<figure><img src="image_1.png" /></figure>

# The Metal-poor non-Sagittarius (?) Globular Cluster NGC 5053: Orbit and Mg, Al, and Si abundances

Baitian Tang<fnref n="1" />,<fnref n="2" />, J. G. Fernández-Trincado<fnref n="2" />,<fnref n="3" />, Doug Geisler<fnref n="2" />, Olga Zamora<fnref n="4" />,<fnref n="5" />, Szabolcs Mészáros<fnref n="6" />,<fnref n="16" />, Thomas Masseron<fnref n="4" />,<fnref n="5" />, Roger E. Cohen<fnref n="7" />, D. A. García-Hernández<fnref n="4" />,<fnref n="5" />, Flavia Dell'Agli<fnref n="4" />,<fnref n="5" />, Timothy C. Beers<fnref n="8" />, Ricardo P. Schiavon<fnref n="9" />, Sangmo Tony Sohn<fnref n="7" />, Sten Hasselquist<fnref n="10" />, Annie C. Robin<fnref n="3" />, Matthew Shetrone<fnref n="11" />, Steven R. Majewski<fnref n="12" />, Sandro Villanova<fnref n="2" />, Jose Schiappacasse Ulloa<fnref n="2" />, Richard R. Lane<fnref n="13" />, Dante Minnti<fnref n="13" />, Alexandre Roman-Lopes<fnref n="14" />, Andres Almeida<fnref n="14" />, and E. Moreno<fnref n="15" />

Received 2017 November 7; revised 2018 January 24; accepted 2018 January 24; published 2018 March 5

## Abstract

Metal-poor globular clusters (GCs) exhibit intriguing Al–Mg anti-correlations and possible Si–Al correlations, which are important clues to decipher the multiple-population phenomenon. NGC 5053 is one of the most metal-poor GCs in the nearby universe and has been suggested to be associated with the Sagittarius (Sgr) dwarf galaxy, due to its similarity in location and radial velocity with one of the Sgr arms. In this work, we simulate the orbit of NGC 5053, and argue against a physical connection between Sgr and NGC 5053. On the other hand, the Mg, Al, and Si spectral lines, which are difficult to detect in the optical spectra of NGC 5053 stars, have been detected in the near-infrared APOGEE spectra. We use three different sets of stellar parameters and codes to derive the Mg, Al, and Si abundances. Regardless of which method is adopted, we see a large Al variation, and a substantial Si spread. Along with NGC 5053, metal-poor GCs exhibit different Mg, Al, and Si variations. Moreover, NGC 5053 has the lowest cluster mass among the GCs that have been identified to exhibit an observable Si spread until now.

**Key words:** globular clusters: individual (NGC 5053) – stars: abundances – stars: evolution

## 1. Introduction

The multiple-population (MP) phenomenon has now been observed in most of the evolutionary sequences of globular clusters (GCs): main-sequence (MS), subgiant branch (SGB), red giant branch (RGB), horizontal branch (HB), and asymptotic giant branch (AGB). While photometry is an efficient way of revealing MPs in most stellar phases, and particularly, fainter phases (e.g., Milone et al. 2015; Piotto et al. 2015), high-resolution spectroscopy allows deeper insights into GC formation and internal stellar evolution, providing detailed abundances for a number of elements with a variety of nucleosynthetic origins (e.g., García-Hernández et al. 2015; Mészáros et al. 2015; Schiavon et al. 2017; Tang et al. 2017). The Al–Mg anti-correlations, and the less frequent Si–Al correlations are of great interest, because these chemical patterns indicate that the polluting stars must have reached temperatures above 90 MK (Prantzos et al. 2007; Ventura et al. 2012; D’Antona et al. 2016), which is a strong constraint on the nature of these stars. A significant silicon spread is observed in a few GCs, mainly metal-poor or massive GCs

(e.g., Carretta et al. 2009b; Mészáros et al. 2015). Further investigations of metal-poor GCs would tell us more about the environment that stimulates the Si variation.

NGC 5053 is one of the most metal-poor GCs known ([Fe/H] = −2.27, Harris 1996; 2010 version). It is located close to the Galactic north pole (αJ2000 = 13h16m27s1, δJ2000 = +17°42′01″, l = 335°70, b = +78°95). With similar location and radial velocity<fnref n="17" /> (RV) to one of the Sagittarius (Sgr) arms (Law & Majewski 2010), NGC 5053 has been speculated to be associated with the Sgr stream, but a firm association is still under debate (Palma et al. 2002; Bellazzini et al. 2003; Law & Majewski 2010). A similar discussion is also found for its close companion, M53 (Figure 1). NGC 5053 and M53 have similar Galactocentric radii (17.8 and 18.4 kpc, respectively). Based on the X, Y, and Z positions from the Harris catalog, these two GCs are currently only ~500 pc away from each other. Furthermore, Chun et al. (2010) suggested that these two GCs also share a tidal bridge. Palma et al. (2002) suggested that the Sgr association is unlikely for these two GCs because they are more metal poor than previously identified clusters ([Fe/H] = −2.27 for NGC 5053 and [Fe/H] = −2.10

<footnote n="1">¹ School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, People's Republic of China</footnote>

<footnote n="2">² Departamento de Astronomía, Casilla 160-C, Universidad de Concepción, Concepción, Chile</footnote>

<footnote n="3">³ Institut Utinam, CNRS UMR 6213, Université Bourgogne-Franche-Comté, OSU THETA Franche-Comté, Observatoire de Besançon, BP 1615, F-25010 Besançon Cedex, France</footnote>

<footnote n="4">⁴ Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain</footnote>

<footnote n="5">⁵ Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain</footnote>

<footnote n="6">⁶ ELTE Eötvös Loránd University, Gothard Astrophysical Observatory, Szombathely, Hungary</footnote>

<footnote n="7">⁷ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA</footnote>

<footnote n="8">⁸ Department of Physics and JINA Center for the Evolution of the Elements, University of Notre Dame, Notre Dame, IN 46556 USA</footnote>

<footnote n="9">⁹ Astrophysics Research Institute, Liverpool John Moores University, Liverpool, UK</footnote>

<footnote n="10">¹⁰ New Mexico State University, Las Cruces, NM 88003, USA</footnote>

<footnote n="11">¹¹ Department of Astronomy, University of Texas at Austin, Austin, TX 78712, USA</footnote>

<footnote n="12">¹² Department of Astronomy, University of Virginia, Charlottesville, VA 22904-4325, USA</footnote>

<footnote n="13">¹³ Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuna Mackenna 4860, 782-0436 Macul, Santiago, Chile</footnote>

<footnote n="14">¹⁴ Instituto de Investigación Multidisciplinario en Ciencia y Tecnología, Universidad de La Serena, Benavente 980, La Serena, Chile</footnote>

<footnote n="15">¹⁵ Instituto de Astronomía, Universidad Nacional Autónoma de México, Apartado Postal 70-264, 04510-México DF, Mexico</footnote>

<footnote n="16">¹⁶ Premium Postdoctoral Fellow of the Hungarian Academy of Sciences.</footnote>

<footnote n="17">¹⁷ The radial velocities in this work are heliocentric radial velocities.</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Locations of the stars in the APOGEE field of NGC 5053. The NGC 5053 member stars are indicated by filled circles. The magenta circle indicates the cluster tidal radius. Note that the star cluster in the upper left is M53.</figcaption></figure>

for M53, Harris catalog). Bellazzini et al. (2003) considered NGC 5053 to be one of the Sgr GCs based on its location and radial velocity, while M53 was not discussed. Law & Majewski (2010) showed that the proper motion of M53 along the right ascension axis ($\mu_o \cos\delta$) is not consistent with any of the Sgr tidal arms, and concluded that M53 is probably not physically associated with Sgr. Meanwhile, the location and radial velocity of NGC 5053 are consistent with the T1 Sgr tidal arm, but the cluster's proper motion was not available at that time. Below, we simulate the orbit of NGC 5053 using newly obtained proper motion<fnref n="18" /> and our new software for dynamical modeling GravPot16 (J. Fernández-Trincado et al. 2018, in preparation).

In terms of chemical abundances, Sbordone et al. (2015) analyzed HIRES spectra (438–678 nm, *R* = 48,000) down-loaded from the Keck Observatory archive for one RGB star in NGC 5053. Because the spectral lines are generally weak in metal-poor stars, only 13 element species were investigated. We note that Mg, Al, and Si are not in their list of elements. Boberg et al. (2015, B15) observed 17 member stars using the Wisconsin–Indiana–Yale-NOAO-Hydra (WIYN) multi-object spectrograph. After analyzing the medium-resolution spectra (R ~ 13,000), they measured the abundances of Fe, Ca, Ti, Ni, Ba, Na, and O. Boberg et al. found bimodality in the Na distribution, suggesting the existence of multiple populations in this GC. Previous work on elemental abundances provides evidence for a possible chemical connection between NGC 5053 and Sgr, including a very low yttrium abundance (Sbordone et al. 2015). However, a firm association has not been obtained yet. In this work, we focus on deriving the Mg, Al, and Si abundances from the APOGEE (Apache Point Observatory Galactic Evolution Experiment) spectra (Section 5), where relatively strong spectral lines are seen for these elements. These are the first measurements of Mg, Al, and Si in NGC 5053. These abundances are important indicators of the nature of the polluting stars that are responsible for multiple populations (Section 6).

## 2. Sample Selection and Data Reduction

APOGEE (Majewski et al. 2017) was one of the programs operating during the Sloan Digital Sky Survey III (SDSS-III, Eisenstein et al. 2011). The multi-object NIR fiber spectrograph on the 2.5 m telescope at the Apache Point Observatory (Gunn et al. 2006) delivers high-resolution (R ~ 22,500) H-band spectra ($\lambda$ = 1.51–1.69 µm), and the APOGEE survey targeted a color-selected sample that predominantly consists of RGB stars across the Milky Way (Zasowski et al. 2017). APOGEE data reduction software is applied to reduce multiple 3D raw data cubes into calibrated, well-sampled, combined 1D spectra (Nidever et al. 2015). In addition, the APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP; García Pérez et al. 2016) derives stellar parameters and elemental abundances by comparing observed spectra to libraries of theoretical spectra (Zamora et al. 2015), constructed using extensive molecular/atomic linelists (Shetrone et al. 2015), in order to find the closest model match, using $\chi^2$ minimization in a multi-dimensional parameter space. In the current public SDSS Data Release 14 (DR14), up to more than 20 chemical elements were identified, and measured abundances provided (Holtzman et al. 2015). DR14 includes all APOGEE-1 data, and APOGEE-2N data taken between 2014 July and 2016 July.

To select stars that are members of NGC 5053, we first restrict the sample to stars within the tidal radius (11.43') given by Harris (1996; 2010 version). Then we exclude probable field stars by applying two generous criteria: $[Fe/H]_{NGC5053} \pm 0.3$, $RV_{NGC5053} \pm 15 \text{ km s}^{-1}$, where $[Fe/H]_{NGC5053} = -2.27$ and $RV_{NGC5053} = 44.0 \text{ km s}^{-1}$ from the Harris catalog. We identify 11 stars using the metallicities and RVs provided by APOGEE DR14. Given that NGC 5053 may have tidal structure (Lauchner et al. 2006), we also relax the search area to 3 times the tidal radius, but no further members in DR14 are identified in this way. Since NGC 5053 is far away from the Galactic plane, relaxing the [Fe/H] and RV criteria ($\pm 0.6$ dex and $\pm 30 \text{ km s}^{-1}$) also does not increase the number of members. After checking the color–magnitude diagram (CMD) and stellar parameters, we further exclude one star (APOGEE_ID=2M13161337+1743552), because its location in the CMD is away from the RGB (Figure 2), and its ASPCAP stellar parameters also deviate from the isochrone (Figure 6). The stellar parameters are given in Section 4. Thus, our final list consists of 10 stars (Figure 1). We have also checked the photometry from P. Stetson<fnref n="19" /> for possible AGB (Asymtoptic Giant Branch) stars in our sample. García-Hernández et al. (2015) showed that *U* versus (*U* − *I*) CMD is able to distinguish AGB stars from RGB stars. We have checked the *U* versus (*U* − *I*) CMD for NGC 5053, where eight stars from our sample are identified. No obvious AGB star is found. Among our 10 sample stars, 6 of them were also selected as members in B15 (Table 1, also see Figure 2).

## 3. TRACKING THE ORBIT OF NGC 5053

### 3.1. *Adopted Observational Data for NGC 5053 and Sagittarius*

To obtain robust estimates of the orbit of NGC 5053, we employed recent high-quality data. First, we adopted the new

<footnote n="18">¹⁸ The proper motions in this work are absolute proper motions.</footnote>

<footnote n="19">¹⁹ http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/community/STETSON/standards/</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** *V* vs. *B*−*V* CMD of NGC 5053. The APOGEE selected members are indicated by black dots. The red open circles show the stars observed by B15. The blue open circle is the one RGB star observed in Sbordone et al. (2015). The cross is the one star that we exclude by CMD and isochrone selection.</figcaption></figure>

proper motion measurements based on multi-epoch Hubble
Space Telescope (HST) observations separated by ~11 years in
time. Details of this measurement, including the proper motion
result for NGC 5053, will be presented in a forthcoming paper
(T. Sohn et al. 2018, in preparation). In short, we utilized the
same established method of Sohn et al. (2012, 2013, 2017) to
achieve a one-day proper motion uncertainty of ~0.07 mas yr⁻¹
for NGC 5053. The only other proper motion measurement found
in the literature is provided by Kharchenko et al. (2013), and for
comparison, we integrate orbits using their measurement
separately (see Figure 3 for details).

The heliocentric distance of NGC 5053 was presented in the
Harris catalog and Arellano Ferro et al. (2010) using RR Lyrae
stars. Being standard candles, RR Lyrae stars are particularly
suitable to derive cluster distances with a high degree of
confidence. The Harris catalog suggested a distance of 16.4 kpc
for NGC 5053, which assumes *V*(HB) = 16.65 (Sarajedini
& Milone 1995), [Fe/H] = −2.29, extinction ratio *R* = 3.0,
*E*(B − *V*) = 0.04, and the relation *M*<sub>V</sub> = 0.15[Fe/H] + 0.80.
Arellano Ferro et al. (2010) derived a mean distance modulus of
16.12 ± 0.4, which corresponds to a distance of 16.7 ± 0.3 kpc.
They assume [Fe/H] = −1.97, *R* = 3.2, *E*(B − *V*) = 0.018.
Even though different parameters were assumed in two studies,
the derived distances agree with each other. We adopt the latter
distance 16.7 ± 0.3 kpc in this work.

Using the APOGEE spectra, we have visually inspected the
strong Mg, Al, and Si spectral lines (Section 5), and list the
derived RV in Table 2. We obtain a mean RV of

43.4 ± 2.2 km s⁻¹, which is consistent with the value from
the Harris catalog (44.0 ± 0.4 km s⁻¹). The detailed values that
we adopted in our simulations are shown in Table 3.

3.2. *Orbits and Implications*

By combining our Milky Way potential model (see the
Appendix) with measurements of radial velocity, absolute
proper motion, distance, and sky position for NGC 5053 and
Sagittarius, we ran N<sub>total</sub> = 1 × 10<sup>4</sup> pairs of orbits NGC 5053
—Sagittarius, taking into account the uncertainties in the input
data considering 1σ variations in a Gaussian Monte Carlo
approach. For each generated set of parameters, the orbit of
NGC 5053 was computed backward in time, up to 2.5 Gyr. All
orbital computations were made with a Runge–Kutta algorithm
of the seventh order, with a variable time step determined at the
initial conditions and conserved to 1 part in 10<sup>−14</sup>.

From the integrated set of orbits, we compute (1) the orbital
eccentricity, defined as $e = (r_{apo} - r_{per})/(r_{apo} + r_{per})$, with $r_{apo}$
and $r_{per}$ as successive apogalactic and perigalactic distances,
(2) the maximun vertical amplitude $Z_{max}$ as well as (3) the
orbital Jacobi constant per unit mass, $E_J$, and (4) the
“characteristic” orbital energy, $(E_{min} + E_{max})/2$, as defined in
Moreno et al. (2015).

The major assumptions and limitations in our computations
are (i) we do not consider the effects of dynamical friction of
NGC 5053 and Sagittarius, which is expected to bring both
systems closer to the Galactic center; (ii) we ignore secular
changes in our Milky Way potential over time, which are
expected although the Milky Way has had a quiet recent
accretion history; (iii) we ignore the possibility that the pair
NGC 5053—Sagittarius were likely more massive in the past
and have tidally lost some of that mass, which reduces the
absolute probabilities we find.

Our simulation results (Figure 3) show that the orbit of NGC
5053 does not resemble that of Sgr, suggesting no association
between the two objects. Figure 4 shows results for the
“characteristic” orbital energy ($E_{max} + E_{min}/2$) versus the
orbital Jacobi energy ($E_J$) in the potential mentioned above
(including $1 \times 10^4$ random orbital realizations), the Galactic
noninertial frame is employed to compute the orbits. This plot
shows a noticeable difference between NGC 5053 and Sgr. The
Sgr occupies a very distinct region in these spaces, with an
overdensity at $E_J \sim -1400 \times 10^5 \text{ km}^2 \text{s}^{-2}$ and $E_{max} + E_{min}/2 \sim -1000 \text{ km}^2 \text{s}^{-2}$, with most of the NGC 5053 orbits shifted
toward a lower distribution both in “characteristic” orbital
energy and $E_J$. Therefore, an association of NGC 5053 with Sgr
appears implausible.

In Figure 5, we compared the eccentricity distribution for
Sgr and NGC 5053, considering the HST and Kharchenko et al.
(2013) absolute proper motions. This figure reassuringly shows
that the eccentricity distributions of NGC 5053 and Sgr are
decidedly different, even after taking errors into account, which
means that NGC 5053 is characterized by different orbital
configurations than Sgr. Therefore, our results suggest that it is
unlikely that NGC 5053 comes from a dwarf galaxy (Sgr) that,
on average, has significantly higher orbital energy.

4. Chemical Abundance Derivation

Since some of the spectral lines in metal-poor stars become
too weak for analysis, stellar parameters (T<sub>eff</sub>, log g, [Fe/H])
derived from χ<sup>2</sup> fitting in ASPCAP may be problematic.
<table><caption>**Table 1**

Photometric Properties of the NGC 5053 Members</caption><thead><tr><th>#</th><th>APOGEE_ID</th><th>R.A.<sub>J2000</sub> (°)</th><th>Decl.<sub>J2000</sub> (°)</th><th>B</th><th>V</th><th>2MASS J</th><th>2MASS H</th><th>2MASS K<sub>S</sub></th><th>B15 ID</th></tr></thead><tbody><tr><td>Star1</td><td>2M13160457+1747017</td><td>199.019064</td><td>17.783821</td><td>16.37</td><td>15.53</td><td>13.775</td><td>13.208</td><td>13.116</td><td>...</td></tr><tr><td>Star2</td><td>2M13161223+1746228</td><td>199.050959</td><td>17.773018</td><td>15.20</td><td>14.08</td><td>11.956</td><td>11.377</td><td>11.243</td><td>3</td></tr><tr><td>Star3</td><td>2M13162073+1741059</td><td>199.086404</td><td>17.684973</td><td>15.99</td><td>15.10</td><td>13.293</td><td>12.752</td><td>12.633</td><td>15</td></tr><tr><td>Star4</td><td>2M13162226+1741536</td><td>199.092771</td><td>17.698231</td><td>16.12</td><td>15.25</td><td>13.140</td><td>12.776</td><td>12.608</td><td>20</td></tr><tr><td>Star5</td><td>2M13162279+1739074</td><td>199.094981</td><td>17.652067</td><td>16.30</td><td>15.44</td><td>14.101</td><td>13.655</td><td>13.513</td><td>...</td></tr><tr><td>Star6</td><td>2M13163419+1743530</td><td>199.142482</td><td>17.731409</td><td>16.45</td><td>15.71</td><td>13.471</td><td>12.873</td><td>12.856</td><td>19</td></tr><tr><td>Star7</td><td>2M13163790+1745355</td><td>199.157922</td><td>17.759867</td><td>16.11</td><td>15.24</td><td>13.180</td><td>12.637</td><td>12.541</td><td>14</td></tr><tr><td>Star8</td><td>2M13164030+1740254</td><td>199.167950</td><td>17.673727</td><td>15.96</td><td>15.04</td><td>13.926</td><td>13.424</td><td>13.348</td><td>...</td></tr><tr><td>Star9</td><td>2M13164077+1747338</td><td>199.169899</td><td>17.792746</td><td>16.47</td><td>15.66</td><td>13.345</td><td>12.793</td><td>12.688</td><td>...</td></tr><tr><td>Star10</td><td>2M13165764+1738050</td><td>199.240180</td><td>17.634743</td><td>15.76</td><td>14.83</td><td>12.962</td><td>12.388</td><td>12.295</td><td>11</td></tr></tbody></table>

Note. B and V apparent magnitudes come from Sarajedini & Milone (1995).

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Representative orbits of Sgr (gray), NGC 5053 with HST proper motion (red), and NGC 5053 with old proper motion (green) in the reference frame where the bar is at rest. Left: equatorial Galactic orbits. Right: meridional Galactic orbits. The orbits of NGC 5053 do not resemble that of Sgr, suggesting that the proposed connection between these two systems may be unlikely.</figcaption></figure>

<figure><img src="image_5.png" /></figure>

Mészáros et al. (2015) suggested that manual analysis is required for stars more metal-poor than [Fe/H] = −1. Furthermore, some of the windows for a given element may be dominated by noise when the signal is too weak, which complicates the abundance derivation. Therefore, we derive chemical abundances manually for our sample of metal-poor stars in NGC 5053. However, note that all of our spectra have S/N > 75 (Table 3), and most have S/N > 100.

First, we estimated the stellar parameters using B, V, I (Sarajedini & Milone 1995) and 2MASS J, H, K photometry (Table 1). The photometric $T_{\text{eff}}$ is the mean value of the $T_{\text{eff}}$ calculated with B − V and V − K$_{s}$ colors using the equations of González Hernández & Bonifacio (2009). The foreground extinction for each band is given by Schlafly & Finkbeiner (2011)$^{20}$ and is very low ($E(B-V) = 0.015$). To derive log g, we use the Dartmouth Stellar Evolution Database (DSED, Dotter et al. 2008) isochrone of age = 13 Gyr, [Fe/H] = −2.27, [α/Fe] = +0.20. The log g for each star is read from the isochrone for its given photometric $T_{\text{eff}}$.

Figure 6 shows the isochrone, stellar parameters (SPs) from ASPCAP and from photometry. We find that (1) the ASPCAP derived SPs agree well with the isochrone; (2) the photometric derived SPs also agree well with the isochrone by definition; (3) the B15 SPs have higher log g or lower $T_{\text{eff}}$ than the isochrone; (4) and the number distribution of stars along the isochrone for ASPCAP SPs agrees well with that of CMD in Figure 2, while photometric derived SPs suggest that most stars have low log g and low $T_{\text{eff}}$.

The iron abundances of NGC 5053 stars have been determined by several optical investigations (e.g., B15, Sbordone et al. 2015), and the results from the literature are generally around −2.1 to −2.5 (see B15 for a list of literature results). The value given in the Harris catalog is [Fe/H] = −2.27. After visually inspecting the iron lines in the spectra, we find that the iron lines are hard to detect even with S/N ~ 100. Given that the derived chemical abundances are affected by the uncertainties of adopted stellar parameters, we decided to derive the elemental abundances using three different sets of stellar parameters:

<footnote>$^{20}$ NED. https://ned.ipac.caltech.edu.</footnote>
<table><caption>**Table 2**

Stellar Parameters of the NGC 5053 Members from ASPCAP</caption><thead><tr><th rowspan="2">#</th><th>RV</th><th>δ<sub>RV</sub></th><th>[Fe/H]</th><th>δ<sub>[Fe/H]</sub></th><th>T<sub>eff</sub></th><th>δ<sub>T<sub>eff</sub></sub></th><th>log g</th><th>δ<sub>log g</sub></th><th>SNR</th></tr><tr><th colspan="4">(km s<sup>-1</sup>)</th><th colspan="4">(K)</th></tr></thead><tbody><tr><td>Star1</td><td>43.81</td><td>0.17</td><td>-2.28</td><td>0.02</td><td>4923.7</td><td>99.3</td><td>1.85</td><td>0.13</td><td>108</td></tr><tr><td>Star2</td><td>44.56</td><td>0.06</td><td>-2.36</td><td>0.02</td><td>4497.3</td><td>67.7</td><td>0.82</td><td>0.11</td><td>187</td></tr><tr><td>Star3</td><td>45.19</td><td>0.06</td><td>-2.24</td><td>0.02</td><td>4855.6</td><td>96.3</td><td>1.63</td><td>0.13</td><td>105</td></tr><tr><td>Star4</td><td>46.02</td><td>0.15</td><td>-2.31</td><td>0.02</td><td>4819.1</td><td>94.2</td><td>1.54</td><td>0.13</td><td>105</td></tr><tr><td>Star5</td><td>47.12</td><td>0.10</td><td>-2.52</td><td>0.03</td><td>4991.9</td><td>112.0</td><td>1.93</td><td>0.15</td><td>76</td></tr><tr><td>Star6</td><td>40.68</td><td>0.13</td><td>-2.35</td><td>0.02</td><td>4975.2</td><td>95.3</td><td>1.87</td><td>0.12</td><td>138</td></tr><tr><td>Star7</td><td>41.97</td><td>0.18</td><td>-2.25</td><td>0.02</td><td>4996.4</td><td>104.3</td><td>1.89</td><td>0.14</td><td>112</td></tr><tr><td>Star8</td><td>41.86</td><td>0.38</td><td>-2.48</td><td>0.03</td><td>5048.9</td><td>112.2</td><td>2.06</td><td>0.15</td><td>91</td></tr><tr><td>Star9</td><td>40.77</td><td>0.15</td><td>-2.44</td><td>0.02</td><td>4701.9</td><td>88.6</td><td>1.36</td><td>0.14</td><td>104</td></tr><tr><td>Star10</td><td>41.81</td><td>0.10</td><td>-2.35</td><td>0.02</td><td>4876.2</td><td>88.0</td><td>1.65</td><td>0.12</td><td>153</td></tr></tbody></table>

Note. The RVs have been corrected by visual inspection of the strong Mg, Al, and Si spectral lines. See the text for more details.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** This diagram plots the “characteristic” orbital energy ($E_{\text{min}} + E_{\text{max}}$)/2 vs. the orbital Jacobi constant ($E_j$), in units of $1 \times 10^5$ km$^2$ s$^{-2}$, in the reference frame of the bar, and considering $1\sigma$ variations in a Gaussian Monte Carlo sampling ($1 \times 10^4$ orbits). Gray dots are for the Sagittarius dwarf galaxy, green dots for NGC 5053 considering the absolute proper motion from Kharchenko et al. (2013), and red dots considering absolute proper motion from HST observations.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Histogram of the distribution of eccentricities for NGC 5053 and Sagittarius considering $1\sigma$ variations in a Gaussian Monte Carlo sampling ($1 \times 10^4$ orbits). The Sagittarius eccentricity is shown with a gray histogram, while NGC 5053, adopting HST absolute proper motion are represented with a red histogram, and from adopted absolute proper motion from Kharchenko et al. (2013) is represented with a green histogram.</figcaption></figure>

1. SP1: Photometric derived $T_{\text{eff}}$ and log g from the isochrone, [Fe/H] derived from the iron lines;

2. SP2: ASPCAP-calibrated $T_{\text{eff}}$ and log g, but assumed $[\text{Fe/H}] = -2.27$;

3. SP3: B15 derived stellar parameters.

The microturbulence velocity ($v_t$) is calculated using the equation from Mészáros et al. (2015):

$$v_t = 2.24 - 0.3 \times \log g. \quad (1)$$

After visually inspecting the APOGEE spectra of the member stars, we find that only Mg, Al, and Si can be reliably derived for most of the stars, due to their extreme metal-poor nature. We use the MARCS/Turbospectrum stellar libraries from Zamora et al. (2015), where we interpolate the atmospheric model spectra of each star from these model grids. The

line list used in this work is the latest internal DR14 atomic/molecular line list (line list.20170418). The wavelengths of the line centers of the Mg, Al, and Si atomic lines are taken from Souto et al. (2016). We first inspect the strong lines, and apply additional RV shifts on top of the APOGEE RV correction if necessary. Note that APOGEE pipeline determined RV may have a small offset from the true value in the case of weak spectral lines. The line-by-line analysis is done using two codes: (1) A simple python script written by us, based on the 1D LTE spectral synthesis code Turbospectrum (Plez 2012). We call this TBS for short; and (2) BACCHUS, which is also based on Turbospectrum. We use TBS for stellar parameters SP2 and SP3, and use BACCHUS for stellar parameters SP1.

We first briefly introduce TBS. Each spectrum is normalized locally to avoid possible offset in flux, then the $\chi^2$ minimum is searched between the observed and model spectra. An example
<figure><img src="image_8.png" /><figcaption>**Figure 6.** *T*<sub>eff</sub> vs. log *g*. The ASPCAP results are labeled with blue dots. The error bars for ASPCAP results are shown in the bottom right. The photometric stellar parameters using the González Hernández & Bonifacio (2009) relations are labeled with plus signs. The B15-derived stellar parameters of the stars in common between our work and B15 are labeled with open circles. The DSED isochrone of 13 Gyr and [Fe/H] = −2.27, [α/Fe] = +0.20 is shown as a dotted line. The cross is the one star that we exclude by CMD and isochrone selection.</figcaption></figure>

is given in Figure 7. At this stage, visual inspection is required
to weed out extremely weak lines and bad fits. Finally, the
means of individual measurements are taken as the chemical
abundances, and standard deviations as errors (Table 4). For
BACCHUS, readers are referred to Masseron et al. (2016) for a
detailed description. Here we only briefly describe the basic
features in BACCHUS. First, a sigma-clipping is applied on the
selected continuum points around the targeted line, then a
linear fit is computed over the remaining points. Line
broadening effects include not only the one caused by
microturbulence, but also instrumental broadening. The code
can detect significantly bad fits, like a sudden drop in the
spectrum due to bad pixels in the detectors. Observed spectra
and model spectra are compared in four different ways to
determine abundances: χ² minimization, line intensity, equiva-
lent width, and spectral synthesis. We use χ² minimization in
this work for consistency between the two codes. Similar to
TBS, the means of individual measurements are taken as the
chemical abundances, and standard deviations as errors.
Between these two codes, BACCHUS is faster and also more
sophisticated in handling the continuum fitting, line broad-
ening, and other issues, while visual inspection in TBS ensures
that our results are not overly influenced by the noise in the
spectra. The measured chemical abundances are given with
respect to the solar abundances from Asplund et al. (2005).

5. Results

5.1. *Multiple Populations in NGC 5053*

We derive the iron abundances using BACCHUS, listed in Table 5. The mean iron abundance is −2.20 with a standard deviation of 0.02 dex. Our measurements basically agree with the iron abundance given by the Harris catalog ([Fe/H] = −2.27). The iron lines in NIR are generally weaker and less numerous compared to those in the optical; therefore, an offset of ~0.1 dex between the iron abundances derived from the NIR and from the optical is acceptable.

Visual inspection suggests that for three stars (Star5, Star8, Star9) we have no reliable Al measurements because the lines are too weak. However, we managed to inspect these lines individually to estimate upper limits. We plot the measured abundances and upper limits for the three different sets of stellar parameters in Figure 8. To study the multiple populations in metal-poor GCs in context, we also plot three metal-poor GCs (M15, M92, M53) from Mészáros et al. (2015) that have [Fe/H] < −2. The first and second generations that were defined in Mészáros et al. (2015) are distinguished by red circles and blue triangles, respectively. Interestingly, M53 ([Fe/H] = −2.10), which is a close companion of NGC 5053 in the sky, was also included in that work. We label the M53 stars with filled symbols.

A clear Al variation as large as 0.8 dex is found in NGC 5053, and we can easily separate two groups of stars with different Al abundances. This is true for all three sets of SPs. We note that six stars are in common between our sample and B15 (Table 1), and four of them have [Na/Fe] measurements from optical spectra (Table 6). The only first-generation (FG) star (Star2) in common shows a low [Na/Fe] (< 0), and three second-generation (SG) stars in common show [Na/Fe] ~ 0.9. Thus, our stellar generation division by Al is supported by the Na abundances from B15. The two stellar generations of NGC 5053 also fit well into the two stellar generations defined by the other metal-poor GCs, though we note that three FG stars in this work (Star2, Star8, Star9) lie at the limit that separates the two stellar generations, although two of these stars only have Al upper limits from our data and therefore could actually lie closer to the FG star region. Meanwhile, Mg shows no strong variation between the two stellar populations. In all three sets of measurements, we do not find stars with [Mg/Fe] < 0.0. The Mg-Al anti-correlation of NGC 5053 does not resemble that of M92 or M15 ([Fe/H] ~ -2.3, open symbols), but resembles that of M53 ([Fe/H] ~ -2.1, filled symbols); in the sense that no strong Mg depletion is seen in NGC 5053, even in SG stars.

All three sets of chemical measurements suggest a substantial Si abundance variation (≥0.25 dex), which leads to a Si-Al correlation. Note that the Si separation between the two stellar generations is smaller than the Al separation. In terms of Si distribution, NGC 5053 stars resemble those of M92 or M15, but not of M53. The different behaviors of Mg and Si among metal-poor GCs suggest that metallicity is not the only parameter that regulates the MP phenomenon (see Section 6.2).

5.2. Robustness of the Measurements

In this work, we derive elemental abundances adopting
different sets of stellar parameters and different codes. SP3
(B15) usually yields higher elemental abundances due to the
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Example of spectral line fitting. In the left panel, the observed spectral line is shown as discrete dots, while models with different Al abundances are shown as lines with different colors. In the right panel, the $\chi^2$ of models with different Al abundances are plotted. A quadratic polynomial interpolation is used to find the $\chi^2$ minimum, as indicated by the vertical line.</figcaption></figure>

assumed low metallicities ([Fe/H] ~ -2.45). Conversely, SP1 usually yields lower elemental abundances: for example, the [Mg/Fe] abundances are lower in the SG stars, where an Al–Mg anti-correlation is barely seen. Bearing these uncertainties in mind, our conclusions, namely, that there is a range of Al and Si abundances in NGC 5053 stars, and that those are correlated, are insensitive to the choice of stellar parameters adopted in the analysis.

Figure 9 compares the elemental abundances derived by ASPCAP and the BACCHUS+SP1 method. ASPCAP derived [Mg/Fe] and [Si/Fe] are higher than those of the BACCHUS results, partially due to the lower [Fe/H] from the ASPCAP pipeline ([Fe/H] = -2.36 ± 0.09). There is no one-to-one correlation between the two sets of results. On the other hand, the [Al/Fe] abundances are similar between the two methods, though we note that the upper limits of the chemical abundances can only be given after visual inspection under the circumstance of very weak lines. We find a similar situation if we compare the elemental abundances derived by ASPCAP and the TBS+SP2 method (Figure 10). Though the systematic offset between the Mg (and Si) abundances from these two methods is smaller, their comparison does not show a one-to-one correlation. However, the [Al/Fe] abundances derived from the two methods follow a one-to-one correlation, with possible systematic offset. Therefore, we emphasize that it is necessary to derive chemical abundances manually in the case of very metal-poor stars, especially for those stars with [Fe/H] < -2. We note that the ASPCAP performance at extremely low [Fe/H] has been a known issue in the ASPCAP team.

# 6. Discussion

## 6.1. Is NGC 5053 Associated with Sgr?

Using the newly obtained, high-precision proper motion of NGC 5053 and our software GravPot16, we have shown that the orbit of NGC 5053 is significantly different from that of Sgr. Our simulation results strongly argue against a connection between NGC 5053 and Sgr.

In terms of chemistry, we first take a look at [Mg/Fe] versus [Fe/H], since the Mg abundances of NGC 5053 are newly obtained in this work, and Hasselquist et al. (2017) have shown that the Milky Way (MW) thin disk, thick disk, and Sgr core stars are distinguishable in this parameter space. To visualize the MW thin disk, thick disk, and halo, we first select giants from APOGEE DR14 with the following criteria: (1) $3500 < T_{\text{eff}} < 5000$ K; (2) $\log g < 2.0$; (3) SNR > 70; (4) [Fe/H] and [Mg/Fe] measurements are available. The number density of these stars on a logarithmic scale is indicated by a grayscale map in Figure 11, where high number density regions are darker. The stars selected by Hasselquist et al. are plotted as magenta triangles. Besides NGC 5053, we also try to identify other possible Sgr-associated GCs in APOGEE. We preliminarily identify five stars from M54, using a similar method to that described in Section 2. We have checked the strong Mg lines manually, and find that the ASPCAP fits are reasonable. Therefore, we use the ASPCAP values instead of performing another manual analysis. We note that more observations of M54 stars have been scheduled by the APOGEE team; a careful analysis of M54 stars will be left to a future publication.
<table><caption>**Table 3**
RVs, Distances, and Proper Motions Adopted in This Work</caption><thead><tr><th rowspan="2">#</th><th>RV</th><th>RV Err</th><th>d</th><th>d Err</th><th>μ<sub>a</sub>cosδ</th><th>μ<sub>a</sub>cosδ Err</th><th>μ<sub>δ</sub></th><th>μ<sub>δ</sub> Err</th></tr><tr><th colspan="3">(km s<sup>-1</sup>)</th><th colspan="3">(pc)</th><th colspan="2">(mas yr<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Sgr</td><td>171.0</td><td>17.0</td><td>24.8</td><td>0.8</td><td>-2.75</td><td>0.2</td><td>-1.65</td><td>0.22</td></tr><tr><td>NGC 5053 old proper motion</td><td>43.4</td><td>2.2</td><td>16.7</td><td>0.3</td><td>-5.81</td><td>0.53</td><td>-2.76</td><td>0.53</td></tr><tr><td>NGC 5053 HST proper motion</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>T. Sohn et al. (2018 in preparation)</td></tr></tbody></table>

Note. For NGC 5053, RV comes from APOGEE observation; distance comes from Arellano Ferro et al. (2010); the old proper motion comes from Kharchenko et al. (2013); the HST proper motion will be shown in T. Sohn et al. (2018, in preparation) For Sgr, RV comes from Kunder & Chaboyer (2009); distance comes from Law & Majewski (2010); and proper motion comes from Pryor et al. (2010).

<table><caption>**Table 4**
Manually Derived Chemical Abundances of the NGC 5053 Members</caption><thead><tr><th colspan="7">BACCHUS+SP1</th></tr><tr><th>#</th><th>[Mg/Fe]</th><th>δ<sub>[Mg/Fe]</sub></th><th>[Al/Fe]</th><th>δ<sub>[Al/Fe]</sub></th><th>[Si/Fe]</th><th>δ<sub>[Si/Fe]</sub></th></tr></thead><tbody><tr><td>star1</td><td>0.14</td><td>0.07</td><td>0.93</td><td>0.18</td><td>0.45</td><td>0.10</td></tr><tr><td>star2</td><td>0.26</td><td>0.05</td><td>0.26</td><td>0.04</td><td>0.40</td><td>0.08</td></tr><tr><td>star3</td><td>0.18</td><td>0.08</td><td>1.01</td><td>0.13</td><td>0.55</td><td>0.02</td></tr><tr><td>star4</td><td>0.12</td><td>0.02</td><td>0.96</td><td>0.20</td><td>0.54</td><td>0.09</td></tr><tr><td>star5</td><td>0.22</td><td>0.01</td><td>...</td><td>...</td><td>0.51</td><td>0.10</td></tr><tr><td>star6</td><td>0.12</td><td>0.03</td><td>0.83</td><td>0.07</td><td>0.51</td><td>0.03</td></tr><tr><td>star7</td><td>0.21</td><td>0.07</td><td>0.79</td><td>0.16</td><td>0.46</td><td>0.05</td></tr><tr><td>star8</td><td>0.30</td><td>0.06</td><td>...</td><td>...</td><td>0.37</td><td>0.07</td></tr><tr><td>star9</td><td>0.22</td><td>0.04</td><td>...</td><td>...</td><td>0.32</td><td>0.07</td></tr><tr><td>star10</td><td>0.18</td><td>0.05</td><td>0.81</td><td>0.12</td><td>0.48</td><td>0.09</td></tr></tbody><thead><tr><th colspan="7">TBS+SP2</th></tr><tr><th>#</th><th>[Mg/Fe]</th><th>δ<sub>[Mg/Fe]</sub></th><th>[Al/Fe]</th><th>δ<sub>[Al/Fe]</sub></th><th>[Si/Fe]</th><th>δ<sub>[Si/Fe]</sub></th></tr></thead><tbody><tr><td>star1</td><td>0.23</td><td>0.09</td><td>0.93</td><td>0.08</td><td>0.60</td><td>0.13</td></tr><tr><td>star2</td><td>0.30</td><td>0.06</td><td>0.33</td><td>0.06</td><td>0.40</td><td>0.04</td></tr><tr><td>star3</td><td>0.22</td><td>0.08</td><td>1.08</td><td>0.11</td><td>0.66</td><td>0.06</td></tr><tr><td>star4</td><td>0.22</td><td>0.03</td><td>0.98</td><td>0.17</td><td>0.63</td><td>0.09</td></tr><tr><td>star5</td><td>0.19</td><td>0.04</td><td>...</td><td>...</td><td>0.63</td><td>0.08</td></tr><tr><td>star6</td><td>0.27</td><td>0.07</td><td>1.00</td><td>0.10</td><td>0.66</td><td>0.06</td></tr><tr><td>star7</td><td>0.37</td><td>0.07</td><td>1.02</td><td>0.13</td><td>0.71</td><td>0.06</td></tr><tr><td>star8</td><td>0.31</td><td>0.04</td><td>...</td><td>...</td><td>0.40</td><td>0.04</td></tr><tr><td>star9</td><td>0.27</td><td>0.08</td><td>...</td><td>...</td><td>0.37</td><td>0.07</td></tr><tr><td>star10</td><td>0.32</td><td>0.06</td><td>0.97</td><td>0.07</td><td>0.63</td><td>0.10</td></tr></tbody><thead><tr><th colspan="7">TBS+SP3</th></tr><tr><th>#</th><th>[Mg/Fe]</th><th>δ<sub>[Mg/Fe]</sub></th><th>[Al/Fe]</th><th>δ<sub>[Al/Fe]</sub></th><th>[Si/Fe]</th><th>δ<sub>[Si/Fe]</sub></th></tr></thead><tbody><tr><td>star2</td><td>0.40</td><td>0.05</td><td>0.40</td><td>0.06</td><td>0.52</td><td>0.09</td></tr><tr><td>star3</td><td>0.32</td><td>0.05</td><td>1.15</td><td>0.12</td><td>0.74</td><td>0.04</td></tr><tr><td>star4</td><td>0.33</td><td>0.02</td><td>1.09</td><td>0.17</td><td>0.75</td><td>0.05</td></tr><tr><td>star6</td><td>0.30</td><td>0.06</td><td>1.00</td><td>0.11</td><td>0.66</td><td>0.05</td></tr><tr><td>star7</td><td>0.41</td><td>0.08</td><td>1.02</td><td>0.14</td><td>0.72</td><td>0.05</td></tr><tr><td>star10</td><td>0.35</td><td>0.06</td><td>0.98</td><td>0.10</td><td>0.64</td><td>0.09</td></tr></tbody></table>

We also gather data for other possible Sgr-associated GCs from literature: Terzan 8 (Carretta et al. 2014), M54 (Carretta et al. 2010b), Palomar 12 (Cohen 2004), Terzan 7 (Sbordone et al. 2007), Arp 2 (Mottini et al. 2008), and NGC 6534 (Carretta et al. 2017). The [Fe/H] and [Mg/Fe] from the literature are shown as green squares in Figure 11 with associated measurement errors. Note that [Fe/H] and [Mg/Fe] measured by Carretta et al. (2010b) and APOGEE are consistent within their uncertainty ranges.

We see that the MW thin disk, thick disk, and the Sgr core sequences are indeed well separated at [Fe/H] > −1.0 (Figure 11). At lower metallicity, the MW thin disk and thick disk do not have many stars in this region. The stars between −2.0 < [Fe/H] < −0.9 are suggested to be halo stars with two different chemical and dynamical properties (Hayes et al. 2018; Fernández-Alvar et al. 2018). We run out of Sgr stars at [Fe/H] < −1.7, and the MW halo sequence becomes wide and sparse, so it is difficult to estimate whether NGC 5053 is chemically similar to the Sgr or MW halo using only [Mg/Fe] and [Fe/H]. On the other hand, the possible Sgr-associated GCs loosely form a sequence in the low metallicity regime (green squares). The average Mg abundance of NGC 5053 appears lower than the barely seen MW halo sequence and its value (~0.2 dex) is lower than that of Terzan 8 ([Mg/Fe] = 0.47 dex), which has similar metallicity to that of NGC 5053 ([Fe/H] = −2.27, Carretta et al. 2014). This indicates that NGC 5053 may be chemically different from other Sgr GCs, though we caution that the Mg abundances of SG stars may be slightly affected by the Mg–Al reaction chains and that the Sgr GC trend is highly dependent on the three most metal-poor GCs. Meanwhile, studies of metals (e.g., Ni), and heavy elements (e.g., Y and Ba) in NGC 5053, have not shown conclusive evidence of an Sgr connection (Sbordone et al. 2015). Unfortunately, Ni and s-process elements (e.g., Nd and Ce) do not show any measurable lines in our APOGEE spectra.

To summarize, we find tentative chemical evidence to dismiss a connection between NGC 5053 and Sgr, and our simulated orbit of NGC 5053 also argues against such a connection.

## 6.2. Multiple Populations in the Metal-poor Regime

After carefully inspecting three elements involved in the Mg–Al nuclear chain for four metal-poor GCs with different GC cluster masses (Table 7), we see interesting behaviors in their abundance variations. The Mg–Al nuclear chain and the associated Si leakage are supposed to be activated at temperatures above 90 MK (Prantzos et al. 2007; Ventura et al. 2012; D’Antona et al. 2016), with stronger Si leakage at higher temperature. Strong Mg depletion is observed in the two more metal-poor ([Fe/H] ~ −2.3) and massive GCs M92 and M15, but not in the similar metallicity but less massive GC NGC 5053, or in the less metal-poor ([Fe/H] ~ −2.1) but massive GC M53. On the other hand, a Si spread is found for the three most metal-poor GCs M92, M15, and NGC 5053, regardless of their cluster masses, while a Si spread is not found in the less metal-poor, massive GC M53. Therefore, the correlations among Mg, Al, and Si for MPs are not only
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Left column: [Al/Fe] vs. [Mg/Fe]. Right column: [Al/Fe] vs. [Si/Fe]. Top row: SP1 and BACCHUS. Middle row: SP2 and TBS. Bottom row: SP3 and TBS. The NGC 5053 stars are black dots. The two generations of stars in the metal-poor GCs from Mészáros et al. (2015) are labeled as red circles (FG) and blue triangles (SG), with M15 and M92 as open symbols, and M53 as filled ones. Three stars with estimated Al upper limits are indicated by arrows.</figcaption></figure>

affected by metallicity, other parameters may also play important roles. Cluster mass has been suggested to be another parameter that affects the elemental abundances of MPs (e.g., Carretta et al. 2010a; Pancino et al. 2017). In our work, we notice that NGC 5053 has a lower cluster mass (Table 7) and exhibits less prominent Al–Mg anti-correlation compared to M15 and M92. This qualitatively agrees with the trend given in Pancino et al. (2017), where the standard deviation of the [Al/Mg] distribution and its maximum variation of low-mass GCs tend to be smaller in a given [Fe/H].

Carretta et al. (2009b) suggested that Si variation is limited to massive or metal-poor GCs, based on the four GCs that show

Si variation in their observations. This observational evidence agrees with our understanding of the nucleosynthesis reaction chains that are responsible for MPs, since more massive stars, or more metal-poor stars, tend to have higher reaction temperatures, which is required for the Mg–Al nuclear chain reaction and the associated Si leakage (Arnould et al. 1999). Including the GCs that show Si variation in their sample, NGC 2808, NGC 6388, NGC 6752, and NGC 7078 (M15), we found that NGC 5053 has the lowest cluster mass (Table 7). Depending on the mass estimation methods (McLaughlin & van der Marel 2005; Baumgardt 2017), the masses of the clusters might be slightly different. However, we notice that the
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Comparison between the BACCHUS+SP1 and ASPCAP pipeline results. The dotted lines represent the one-to-one line.</figcaption></figure>

mass of NGC 5053 is constantly about one order of magnitude lower than other GCs. Therefore, this cluster likely has the lowest cluster mass among the GCs that have been identified to exhibit an observable Si spread until now.

Nevertheless, we caution that our sample size is limited. Ten stars are a reasonably statistically significant sample, but there is still a small chance that we may be missing the strong Mg-depleted stars. Besides the 10 stars that we study in this work, the CMD of NGC 5053 (Figure 2) indicate that other ~10 bright, RV-identified cluster members (B15) may be observable with the

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Comparison between the TBS+SP2 and ASPCAP pipeline results. The dotted lines represent the one-to-one line.</figcaption></figure>

APOGEE-2 spectrograph (without considering fiber collision). Since the Mg, Al, and Si lines are more difficult to be detected in the optical for metal-poor stars (Sbordone et al. 2015), NIR high-resolution spectroscopy, e.g., APOGEE-2, is more appropriate.

## 7. Summary

Driven by the desire to understand multiple populations in the oldest, most metal-poor stellar systems in the nearby universe, we have carefully studied the orbit and chemical
<figure><img src="image_13.png" /><figcaption>**Figure 11.** [Mg/Fe] vs. [Fe/H]. The Sgr stars selected by Hasselquist et al. (2017) are plotted as magenta triangles. The red open circle represents the average [Mg/Fe] and [Fe/H] abundances for NGC 5053 (BACCHUS+SP1). The blue open square represents the average [Mg/Fe] and [Fe/H] abundances of the M54 members. GCs with possible Sgr origins are shown as green filled squares, and their GC names are labeled. We select a sample of stars from the APOGEE survey to visualize the thin disk, thick disk, and halo (see the text). The grayscale map indicates the number density of these selected stars on a logarithmic scale.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 12.** Rotation curve (blue) of a boxy bulge from 3D test particle simulations evolved in 3D steady-state potential model (GravPot16) compared to BRAVA (black) data (Howard et al. 2008; Kunder et al. 2012). Taken from Figure 5.12 in Fernández-Trincado (2017).</figcaption></figure>

abundances of one of the most metal-poor GCs, NGC 5053. Given the similar location and RV between NGC 5053 and one of the Sgr arms, NGC 5053 has been speculated to be

associated with Sgr. However, using our dynamical code GravPot16, we argue that a physical connection between Sgr and NGC 5053 is unlikely.
<table><caption>**Table 5**
Stellar Parameters 1 (SP1)</caption><thead><tr><th>#</th><th>T<sub>eff</sub></th><th>log g</th><th>[Fe/H]</th></tr></thead><tbody><tr><td>star1</td><td>4722.05</td><td>1.34</td><td>-2.18</td></tr><tr><td>star2</td><td>4395.42</td><td>0.66</td><td>-2.19</td></tr><tr><td>star3</td><td>4648.89</td><td>1.18</td><td>-2.21</td></tr><tr><td>star4</td><td>4593.50</td><td>1.06</td><td>-2.17</td></tr><tr><td>star5</td><td>4954.46</td><td>1.86</td><td>-2.20</td></tr><tr><td>star6</td><td>4651.53</td><td>1.19</td><td>-2.20</td></tr><tr><td>star7</td><td>4570.49</td><td>1.01</td><td>-2.19</td></tr><tr><td>star8</td><td>5045.27</td><td>2.09</td><td>-2.17</td></tr><tr><td>star9</td><td>4529.76</td><td>0.93</td><td>-2.24</td></tr><tr><td>star10</td><td>4582.29</td><td>1.04</td><td>-2.20</td></tr></tbody></table>

<table><caption>**Table 6**
Stellar Parameters (SP3) and Abundances Derived from Optical Spectra (B15)</caption><thead><tr><th>#</th><th>T<sub>eff</sub></th><th>log g</th><th>[Fe/H]</th><th>[Na/Fe]</th></tr></thead><tbody><tr><td>star2</td><td>4400</td><td>0.80</td><td>-2.43</td><td>&lt;0.0</td></tr><tr><td>star3</td><td>4630</td><td>1.40</td><td>-2.48</td><td>...</td></tr><tr><td>star4</td><td>4700</td><td>1.51</td><td>-2.45</td><td>0.9</td></tr><tr><td>star6</td><td>4650</td><td>1.40</td><td>-2.45</td><td>...</td></tr><tr><td>star7</td><td>4630</td><td>1.40</td><td>-2.47</td><td>0.8</td></tr><tr><td>star10</td><td>4570</td><td>1.20</td><td>-2.44</td><td>1.0</td></tr></tbody></table>

We have identified 10 cluster members in the APOGEE DR14 using their spatial location, RV, [Fe/H], and CMD location. We detected strong Mg, Al, and Si spectral lines in the APOGEE spectra, which are otherwise difficult to see in optical spectra. We manually analyzed the spectra with three different combinations of stellar parameters and codes. We proved that the large Al variation and the substantial Si spread are independent of the adopted measured method. Along with NGC 5053, metal-poor GCs exhibit different Mg, Al, and Si variations, which agrees with the claim that metallicity is not the only parameter that is fundamental to the MP phenomenon. Parameters such as cluster mass, must also play important roles. Interestingly, NGC 5053 has the lowest cluster mass among all the GCs that are currently found to exhibit Si variations. This may be the lower mass limit to generate an observable Si spread.

We thank the anonymous referee for insightful comments. B.T., J.G.F.T., D.G., and S.V. gratefully acknowledge support from the Chilean BASAL Centro de Excelencia en Astrofísica y Tecnologías A fines (CATA) grant PFB-06/2007. B.T. acknowledges support from the One Hundred Talents project of Sun Yat-Sen University. S.V. gratefully acknowledges the support provided by Fondecyt reg. n. 1170518. O.Z., T.M., D.A.G.H., and F.D. acknowledge support provided by the Spanish Ministry of Economy and Competitiveness (MINECO) under grant AYA-2014-58082-P. D.A.G.H. was also funded by the Ramón y Cajal fellowship number RYC-2013-14182. Sz.M. has been supported by the Premium Postdoctoral Research Program of the Hungarian Academy of Sciences, and by the Hungarian NKFI Grants K-119517 of the Hungarian National Research, Development and Innovation Office. T.C.B. acknowledges partial support from grant PHY 14-30152; Physics Frontier Center/JINA Center for the Evolution of the

<table><caption>**Table 7**
Basic Parameters for GCs in This Paper</caption><thead><tr><th>ID</th><th>Name</th><th>[Fe/H]<sup>a</sup></th><th>δ<sub>[Fe/H]</sub><sup>a</sup></th><th>log Mass<sup>1</sup> (M<sub>☉</sub>)</th><th>Mass<sup>2</sup> (M<sub>☉</sub>)</th></tr></thead><tbody><tr><td>NGC 5053</td><td></td><td>-2.30</td><td>0.08</td><td>4.81 ± 0.01</td><td>5.37 ± 1.32 × 10<sup>4</sup></td></tr><tr><td>NGC 7078</td><td>M15</td><td>-2.33</td><td>0.02</td><td>...</td><td>5.01 ± 0.06 × 10<sup>5</sup></td></tr><tr><td>NGC 6341</td><td>M92</td><td>-2.35</td><td>0.05</td><td>5.45 ± 0.01</td><td>3.05 ± 0.04 × 10<sup>5</sup></td></tr><tr><td>NGC 5024</td><td>M53</td><td>-2.06</td><td>0.09</td><td>5.66 ± 0.01</td><td>3.83 ± 0.51 × 10<sup>5</sup></td></tr><tr><td>NGC 2808</td><td></td><td>-1.18</td><td>0.04</td><td>5.93 ± 0.01</td><td>8.29 ± 0.06 × 10<sup>5</sup></td></tr><tr><td>NGC 6388</td><td></td><td>-0.45</td><td>0.04</td><td>6.05 ± 0.05</td><td>1.24 ± 0.01 × 10<sup>6</sup></td></tr><tr><td>NGC 6752</td><td></td><td>-1.55</td><td>0.01</td><td>...</td><td>2.34 ± 0.04 × 10<sup>5</sup></td></tr></tbody></table>

**Notes.**

Elements (JINA-CEE), awarded by the US National Science Foundation. S.T.S. acknowledges support by NASA through grants GO-14235 from the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS5-26555. Funding for the GravPot16 software has been provided by the Centre national d'etudes spatiales (CNES) through grant 0101973 and UTINAM Institute of the Université de Franche-Comté supported by the Région de Franche-Comté and Institut des Sciences de l'Univers (INSU).

Monte Carlo simulations have been executed on computers from the Utinam Institute of the Université de Franche-Comté supported by the Région de Franche-Comté and Institut des Sciences de l'Univers (INSU).

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 http://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 Astrofísica 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.

<footnote><sup>a</sup> From Carretta et al. (2009a).</footnote>

<footnote><sup>b</sup> From McLaughlin & van der Marel (2005).</footnote>

<footnote><sup>c</sup> From Baumgardt (2017).</footnote>
## Appendix
Galactic Model

For the Galactic model, we employ a 3D steady-state gravitational potential of the Galaxy, assumed to be made up of the superposition of many composite stellar populations belonging to the thin disk, the thick disk, the Interstellar Matter (ISM), the stellar and dark matter halo, and a rotating Galactic bar component, that fit fairly well the structural and dynamical parameters of the Milky Way. The mass density distribution of each stellar and nonstellar component is described in detail in Robin et al. (2003, 2012, 2014) and the consequent semianalytic Milky Way potential shape will be fully described in a forthcoming paper (J. Fernández-Trincado et al. 2017, in preparation). Here, we present a summary of the main structural parameters of our 3D steady-state potential model; which have been adopted in a score of papers (see, e.g., Fernández-Trincado et al. 2016; Abolfathi et al. 2017; Anders et al. 2017; Fernández-Trincado et al. 2017a, 2017b, 2017c; Recio-Blanco et al. 2017; Libralato et al. 2018).

The model is made up of the sum of an axisymmetric background potential and a nonaxisymmetric one. The axisymmetric potential is dominated by the superposition of homogeneous oblate spheroids, which approximate the density models of Einasto (1979) thin disks (see, e.g., Robin et al. 2003), while the ISM and the thick disks are the analytic expressions as introduced in Smith et al. (2015), which approximate the density profiles in Robin et al. (2003, 2014). The nonaxisymmetric part includes a rotating bar, where the corresponding potential model consists of triaxial inhomogeneous ellipsoids similar to Pichardo et al. (2004), which approximate the dimensions and density model of Robin et al. (2012). In this work, the overall Galactic potential has been scaled to the Sun's Galactocentric distance, 8 pc, and the local rotation velocity of 244.5 km s⁻¹ (e.g., Sofue 2015). The adopted values for the Sun's orbital velocity vector are $[U_⊙, V_⊙, W_⊙] = [13.12 \pm 1.47, 0.92 \pm 0.29, 7.03 \pm 0.18]$ km s⁻¹ (e.g., Robin et al. 2017). For reference, we have adopted a righthanded coordinate system for *U*, *V* and *W*, so that they are positive in the directions of the Galactic center, Galactic rotation, and North Galactic Pole, respectively.

For the structural parameters of the bar potential, we adopted the dynamical constraints from 3D test particle simulations evolved in the 3D steady-state Milky Way potential mentioned above (Fernández-Trincado 2017; Fernández-Trincado et al. 2017b), which is able to reproduce the velocity rotation curve of stars in the bulge at different Galactic longitude and latitudes, as illustrated in Figure 12. For our computations, we have considered the total mass for the bar, $1.1 \times 10^{10} M_⊙$, the present-day orientation of the major axis of the Galactic bar, $\phi = 20°$, and a pattern speed, $\Omega_B = 35$ km s⁻¹ kpc⁻¹. These values are consistent with the recent estimates from literature (see Portail et al. 2015 for instance).

## ORCID iDs

Baitian Tang https://orcid.org/0000-0002-0066-0346

Doug Geisler https://orcid.org/0000-0002-3900-8208

Timothy C. Beers https://orcid.org/0000-0003-4573-6233

Matthew Shetrone https://orcid.org/0000-0003-0509-2656

Steven R. Majewski https://orcid.org/0000-0003-2025-3147

Alexandre Roman-Lopes https://orcid.org/0000-0002-1379-4204

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