Federal do Rio Grande do Sul, Instituto de Física, Av. Bento Gonçalves 9500,
Porto Alegre, RS, Brazil 2424institutetext: Instituto de Astronomía,
Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile
2525institutetext: Departamento de Astronomía, Universidad de Chile, Camino
del Observatorio 1515, Las Condes, Santiago, Chile 2626institutetext: Visiting
astronomer, Cerro Tololo Inter-American Observatory, National Optical
Astronomy Observatory, which is operated by the Association of Universities
for Research in Astronomy (AURA) under a cooperative agreement with the
National Science Foundation, Chile 2727institutetext: Department of Physics
and Astrophysics, University of Delhi, Delhi-110007, India 2828institutetext:
European Southern Observatory, Alonso de Córdova 3107, 7630000 Vitacura,
Santiago, Chile 2929institutetext: University of Nariño Observatory,
Universidad de Nariño, Sede VIIS, Avenida Panamericana, Pasto, Nariño,
Colombia 3030institutetext: Departamento de Física de la Universidad de
Nariño, Torobajo Calle 18 Carrera 50, Pasto, Nariño, Colombia

# APOGEE discovery of a chemically atypical star disrupted from NGC 6723 and
captured by the Milky Way bulge

José G. Fernández-Trincado To whom correspondence should be addressed; E-mail:
<EMAIL_ADDRESS>and/or<EMAIL_ADDRESS>Timothy C. Beers 33
Dante Minniti 4455 Leticia Carigi 66 Vinicius M. Placco 77 Sang-Hyun Chun 88
Richard R. Lane 11 Doug Geisler 9910101111 Sandro Villanova 99 Stefano O.
Souza 1212 Beatriz Barbuy 1212 Angeles Pérez-Villegas 1313 Cristina Chiappini
14141515 Anna. B. A. Queiroz 1414 Baitian Tang 1616 Javier Alonso-García
17171818 Andrés E. Piatti 19192020 Tali Palma 21212222 Alan Alves-Brito 2323
Christian Moni Bidin 2424 Alexandre Roman-Lopes 1010 Ricardo R. Muñoz 25252626
Harinder P. Singh 2727 Richa Kundu 27272828 Leonardo Chaves-Velasquez 29293030
María Romero-Colmenares 1717 Penelope Longa-Peña 1717 Mario Soto and Katherine
Vieira 1111

(Received: XX/XX/XXXX; Accepted: XX/XX/XXXX)

The central (‘bulge’) region of the Milky Way is teeming with a significant
fraction of mildly metal-deficient stars with atmospheres that are strongly
enriched in cyanogen (12C14N). Some of these objects, which are also known as
nitrogen-enhanced stars, are hypothesised to be relics of the ancient assembly
history of the Milky Way. Although the chemical similarity of nitrogen-
enhanced stars to the unique chemical patterns observed in globular clusters
has been observed, a direct connection between field stars and globular
clusters has not yet been proven. In this work, we report on high-resolution,
near-infrared spectroscopic observations of the bulge globular cluster NGC
6723, and the serendipitous discovery of a star, 2M18594405$-$3651518, located
outside the cluster (near the tidal radius) but moving on a similar orbit,
providing the first clear piece of evidence of a star that was very likely
once a cluster member and has recently been ejected. Its nitrogen abundance
ratio ([N/Fe]$\gtrsim+0.94$) is well above the typical Galactic field-star
levels, and it exhibits noticeable enrichment in the heavy $s$-process
elements (Ce, Nd, and Yb), along with moderate carbon enrichment; all
characteristics are known examples in globular clusters. This result suggests
that some of the nitrogen-enhanced stars in the bulge likely originated from
the tidal disruption of globular clusters.

###### Key Words.:

stars: abundances – stars: chemically peculiar – Galaxy: globular clusters:
NGC 6723 – techniques: spectroscopic

##  1 Introduction

Figure 1: Properties of the extra-tidal star compared with likely members of
NGC 6723. Panel (a): The metallicity – radial velocity plane for stars in the
APOGEE-2 catalogue in the region of NGC 6723 (green triangles). The black open
circles are potential members of NGC 6723; sizes reflect their ${\rm V_{o}}$
magnitudes, with decreasing size for fainter magnitudes. The pink line and
shaded region indicate the $\langle$[Fe/H]$\rangle\pm\sigma_{\rm[Fe/H]}$ of
the extra-tidal star. The black dotted lines indicate the nominal [Fe/H] and
radial velocity of NGC 6723 from Harris (1996, 2010 edition). The red unfilled
diamonds refer to probable members analysed in the literature (Crestani et al.
2019). The blue rectangle indicates the region adopted to choose potential
cluster members, based on radial velocity and metallicity (see Section 2).
Panel (b): Positions for stars in the APOGEE-2 and Gaia EDR3 (grey dots)
catalogues in the region of NGC 6723. The magenta cross symbol indicates the
Gaia astrometric uncertainty. The big red and shadow circumference show the
cluster tidal radius ($r_{t}=9.14\pm 0.49$ ′) of NGC 6723 determined in this
work from HST $+$ Gaia EDR3 data set (see Section 8). The orbital paths of the
cluster (black line) and the extra-tidal star (magenta line) are shown, along
with the proper motion vectors (black arrow) of the cluster from Baumgardt et
al. (2019), and the extra-tidal star (magenta arrow); their lengths (scaled up
for visibility) and directions are essentially identical. Panel (c): Proper-
motion plane for the selected candidates. Panels (d) and (e): Vo versus (B-V)o
and 2MASS Ho versus (J-Ks)o Colour-Magnitude Diagram (CMD) centred on NGC
6723, showing all the stars within the cluster tidal radius, and the probable
cluster members (cyan symbols) within a 2$\sigma$ deviation from the best
isochrone fitting (Souza et al. 2020; Oliveira et al. 2020). The largest open
circle in all panels indicate the extra-tidal star.

The great majority of stars in the halo of the Milky Way (MW) have elemental-
abundance ratios, spanning a wide range of metallicities
($-7.5<{\rm[Fe/H]}<0.0$) that are similar to one another and overall track the
general level of metallicity. However, there are a number of important
exceptions, including carbon-enhanced ([C/Fe] $\gtrsim+0.7$) metal-poor (CEMP)
stars, in particular at very low metallicities ([Fe/H] $<-2.0$)–(Frebel et al.
2006; Lee et al. 2013; Placco et al. 2014, 2018; Yoon et al. 2019) and the
class of CH stars (with $-2.0<$[Fe/H]$<-0.2$)–(Karinkuzhi & Goswami 2014), as
well as the carbon-deficient stars (with [C/Fe]$\lesssim+0.5$,
$-2<{\rm[Fe/H]}<+0.1$) with light-element abundances (e.g. N, Al, and Si)
whose chemical compositions mimic the abundance patterns observed in some of
the stars in Galactic (and extragalactic) globular cluster (GC) populations
(e.g. Fernández-Trincado et al. 2017; Schiavon et al. 2017b; Bekki 2019; Hanke
et al. 2020; Mészáros et al. 2020; Fernández-Trincado et al. 2020b).

Multiple potentially pieces of evidence support the origin of CEMP stars in
low-mass galaxies that have been accreted by the MW (Yoon et al. 2019), either
due to mass-transfer binaries (CEMP-$s$ stars, Beers & Christlieb 2005) or
from natal gas polluted by high-mass stars in the early Galaxy (CEMP-no stars,
Beers & Christlieb 2005). However, the mildly metal-poor giants with stellar
atmospheres that are strongly enriched in 12C14N (in cases with available
data, with distinctive Al and Si abundances as well), are referred to as
nitrogen-enhanced (N-rich) stars (Fernández-Trincado et al. 2016a; Fernández-
Trincado et al. 2017; Schiavon et al. 2017b; Fernández-Trincado et al. 2019b)
or NRS (Bekki 2019), and defined in Johnson et al. (2007) as nitrogen-enriched
metal-poor (NEMP) stars, which are CEMP stars with [C/N]$<-0.5$ and
[N/Fe]$>+0.5$. They have resisted a unifying explanation of the
nucleosynthetic processes responsible for their abundance anomalies. These
stars share chemical-abundance patterns that are hypothesised to be associated
with the so-called second-generation stars in GCs (see e.g. Schiavon et al.
2017a; Fernández-Trincado et al. 2019d, 2020e; Mészáros et al. 2020), with
only a handful of exceptions, such as the binary hypothesis (see e.g.
Fernández-Trincado et al. 2019c). There are also a handful of known early
asymptotic giant branch (early-AGB) stars in GCs (see, e.g. Mészáros et al.
2020), which exhibit a nitrogen enrichment similar to that of the N-rich
stars, but with a modest enrichment in carbon ([C/Fe]$>+0.15$.

Recent studies (Bekki 2019; Fernández-Trincado et al. 2020d, c, a) have found
that a significant fraction ($\sim 66$%) of the known metal-poor N-rich stars
in the Galactic field currently reside in the inner MW. However, the site and
process for the formation of these stars remain as long-standing questions
(Bekki 2019). The metal-poor N-rich stars stand out among the variety of
metal-poor stars in our own MW, as they are uniquely suited to the application
of chemical tagging, with direct bearing on the origin of the in situ
structure of the inner halo and bulge. As such, these stars play a crucial
role in reconstructing the formation and evolutionary history of the MW.

NGC 6723 is an old ($\gtrsim$12.50 Gyr; Dotter et al. 2010; Oliveira et al.
2020), massive (1.72$\times 10^{5}$ M⊙: Baumgardt et al. 2019) GC situated in
the bulge region ($d_{\odot}\sim$8.3 kpc), with an orbit constraining it to
lie $\lesssim 2.85$ kpc from the Galactic Centre (Baumgardt et al. 2019). It
is currently located at a position where the foreground interstellar reddening
is low, E(B-V) $\sim 0.063$ (Lee et al. 2014), making it an excellent target
to identify and study the family of N-rich stars in the bulge region of the
MW, in order to probe for a linkage between GC environments and field stars
with nitrogen over-abundances.

The Apache Point Observatory Galactic Evolution Experiment (APOGEE-2, Majewski
et al. 2017) is a cornerstone mission of the Sloan Digital Sky Survey IV
(SDSS-IV, Blanton et al. 2017), which has been designed primarily to
investigate the chemical history of the MW. APOGEE and APOGEE-2 have delivered
an exquisite data set by combining high-resolution near-IR spectroscopic
observations from the Sloan 2.5m telescope at Apache Point Observatory (APO)
and the Irénée du Pont 2.5m telescope at Las Campanas Observatory (LCO): the
largest and most precise census of more than 24 chemical species for hundreds
of thousands of stars throughout the MW. These surveys have revealed numerous
giant stars with light-element abundances that deviate from the general
patterns, and are at odds with current chemical-evolution models. Their
origins have remained obscure, due to limitations on the numbers of such stars
and the precision of the previously available data.

In this work, we take advantage of the APOGEE-2 data set to alleviate the lack
of data towards the Galactic Bulge. We report on the discovery of an extra-
tidal star candidate in the vicinity of a GC (NGC 6723) toward the bulge
region, with nitrogen over-abundances well above that of normal Galactic field
stars, and with a modest carbon enrichment. The other properties of this star,
including metallicity and kinematics, strongly suggest it was once a cluster
member. This is the first demonstration of a direct link between a mildly
metal-poor N-rich field star with a modest carbon enrichment and a parent GC
in the bulge region of the MW.

##  2 Data and sample selection

We present a spectroscopic study of the bulge GC NGC 6723, and its surrounding
regions, based on high-resolution ($R\sim$ 22,000) near-infrared H-band
($\lambda\sim$ 15,145 Å to 16,960 Å, vacuum wavelengths) spectra taken as part
of the APOGEE-2 survey (Majewski et al. 2017; Zasowski et al. 2017), included
within the sixteenth SDSS-IV (Blanton et al. 2017) data release (DR16, Ahumada
et al. 2020). The observations were taken at the twin APOGEE-2 spectrographs
mounted on the 2.5m Sloan Foundation telescope (Gunn et al. 2006) at the
Apache Point Observatory in New Mexico, and on the 2.5m Irénée du Pont
telescope (Bowen & Vaughan 1973) at Las Campanas Observatory in Chile. We
refer the reader to the APOGEE-2 technical papers for further details
regarding the data reduction pipeline for APOGEE-2 (see, e.g. Nidever et al.
2015; García Pérez et al. 2016; Holtzman et al. 2018) .

We have analysed the available APOGEE-2 spectra towards the bulge GC NGC 6723,
included in the APOGEE-2 fields 000-17-C and 359-17-C, which contain reliable
spectral information for 526 stars. Probable cluster members were selected
based on the nominal radial velocity (RV) of the cluster (with a velocity
difference no larger than 15 km s-1), and metallicity within 0.25 dex from the
value reported in Harris (1996, 2010 edition). The initial search was made
within the blue box highlighted in panel (a) of Figure 1, and limited to
spectra with a SNR $>$ 60 pixel-1.

We decided to adopt the uncalibrated ASPCAP [M/H] scale, which tracks all
metals relative to the Sun (listed in Table 1), as a first guess to the
stellar metallicity. This gives the overall metallicity of the stars, as it is
derived by fitting the entire wavelength region covered by the APOGEE-2
spectrographs. Finally, we use Fe I lines to measure the [Fe/H].

The final sample contains eight potential members of NGC 6723. We find that
seven of these stars are located inside the tidal radius, as shown in panel
(b) of Figure 1. There is one star, 2M18594405$-$3651518 (referred to here as
the extra-tidal star), which has a RV and proper motions (see panels (a) and
(c) of Figure 1), and an orbital path similar to that of the NGC 6723 members.
These very probable members lie in the upper part of the prominent red giant
branch (RGB) in the extinction-corrected 2MASS and Vo versus (B-V)o Colour-
Magnitude Diagrams (CMDs), as displayed in panels (d) and (e) of Figure 1, and
have Gaia proper motions similar to the nominal value for the cluster.

Following the same methodology and techniques described in several APOGEE
papers (Fernández-Trincado et al. 2016a; Hawkins et al. 2016; Fernández-
Trincado et al. 2017; Fernández-Trincado et al. 2019a, c, b, d, 2020e), we
employed the BACCHUS software (Masseron et al. 2016) to manually analyze each
star of our sample, in order to re-examine the reliability of each atomic and
molecular line present in each spectrum, and provide chemical abundances for
14 chemical species, listed in Table 1. These abundances have been computed
adopting a line-by-line approach under the assumption of local thermodynamic
equilibrium (LTE). With this independent methodology, we obtain complementary
abundance ratios not provided by the ASPCAP pipeline (García Pérez et al.
2016), in particular for the heavy neutron-capture (s-process) elements (Ce
II, Nd II, and Yb II). Figure 2 illustrates the best spectral-synthesis
calculation on clean selected features for the extra-tidal star.

Figure 2: High-resolution near-IR H-band spectrum of the extra-tidal star. The
spectral regions are shown with orange squares. Superimposed is the best-fit
of a MARCS/BACCHUS spectral synthesis (black line). The light blue shaded
regions show the strength of the molecules (12C16O, 12C14N, 16OH), and the
atomic lines, namely the $\alpha$-elements (Mg I, Si I, Ca I, Ti I), the odd-Z
elements (Al I, K I), the iron-peak elements (Fe I, Ni I), and the s-process
elements (Ce II, ND II, Yb II), expressed in air wavelengths. The legends in
each panel show the absolute abundance, $A$(X), of the species under
consideration, and the signal-to-noise (S/N) in the regions of the features,
respectively.

Importantly, none of the newly identified stars in this work have strong RV
variability over the temporal span of the APOGEE-2 observations (visit-to-
visit variations, $\sigma RV<1$ km s-1), which were obtained during 2018-05-24
(visit 1) and 2018-05-25 (visit 2). Therefore, with the current data there is
no evidence that any of these objects are members of binary systems.

Furthermore, we found that our sample has a Gaia re-normalised unit weight
error (RUWE) value $<$ 1.4, as listed in Table 1, indicating that they are
astrometrically well-behaved sources in the Gaia Early Data Release 3 (Gaia
EDR3) catalogue (Gaia Collaboration et al. 2020).

Panels (a) to (c) of Figure 1 show the metallicity versus kinematic, sky
positions, and astrometric properties of our sample, as well as the
serendipitous discovery of an chemically atypical extra-tidal star in the
vicinity of NGC 6723; a result not previously seen. We find that 5 of the 7
cluster members are strongly enhanced in nitrogen, [N/Fe]$>+0.86$, well above
the Galactic levels (which is typically $\lesssim+0.5$), and a clear indicator
of the presence of nitrogen-enhanced stars in NGC 6723. The CMDs displayed in
Figures 1 (d) and (e) show that most of the stars in our sample lie in the
upper part of the prominent red giant-branch (RGB) of NGC 6723, and do not
exhibit a wide metallicity variation. This is also supported by the
spectroscopic values.

##  3 Atmospheric parameters and elemental abundances

Figure 3: Comparison of elemental-abundance ratios of likely member stars for
NGC 6723 with other GCs of similar metallicity, and the extra-tidal star with
RGB and early-AGB (eAGB) cluster stars, and IRAS07134 star. Panel (a):
Elemental-abundance patterns for our sample (black boxes and red dot) compared
to the spectroscopic study of NGC 6723 (Crestani et al. 2019) (light blue
boxplots). Panel (b): Comparison with M 107 (Mészáros et al. 2020). Panel (c):
Comparison with NGC 362 (Mészáros et al. 2020). Panel (d): Elemental-abundance
patterns for the extra-tidal star compared to those of RGB GC stars. Panel
(e): Compared with early-AGB GC stars (Mészáros et al. 2020). Panel (f):
Comparison with a field post-AGB star, IRAS 07134 (De Smedt et al. 2016), with
comparable atmospheric parameters. Boxes represent the inter-quartile ranges
(IQR), whiskers the 1.5$\times$IQR limits, and blue lines the medians.

We used the BACCHUS code (Masseron et al. 2016) to derive the metallicity
(from Fe I lines), broadening parameters, and chemical abundances for the
stars in our sample, based on careful line selection, and carried out a
detailed inspection of each APOGEE-2 spectrum in order to examine the
reliability of the abundance ratios, in the same manner as described in
Fernández-Trincado et al. (2019b). The adopted atmospheric parameters and the
typical uncertainties are listed in Table 1.

The BACCHUS code relies on the radiative transfer code Turbospectrum (Alvarez
& Plez 1998; Plez 2012) and the MARCS model atmosphere grid (Gustafsson et al.
2008). For each element and each line, the abundance determination proceeds as
in previous APOGEE-2 works (Hawkins et al. 2016). In summary, the steps are:
(i) a spectrum synthesis, using the full set of (atomic and molecular) lines
to find the local continuum level via a linear fit; (ii) cosmic and telluric
line rejections are performed; (iii) the local signal-to-noise ratio (S/N) per
element is estimated; (iv) a series of flux points contributing to a given
absorption line are automatically selected; and (v) abundances are then
derived by comparing the observed spectrum with a set of convolved synthetic
spectra characterised by different abundances.

Four different abundance determinations are used: (i) line-profile fitting;
(ii) core line-intensity comparison; (iii) global goodness-of-fit estimate;
and (iv) equivalent-width comparison. Each diagnostic yields validation flags.
Based on these flags, a decision tree then rejects or accepts the line,
keeping the best-fit abundance. We adopted the $\chi^{2}$ diagnostic as the
abundance determinant, because it is considered to be the most robust.
However, we stored the information from the other diagnostics, including the
standard deviation between all four methods. The line list used in this work
is the latest internal DR14 atomic/molecular linelist (linelist.20170418),
including the $s$-process elements (Ce II, Nd II, and Yb II)–(Hasselquist et
al. 2016; Cunha et al. 2017). For a more detailed description of these lines,
we refer the reader to a forthcoming paper (Holtzman et al. in preparation).

In particular, a mix of heavily CN-cycled and $\alpha$-poor MARCS models were
used, as well as the same molecular lines adopted by APOGEE-2 (Smith et al.
2013), in order 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; that is to say, we first derive 16O abundances from 16OH
lines, then derive 12C from 12C16O lines, and 14N from 12C14N lines; the C–N–O
abundances were derived iteratively to minimize the 16OH, 12C16O, and 12C14N
dependences (Smith et al. 2013).

It is important to perform consistent chemical-abundance analyses using
atmospheric parameters determined independently, in order to check for any
significant deviation in the derived abundances. To achieve this, the
photometric effective temperatures were calculated using the $J-K_{s}$ (2MASS)
colour-relation methodology (González Hernández & Bonifacio 2009). For the
extra-tidal star, we adopted the extinction correction obtained from the
Rayleigh Jeans Colour Excess (RJCE) method (Majewski et al. 2011). Thus, the
photometry is extinction corrected, adopting E(B-V)$=$ 0.063 (see, e.g., Lee
et al. 2014) for stars inside the cluster tidal radius, and assuming an E(B-V)
= 0.520 (Majewski et al. 2011) for the extra-tidal star, which lies at a
region outside the cluster that is severely affected by extinction, given
their position toward the Galactic bulge where the reddening variation may be
substantial (see, e.g. Alonso-García et al. 2017), even if the projected
distance between the extra-tidal star and cluster is small.

We assumed a surface gravity from the PARSEC isochrones (Bressan et al. 2012),
using $\approx$12.5 Gyr as the estimated age of NGC 6723 (Dotter et al. 2010;
Oliveira et al. 2020), and the uncalibrated metallicity ([M/H]), as derived by
ASPCAP/APOGEE-2 runs. The adopted stellar parameters are listed in Table 1.

The adoption of a purely photometric temperature scale enables us to be
somewhat independent of the ASPCAP/APOGEE-2 pipeline, which provides important
comparison data for future pipeline validation. The final results presented in
this paper are based on computations done with the BACCHUS code using the
mentioned photometry and atmospheric parameters, as listed in Table 1.

Figure 4: Distributions of various elemental-abundance ratios from the
APOGEE-2 survey for bulge field stars in close proximity to the Galactic
Centre ($-20^{\circ}<l<20^{\circ}$ and $|b|<20^{\circ}$), and comparison with
stars in NGC 6723. The field-star abundances are represented by orange iso-
abundance contours. The member stars of NGC 6723 and the extra-tidal star
analyzed in this work are shown with black and red open circles, respectively.
The circle sizes reflect their ${\rm V_{o}}$ magnitudes, with decreasing size
for fainter magnitudes. The blue cross symbol denotes the average
$\langle$[Xi/Fe]$\rangle$ and its associated star-to-star scatter
($\sigma_{\rm\langle[X_{i}/Fe]\rangle}$) of the abundance derived from the
seven member NGC 6723 stars analyzed in this work.

The abundance values are sensitive to all of the atmospheric parameters,
depending on the chemical species. To estimate their uncertainties, we have
varied the atmospheric parameters one at a time by the typical values of
$\Delta$T${}_{\rm eff}=\pm 100$ K, $\Delta\log g=\pm 0.3$ dex, and
$\Delta\xi_{t}=\pm 0.05$ km s-1, and then computed the abundances for all
species for each of these possibilities for two stars – one cluster member
(2M18594898$-$3635401) and the extra-tidal star (2M18594405$-$3651518). Thus,
each line for each star has a corresponding $\sigma_{\rm T_{eff}}$, which
refers to its response to $\Delta{\rm T_{eff}}$; $\sigma_{\log g}$ the
response to $\Delta{\log g}$; $\sigma_{\rm\xi_{t}}$ the response to
$\Delta{\rm\xi_{t}}$, and the uncertainties on the mean due to line-to-line
scatter. The uncertainties are propagated in quadrature to compute the
uncertainty of each chemical species in the two stars. The computed
uncertainties are listed in Table 2.

Even though the BACCHUS code has its own procedure to include or reject lines
on a star-by-star basis, it is still important to select the lines beforehand,
due to the uncertainty related to the synthesis approach, such as line
saturation. All the selected atomic and molecular lines were visually
inspected to ensure that the spectral fit was adequate.

The individual oxygen abundances are also listed in Table 1. We caution about
the accuracy of [O/Fe], as they display larger scatter, which may be due to
telluric features and uncertain determinations in the Teff regime of our
objects. As highlighted by previous works, the uncertainty arises because
BACCHUS determines these abundances from the strengths of 12C14N and 12C16O
lines, which become too weak for stars at relatively low metallicities
([Fe/H]$\lesssim-1.0$). Figures 2 and 3 clearly shows that K I, Ce II, Nd II,
and Yb II enhancement of the extra-tidal star compared to other NGC 6723 stars
can be convincingly claimed. Consequently, we conclude that the Ce, Nd, and Yb
enhancement was likely inherited from the initial gas composition of NGC 6723.

##  4 Results

###  4.1 NGC 6723 stars

Figure 5: Predicted abundance ratios, as a function of the initial stellar
mass, for low-and-intermediate-mass stars. ${\rm[X_{i}/Fe]}$ values were
obtained from stellar yields by Karakas et al. (2014, 2018). For comparison,
the red line and shaded red bands represent the observed abundance ratios and
sensitivities for our extra-tidal star.

For the selected stars, we derive abundance ratios covering the main element
families, namely the light elements (C, N), the $\alpha$-elements (O, Mg, Si,
Ca, Ti), the odd-Z elements (Al, K), the iron-peak elements (Fe, Ni), and
products of the slow neutron-capture (s-) process (Ce, Nd, Yb), and have
abundance determinations from spectra in the H-band of APOGEE-2 (Mészáros et
al. 2020). For the cluster members, we find metallicity consistent with
previous estimates for this cluster, $\langle$[Fe/H]$\rangle$ $=-1.00$, with a
small, 0.06 dex, star-to-star scatter, commensurate with recent results based
on high-resolution spectroscopy (Rojas-Arriagada et al. 2016; Crestani et al.
2019), which indicate a mono-[Fe/H] behaviour.

We obtained a mean nitrogen abundance ratio of [N/Fe] $=+0.95$, with an
observed star-to-star scatter ($0.34$ dex) that well exceeds the observational
uncertainties. The abundance ratios for the other elements up to the iron peak
(O, Mg, Al, Si, K, Ca, Ti, and Ni) appear to be homogeneous within the
permitted error variation, and replicate the chemical patterns observed for
Galactic GCs of comparable metallicity, as shown in panels (b) and (c) of
Figure 3. The heavy s-process elements, such as Ce and Nd, are lower ([Ce/Fe],
[Nd/Fe] $\lesssim+0.29$) compared to M107, a GC with similar metallicity as
NGC 6723, excepting Yb, which we find to be higher in some NGC 6723 stars. It
has been noted previously that s-process-element enhancements $\gtrsim+0.4$
are usually rare, and are reported for only a few clusters (Mészáros et al.
2020), particularly at the metallicity of NGC 6723, suggesting they arise from
pollution by AGB stars (Ventura et al. 2016; Mészáros et al. 2020).

The large star-to-star abundance variation inside the cluster – especially in
the case of N – is indicative of the presence of multiple populations (MPs) in
NGC 6723, as found in other massive ($\gtrsim 10^{5}$M⊙) GCs at all
metallicities. There is thus strong evidence for an intrinsic spread in
[N/Fe], including a clear C–N anti-correlation. However, we find no clear Al–N
correlation or Al–O anti-correlation (see Figure 4). In other words, NGC 6723
exhibits MPs based on the N abundances, despite appearing to have single
populations in the Al abundances. This is similar to other Galactic GCs at
this metallicity (Mészáros et al. 2020), for which it has been suggested that
lower spreads in Al could be ascribed to operation of a modest Mg-Al cycle. If
the intra-cluster polluters were in fact low-mass ($\lesssim 3$ M⊙) stars, we
would expect low Al production (Mészáros et al. 2020) in NGC 6723. The low
mean abundance and small Al spread ($\langle$ [Al/Fe]$\rangle=+0.28\pm 0.12$)
measured for the NGC 6723 sample supports this conclusion.

The stars we have studied in NGC 6723 have [C/Fe]$<-0.17$, and display a
similar C–N anti-correlation as M107, with $\langle$[C/Fe]$\rangle=-0.35\pm
0.16$. Additionally, NGC 6723 exhibits a star-to-star [Mg/Fe] scatter with no
significant [Al/Fe] spread. No Mg-Al anti-correlation is apparent, and the
scatter is small. In addition, inspection of the [Si/Fe] ratio, as a function
of [Al/Fe] or [Mg/Fe], for the few stars with reliable Si measurements, did
not reveal any clear trend. This suggests no net production of these elements,
but rather is the likely result of the conversion of Mg into Al during the Mg-
Al cycle (Mészáros et al. 2020).

Figure 4 compares the C, N, O, Mg, Al, Si, Ca, Ti, Ni, and Ce abundances of
our sample with Galactic Bulge stars. The behaviour of those chemical species
matches the mean [Xi/Fe] (with Xi meaning the chemical species) of MW stars at
similar metallicity, while the [N/Fe] abundance ratios are clearly super-
Solar. Our results for [Si/Fe] are in reasonable agreement with optical
observations (Rojas-Arriagada et al. 2016; Crestani et al. 2019).

NGC 6723 has a uniform and constant [Ca/Fe] abundance ratio
($\langle$[Ca/Fe]$\rangle=+0.25\pm 0.10$), in agreement with optical
observations (Crestani et al. 2019), which indicates that it is not affected
by the H-burning process (Mészáros et al. 2020), as Ca is mostly produced by
supernovae. For the odd-Z element K, we find that NGC 6723 exhibits a weak
K–Mg anti-correlation, with $\langle$[K/Fe]$\rangle=+0.15\pm 0.10$, suggesting
that this population might have formed from super-AGB ejecta (Ventura et al.
2012).

For the remaining chemical species, we find that the average
$\langle$[O/Fe]$\rangle$ ($+$0.40 $\pm$0.17), $\langle$[Ti/Fe]$\rangle$
($+0.27\pm 0.14$), $\langle$[Ni/Fe]$\rangle$ ($-$0.01$\pm$0.05),
$\langle$[Ce/Fe]$\rangle$ ($+0.14\pm 0.08$), $\langle$[Nd/Fe]$\rangle$
($+0.15\pm 0.07$), and $\langle$[Yb/Fe]$\rangle$ ($+0.68\pm 0.09$) ratios are
comparable to values for M107 and NGC 362, and in agreement with previous
results (Rojas-Arriagada et al. 2016; Crestani et al. 2019). However, some
differences are noteworthy for Nd, compared to GCs at similar metallicity, but
it does agree with the production of other $s$-process species such as Ba
(Rojas-Arriagada et al. 2016), with small star-to-star scatter.

Figure 6: Thousand-orbit realisations of NGC 6723 and the extra-tidal star
time-integrated for 2 Gyr. The dark colours correspond to the most probable
regions of the space, which are crossed more frequently by the simulated
orbits, assuming three different values of the angular velocity of the bar
($\Omega_{\rm bar}=33,43,$ and 53 km s-1 kpc). Panels (a), (b), and (c) show
the orbits of NGC 6723, using as initial conditions the observed values from
Baumgardt et al. (2019); the middle and bottom rows show the orbits of the
extra-tidal star, adopting the observed values from the Table 1, and an
assumed heliocentric distance at 8.3 kpc (panels d, e, and f), and 6.24 kpc
(panels g, h, and i).

###  4.2 Extra-tidal star candidate

Panels (d) and (e) of Figure 1 show the existence of an extra-tidal star in
the smoothly curved morphology of the upper RGB in the Vo versus (B-V)o (Lee
et al. 2014), and Ho versus (J-Ks)o diagrams, extending from the cluster
centre out to $\sim$1.3 tidal radii. The brightness and bluish offset in all
three diagrams from the equally bright RGB stars indicate that this extra-
tidal star is in reasonable agreement with the expected behaviour for AGB
stars in GCs. Figure 1 (a) also shows that this extra-tidal star has similar
metallicity and radial velocity, and Figures 1 (b) and (c) demonstrate the
similarity of the orbital paths and proper motions to NGC 6723 member stars as
well. Thus, these properties are vetted not only by chemical abundances, but
by photometry and kinematics as well.

The $\alpha-$element (Mg, Si, Ca, and Ti), the odd-Z element (Al and K), and
the iron-peak element Ni abundance ratios fall between $-0.09$ and $+0.52$ for
our extra-tidal star. This is similar to the members of NGC 6723 and other GC
stars with comparable metallicity, within the uncertainties (see Table 2 and
Figure 3). Figure 3 also shows that the extra-tidal star is strongly enhanced
in the s-process elements (Ce II, Nd II, and Yb II), which is in agreement
with other GC stars at similar metallicity (Mészáros et al. 2020).

Figure 2 reveal that the newly identified extra-tidal star has a stellar
atmosphere strongly enriched in 12C14N features, which indicates a high
enrichment in nitrogen ([N/Fe]$=+0.94$), well above usual Galactic levels.
However, this particular star has a carbon abundance higher than the abundance
ratios measured for NGC 6723 member stars as shown in panel (a) of Figure 3,
but in reasonable agreement with the most C-rich stars in GCs of comparable
metallicity (see panels (b) and (c) of Figure 3). This atypical chemical
pattern suggests that the extra-tidal star is not a genuine second-generation
star as other typical N-rich field /GC stars, but indeed is part of a second-
type of N-rich star with modest carbon enrichment, likely a GC star with AGB-
like chemical patterns. Figures 2 and 3 also clearly show that K I, and Ce II
enhancement of the extra-tidal star can be convincingly claimed. Thus, we
conclude that the Ce, Nd, and Yb enhancement was inherited from the initial
gas composition of NGC 6723.

We also find that the oxygen abundance is in reasonable agreement with levels
seen for NGC 6723 stars (Rojas-Arriagada et al. 2016; Crestani et al. 2019).
From the strength of the 12C16O and 16OH molecular features (see Figure 2),
one would expect that more oxygen in the atmosphere means that more carbon is
locked into 12C16O, and is not available to form 12C14N, as the strength of
the 12C14N features is anti-correlated with [O/Fe]. From Table 1, even a small
change in the surface temperature and $\log g$ requires some adjustment to the
carbon and oxygen abundance, but [N/Fe] is relatively insensitive to small
Teff and surface gravity changes, and we can be confident that this star is
indeed nitrogen enriched.

##  5 Possible origins for the observed chemical composition of the extra-
tidal star

There are several competing scenarios that might explain the unusual chemical
abundances of our extra-tidal star, in the context of an escaped member of NGC
6723 that was tidally disrupted and captured by the MW’s bulge.

It appears likely that some stars (C-poor or C-enriched) belonging to the
family of mildly metal-poor N-rich stars (peaking at [Fe/H] $\sim-1.0$) could
be relics of initially massive clusters such as NGC 6723. It is reasonable to
assume that some of those objects were formed in Galactic GCs and later
dynamically ejected into the Galactic field when their parent GCs were
ultimately disrupted and destroyed, possibly during disc–bulge crossing events
(see, e.g., Leon et al. 2000; Lane et al. 2010; Fernández-Trincado et al.
2015a, b, 2016b; Kundu et al. 2019b, a, 2020; Hanke et al. 2020; Sollima
2020). However, this has not heretofore been directly demonstrated.

With the newly analyzed extra-tidal star, we want to investigate the possible
origin of neutron-capture (s-process) enrichment, simultaneous with the
observed enrichment in nitrogen and its apparent carbon enrichment.

Figure 5 shows the observed photospheric abundances of our target star, along
with theoretical (C, N, Mg, Al, Ce, Nd, and Yb) abundance ratios from
nucleosynthetic AGB models closest to [M/H] $\sim-1.09$. We obtained these
models by interpolating the stellar yields from Karakas et al. (2014) and
Karakas et al. (2018). From inspection, an over-abundance of the elements
created by the s-process (Ce II, Nd II, and Yb II) support the idea that AGB
stars with initial masses of $\sim$3.7 M⊙ could reasonably explain the
observed s-process enrichment. As also seen in this figure, the C and N
enrichments could be explained, at $\sim$2$\sigma$, with initial masses of
$\sim$3.7 and $\sim$2.5 M⊙, respectively, while Mg and Al suggest an initial
mass of $\sim$2.5 M⊙. Thus, most of these species are in agreement with
production by an AGB star having an initial mass $\sim$2.5 or 3.7 M⊙, which
underwent a mass-transfer event, resulting in pollution of an intermediate-
mass companion that today has evolved to the tip of the RGB. We caution about
the accuracy of the estimated [O/Fe] values, as they display a larger scatter,
possibly due to telluric features and uncertain determinations in the Teff
regime of our objects. As highlighted in previous works, the uncertainty
arises because BACCHUS determines these abundances from the strengths of
12C14N and 12C16O lines, which become too weak for stars at relatively low
metallicities ([Fe/H] $-1.0$). For this reason, we do not draw conclusive
constraints in the mass of the progenitor based on the individual oxygen
abundance listed in Table 1.

It is also possible that this star is itself an AGB star (perhaps with no
relationship to NGC 6723), which could also explain the puzzle of its high
nitrogen and s-process enrichment. However, such a range in mass would
correspond to a very young star ($\sim$0.5 – 0.7 Gyr), which is likely too low
to support this hypothesis. The AGB stage of stellar evolution is also very
short-lived, so there is a low probability of finding an AGB star.

Taking into account the above results, we speculate on several possible
scenarios that could be viable to explain the unusual nature of our object, in
the context of an escaped member of NGC 6723 that was tidally disrupted and
captured by the bulge of the MW.

  * i.

Extrinsic mechanism (binary-mass transfer system). The over-abundance of
s-process elements could come from the accretion of s-process-rich matter from
a former thermally pulsing (TP)-AGB companion during its heavy mass-loss phase
on the AGB (Brown et al. 1990), which has since evolved into a faint white
dwarf (see, Fernández-Trincado et al. 2019c, for instance). Figure 5 indicates
that our measured abundance ratios, from the light elements (C, N), the
$\alpha$-element (Mg), and the odd-Z element (Al), to the $s$-process elements
(Ce, Nd, and Yb), could have originated from material previously enriched in a
TP-AGB companion with an initial mass of $\sim 2.5$ and $\sim 3.7$ M⊙,
respectively.

Consequently, if the case of an extrinsic mechanism is favoured, and the
extra-tidal star is/was part of a binary system before/after leaving the
cluster, it would be possible that the star accreted N-rich material from the
companion when the latter reached the AGB phase with the inferred mass. In
this case, the abundances that we measure are not its original ones, but they
reflect the chemical composition of the interior of the companion, plus some
degree of dilution in the convective envelope of the accreting star. In
addition to the nitrogen and s-process enrichment, carbon should also be over-
abundant, as a result of a third dredge-up episode in the donor. Such a star
could have polluted the extra-tidal star with C, N, and s-process-rich
material, but lost so much mass that the binary may be disrupted, or become so
wide that RV variations would be very small, which could explain the lack of a
detectable white dwarf companion. However, the current PMs and radial velocity
of the extra-tidal star appear to support that this object was detached from
the cluster by tidal disruption, consistent with the low relative velocity
between this cluster and the star during close encounters. In such a case, the
possibility that our object was part of a binary system before departure from
the cluster would not be supported (see e.g. Fernández-Trincado et al. 2016a).

The absence of RV variation over the temporal span of the APOGEE-2
observations ($<1$ day) and Gaia EDR3 ($-93.22\pm 1.23$ km s-1) provide no
evidence that our object (the extra-tidal star) is currently a binary with a
white dwarf companion. Long-term RV monitoring of this unusual object would
naturally be the best course to rule out an origin by the binary channel.

If there is any possibility to support the binary hypothesis in the future,
perhaps from careful long-term RV monitoring, then it is worth mentioning
that, if the donor material was lost in a wind from a $\sim$2.5–3.7 M⊙ AGB
star, it must have been shed very recently. However, this scenario is not
compatible with its apparent brightness in Figure 1 (d) and (e), as the object
is intrinsically bluer and more luminous than other observed stars in NGC
6723.

  * $\bullet$

Intrinsic mechanism. A second scenario is that our unusual object could itself
be an AGB star. In this case, it was enhanced in s-process elements via the
third dredge-up of nucleosynthetic products created in the stellar interior
and shell helium-burning (via thermal pulses), followed by subsequent mixing
that can result in an over-abundance of C and N at the surface (Karakas et al.
2014). Moreover, if the extra-tidal star is an actual evolved object, possibly
an early-AGB or an AGB star, it would have a mass in the range $\sim 2.5$ to
$\sim 3.7$ M⊙ to explain the observed photospheric chemical composition. As
pointed out above, this would imply that a GC origin of this star is ruled
out.

  * $\bullet$

A third possibility could be that our star is an s-process-enriched red giant
that is the result of star formation in an already s-process-enriched medium,
where AGB stars have played a more dominant role in chemical evolution
(Ventura et al. 2016). Hence, a valid possibility is that the extra-tidal star
inherited its present chemical composition while it was still a cluster
member, likely from gas lost by a previous generation of $\sim$2.5–3.7 M⊙ AGB
stars. This mass range is also fairly well-supported by the observed [Mg/Fe],
and [Al/Fe] abundance ratios, as shown in Figure 5.

  * $\bullet$

A fourth plausible interpretation is that N-rich stars towards the bulge
region are among the oldest in the Galaxy, and their abundances are in fact
the imprints of the very early chemical enrichment by spinstars, metal-poor,
fast-rotating massive stars (Chiappini et al. 2011; Barbuy et al. 2014), which
polluted the interstellar medium from which bulge GCs formed. An enhancement
in N and modest enhancement in C, as well as some contribution to the neutron-
capture elements (s-process nucleosynthesis) might be expected. This scenario
would predict that all of the stars in NGC 6723 (and indeed in all bulge GCs
formed in situ) would be N-rich stars, whereas if the third possibility is
correct, then there should exist first-generation stars in the cluster that do
not exhibit enhanced nitrogen.

We conclude that it is very likely that we have identified a former cluster
member (the extra-tidal star), with observed abundances consistent with
production by AGB stars that played an important role in the chemical
enrichment of NGC 6723, which is in-line with previous results for GCs at
similar metallicity (Ventura et al. 2016; Mészáros et al. 2020).

It is important to note that, at [Fe/H] $\sim-1.17$, it seems likely that the
s-process would dominate the production of such elements, invoking the AGB
progenitor (Kobayashi et al. 2020) rather that other possible sources such as
binary neutron star (NS–NS) mergers (Wanajo et al. 2014). In addition, if we
were to assume that the n-capture came from an NS-NS merger, then we would
need a second progenitor to account for the N and other light elements.

We also note some differences between the extra-tidal star and MW field stars.
Figure 4 shows a comparison between this star (red symbol) and bulge field
stars at similar metallicity from the APOGEE-2 survey. While this result
reinforces that N-rich stars of different generations (Martell et al. 2016)
populate different regions of the canonical abundance planes, some
similarities are noteworthy with Galactic field stars. The unique nature of
our star is clear in the [C/Fe]–[N/Fe], [N/Fe]–[Al/Fe], [O/Fe]–[Al/Fe],
[Mg/Fe]–[Al/Fe], [Mg/Fe]–[Si/Fe], [Mg/Fe]–[K/Fe], and [Ca/Fe]–[Ti/Fe] planes,
which slightly exceed the Galactic levels, while some similarities remain for
the $\alpha-$elements Mg, Si, Ca, and Ti, the odd-Z elements Al and K, and the
iron-peak element Ti. In contrast to bulge field stars, the extra-tidal star
clearly has higher [C, N, O/Fe] abundance ratios ($>+0.5$). These differences
(and similarities) suggest that the extra-tidal star exhibits the typical
chemical patterns similar to those of evolved stars in GC at [Fe/H]$\sim-1.0$
(Mészáros et al. 2020), as shown in panel (e) of Figure 3. However, it is
important to note that our extra-tidal star shows a lower metallicity compared
to the cluster mean, but all its chemical patterns show good agreement with
the other members of NGC 6723. This low-metallicity effect could be explained
if some variability signature is detected in this star, as there is some
evidence in the literature (Muñoz et al. 2018) that variability affects the
measurement of the iron abundance in some way, causing a large offset with
respect to the cluster mean. Another detailed photometric/spectroscopic
analysis of this star is needed to investigate possible variability effects on
the metallicity derivation. We note that, according to its radial velocity,
proper motions, position in the CMD, and atmospheric parameters, this star
is/was very likely a cluster member.

##  6 Expected Radial Profile of halo field stars with a globular cluster-like
abundance patterns toward NGC 6723

We compute the predicted number ($N_{gc}$) of halo field stars with globular
cluster-like abundance patterns observed in APOGEE-2 (see, e.g., Fernández-
Trincado et al. 2016a; Fernández-Trincado et al. 2017; Schiavon et al. 2017b;
Fernández-Trincado et al. 2019b) towards the field of NGC 6723 using the
smooth halo density relations presented in Horta et al. (2021), and by
adopting the same Monte Carlo implementation of the Von Neumann Rejection
Technique (Press et al. 2002) as in Eq. 1 in Mateu et al. (2009) and Eq. 7 in
(Fernández-Trincado et al. 2015b).

We find the expected number of observed APOGEE-2 halo field stars with a
possible GC origin in the range $5.5$ kpc $<d_{\odot}<9.5$ kpc, over a
circular sky area of one-degree radius centred in NGC 6723, and with
astrometric and kinematic properties as the cluster to be $N_{gc}<0.05$ (from
1000 Monte Carlo realisations). This indicates that the region around NGC 6723
is underdense, not overdense, in Galactic halo field stars with globular
cluster-like abundance patterns, leaving enough room to favour the scenario of
a genuine extra-tidal star associated with NGC 6723.

##  7 Galactic orbit

We used the GravPot16111https://gravpot.utinam.cnrs.fr algorithm for the
calculation of the orbital path of both NGC 6723 and the extra-tidal star
around the MW. The GravPot16 model is composed of multiple potentials for the
Galactic disc and a box/peanut bulge. For the Sun’s position in the MW we
assumed a distance to the Galactic Centre of $R_{\odot}=$8 kpc. In order to
correct for the solar motion, we used the Sun’s velocity respect to the local
standard of rest ($U_{\odot}$, $V_{\odot}$, $W_{\odot}$)
$=$($11.10,12.24,7.25$) km s-1 (Brunthaler et al. 2011) and the velocity of
the local standard of rest (LSR) $\nu_{LSR}=244.5$ km s-1, based on $R_{\rm
o}$ and assuming the composite rotation curve of Sofue (2015).

For NGC 6723 and the extra-tidal star, we integrated over a 2 Gyr timespan,
and calculated their orbital paths and orbital parameters using three
different values of the angular velocity of the bar $\Omega_{\rm bar}=33,43,$
and 53 km s-1 kpc-1. For NGC 6723, we adopted the observational parameters
from Baumgardt et al. (2019); for the extra-tidal star, we adopted the
observational parameters given in Table 1, except for the distance, for which
we assumed two different values, e.g., $8.3\pm 0.83$ kpc, the same
heliocentric distance as NGC 6723 (Baumgardt et al. 2019), and $6.24\pm 1.69$
kpc, the estimated distance from the StarHorse code (Anders et al. 2019) (the
algorithm combines the Gaia astrometric information with multiband photometric
information and a number of Galactic priors), which have smaller uncertainties
at large ranges, as previously expected, and which have been proven to be an
useful tool in confirming the dichotomy with APOGEE-2/DR16 and dissecting the
bulge stellar populations (Queiroz et al. 2018, 2020).

A simple Monte Carlo analysis was performed for the complete calculation,
taking into account the errors in distance, RV, and proper motions, which were
randomly propagated as 1$\sigma$ variations, assumed to follow Gaussian
distributions. For both objects we computed 1000 orbits. Figure 6 shows the
probability densities of the resulting orbits on the X–Y, X–Z, and Y–Z planes
in the non-inertial reference frame where the bar is at rest, where the dark
area correspond to the most probable regions of the space, which are crossed
more frequently by the simulated orbits. We found that both cluster and extra-
tidal star are situated in the inner region of the bulge. For the full
ensemble of orbits, we also calculated the deviations in the orbital
parameters due to the different values of the angular velocity of the bar,
($\Delta{}r_{peri}$, $\Delta{}r_{apo}$, $\Delta{}Z_{max}$, $\Delta{}e$): NGC
6723 (0.02 kpc, 0.65 kpc, 0.37 kpc, 0.01), extra-tidal star at $d_{\odot}=8.3$
kpc (0.01 kpc, 0.52 kpc, 0.29 kpc, 0.01), and extra-tidal star at
$d_{\odot}=6.24$ kpc (0.06 kpc, 0.07 kpc, 0.05 kpc, 0.03). With the different
values of $\Omega_{\rm bar}$, we can see that the predicted orbits are not
significantly affected by the change of this parameter, and consequently, it
does alter our conclusions.

Figure 7: Modified Figure 10 from Chun et al. (2015). The red ‘star’ symbol
shows the position of the newly identified extra-tidal star. The orange circle
indicates the cluster tidal radius ($r_{t}=9.14\pm 0.49$ ′, see Section 8),
and the red arrow defines the proper motion of NGC 6723 from Baumgardt et al.
(2019). The orange solid and dashed line shows the direction of the Galactic
Centre and Galactic plane, respectively. The top-left panel is the star-count
map around the cluster; the top-right panel is the surface-density map,
smoothed by a Gaussian kernel 0.07∘; the lower-left panel is the same data,
but smoothed with a 0.11∘ kernel; the bottom-right panel shows the
distribution map of E(B-V). The iso-density contour levels shown are
2.0$\sigma$, 2.5$\sigma$, 3.0$\sigma$, 4.0$\sigma$, 5.0$\sigma$, and
7.0$\sigma$. The orbital path of the cluster (black line) and the extra-tidal
star (purple line) is over-plotted.

The median orbital parameters, assuming $\Omega_{\rm bar}=43$ km s-1 kpc for
NGC 6723 and the extra-tidal star, are as follows: ($r_{peri}$, $r_{apo}$,
$Z_{max}$, $e$): NGC 6723 ($0.05\pm 0.08$ kpc, $3.28\pm 0.12$ kpc, $3.87\pm
0.12$ kpc, $0.97\pm 0.04$), extra-tidal star at $d_{\odot}=8.3$ kpc ($0.06\pm
0.14$ kpc, $3.36\pm 0.10$ kpc, $3.98\pm 0.12$ kpc, $0.97\pm 0.07$), and extra-
tidal star at $d_{\odot}=6.24$ kpc ($1.56\pm 1.07$ kpc, $4.28\pm 0.66$ kpc,
$2.46\pm 0.82$ kpc, $0.46\pm 0.24$). We confirm that both NGC 6723 and the
newly found extra-tidal star possess trajectories indicating that they are
confined to the bulge region ($\lesssim 4$ kpc) and have similar orbital
properties, suggesting that the extra-tidal star shares an identical dynamical
history as NGC 6723, as expected of stripped cluster stars. Figure 1 (b) and
Figure 7 show that the extra-tidal star is in-line with the cluster’s orbit.
Figure 7 also suggests that the orbital path of NGC 6723 is tracing out the
trailing arm, and our extra-tidal star candidate is located along the leading
arm.

Figure 8: Stellar-density profile of NGC 6723 determined from the HST$+$Gaia
EDR3 data set. Small orange symbols show densities before background
subtraction. The-best fit King (1966) profile is shown in lime and cyan,
respectively. The red dashed line show the determined tidal radius
($r_{t}=9.14\pm 0.49$ ′) in this work, while the black line in 1.1 ′separate
the HST from Gaia EDR3 data set.

##  8 Comments on the tidal radius

The tidal radius for NGC 6397 has been measured by several studies, resulting
in different values. For instance, a recent work by de Boer et al. (2019)
using Gaia DR2 data determined a tidal radius that peaks at $r_{t}=67.66\pm
9.50$ pc ($\sim 26.7^{\prime}$) from a generalised lowered isothermal LIMEPY
model. This is considerably larger than previously thought. The Baumgardt et
al. (2019) value, using the same data set and a different analysis method,
adopted $r_{t}=36.95$ pc ($\sim$14.6′), which is substantially larger than the
value of $r_{t}=10.51^{\prime}$ listed by Harris (1996, 2010, 2010 edition).

Moreover, simulations from Moreno et al. (2014) calculated tidal radii between
29 – 31.4 pc using a 6-D dataset in an axisymmetric and non-axisymmetric
Galactic potential, including a rotating Galactic bar and a 3-D model for the
spiral arms. Their results indicate good agreement with the tabulated value
from Harris’s compilation and the cluster Jacobi radii determined in Piatti et
al. (2019). Furthermore, the observed cluster stellar-density maps from near-
infrared observations (see, e.g., Chun et al. 2015) suggest the existence of
over-density features of some number of stars from $\sim 6.3^{\prime}$
$\lesssim r\lesssim 15.77^{\prime}$, exhibiting azimuthally irregular
patterns. Our newly identified extra-tidal star lies in this region as shown
in Figure 7, and placed well outside the Jacobi radius ($\gtrsim 11\arcmin$;
Piatti et al. 2019). This called our attention to the recent derived slightly
larger $r_{t}$ values from de Boer et al. (2019), based on Gaia DR2. This
value, should be viewed with caution, as it has its own limitations toward the
bulge regions, and could lead to fitting non-physically motivated core King
(1962) and tidal radii.

With the new improved data from Gaia EDR3 (Gaia Collaboration et al. 2020),
and the available Hubble Space Telescope (HST) imaging data within 1.1 ′from
the cluster center (Sarajedini et al. 2007), we can determine updated
structural parameters with better precision. To construct number density
profiles, we make use of star counts by adopting the same technique as in
Cohen et al. (2020) to combine both surveys. Briefly, the stellar density is
found in annuli of varying radii around the centre of the cluster, and these
density values are fitted by a King profile (King 1966). The HST$+$Gaia EDR3
data is fairly well-fit by the (King 1966) profile. The stellar-density
profile is shown in Figure 8. For NGC 6723 we have determined a radius
$r_{t}=9.14\pm 0.49$ ′, which is in good agreement with the values reported in
Harris (1996, 2010 edition), and by dynamical studies of NGC 6723 (see, e.g.,
Moreno et al. 2014; Piatti et al. 2019).

Our finding is in line with recent studies in the vicinity of NGC 6723, for
example, near-infrared J-, H-, and K-band observations from the WFCAM camera
on the 3.8 m UKIRT Chun et al. (2015), suggesting the existence of extra-tidal
features $\gtrsim 11^{\prime}$ (Fig. 7), and is in good agreement with a
rather high destruction ratio of $\nu_{tot}/\nu_{evap}\sim 0.81-2.0$ Gnedin &
Ostriker (1997); Moreno et al. (2014) (where $\nu_{tot}$ is the total
destruction rate of this cluster, and $\nu_{evap}$ is the evaporation rate per
Hubble time). The newly identified extra-tidal star lie near the weak extended
substructure beyond the tidal radius in the southern region of NGC 6723 (see,
e.g., Chun et al. 2015) as highlighted in Figure 7, suggesting that this star
has left the GC’s potential. Thus, our findings provide strong support for the
idea of linking N-rich field stars to GCs in the bulge region of the MW (Bekki
2019).

##  9 Concluding remarks

Our finding is in-line with recent studies in the vicinity of NGC 6723, e.g.,
near-infrared J-, H-, and K-band observations from the WFCAM camera on the 3.8
m UKIRT (Chun et al. 2015), suggesting the existence of extra-tidal features
around this cluster (see Figure 7). Thus, our findings provide strong support
for the idea of linking some of the observed N-rich field stars to GCs in the
bulge region of the MW (e.g., Schiavon et al. 2017b; Fernández-Trincado et al.
2019b).

We also conclude that it is very likely that we have identified a former
cluster member, with observed abundances consistent with production by AGB
stars that played an important role in the chemical enrichment of NGC 6723,
which is in-line with previous results for GCs at similar metallicity
(Mészáros et al. 2020).

There are also several competing scenarios that might explain the unusual
chemical abundances of the newly identified extra-tidal star, in the context
of an escaped member of NGC 6723 that was tidally disrupted and captured by
the MW’s bulge. In summary:

  * $\bullet$

Extrinsic mechanism: The over-abundance of the s-process elements in this star
could come from the accretion of s-process-rich matter from a former thermally
pulsing AGB companion during its heavy mass-loss phase on the AGB, which has
since evolved into a faint white dwarf star.

  * $\bullet$

Intrinsic mechanism: This star could be an intrinsic AGB star, enhanced in
s-process elements during the third dredge-up of nucleosynthetic products
created in the stellar interior and shell helium-burning (via thermal pulses),
followed by subsequent mixing that can result in an over-abundance of carbon
and nitrogen at the surface.

  * $\bullet$

This star could be an s-process-enriched red giant resulting from star
formation in an already s-process-enriched medium, where low-mass AGB stars
have played a dominant role in chemical evolution.

Finally, the newly identified extra-tidal star displays a [N/Fe] ratio similar
to other metal-poor N-rich field stars, but which are not carbon enriched (one
of the typical signatures of second-generation GC stars)–(see e.g., Fernández-
Trincado et al. 2016a; Fernández-Trincado et al. 2017; Schiavon et al. 2017b;
Fernández-Trincado et al. 2019b), suggesting that the extra-tidal star is not
a genuine second-generation star, but it is part of a sub-family of the N-rich
stars with modest carbon enrichment as that observed in some Galactic GC stars
at similar metallicity, likely associated with the intermediate-mass
($\lesssim$3 M⊙) population of early-AGB stars.

Table 1: Top table: Final abundances for the stars analyzed in this work ,
adopting stellar atmospheric parameters from photometry (Teff) and log $g$
from 12.5 Gyr PARSEC isochrones, as determined using local thermodynamic
equilibrium (LTE) model atmospheres. Middle table: The final abundances as
determined by the ASPCAP pipeline. Bottom table: List of the main physical
parameters of our stars.

APOGEE$\\_$ID |  Teff |  log $g$ | [M/H] | $\xi_{t}$ | [C/Fe] | [N/Fe] | [O/Fe] | [Mg/Fe] | [Al/Fe] | [Si/Fe] | [K/Fe] | [Ca/Fe] | [Ti/Fe] | [Fe/H] | [Ni/Fe] | [Ce/Fe] | [Nd/Fe] | [Yb/Fe]
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
This work | (K) |  |  |  km s-1 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2M18590940$-$3640192 | 4397 | $1.28$ | $-1.11$ | 1.766 | $-0.45$ | $+1.02$ | $+0.46$ | $+0.37$ | $+0.16$ | $+0.42$ | $-0.01$ | $+0.09$ | $+0.29$ | $-0.93$ | $-0.06$ | $+0.04$ | … | …
2M18592786$-$3636509 | 4425 | $1.41$ | $-0.96$ | 1.931 | $-0.58$ | $+1.53$ | $+0.55$ | $+0.32$ | $+0.40$ | $+0.29$ | $+0.19$ | $+0.30$ | $+0.47$ | $-0.91$ | $-0.07$ | $+0.29$ | … | …
2M18593255$-$3641374 | 4349 | $1.27$ | $-1.02$ | 1.817 | $-0.17$ | $+0.56$ | $+0.60$ | $+0.30$ | $+0.24$ | $+0.35$ | $+0.21$ | $+0.36$ | $+0.19$ | $-1.02$ | $+0.01$ | $+0.15$ | $+0.22$ | …
2M18593691$-$3641280 | 4498 | $1.62$ | $-0.87$ | 1.549 | $-0.20$ | $+0.86$ | $+0.14$ | $+0.33$ | $+0.52$ | $+0.37$ | $+0.14$ | $+0.21$ | $+0.08$ | $-1.00$ | $+0.05$ | $+0.11$ | … | …
2M18594472$-$3639043 | 4364 | $1.30$ | $-1.05$ | 1.761 | $-0.53$ | $+1.06$ | $+0.16$ | $+0.31$ | $+0.19$ | $+0.41$ | $+0.02$ | $+0.14$ | $+0.19$ | $-0.99$ | $-0.09$ | $+0.05$ | … | …
2M18594565$-$3637016 | 4056 | $0.74$ | $-1.01$ | 2.046 | $-0.21$ | $+0.45$ | $+0.47$ | $+0.31$ | $+0.24$ | $+0.35$ | $+0.21$ | $+0.32$ | $+0.19$ | $-1.02$ | $+0.03$ | $+0.13$ | $+0.07$ | $+0.59$
2M18594898$-$3635401 | 4054 | $0.74$ | $-0.97$ | 2.812 | $-0.29$ | $+1.18$ | $+0.39$ | $+0.10$ | $+0.21$ | $+0.31$ | $+0.31$ | $+0.35$ | $+0.45$ | $-1.12$ | $+0.03$ | $+0.22$ | … | $+0.76$
2M18594405$-$3651518 | 4130 | $0.80$ | $-1.09$ | 2.733 | $+0.55$ | $+0.94$ | $+0.54$ | $+0.18$ | $+0.17$ | $+0.38$ | $+0.33$ | $+0.24$ | $+0.37$ | $-1.17$ | $+0.11$ | $+1.19$ | $+1.54$ | $+1.29$
APOGEE$\\_$ID |  Teff |  log $g$ | [M/H] | $\xi_{t}$ | [C/Fe] | [N/Fe] | [O/Fe] | [Mg/Fe] | [Al/Fe] | [Si/Fe] | [K/Fe] | [Ca/Fe] | [Ti/Fe] | [Fe/H] | [Ni/Fe] | [Ce/Fe] | [Nd/Fe] | [Yb/Fe]
ASPCAP | (K) |  |  |  km s-1 |  |  |  |  |  |  |  |  |  |  |  |  |  |
2M18590940$-$3640192 | 4377 | $1.32$ | $-1.11$ | 2.503 | $-0.22$ | $+0.71$ | $+0.28$ | $+0.28$ | $-0.03$ | $+0.26$ | $+0.10$ | $+0.16$ | $+0.06$ | $-1.11$ | $-0.03$ | $-0.07$ | … | …
2M18592786$-$3636509 | 4391 | $1.65$ | $-0.96$ | 2.126 | $-0.24$ | $+0.99$ | $+0.22$ | $+0.24$ | $+0.19$ | $+0.23$ | $+0.24$ | $+0.23$ | $+0.31$ | $-0.98$ | $+0.01$ | $+0.24$ | … | …
2M18593255$-$3641374 | 4327 | $1.53$ | $-1.03$ | 1.849 | $-0.06$ | $+0.09$ | $+0.28$ | $+0.24$ | $+0.02$ | $+0.31$ | $+0.25$ | $+0.22$ | … | $-1.02$ | $+0.04$ | $+0.00$ | … | …
2M18593691$-$3641280 | 4847 | $2.29$ | $-0.88$ | 2.017 | $-0.20$ | $+1.01$ | $+0.14$ | $+0.18$ | $+0.48$ | $+0.22$ | $+0.27$ | $+0.26$ | $+0.42$ | $-0.90$ | $+0.04$ | $+0.49$ | … | …
2M18594472$-$3639043 | 4597 | $1.58$ | $-1.05$ | 2.545 | $-0.26$ | $+0.88$ | $+0.22$ | $+0.22$ | $+0.05$ | $+0.22$ | $+0.14$ | $+0.13$ | $+0.23$ | $-1.06$ | $+0.01$ | $+0.30$ | … | …
2M18594565$-$3637016 | 4121 | $1.14$ | $-1.01$ | 2.025 | $-0.13$ | $+0.17$ | $+0.28$ | $+0.33$ | $+0.05$ | $+0.28$ | $+0.24$ | $+0.24$ | … | $-1.00$ | $+0.02$ | … | … | …
2M18594898$-$3635401 | 4204 | $1.31$ | $-0.98$ | 2.123 | $-0.24$ | $+0.94$ | $+0.22$ | $+0.25$ | $+0.21$ | $+0.21$ | $+0.29$ | $+0.28$ | … | $-0.99$ | $+0.01$ | $+0.13$ | … | …
2M18594405$-$3651518 | 4058 | $-0.19$ | $-1.09$ | 1.995 | $+0.04$ | $+0.82$ | $+0.04$ | $+0.33$ | $+0.11$ | $+0.19$ | $+0.30$ | $+0.18$ | … | $-1.15$ | $-0.13$ | … | … | …
APOGEE_ID | S/N | $RV$ | $\sigma RV$ | E(B-V) |  Vo |  (B-V)o |  Ho |  (J-Ks)o | $\mu_{\alpha}\cos(\delta)$ | $\mu_{\delta}$ | RUWE | # Visits |  |  |  |  |  |
|  |  km s-1 |  km s-1 |  |  |  |  |  |  |  (mas yr-1) |  (mas yr-1) |  |  |  |  |  |  |
|  |  |  | CTIO | CTIO | 2MASS | 2MASS |  |  |  |  |  |  |  |  |  |  |
2M18590940$-$3640192 | 128 |  $-$96.5 | 0.01 | 0.063 | 13.34 | 1.19 | 10.51 | 0.76 |  0.92$\pm$0.02 |  $-$2.47$\pm$0.01 | 1.18 | 2 |  |  |  |  |  |
2M18592786$-$3636509 | 187 |  $-$91.3 | 0.00 | 0.063 | 13.45 | 1.25 | 10.45 | 0.75 |  0.84$\pm$0.02 |  $-$2.51$\pm$0.02 | 1.16 | 2 |  |  |  |  |  |
2M18593255$-$3641374 | 123 |  $-$89.5 | 0.04 | 0.063 | 13.69 | 1.19 | 10.83 | 0.78 |  0.89$\pm$0.02 |  $-$2.28$\pm$0.02 | 1.18 | 2 |  |  |  |  |  |
2M18593691$-$3641280 | 98 |  $-$91.4 | 0.11 | 0.063 | 14.52 | 1.02 | 11.86 | 0.72 |  1.04$\pm$0.03 |  $-$2.37$\pm$0.02 | 1.10 | 2 |  |  |  |  |  |
2M18594472$-$3639043 | 165 |  $-$100.1 | 0.01 | 0.063 | 13.54 | 1.13 | 10.81 | 0.77 |  1.25$\pm$0.02 |  $-$2.45$\pm$0.02 | 1.20 | 2 |  |  |  |  |  |
2M18594565$-$3637016 | 258 |  $-$91.9 | 0.29 | 0.063 | 13.22 | 1.37 | 10.01 | 0.89 |  0.84$\pm$0.02 |  $-$2.53$\pm$0.02 | 1.13 | 2 |  |  |  |  |  |
2M18594898$-$3635401 | 281 |  $-$93.7 | … | 0.063 | 13.08 | 1.43 | 9.77 | 0.91 |  0.93$\pm$0.02 |  $-$2.55$\pm$0.02 | 1.21 | 2 |  |  |  |  |  |
2M18594405$-$3651518 | 270 |  $-$94.5 | 0.06 | 0.520 | 12.72 | 1.38 | 9.78 | 0.86 |  1.06$\pm$0.02 |  $-$2.32$\pm$0.02 | 1.19 | 2 |  |  |  |  |  |

222Note: The synthetic spectra were based on 1D Local Thermodynamic
Equilibrium (LTE) model atmospheres calculated using MARCS models (Gustafsson
et al. 2008) and the Solar abundances from Asplund et al. (2005), except for
Ce II, Nd II, and Yb II, for which we have adopted the Solar abundances from
Grevesse et al. (2015).

Table 2: Abundance-ratio uncertainties for the model parameters with
$\Delta$T${}_{\rm eff}=100$ K, $\Delta\log g$ $=$ 0.3 dex,
$\Delta\xi_{t}=0.05$ km s-1, the uncertainties on the mean due to line-to-line
scatter ( $\sigma_{\rm[X/H],mean}$), and corresponding total error.

2M18594405 | $\sigma_{\rm[X/H],\log g}$ | $\sigma_{\rm[X/H],T_{\rm eff}}$ | $\sigma_{\rm[X/H],\xi_{t}}$ | $\sigma_{\rm[X/H],mean}$ | $\sigma_{\rm[X/H],total}$
---|---|---|---|---|---
$-$3651518 |  |  |  |  |
| [dex] | [dex] | [dex] | [dex] | [dex]
12C16O $\rightarrow$ 12C | 0.065 | 0.018 | 0.004 | 0.110 | 0.129
12C14N $\rightarrow$ 14N | 0.075 | 0.094 | 0.023 | 0.071 | 0.142
16OH $\rightarrow$ 16O | 0.018 | 0.097 | 0.014 | 0.068 | 0.121
Mg I | 0.005 | 0.089 | 0.022 | 0.052 | 0.106
Al I | 0.011 | 0.080 | 0.006 | 0.117 | 0.142
Si I | 0.045 | 0.023 | 0.006 | 0.094 | 0.107
K I | 0.025 | 0.044 | 0.009 | 0.137 | 0.146
Ca I | 0.023 | 0.023 | 0.007 | 0.085 | 0.091
Ti I | 0.007 | 0.070 | 0.033 | 0.246 | 0.258
Fe I | 0.016 | 0.042 | 0.005 | 0.154 | 0.161
Ni I | 0.027 | 0.047 | 0.010 | 0.155 | 0.165
Ce II | 0.123 | 0.067 | 0.025 | 0.125 | 0.189
Nd II | 0.075 | 0.071 | 0.023 | 0.130 | 0.168
Yb II | 0.092 | 0.024 | 0.004 | 0.020 | 0.097
2M18594898 | $\sigma_{\rm[X/H],\log g}$ | $\sigma_{\rm[X/H],T_{\rm eff}}$ | $\sigma_{\rm[X/H],\xi_{t}}$ | $\sigma_{\rm[X/H],mean}$ | $\sigma_{\rm[X/H],total}$
$-$3635401 |  |  |  |  |
| [dex] | [dex] | [dex] | [dex] | [dex]
12C16O $\rightarrow$ 12C | 0.035 | 0.064 | 0.009 | 0.052 | 0.090
12C14N $\rightarrow$ 14N | 0.042 | 0.108 | 0.004 | 0.069 | 0.135
16OH $\rightarrow$ 16O | 0.049 | 0.139 | 0.003 | 0.035 | 0.152
Mg I | 0.025 | 0.073 | 0.016 | 0.017 | 0.081
Al I | 0.014 | 0.111 | 0.009 | 0.116 | 0.161
Si I | 0.033 | 0.007 | 0.003 | 0.079 | 0.086
K I | 0.038 | 0.009 | 0.004 | 0.014 | 0.042
Ca I | 0.037 | 0.033 | 0.003 | 0.026 | 0.056
Ti I | 0.067 | 0.070 | 0.043 | 0.199 | 0.225
Fe I | 0.036 | 0.072 | 0.008 | 0.116 | 0.141
Ni I | 0.011 | 0.021 | 0.003 | 0.070 | 0.074
Ce II | 0.059 | 0.013 | 0.004 | 0.069 | 0.092
Nd II | 0.049 | 0.043 | 0.005 | 0.043 | 0.078
Yb II | 0.150 | 0.027 | 0.002 | 0.047 | 0.159

Note: The total error is defined as: $\sigma_{\rm[X_{\rm
i}/Fe],total}=\sqrt{\sigma^{2}_{\rm[X_{\rm i}/Fe],\log
g}+\sigma^{2}_{\rm[X_{\rm i}/Fe],T_{\rm eff}}+\sigma^{2}_{\rm[X_{\rm
i}/Fe],\xi_{t}}+\sigma^{2}_{\rm[X_{\rm i}/Fe],mean}}$.

###### Acknowledgements.

We thank the anonymous referee for helpful comments that greatly improved the
paper. We thank Dr. Lee Y.-W. J.G.F-T is supported by FONDECYT No. 3180210.
T.C.B. acknowledge partial support for this work 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. D.M. is supported by the
BASAL Center for Astrophysics and Associated Technologies (CATA) through grant
AFB 170002, and by project FONDECYT Regular No. 1170121. 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). S.V. gratefully acknowledges the support provided
by Fondecyt reg. n. 1170518. S.O.S. acknowledges the FAPESP PhD fellowship
2018/22044-3. B.B. acknowledge partial financial support from FAPESP, CNPq,
and CAPES - Finance Code 001. A.P-V. and S.O.S acknowledge the DGAPA-PAPIIT
grant IG100319. B.T. gratefully acknowledges support from the National Natural
Science Foundation of China under grant No. U1931102 and support from the
hundred-talent project of Sun Yat-sen University. J.A.-G. acknowledges support
from Fondecyt Regular 1201490 and from ANID, Millennium Science Initiative
ICN12_009, awarded to the Millennium Institute of Astrophysics (MAS). We
acknowledge UA VRIIP for the fund ”Asistentes de Investigación” financed by
projects ANT1855 and ANT1856 from Ministerio de Educación, Chile. T.P.
acknowledge support from the Argentinian institutions CONICET and SECYT
(Universidad Nacional de Córdoba). A.R-L acknowledges financial support
provided in Chile by Agencia Nacional de Investigación y Desarrollo (ANID)
through the FONDECYT project 1170476. R.R.M. acknowledges partial support from
project BASAL AFB-$170002$ as well as FONDECYT project N${}^{\circ}1170364$.
L.C-V thanks the Fondo Nacional de Financiamiento para la Ciencia, La
Tecnología y la innovación ”FRANCISCO JOSÉ DE CALDAS”, MINCIENCIAS, and the
VIIS for the economic support of this research.
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, the
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.

## References

  * Ahumada et al. (2020) Ahumada, R., Allende Prieto, C., Almeida, A., et al. 2020, ApJS, 249, 3
  * Alonso-García et al. (2017) Alonso-García, J., Minniti, D., Catelan, M., et al. 2017, ApJ, 849, L13
  * Alvarez & Plez (1998) Alvarez, R. & Plez, B. 1998, A&A, 330, 1109
  * Anders et al. (2019) Anders, F., Khalatyan, A., Chiappini, C., et al. 2019, A&A, 628, A94
  * Asplund et al. (2005) Asplund, M., Grevesse, N., & Sauval, A. J. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 336, Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, ed. I. Barnes, Thomas G. & F. N. Bash, 25
  * Barbuy et al. (2014) Barbuy, B., Chiappini, C., Cantelli, E., et al. 2014, A&A, 570, A76
  * Baumgardt et al. (2019) Baumgardt, H., Hilker, M., Sollima, A., & Bellini, A. 2019, MNRAS, 482, 5138
  * Beers & Christlieb (2005) Beers, T. C. & Christlieb, N. 2005, ARA&A, 43, 531
  * Bekki (2019) Bekki, K. 2019, MNRAS, 490, 4007
  * Blanton et al. (2017) Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017, AJ, 154, 28
  * Bowen & Vaughan (1973) Bowen, I. S. & Vaughan, A. H., J. 1973, Appl. Opt., 12, 1430
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Brown et al. (1990) Brown, J. A., Wallerstein, G., & Oke, J. B. 1990, AJ, 100, 1561
  * Brunthaler et al. (2011) Brunthaler, A., Reid, M. J., Menten, K. M., et al. 2011, Astronomische Nachrichten, 332, 461
  * Chiappini et al. (2011) Chiappini, C., Frischknecht, U., Meynet, G., et al. 2011, Nature, 472, 454
  * Chun et al. (2015) Chun, S.-H., Kang, M., Jung, D., & Sohn, Y.-J. 2015, AJ, 149, 29
  * Cohen et al. (2020) Cohen, R. E., Bellini, A., Libralato, M., et al. 2020, arXiv e-prints, arXiv:2012.00791
  * Crestani et al. (2019) Crestani, J., Alves-Brito, A., Bono, G., Puls, A. A., & Alonso-García, J. 2019, MNRAS, 487, 5463
  * Cunha et al. (2017) Cunha, K., Smith, V. V., Hasselquist, S., et al. 2017, ApJ, 844, 145
  * de Boer et al. (2019) de Boer, T. J. L., Gieles, M., Balbinot, E., et al. 2019, MNRAS, 485, 4906
  * De Smedt et al. (2016) De Smedt, K., Van Winckel, H., Kamath, D., et al. 2016, A&A, 587, A6
  * Dotter et al. (2010) Dotter, A., Sarajedini, A., Anderson, J., et al. 2010, ApJ, 708, 698
  * Fernández-Trincado et al. (2020a) Fernández-Trincado, J. G., Beers, T. C., & Minniti, D. 2020a, A&A, 644, A83
  * Fernández-Trincado et al. (2020b) Fernández-Trincado, J. G., Beers, T. C., Minniti, D., et al. 2020b, ApJ, 903, L17
  * Fernández-Trincado et al. (2020c) Fernández-Trincado, J. G., Beers, T. C., Minniti, D., et al. 2020c, A&A, 643, L4
  * Fernández-Trincado et al. (2019a) Fernández-Trincado, J. G., Beers, T. C., Placco, V. M., et al. 2019a, ApJ, 886, L8
  * Fernández-Trincado et al. (2019b) Fernández-Trincado, J. G., Beers, T. C., Tang, B., et al. 2019b, MNRAS, 488, 2864
  * Fernández-Trincado et al. (2020d) Fernández-Trincado, J. G., Chaves-Velasquez, L., Pérez-Villegas, A., et al. 2020d, MNRAS, 495, 4113
  * Fernández-Trincado et al. (2019c) Fernández-Trincado, J. G., Mennickent, R., Cabezas, M., et al. 2019c, A&A, 631, A97
  * Fernández-Trincado et al. (2020e) Fernández-Trincado, J. G., Minniti, D., Beers, T. C., et al. 2020e, A&A, 643, A145
  * Fernández-Trincado et al. (2016a) Fernández-Trincado, J. G., Robin, A. C., Moreno, E., et al. 2016a, ApJ, 833, 132
  * Fernández-Trincado et al. (2016b) Fernández-Trincado, J. G., Robin, A. C., Reylé, C., et al. 2016b, MNRAS, 461, 1404
  * Fernández-Trincado et al. (2015a) Fernández-Trincado, J. G., Robin, A. C., Vieira, K., et al. 2015a, A&A, 583, A76
  * Fernández-Trincado et al. (2015b) Fernández-Trincado, J. G., Vivas, A. K., Mateu, C. E., et al. 2015b, A&A, 574, A15
  * Fernández-Trincado et al. (2017) Fernández-Trincado, J. G., Zamora, O., García-Hernández, D. A., et al. 2017, ApJ, 846, L2
  * Fernández-Trincado et al. (2019d) Fernández-Trincado, J. G., Zamora, O., Souto, D., et al. 2019d, A&A, 627, A178
  * Frebel et al. (2006) Frebel, A., Christlieb, N., Norris, J. E., et al. 2006, ApJ, 652, 1585
  * Gaia Collaboration et al. (2020) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2020, arXiv e-prints, arXiv:2012.01533
  * García Pérez et al. (2016) García Pérez, A. E., Allende Prieto, C., Holtzman, J. A., et al. 2016, AJ, 151, 144
  * Gnedin & Ostriker (1997) Gnedin, O. Y. & Ostriker, J. P. 1997, ApJ, 474, 223
  * González Hernández & Bonifacio (2009) González Hernández, J. I. & Bonifacio, P. 2009, A&A, 497, 497
  * Grevesse et al. (2015) Grevesse, N., Scott, P., Asplund, M., & Sauval, A. J. 2015, A&A, 573, A27
  * Gunn et al. (2006) Gunn, J. E., Siegmund, W. A., Mannery, E. J., et al. 2006, AJ, 131, 2332
  * Gustafsson et al. (2008) Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951
  * Hanke et al. (2020) Hanke, M., Koch, A., Prudil, Z., Grebel, E. K., & Bastian, U. 2020, A&A, 637, A98
  * Harris (1996) Harris, W. E. 1996, AJ, 112, 1487
  * Harris (2010) Harris, W. E. 2010, arXiv e-prints, arXiv:1012.3224
  * Hasselquist et al. (2016) Hasselquist, S., Shetrone, M., Cunha, K., et al. 2016, ApJ, 833, 81
  * Hawkins et al. (2016) Hawkins, K., Masseron, T., Jofré, P., et al. 2016, A&A, 594, A43
  * Holtzman et al. (2018) Holtzman, J. A., Hasselquist, S., Shetrone, M., et al. 2018, AJ, 156, 125
  * Horta et al. (2021) Horta, D., Mackereth, J. T., Schiavon, R. P., et al. 2021, MNRAS, 500, 5462
  * Johnson et al. (2007) Johnson, J. A., Herwig, F., Beers, T. C., & Christlieb, N. 2007, ApJ, 658, 1203
  * Karakas et al. (2018) Karakas, A. I., Lugaro, M., Carlos, M., et al. 2018, MNRAS, 477, 421
  * Karakas et al. (2014) Karakas, A. I., Marino, A. F., & Nataf, D. M. 2014, ApJ, 784, 32
  * Karinkuzhi & Goswami (2014) Karinkuzhi, D. & Goswami, A. 2014, MNRAS, 440, 1095
  * King (1962) King, I. 1962, AJ, 67, 471
  * King (1966) King, I. R. 1966, AJ, 71, 64
  * Kobayashi et al. (2020) Kobayashi, C., Karakas, A. I., & Lugaro, M. 2020, ApJ, 900, 179
  * Kundu et al. (2019a) Kundu, R., Fernández-Trincado, J. G., Minniti, D., et al. 2019a, MNRAS, 489, 4565
  * Kundu et al. (2019b) Kundu, R., Minniti, D., & Singh, H. P. 2019b, MNRAS, 483, 1737
  * Kundu et al. (2020) Kundu, R., Navarrete, C., Fernández-Trincado, J. G., et al. 2020, arXiv e-prints, arXiv:2011.10525
  * Lane et al. (2010) Lane, R. R., Kiss, L. L., Lewis, G. F., et al. 2010, MNRAS, 406, 2732
  * Lee et al. (2014) Lee, J.-W., López-Morales, M., Hong, K., et al. 2014, ApJS, 210, 6
  * Lee et al. (2013) Lee, Y. S., Beers, T. C., Masseron, T., et al. 2013, AJ, 146, 132
  * Leon et al. (2000) Leon, S., Meylan, G., & Combes, F. 2000, A&A, 359, 907
  * Majewski et al. (2017) Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94
  * Majewski et al. (2011) Majewski, S. R., Zasowski, G., & Nidever, D. L. 2011, ApJ, 739, 25
  * Martell et al. (2016) Martell, S. L., Shetrone, M. D., Lucatello, S., et al. 2016, ApJ, 825, 146
  * Masseron et al. (2016) Masseron, T., Merle, T., & Hawkins, K. 2016, BACCHUS: Brussels Automatic Code for Characterizing High accUracy Spectra
  * Mateu et al. (2009) Mateu, C., Vivas, A. K., Zinn, R., Miller, L. R., & Abad, C. 2009, AJ, 137, 4412
  * Mészáros et al. (2020) Mészáros, S., Masseron, T., García-Hernández, D. A., et al. 2020, MNRAS, 492, 1641
  * Moreno et al. (2014) Moreno, E., Pichardo, B., & Velázquez, H. 2014, ApJ, 793, 110
  * Muñoz et al. (2018) Muñoz, C., Geisler, D., Villanova, S., et al. 2018, A&A, 620, A96
  * Nidever et al. (2015) Nidever, D. L., Holtzman, J. A., Allende Prieto, C., et al. 2015, AJ, 150, 173
  * Oliveira et al. (2020) Oliveira, R. A. P., Souza, S. O., Kerber, L. O., et al. 2020, ApJ, 891, 37
  * Piatti et al. (2019) Piatti, A. E., Webb, J. J., & Carlberg, R. G. 2019, MNRAS, 489, 4367
  * Placco et al. (2018) Placco, V. M., Beers, T. C., Santucci, R. M., et al. 2018, AJ, 155, 256
  * Placco et al. (2014) Placco, V. M., Frebel, A., Beers, T. C., et al. 2014, ApJ, 781, 40
  * Plez (2012) Plez, B. 2012, Turbospectrum: Code for spectral synthesis
  * Press et al. (2002) Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 2002, Numerical recipes in C++ : the art of scientific computing
  * Queiroz et al. (2020) Queiroz, A. B. A., Anders, F., Chiappini, C., et al. 2020, A&A, 638, A76
  * Queiroz et al. (2018) Queiroz, A. B. A., Anders, F., Santiago, B. X., et al. 2018, MNRAS, 476, 2556
  * Rojas-Arriagada et al. (2016) Rojas-Arriagada, A., Zoccali, M., Vásquez, S., et al. 2016, A&A, 587, A95
  * Sarajedini et al. (2007) Sarajedini, A., Bedin, L. R., Chaboyer, B., et al. 2007, AJ, 133, 1658
  * Schiavon et al. (2017a) Schiavon, R. P., Johnson, J. A., Frinchaboy, P. M., et al. 2017a, MNRAS, 466, 1010
  * Schiavon et al. (2017b) Schiavon, R. P., Zamora, O., Carrera, R., et al. 2017b, MNRAS, 465, 501
  * Smith et al. (2013) Smith, V. V., Cunha, K., Shetrone, M. D., et al. 2013, ApJ, 765, 16
  * Sofue (2015) Sofue, Y. 2015, PASJ, 67, 75
  * Sollima (2020) Sollima, A. 2020, MNRAS, 495, 2222
  * Souza et al. (2020) Souza, S. O., Kerber, L. O., Barbuy, B., et al. 2020, ApJ, 890, 38
  * Ventura et al. (2012) Ventura, P., di Criscienzo, M., Schneider, R., et al. 2012, MNRAS, 420, 1442
  * Ventura et al. (2016) Ventura, P., García-Hernández, D. A., Dell’Agli, F., et al. 2016, ApJ, 831, L17
  * Wanajo et al. (2014) Wanajo, S., Sekiguchi, Y., Nishimura, N., et al. 2014, ApJ, 789, L39
  * Yoon et al. (2019) Yoon, J., Beers, T. C., Tian, D., & Whitten, D. D. 2019, ApJ, 878, 97
  * Zasowski et al. (2017) Zasowski, G., Cohen, R. E., Chojnowski, S. D., et al. 2017, AJ, 154, 198