# Measuring the $\alpha$-abundance of subsolar-metallicity stars in the Milky
Way’s central half-parsec: testing globluar cluster and dwarf galaxy infall
scenarios

Rory O. Bentley  UCLA Galactic Center Group, Physics and Astronomy Department,
UCLA, Los Angeles, CA 90095-1547, USA  Tuan Do  UCLA Galactic Center Group,
Physics and Astronomy Department, UCLA, Los Angeles, CA 90095-1547, USA
Wolfgang Kerzendorf  Department of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  Department of Computational
Mathematics, Science, and Engineering, Michigan State University, East
Lansing, MI 48824, USA  Devin S. Chu  UCLA Galactic Center Group, Physics and
Astronomy Department, UCLA, Los Angeles, CA 90095-1547, USA  Zhuo Chen  UCLA
Galactic Center Group, Physics and Astronomy Department, UCLA, Los Angeles, CA
90095-1547, USA  Quinn Konopacky  Center for Astrophysics and Space Science,
University of California San Diego, La Jolla, CA 92093, USA  Andrea Ghez  UCLA
Galactic Center Group, Physics and Astronomy Department, UCLA, Los Angeles, CA
90095-1547, USA

###### Abstract

While the Milky Way Nuclear star cluster has been studied extensively, how it
formed is uncertain. Studies have shown it contains a solar and supersolar
metallicity population that may have formed in-situ, along with a subsolar
metallicity population that may have formed via mergers of globular clusters
and dwarf galaxies. Stellar abundance measurements are critical to
differentiate between formation scenarios. We present new measurements of
[$M/H$] and $\alpha$-element abundances [$\alpha/Fe$] of two subsolar-
metallicity stars in the Galactic Center. These observations were taken with
the adaptive-optics assisted high-resolution (R=24,000) spectrograph NIRSPEC
in the K-band (1.8 - 2.6 micron). These are the first $\alpha$-element
abundance measurements of sub-solar metallicity stars in the Milky Way nuclear
star cluster. We measure [$M/H$]=$-0.59\pm 0.11$, [$\alpha/Fe$]=$0.05\pm 0.15$
and [$M/H$]= $-0.81\pm 0.12$, [$\alpha/Fe$]= $0.15\pm 0.16$ for the two stars
at the Galactic center; the uncertainties are dominated by systematic
uncertainties in the spectral templates. The stars have an [$\alpha/Fe$] in-
between the [$\alpha/Fe$] of globular clusters and dwarf galaxies at similar
[$M/H$] values. Their abundances are very different than the bulk of the stars
in the nuclear star cluster. These results indicate that the sub-solar
metallicity population in the Milky Way nuclear star cluster likely originated
from infalling dwarf galaxies or globular clusters and are unlikely to have
formed in-situ.

Galaxy: center - stars: abundances - stars: late-type - techniques:
spectroscopic

##  1 Introduction

The Milky Way nuclear star cluster (MW NSC) is a massive ($\sim
10^{7}M_{\odot}$) and very dense collection of stars that surrounds the
supermassive black hole at the very center of our Galaxy (Schödel et al.,
2014b; Chatzopoulos et al., 2015; Feldmeier-Krause et al., 2017). How the MW
NSC formed is not well understood. The two primary scenarios are ’in-situ’
formation (e.g. Milosavljević, 2004; Pflamm-Altenburg & Kroupa, 2009), and
’migration and merger’ (e.g. Tremaine et al., 1975; Capuzzo-Dolcetta, 1993;
Antonini et al., 2012; Antonini, 2013). In in-situ formation, the stars formed
roughly in their present positions. In migration and merger, the stars formed
much further from the center, in globular clusters and dwarf galaxies. These
then migrated inwards through dynamical friction, before being disrupted and
mixed into the present-day MW NSC. However, identifying the origins of stars
and stellar populations is not always simple, as the distinguishing
observational tracers can be difficult to measure.

An important key to understanding the formation history of the stars in the
nuclear star cluster is their metallicity and elemental abundances. Through
determination of stellar metallicities, one can identify when the stars
formed, and at what rate (e.g. Fuhrmann, 1998; Anders et al., 2014; Bensby et
al., 2014). Elemental abundances are very useful tools in disentangling the
different stellar components of the Milky Way. Of particular interest here are
the bulk metallicity [$M/H$] (often used interchangeably with the iron
abundance [$Fe/H$]), and the $\alpha$-element (O, Mg, Si, S, Ca, and Ti)
abundance [$\alpha/Fe$]. These two parameters change dramatically in a star
depending on the environment in which a star formed. Comparisons between the
stellar populations of the Galactic disk, bulge, halo, and surrounding dwarf
galaxies find very different [$M/H$] and [$\alpha/Fe$] values from population
to population (e.g. Bonifacio et al., 2004; Monaco et al., 2005; Letarte et
al., 2010; Hayden et al., 2015; Norris et al., 2017; Hill et al., 2019;
Zasowski et al., 2019; Schultheis et al., 2020).

Early spectroscopic studies of the MW NSC were hampered by the $\sim$30
magnitudes of extinction in optical bands (where abundance studies usually
take place), and the intense stellar crowding in the Galactic center. Initial
infrared studies in the K-band and H-band were able to observe a dozen stars
in the Milky Way’s central $\lesssim$10 pc, and found solar to supersolar iron
abundances (Carr et al., 2000; Ramírez et al., 2000; Blum et al., 2003; Cunha
et al., 2007). The stellar crowding at the Galactic center meant that only the
brightest stars could be observed (K < 9.5 mag). Reaching fainter magnitudes
allows for more available targets (making it easier to study the stellar
population in more detail), and allows one to study stars which are typically
longer lived (making it possible to study a longer period of history,
Feldmeier-Krause et al. (2017)).

Medium spectral-resolution (R $\sim$ 5,000) integral-field spectroscopy in
recent years have found that the stars have a broad range of [$M/H$] values,
spanning from -1.0 to above 0.5 dex (Figure 1, Do et al., 2015; Feldmeier-
Krause et al., 2017). These findings are consistent with smaller samples
observed at higher spectral resolution (Schultheis et al., 2015; Ryde et al.,
2016; Rich et al., 2017; Do et al., 2018; Thorsbro et al., 2020). This
variation indicates a complex metal enrichment history of the MW NSC. The high
metallicity stars likely formed in-situ or in the nearby bulge from gas
enriched by metals from past generations of Milky Way stars. However, the
subsolar metallicity population may have had a different origin, potentially
being the remnant of a globular cluster or dwarf galaxy infall. The recent
discovery of dynamical distinctions between the subsolar and supersolar
metallicity populations in the central 10 pc suggests that the subsolar
metallicity stars may be the remnants of an infall (Feldmeier-Krause et al.,
2020a; Do et al., 2020). Additionally, the discovery of RR Lyrae variables in
the bulge in Minniti et al. (2016), provides additional tracers of past infall
events. An infall origin hypothesis could be tested by higher spectral
resolution studies of the stars probing [$\alpha/Fe$], which has a small
effect on the spectra and cannot be measured at medium resolution.

Figure 1: The metallicity distributions of stars at the Galactic Center (solid
black histogram Feldmeier-Krause et al., 2017), inner Milky Way bulge (dashed
black histogram Ahumada et al., 2019), and several globular clusters (red
line) and dwarf galaxies (green lines). The Galactic center metallicity
distribution is very wide, spanning a factor of $\sim 100$ in metal abundance.
Differences in the origins of these stars may be reason for this large
variation in [$M/H$]. In this work, we test the hypothesis that the low-
metallicity stars ([$M/H$] < -0.5) may have been brought to the Galactic
center by infalling globular clusters or dwarf galaxies by using both [$M/H$]
and [$\alpha/Fe$].

Although there have been studies of [$\alpha/Fe$] within the MW NSC (Rich et
al., 2017; Do et al., 2018; Thorsbro et al., 2020), the small sample sizes
($\lesssim$ 10 stars) have missed the subsolar metallicity population, which
comprises $\lesssim$10$\%$ of the total population (Do et al., 2015;
Feldmeier-Krause et al., 2017). Schultheis et al. (2015) and Ryde et al.
(2016) analyzed an adaptive optics assisted high resolution (R $\sim$ 24,000)
spectrum of an inner bulge red giant, and found [$\alpha/Fe$] = 0.4 and
[$Fe/H$] = -1.0. This star is located 58 pc from the MW NSC, within the Milky
Way bulge but outside the MW NSC, which has an effective radius $r_{eff}$ =
4.2$\pm$0.4 (Schödel et al., 2014a).

In this paper, we measure for the first time both the metallicity and alpha-
abundance of sub-solar metallicity stars within 1 pc of the supermassive black
hole at the Galactic center with new high-resolution K-band spectra ($R\sim
24,000$). Our aim is to constrain the physical origins of this population by
comparing their composition to globular clusters and dwarf galaxies to assess
the infall and merger hypothesis. If these stars are in fact mergers, we may
expect the relationship between [$M/H$] and [$\alpha/Fe$] to be comparable to
these objects (Searle & Zinn, 1978). Similarly, these measurements could also
show whether they are formed in-situ like most other stars in the inner bulge
Feltzing & Chiba (2013).

In this work, we use full spectrum fitting to obtain our [$\alpha/Fe$] and
[$M/H$] measurements, and provide the first full spectrum fitting calibrations
at high spectral resolution in K-band. In full-spectrum fitting, a large
portion of the observed spectrum is fit to a synthetic spectrum over a range
of model-dependant physical parameters. This method can measure stellar
parameters (effective temperature $T_{eff}$, surface gravity log $g$, [$M/H$],
and [$\alpha/Fe$]) and was used in in APOGEE (Holtzman et al., 2015), along
with several of the Galactic Center studies discussed above (Do et al., 2015,
2018; Feldmeier-Krause et al., 2017). As part of this calibration, we also
compare fitting with two spectral grids that cover the region of parameter
space for our study: the BOSZ grid and the PHOENIX grid. The BOSZ grid (Bohlin
et al., 2017), designed for flux calibration of standard stars for the James
Webb Space Telescope, and the PHOENIX grid (Husser et al., 2013), a widely-
used grid designed for a range of stellar astrophysics applications, are of
particular interest for high-resolution near-infrared spectroscopy.

Section 2 describes the observations and data. Section 3 describes the full-
spectrum fitting, summarizes the experiments to test the quality and
robustness of our fits, and our fit results for the Galactic center stars.
Section 5 provides discussion, and Section 6 is a conclusion. Section 8
contains more in-depth discussion of the experiments in Section 4.

##  2 Observations and Data

###  2.1 NIRSPAO Observations

The observations in this study were taken between April 2016 and July 2017
with NIRSPAO, which consists of the NIRSPEC spectrograph (McLean et al., 1998;
McLean, 2005), behind laser guide star AO (Wizinowich et al., 2006; van Dam et
al., 2006) at the W. M. Keck Observatory. Observations were taken in echelle
mode, yielding a spectral resolution of R $\sim$ 24,000 (McLean et al., 1998)
with a slit aperture of 0.041"x2.26". Laser guide star was used at the center
of the field of view for each observation, and for lower order tip-tilt
corrections, a R=13.7 mag star USNO 0600-28577051 (17:45:40.720–29:00:11.20)
was used as a natural guide star. Details on the observations are listed in
Table 1.

###  2.2 Sample Selection

The two Galactic center stars are selected from the sample of stars studied in
Do et al. (2015). These stars are part of a program to followup observations
of stars in Do et al. (2015) with K $<$ 13 mag at high spectral resolution in
K-band. Early results from this program were reported in Do et al. (2018).
Here we focus on the two sub-solar metallicity stars with signal-to-noise
ratio (SNR) $>$ 10 from this program (see Appendix 8.7 for discussion about
SNR). The properties of the two stars included in this study, N2-1-002 and
NE1-1-003 are listed in Table 1, and their positions are shown in Figure 2.

Figure 2: An HST WFC3-IR image taken with the F153M filter of the Galactic
center in the near-infrared from Hosek et al. (in prep), that shows the
location of the 2 stars in our sample (red circles). These stars are within 1
pc (blue circle) in projection from Sgr A*. Black dashed line indicates the
Galactic plane.

For calibrations, we observe six stars from open clusters that were used to
calibrate the APOGEE abundance measurements (Mészáros et al., 2013). These
stars have metallicities that span the expected range of metallicities based
on the results of Do et al. (2015). The star 2M18482584+4828027, which is one
of the highest metallicity stars in the APOGEE catalog, was also observed to
provide a calibrator at very high metallicity. The observations of the
calibrators obtained by us are in Table 1, and their physical parameters from
the APOGEE DR16 data release (Ahumada et al., 2019) are listed in 2. As the
APOGEE physical parameter values for the cluster stars are consistent with
previous measurements using different methods, we taking the APOGEE values as
the true physical parameter values.

###  2.3 Calibrators from Archival Data

We use the the Keck Observatory Archive to search for NIRSPEC K-band
observations of stars in open clusters that have been observed in the APOGEE
calibration sample (Mészáros et al., 2013), to be used as additional
calibrators. Three calibrators in the cluster M71, and another observation of
a calibrator we observed (2M19534827+1848021) matched our criteria. These
spectra are from program C118NS (PI: Cohen, J.). The observations were taken
in a very similar manner to our observations outlined in Table 1, except with
a slit aperture of 0.288"x24". The raw spectra were downloaded and reduced
using the method in Section 2.4. These archival observations are also listed
in Table 1, and physical parameters are listed in Table 2.

Table 1: Observed Stars††

Name | K | RA | Dec | Date Observed | Integration Time | Position Angle | Purpose | SN
---|---|---|---|---|---|---|---|---
| (mag) |  |  | (UT) | (s) |  | of Observation |
NE1-1-003 | 11.45 | 8.61† | 3.762† | 2016 April 30 | 2x900 | 356.5 | Science Target | 25
N2-1-002 | 12.12 | 4.398† | 10.997† | 2016 May 16 | 2x900 | 121 | Science Target | 10
2M19205338+3748282 | 9.77 | 19:20:53.38 | 37:48:28.2 | 2016 May 16 | 4x480 | 121 | Calibrator | 45
2M19411705+4010517 | 7.82 | 19:41:17.1 | 40:10:51.8 | 2016 May 16 | 4x180 | 121 | Calibrator | 40
2M19213390+3750202 | 8.80 | 19:21:33.9 | 37:50:20.2 | 2016 May 20 | 4x360 | 155 | Calibrator | 35
2M19413439+4017482 | 7.99 | 19:41:34.4 | 40:17:48.2 | 2016 May 20 | 4x120 | 155 | Calibrator | 40
2M19534827+1848021 | 8.09 | 19:53:48.3 | 18:48:02.3 | 2016 May 20 | 4x60 | 155 | Calibrator | 55
2M15190324+0208032 | 8.50 | 15:19:03.2 | 02:08:03.3 | 2017 July 13 | 4x120 | 0 | Calibrator | 85
2M18482584+4828027 | 9.5 | 18:48:25.9 | 48:28:02.7 | 2017 July 13 | 4x300 | 0 | Calibrator | 60
2M19534827+1848021 | 8.09 | 19:53:48.3 | 18:48:02.3 | 2008 Oct 07 | 2x600 | 81 | Calibrator∗ | 80
2M19535325+1846471 | 8.04 | 19:53:53.3 | 18:46:47.1 | 2008 Oct 07 | 4x600 | 81 | Calibrator∗ | 100
2M19533757+1847286 | 8.42 | 19:53:37.6 | 18:47:28.6 | 2008 Oct 08 | 4x600 | 50 | Calibrator∗ | 90
2M19534525+1846553 | 9.42 | 19:53:45.3 | 18:46:55.4 | 2008 Oct 08 | 2x600 | 50 | Calibrator∗ | 75

∗ Spectrum from Keck Observatory Archive.

† Projected offset in " from the central supermassive black hole at
17:45:40.0409 -29:00:28.118 (Schödel et al., 2010).

†† All observations taken at echelle/cross-disperser setting 63.85/35.65, with
filter Nirspec-7 (K-band). Slit aperture of 0.041"x2.26" used for our
observations, 0.288"x26" for observations from Keck Observatory Archive.

Table 2: Calibrator Stars for this paper, with APOGEE DR16 physical parameters Name | Cluster | H | $T_{eff}$ | log g | [$M/H$] | [$\alpha/Fe$]
---|---|---|---|---|---|---
|  | (mag) | (K) |  |  |
2M19205338+3748282 | NGC 6791 | 9.96$\pm$0.02 | 4032$\pm$65 | 1.50$\pm$0.05 | 0.36$\pm$0.01 | 0.02$\pm$0.01
2M19411705+4010517 | NGC 6819 | 8.01$\pm$0.02 | 4103$\pm$68 | 1.50$\pm$0.05 | 0.00$\pm$0.01 | 0.02$\pm$0.01
2M19213390+3750202 | NGC 6791 | 9.05$\pm$0.02 | 3750$\pm$59 | 1.10$\pm$0.04 | 0.32$\pm$0.01 | 0.04$\pm$0.01
2M19413439+4017482 | NGC 6819 | 8.20$\pm$0.02 | 4185$\pm$69 | 1.75$\pm$0.05 | 0.06$\pm$0.01 | 0.00$\pm$0.01
2M19534827+1848021 | M71 | 8.27$\pm$0.03 | 4077$\pm$73 | 1.24$\pm$0.06 | -0.74$\pm$0.01 | 0.22$\pm$0.01
2M15190324+0208032 | M5 | 8.63$\pm$0.03 | 4022$\pm$76 | 0.70$\pm$0.07 | -1.27$\pm$0.01 | 0.17$\pm$0.01
2M18482584+4828027 |  | 9.60$\pm$0.02 | 5572$\pm$122 | 3.81$\pm$0.07 | 0.44$\pm$0.01 | -0.04$\pm$0.01
2M19535325+1846471 | M71 | 8.20$\pm$0.02 | 4002$\pm$72 | 1.04$\pm$0.06 | -0.82$\pm$0.01 | 0.23$\pm$0.01
2M19533757+1847286 | M71 | 8.68$\pm$0.02 | 4004$\pm$71 | 1.14$\pm$0.06 | -0.74$\pm$0.01 | 0.26$\pm$0.01
2M19534525+1846553 | M71 | 9.56$\pm$0.02 | 4305$\pm$78 | 1.75$\pm$0.07 | -0.73$\pm$0.01 | 0.19$\pm$0.01

###  2.4 Data Reduction

Observations were reduced using the REDSPEC
package111https://www2.keck.hawaii.edu/inst/nirspec/redspec. This is the
standard data reduction package for pre-2019 NIRSPEC observations. Etalon
lamps were used for wavelength solutions, and spatial rectification was
performed with standard stars. The many features of the etalon lamp gives
excellent relative wavelength calibration in each order, but there is a
systematic offset different spectral orders. To account for this, we
simultaneously fit for a relative velocity offset between orders when fitting
the data. The REDSPEC spectral extraction routine was used to obtain the final
spectra. Orders 33 through 37 were reduced and inspected, although only orders
34 through 36 are used in the fitting. Orders 34-36 (covering 2.1-2.3 $\mu$m)
have the highest SN and and best telluric feature subtractions. A portion of
the reduced Galactic center star spectra are shown in Figure 3. Appendix 8.8
shows all of the spectra.

Figure 3: NIRSPAO spectra (black) and best-fit models (blue) of the two
Galactic center stars in our sample, shifted to rest wavelengths. These are
the first high spectral resolution observations of low-metallicity stars
([Fe/H] < -0.5) in the central 1 pc from the supermassive black hole. See
Appendix for all spectral orders of all calibrator stars and Galactic center
stars.

###  2.5 Additional Data

We use Ks photometry for N2-1-002 and NE1-1-003 from Schödel et al. (2010).
Measurements in Schödel et al. (2010) were made from images taken with the
NACO instrument on the ESO VLT unit telescope 4. We use the known offsets of
the two stars from Sgr A* to identify them in the Schödel et al. (2010)
database. The $Ks$ magnitudes are $Ks$=12.12$\pm$0.02 for N2-1-002 and
$Ks$=11.45$\pm$0.02 for NE1-1-003.

Radial velocity measurements of N2-1-002 and NE1-1-003 used in this work are
from Do et al. (2015). They used medium resolution (R=5,400) spectra from NIFS
spectrograph on the Gemini North telescope. We apply a correction for the
motion of the the local standard of rest to the velocities reported in Do et
al. (2015). We find $v_{rad}$=250 km/s for N2-1-002 and $v_{rad}$=146 km/s for
NE1-1-003.

We use proper motion measurements for N2-1-002 and NE1-1-003 from Hosek et al.
(in prep). These measurements were made using HST WFC3-IR observations in the
F153M filter from 2010 to 2020. N2-1-002 has a proper motion of $\mu$=2.2
mas/yr (corresponding to 87 km/s at the Galactic center) and NE1-1-003 has a
proper motion of $\mu$=8.3 mas/yr (corresponding to 265 km/s at the Galactic
center). We use the proper motion and radial velocity information in section
4.2 to constrain the location of these stars to the innermost 0.75 pc of the
MW NSC.

##  3 Methods

In this section, we describe the methodology we employ for parameter
estimation, calibrations, and resulting [$M/H$] and [$\alpha/Fe$] measurements
for stars in our sample. Section 3 describes the Bayesian inference model and
full-spectral fitting method. Section 3.2 describes the calibration of our
method for our K-band spectra, and our choice of spectral grid.

###  3.1 Full-Spectral Fitting with StarKit

We use full-spectral fitting tool StarKit (Kerzendorf & Do, 2015) to fit our
spectra. In this method we compare the observed spectrum to a synthetic model
to determine the best fitting model parameters using Bayes’ Theorem:

$P(\theta|D)=\frac{P(D|\theta)P(\theta)}{P(D)}$ (1)

where $D$ is the observed spectrum, and the model parameters
$\theta=(T_{eff},~{}\log
g,~{}\textrm{[M/H]},\textrm{[}\alpha\textrm{/Fe]},v_{rad},v_{rot},\sigma_{\rm
add,order})$, where $v_{rad}$ is the radial velocity and $v_{rot}$ is the
rotational velocity, and $\sigma_{\rm add,order}$ is the additive uncertainty
to the flux. The priors on the model parameters are $P(\theta)$ and $P(D)$ is
the evidence, which acts as the normalization. The combined likelihood for an
observed spectrum is:

$P(D|\theta)=\prod^{\lambda_{n}}_{\lambda=\lambda_{0}}\frac{1}{\epsilon_{\lambda,obs}\sqrt{2\pi}}\exp{(-(F_{\lambda,obs}-F_{\lambda}(\theta))^{2}/2\epsilon_{\lambda,obs}^{2})},$
(2)

where $F_{\lambda,obs}$ is the observed spectrum, $F_{\lambda}(\theta)$ is the
model spectrum evaluated with a given set of model parameters, and
$\epsilon_{\lambda,obs}$ is the 1 $\sigma$ total uncertainty for each
wavelength. This likelihood assumes that the uncertainty for each flux point
is approximately Gaussian. For computational efficiency, we use the log-
likelihood in place of the likelihood:

$\ln
P(D|\theta)\propto-\frac{1}{2}\sum^{\lambda_{n}}_{\lambda=\lambda_{0}}((F_{\lambda,obs}-F_{\lambda}(\theta))^{2}/\epsilon_{\lambda,obs}^{2}).$
(3)

The total flux uncertainty $\epsilon_{\lambda,obs}$ at each wavelength
includes the observed flux uncertainty, $\sigma_{\lambda,obs}$ and an
additional error component, $\sigma_{\rm add,order}$ to account for systematic
errors in the model grid: $\epsilon_{\lambda,obs}^{2}=\sigma_{\rm
add,order}^{2}+\sigma_{\lambda,obs}^{2}$. This additive error ($\sigma_{\rm
add,order}$) is fitted as part of the likelihood calculation simultaneously
with the model parameters. A single $\sigma_{\rm add,order}$ value is fitted
for each order, which can range between 0 to 10$\%$ of the median flux.

Table 3: Grid Parameter Ranges (full extent and ranges used in fits) Parameter | BOSZ (Step size) | PHOENIX (Step size) | Full BOSZ (Step size) | Full PHOENIX (Step size)
---|---|---|---|---
Wavelength range∗ ($\mu$m) | 2.0-2.4 | 2.0-2.4 | 0.1-32 | 0.05-5.5
$T_{eff}$ (K) | 3500 to 7000 (250) | 2300 to 6000 (100) | 3500 to 30000 (250-1000) | 2300 to 12000 (100-250)
log $g$ | 0.0 to 4.5 (0.5) | 0.0 to 4.5 (0.5) | 0.0 to 5.0 (0.5) | 0.0 to 6.0 (0.5)
$[M/H]$ | -2.0 to 0.75 (0.25) | -2.0 to 1.0 (0.5) | -2.0 to 0.75 (0.25) | -4.0 to 1.0 (0.5-1.0)
$[\alpha/Fe$$]$ | -0.25 to 0.5 (0.25) | -0.2 to 1.0 (0.2) | -0.25 to 0.5 (0.25) | -0.2 to 1.0 (0.2)
R | 50000 | 50000 | 300000 | 500000

StarKit has a modular structure that breaks the steps of constructing the
model from the grid into different steps. Given a set of physical parameters,
StarKit uses a linear interpolator to produce model spectra at arbitrary
values from the spectral grid points. The spectrum is convolved with a
rotational broadening profile, then shifted to the specified radial velocity.
Afterwards, it is convolved with a Gaussian to the resolution of the NIRSPEC
spectrograph (R $\sim$ 24,000) and resampled at the wavelength of
observations. Finally, the model spectrum is normalized using a polynomial to
fit the continuum of the observed spectrum.

We use uniform priors for the Bayesian inference for all fitted parameters
(Table 4). The priors on $T_{eff}$ and $v_{rot}$ were chosen based on the
range of values observed for red giant stars. Prior ranges in [$M/H$] range
from -2.0 to 0.75 when using the BOSZ grid and from -2.0 to +1.0 for the
PHOENIX grid. For [$\alpha/Fe$], the prior ranges from -0.25 to 0.5 for the
for the BOSZ grid and -0.2 to +1.0 for the PHOENIX grid. The upper limits for
the choice of priors on [$M/H$] and [$\alpha/Fe$] are based on limits in the
pre-computed template spectral grids. We investigate both fitting for log $g$
and using photometric information to fix the value of log g for spectral
fitting (Sections 8.3). We also use flat priors to fit for the wavelength
offset between orders.

Table 4: Prior ranges used in fits

Parameter (unit) | Range
---|---
$T_{eff}$ (K) | 3500 to 6000
log $g$∗ | from photometry
$[M/H]$ | -2.0 to 0.75
$[\alpha/Fe$$]$ | -0.25 to 0.5
$v_{rot}$ (km/s) | 0 to 20
$v_{rad}$ (km/s) | -600 to 600
R | 15000 to 40000
Additive flux error (normalized flux) | 0 to 0.1

∗ log $g$ was fixed in the fits that best matched the reference physical
parameters, and the fits to the Galactic center target stars.

We sample the posterior $P(\theta|D)$ using the MuliNest algorithm (Feroz &
Hobson, 2008; Feroz et al., 2009) and report the central 68% confidence
interval for all parameters ($T_{eff}$, log $g$, [$M/H$], [$\alpha/Fe$],
$v_{rot}$, $v_{rad}$). See Do et al. (2018) for additional details about the
fitting.

###  3.2 Calibration of K-band Spectra

In this section, we present our investigation of the most likely sources of
systematic errors in the parameter estimation for $T_{eff}$, log $g$, [$M/H$]
and [$\alpha/Fe$]. We do this by comparing the StarKit fits to K-band spectra
we obtained of open cluster stars previously used APOGEE survey for
calibrations. These stars were used by the APOGEE survey to calibrate their
parameter estimates with H-band spectra (Mészáros et al., 2013), so they have
multiple previous measurements of their physical parameters. We need to do
this cross calibration between K-band and H-band because there has been no
large scale calibration done in K-band at the spectral resolution of our
observations.

###  3.3 Choosing a Spectral Grid

To create the model spectra, StarKit requires a pre-computed grid of spectra,
so the choice of the grid is important. The spectral grids consist of a large
set of synthetic spectra computed from stellar atmosphere models over a range
of model parameters. For this work, the most important parameters are
$T_{eff}$, log $g$, [$M/H$], [$\alpha/Fe$]. For this work we use the BOSZ grid
and PHOENIX grid, the 2 publicly available grid with the wavelength range and
spectral resolution that allows us to measure [$\alpha/Fe$]. To choose between
the two grids, we ran fits using the PHOENIX and BOSZ grids on the 10
calibrator stars. We then examined the fit residuals and the best-fit physical
parameters to compare them with the APOGEE values for these stars (Holtzman et
al., 2015; Ahumada et al., 2019). The parameter ranges of the BOSZ and PHOENIX
grids that were used in the fits are shown in Table 3.

The two grids have important differences. They use different line lists, and
line shape, profile, and depth calculations (see Husser et al. (2013), Bohlin
et al. (2017) for more information). The PHOENIX grid has a lower limit in
$T_{eff}$ of $T_{eff}$=2300 K, compared to $T_{eff}$=3500 K for BOSZ. High
metallicity stars at the Galactic center are likely to have temperatures below
the 3500 K lower edge of the BOSZ grid. We therefore limit our current
analysis to the low-metallicity stars at the Galactic center, which are more
likely to have a temperature above 3500 K. The BOSZ grid allows for the C
abundance [$C/M$] as a free parameter, but we chose to fix [$C/M$]= 0.0, in
order to focus on the bulk properties of the star.

We find that the BOSZ grid is better able to reproduce the observed calibrator
spectra than the PHOENIX grid (Appendix 8.1), showing smaller mean offsets and
at least 1.6 times less scatter in the offsets (7). The best-fit stellar
parameters [$M/H$] has an average offset compared to APOGEE values of
-0.18$\pm$0.16 with the BOSZ grid compared to -0.20$\pm$0.29 with the PHOENIX
grid. Similarly, [$\alpha/Fe$] shows smaller mean offsets and scatter from the
APOGEE values, with $\Delta$[$\alpha/Fe$] =-0.18$\pm$0.18 with the BOSZ grid
and [$\alpha/Fe$]=-0.19$\pm$0.24 with the PHOENIX grid. Table 5 summarizes the
fits. More detail can be found in Appendix )

###  3.4 Surface gravity

We find in our fits of the calibrators that K-band spectra are insensitive to
surface gravity, so additional information such as photometry are required to
constrain log g. This lack of sensitivity is evident by the large scatter in
the best-fit surface gravity for the calibrators compared to their reference
values. This indicates that the spectral features in K-band are insensitive to
changes in log $g$. We therefore fixed log $g$ in our fits to the value from
APOGEE DR16 for the calibrators, or a value derived from stellar isochrones
and photometry for the MW NSC stars. See Appendix 8.3 for more details.

###  3.5 Correcting for Systematic Uncertainties in Best-Parameters

We use comparisons with stellar calibrators discussed above to apply a
correction to the best fit parameters using Starkit for fitting K-band
spectra. This calibration step is similar to that applied by the APOGEE team
in Mészáros et al. (2013) based on similar analyses with stars in open
clusters. To correct for these offsets when fitting our spectra of stars in
the Galactic Center, we use the mean systematic offset and its uncertainty
between the StarKit fits of the calibrator stars and their reference values.
We use the standard deviation in these offsets as an estimate of the
uncertainty of this correction. We subtract this correction for each parameter
and add the scatter in quadrature with the statistical uncertainties to
estimate the final uncertainty for each parameter. Based on our experiments,
we find that the most accurate way to measure stellar parameters in K-band
with NIRSPAO and StarKit is to use the BOSZ grid and to fix log g with prior
information (previous observations for the calibrators, photometrically
derived values for Galactic center stars). The mean offsets and offset
standard deviations used to account for systematic offsets are listed in Table
7 row 3 ($v_{rad}$, log $g$ fixed), and shown in Figure 4.

###  3.6 Investigating Additional Sources of Systematic Uncertainties

We investigate two additional sources of systematic uncertainty that have less
impact on the best-fit parameters than those discussed above. Here, we
summarize our findings for completeness. For details, see the Appendices.

  * •

We try masking different portions of the spectra with large fitting residuals
to see if that would improve the fit. We also experiment with masking regions
that were most sensitive to the physical parameters such as [$M/H$]. None of
the masks result in a significant improvement in the bringing the fits for the
calibrator stars closer to the values from APOGEE.

  * •

We test the effect of noise in our spectra by artificially adding random noise
to our calibrator spectra to examine the SNR where the fits are robust. We add
noise to simulate nine SNR values between 2 and 25 and then compare the fits
to the case without extra noise. This experiment shows that the best-fit
parameters begin to deviate from their values without extra noise at SNR<10\.
From this result, we exclude spectra with SNR<10 from further analysis as
unreliable.

  * •

We also investigate how spectral resolution affects the best-fit parameters
and find that generally, the best-fit parameters are consistent between R =
4000 and 24,000, though with larger uncertainties at lower resolution. We
convolve the R$\sim$24,000 NIRSPAO spectra with a Gaussian filter to simulate
lower spectral resolution. Reducing the resolution to R$\sim$4,000 produce
offsets consistent with what we find at the R$\sim$24,000 spectra to within 1
$\sigma$. Additionally, we fit a sample of R$\sim$2,000 spectra from the SPEX
stellar spectral library to compare the StarKit fits to literature values of
$T_{eff}$, log $g$, and [$M/H$] at an even lower R. The mean offsets for the
SPEX fits to their reference values were similar to the offset we see with
APOGEE calibrators at higher resolutions, but the scatter is $\sim$30$\%$
greater at this lower resolution.

Table 5: Mean offsets and standard deviations of the BOSZ and PHOENIX
comparison fits, and the final offsets that are used in correcting fits.

Experiment | Grid | $T_{eff}$ | log $g$ | [$M/H$] | [$\alpha/Fe$]
---|---|---|---|---|---
|  | K |  |  |
R fixed | BOSZ | -145.0$\pm$178.0 | -0.09$\pm$0.45 | -0.18$\pm$0.16 | -0.18$\pm$0.18
R fixed | PHOENIX | -147.0$\pm$250.0 | -1.22$\pm$1.07 | -0.2$\pm$0.29 | 0.19$\pm$0.24
$v_{rad}$, log $g$ fixed∗ | BOSZ | -117.0$\pm$180.0 | 0.0$\pm$0.0 | -0.16$\pm$0.09 | -0.2$\pm$0.15

∗ These are the final values are used to correct for systematic offsets and
error in the best-fit parameters for the Galactic center fits.

Figure 4: We calibrate the K-band NIRSPAO spectra by using stars in star clusters that have also been observed by the APOGEE survey for their calibration in H-band. We use the offset between the best-fit StarKit model and the APOGEE value to determine the systematic offset and uncertainty in the StarKit model. The circular points are spectra taken for this work, and diamond points are previously observed and available in the Keck Observatory Archive. The blue dashed line is the mean offset and the shaded region is the 1$\sigma$ variation. The black dashed line is at an offset of zero. We find that the [$M/H$] and [$\alpha/Fe$] have a systematic offset of -0.17$\pm 0.09$ and -0.2$\pm 0.15$, respectively. We apply these offsets and their uncertainties to the fits of the Galactic center stars. Table 6: Stellar physical parameters of Galactic Center star fits Name | $T_{eff}$ | log g | [$M/H$] | [$\alpha/Fe$] | $T_{eff}$ | [$M/H$] | [$\alpha/Fe$] | $v_{rot}$ | Avg additive error
---|---|---|---|---|---|---|---|---|---
| K | (fixed) |  |  | K (corrected) | (corrected) | (corrected) | km/s |
NE1-1-003 | 3830.0$\pm$193.0 | 0.6 | -0.75$\pm$0.11 | -0.15$\pm$0.15 | 3947.0$\pm$193.0 | -0.59$\pm$0.11 | 0.05$\pm$0.15 | 9.7$\pm$2.1 | 1.9$\pm$0.1%
N2-1-002 | 4100.0$\pm$201.0 | 0.9 | -0.97$\pm$0.12 | -0.05$\pm$0.16 | 4217.0$\pm$201.0 | -0.81$\pm$0.12 | 0.15$\pm$0.16 | 5.0$\pm$2.6 | 5.8$\pm$0.1%

###  3.7 Results of calibrations

Our work presents the most extensive testing, so far, of full-spectrum fitting
in the K-band at R 24,000. We are able to recover the stellar parameters
$T_{eff}$, [$M/H$], & [$\alpha/Fe$] to an accuracy similar to what other
surveys have found in other wavelengths. This shows that the K-band can be
reliably used for bulk abundance determination with the full-spectrum fitting.
$T_{eff}$, [$M/H$], and [$\alpha/Fe$] were measured to 200 K, 0.10 dex, and
0.15 dex respectively. In comparison, typical APOGEE accuracy for these values
are 200 K, 0.09 dex, and 0.10 dex respectively. We find that the most
difficult parameter to constrain with K-band spectra at R = 24,000 is the
surface gravity. This is likely because of the lack of features in the spectra
sensitive to log $g$ at our spectral resolution in this wavelength range.
While the surface gravity is not well fit, we find that it also is not a
strong source of bias because the spectra are not very sensitive to changes in
the surface gravity. With additional information such as the distance and
brightness of the stars, we also find that we can fix the surface gravity to
values from photometry to further reduce the bias from this parameter.

We find that the uncertainties in are dominated $T_{eff}$, [$M/H$], and
[$\alpha/Fe$] by the systematic effects arising from mismatches in some lines
between the template and observed spectra. In this work, we find that in the
K-band, the lines from 22600-22670Å (eg. 22631Å Ca, 22657Å Ca) and
22050-22090Å (eg. 22056Å Sc, 22068Å Si), along with the Ti line at 22010Å have
larger systematic differences. The remaining regions of the spectra appear to
be well-fit by the models.

In our current work, we focus on the subsolar metallicity stars because their
physical parameters are within the pre-computed BOSZ grid. A large number of
high metallicity stars could be studied in a similar way with additional grid
points at lower temperatures. High metallicity stars are generally much
cooler. Extending the BOSZ grid to lower temperatures ($T_{eff}$ < 3000 K)
will allow a large number of stars to be fit using the full spectral fitting
method.

##  4 Results

###  4.1 Chemical Abundances in the Galactic Center Stars

We find that the two Galactic center stars NE1-1-003 and N2-1-002 have sub-
solar metallicities and have solar alpha-abundances. We fit the K-band spectra
of these stars using the methodology outlined above. For this fit, we use a
prior on value of log $g$ from Ks photometry from Schödel et al. (2010) and
the SPISEA isochrone fitting package (Hosek et al., 2020) with MIST isochrones
(Choi et al., 2016). We infer that log $g$ = 0.6 for NE1-1-003 and log $g$ =
0.9 for N2-1-002 (Appendix 8.3). We apply the empirically determined
corrections to $T_{eff}$, [$M/H$], [$\alpha/Fe$] found in Section 3 to the
best-fit parameters and include the systematic uncertainties added in
quadrature to the statistical uncertainties. We find that NE1-1-003 has
$T_{eff}$ = 3947$\pm$193, [$M/H$] = -0.59$\pm$0.11, [$\alpha/Fe$] =
0.05$\pm$0.15, and N2-1-002 has $T_{eff}$ = 4217$\pm$201, [$M/H$] =
-0.81$\pm$0.12, [$\alpha/Fe$] = 0.15$\pm$0.16 (for other parameters see Table
6).

###  4.2 Constraining Location within the Nuclear Star Cluster

The two stars in our sample are consistent with being less than 0.75 pc from
the supermassive black hole based on their 3D velocity. If we assume a star is
bound to the supermassive black hole and the nuclear star cluster, the escape
velocity at a given projected distance gives the maximum velocity that a star
can have:

$v_{esc}=\sqrt{\frac{2GM(r)}{r}},$ (4)

where $M(r)$ is the mass within a radius $r$ of the black hole, and
$r=\sqrt{R_{2D}^{2}+z^{2}}$, where $R_{2D}$ is the projected distance from the
black hole and $z$ is the line of sight distance. A star’s velocity and
projected distance therefore gives an upper limit to the 3D distance that the
star can be from the black hole. Here we use a black hole mass of $4\times
10^{6}$ $M_{\odot}$ (Gravity Collaboration et al., 2018; Do et al., 2019), and
stellar mass distribution from Schödel et al. (2010). Using the radial
velocities from Do et al. (2015) and proper motion measurements from Hosek et
al. (in prep.), NE1-1-003 likely is located between 0.37 pc and 0.48 pc and
N2-1-002 is between 0.47 pc and 0.60 pc from the black hole (Figure 5).

Figure 5: The maximum escape velocity from the nuclear star cluster,
$v_{escape}$, versus distance from Sgr A* $r$ (blue line). The green and red
points indicate the two stars in the Galactic center studied in this work,
with the dashed lines showing their 3-dimensional velocities. Assuming they
are bound to the nuclear star cluster, their high 3D velocities place them
within 0.6 pc from the supermassive black hole.

##  5 Discussion

Our present study offers new insight into the question of whether some parts
of the Milky Way nuclear star cluster is the result of a merger with a
globular cluster or dwarf galaxy. [$M/H$] and [$\alpha/Fe$] have been shown to
vary between different regions of the Milky Way (Hayden et al., 2015) and in
globular clusters (Pritzl et al., 2005) and dwarf galaxies (Letarte et al.,
2010; Norris et al., 2017; Hill et al., 2019). The two stars in this study,
N2-1-002 ( [$M/H$]=-0.81$\pm$0.12 and [$\alpha/Fe$]=0.15$\pm$0.16) and
NE1-1-003 ([$M/H$]=-0.59$\pm$0.11 and [$\alpha/Fe$]=0.05$\pm$0.15) have sub-
solar metallicity and approximately solar alpha-abundance.

Our measurements for these stars provide the first $\alpha$-abundances for
subsolar metallicity stars in the central 1-pc (Figure 6). There are no high
resolution spectroscopic studies before our work because they represent $<10$%
of the total number of stars in the MW NSC. The small sample sizes (1 to $\sim
10$) of previous high-resolution studies have missed these the sub-solar
metallicity population of the MW NSC, and have measured alpha-abundances for
the solar and super-solar metallicity population (Carr et al., 2000; Ramírez
et al., 2000; Cunha et al., 2007; Davies et al., 2009; Do et al., 2018;
Thorsbro et al., 2020). Previous high spectral resolution $\alpha$-abundance
measurements of metal-poor stars have been made at larger Galactrocentric
distances ($>25pc$) than our study because of the difficulty in resolving
stars without the use of adaptive optics (Figure 6, Schultheis et al. (2015);
Ryde et al. (2016); Ahumada et al. (2019)). These studies outside the nuclear
star clusters showed higher [$\alpha/Fe$] values Schultheis et al. (2015);
Ahumada et al. (2019) compared to N2-1-002 and NE1-1-003 inside the nuclear
star cluster (Figure 7). This suggests that the origin of the subsolar
metallicity stars in the NSC may be different different than in the majority
of the inner bulge.

Figure 6: Metallicity, [$M/H$], as a function of projected distance $r_{proj}$
for several samples of stars studied at high-spectral resolution at the
Galactic center. Red diamonds are the stars from this work, blue circles are
stars from the main bulge population from Thorsbro et al. (2020), the green
circle is the sole metal-poor star from Thorsbro et al. (2020), gold circles
are from Do et al. (2018), and the smaller grey points are inner bulge stars
from APOGEE DR16. Our work explores the abundance of low-metallicity stars
close the supermassive black hole. This work was enabled by adaptive optics
(AO) which can spatially resolve this dense region and having a large sample
of previous medium resolution spectra to find these rare stars.

The [$M/H$] and [$\alpha/Fe$] of the two stars in this study fall between that
of globular clusters and dwarf galaxies suggesting they may be the result of
an infall event. These stars have metallicities much lower than 90$\%$ of
stars in the nuclear star cluster, which suggest that these stars are not
likely to be formed in the same way as the majority of stars in the cluster Do
et al. (2015, 2020); Ryde et al. (2016); Rich et al. (2017); Thorsbro et al.
(2020) (Figures 6, 7). On the other hand, globular clusters have [$M/H$]
ranging from -2.5 to -0.1, with [$\alpha/Fe$] ranging from 0.1 and 0.5. Dwarf
galaxies tend to have large dispersion in both [$M/H$] and [$\alpha/Fe$], with
[$\alpha/Fe$] generally lower than globular clusters at the same [$M/H$]
(Figure 8, Pritzl et al. 2005; Letarte et al. 2010; Norris et al. 2017; Hill
et al. 2019). The two stars in this study have similar metallicity to the Sgr
dSph stars and the globular clusters Terzan 7, Palomar 12, NGC 6342, M71, and
47 Tuc (Pritzl et al., 2005). Given the current uncertainties, we cannot
differentiate these two scenarios at this time.

The presence of dwarf galaxy remnants in the MW NSC would significantly impact
our ideas of how our NSC and supermassive black hole has evolved. Lang et al.
(2013) proposed that a dwarf galaxy containing an intermediate mass black hole
(IMBH) could reach the Galactic center, disrupting gas clouds in the central
$\sim$100 pc, and dragging gas into the MW NSC. Some of this gas could have
accreted onto Sgr A*, causing a burst of accretion activity, and forming the
’Fermi bubbles’, a pair of gamma ray-emitting lobes of gas above and below the
galactic plane (Dobler et al., 2010; Su et al., 2010). The remaining gas could
initiate a burst of star formation in the central $\sim$1 pc, which results in
the young stars we see today (Paumard et al., 2006). This hypothesis can be
tested because the stars belonging to this infalling dwarf should still exist
in the MW NSC today Arca Sedda et al. (2020). The stars in our sample may have
come from such a population, though additional stars are necessary to
differentiate this scenario from an infalling star cluster.

Other recent results also show evidence for infall into the Galactic center.
Minniti et al. (2016) identified a dozen RR Lyrae variables, characteristic
members of old and metal-poor populations, in the Galactic bulge, providing
the first direct observational evidence for past infall events. Feldmeier-
Krause et al. (2020b) found that there are two times as many metal-poor stars
in the Galactic North portion of the MW NSC compared to elsewhere in the
cluster. As infalling clusters are expected to form anisotropic structures
that can persist for Gyr after infall (Perets & Mastrobuono-Battisti, 2014;
Arca Sedda et al., 2020), they suggest that this anisotropy could be evidence
of a recent cluster infall which deposited our metal-poor stars within the MW
NSC. Minniti et al. (2021) investigated the orbits of known globular clusters,
noted a lack of clusters passing within 0.5∘ of the Galactic center. They
discuss that clusters and possibly dwarf galaxy remnants passing into this
region may be disrupted, and the constituent stars mixed into the inner bulge.
In addition, Do et al. (2020) found different kinematic properties in the
subsolar metallicity population compared to the super-solar population, which
also consistent with an infall hypothesis. Our study offers additional
evidence for this by showing that the alpha-abundances are not typical of the
inner Milky Way, and therefore unlikely to be formed in-situ. Also detected
from APOGEE data are signs that parts of the inner bulge was created from
dwarf galaxy mergers (Helmi et al., 2018; Horta et al., 2021). Additional
measurements bridging the APOGEE stars and the MW NSC stars could be used to
test whether the stars in the MW NSC was part of this remnant galaxy.

While metal-poor stars could have formed in-situ at the Galactic center 13
Gyrs ago before significant metal enrichment, the stars in this study are
unlikely to be part of this population. Due to the very fast metal-enrichment
in the bulge, the vast majority of the earliest stars that may have formed in-
situ would be expected to have [$M/H$] $\sim$ -1.0 and $\alpha$-enhanced with
[$\alpha/Fe$] $\sim$ 0.5 (Barbuy et al., 2009; Chiappini et al., 2011; Barbuy
et al., 2014; Schiavon et al., 2017; Thorsbro et al., 2020). While the stars
in our study have similar metallicities, they are not alpha-enriched, which
suggests formation in a system with longer star formation history. In
addition, stellar isochrone fitting work in Chen et al., (in prep) suggests
that the metal-poor component of the MW NSC has ages of 3-5 Gyr, far younger
than the 13 Gyr when the first stars in the bulge are believed to have formed
(Howes et al., 2015). The results of Minniti et al. (2021), showing a lack of
globular clusters in the inner 0.5∘ ( 100 pc) around the Galactic center,
suggests that clusters which enter this region are disrupted. If the stars
from the disrupted clusters remain in the inner 100 pc, some may migrate to
the MW NSC, resulting in the metal-poor stars studied here. In the future,
measurements of specific elemental abundances such as [$C/Fe$] and [$Al/Fe$]
could be used to separate the in-situ versus the merger scenarios, as they
have distinct chemical abundance patterns (Schiavon et al., 2017; Fernández-
Trincado et al., 2019, 2020).

Figure 7: [$\alpha/Fe$] vs [$M/H$] for stars in our sample (red diamonds),
compared with previous observations inside the Milky Way Nuclear star cluster
(gold squares, blue circles Do et al., 2018; Thorsbro et al., 2020), and a
metal-poor star at 40 pc from the Galactic center (green x Schultheis et al.,
2015; Thorsbro et al., 2020). The two stars in our sample occupy a different
region in [$M/H$] and [$\alpha/Fe$] compared to the high metallicity
population inside the nuclear star cluster and the low-metallicity stars
outside the nuclear star cluster; this may indicate that low-metallicity stars
inside the nuclear star cluster may have a different origin than the other
previously studied populations.  Figure 8: The [$\alpha/Fe$] and [$M/H$] for
the stars in our sample (red diamonds) are consistent with both globular
clusters (grey squares, grey dashed line marks median $\alpha/Fe$, Pritzl et
al., 2005) and dwarf galaxies (green X and circles, Monaco et al., 2005; Hill
et al., 2019), within their uncertainties. The low-metallicity nuclear star
cluster stars are also close the observed properties of the Gaia-Enceladus
stream (blue ellipse, Helmi et al., 2018).

At the present time, our understanding of the sub-solar metallicity stars is
limited by the number of Galactic center stars observed at high spectral
resolution and systematic uncertainties in the spectral grid. Increasing the
sample size of metal-poor Galactic center stars will allow us to understand
they lie in [$\alpha/Fe$]-[$M/H$] space, and allow us to differentiate between
a potential globular cluster or in-situ origin, and a dwarf galaxy origin. We
would expect a larger range of both metallicity and alpha-abundance for a
dwarf galaxy origin compared to a globular cluster. A dwarf galaxy will also
tend to have a [$\alpha/Fe$] vs. [$M/H$] relationship that depends on its star
formation history. Measuring this relationship may also allow us to pinpoint
which dissolved dwarf galaxy the Nuclear Star Cluster stars belong to.
Improvements in the atomic data and radiative transfer models will help to
reduce the uncertainties and provide a more precise comparison to other parts
of the Milky Way. A dwarf galaxy infall may also deposit dark matter into the
bulge, while a globular cluster infall would not. However, we cannot
distinguish the effects of dark matter from luminous matter at the present
time.

##  6 Conclusions

We measure the alpha abundance for subsolar metallicity stars in the central
parsec for the first time. We find that [$M/H$] = -0.59$\pm$0.11 and
[$\alpha/Fe$] = 0.05$\pm$0.15 for the star NE1-1-003, and [$M/H$] =
-0.81$\pm$0.12 and [$\alpha/Fe$] = 0.15$\pm$0.16 for the star N2-1-002. We
conducted extensive calibrations using K-band spectra of stars observed in
H-band in the APOGEE survey, and show that our abundances for the calibrators
are consistent with the APOGEE abundances within 0.1 dex in [$M/H$] and 0.15
dex in [$\alpha/Fe$]. The [$\alpha/Fe$] we find for the metal-poor stars are
consistent with the hypothesis that the sub-solar metallicity population may
be the result of a merger of a globular cluster or a dwarf galaxy with the
nuclear star cluster.

Our findings are consistent with other observations that suggest an infall
origin for the sub-solar metallicity population of the Milky Way Nuclear Star
Cluster. The next step in this work is to obtain additional measurements to
differentiate between the infall of a dwarf galaxy and a globular cluster. The
infall of a dwarf galaxy can significantly impact not just the composition of
the nuclear star cluster, but also bring in gas for star formation and
accretion onto the supermassive black hole, which might explain a number of
observed phenomena such as the existence of young stars and the Fermi bubbles.

##  7 Acknowledgements

We would like to thank Jessica R. Lu, Mark Morris, Eric Becklin, and other
members of the UCLA Galactic Center group for providing helpful comments and
discussions. We also would like to thank Matthew Hosek for providing proper
motion data on the two low-metallicity NSC stars, Jennifer Sobeck for
providing information on potential calibrator stars from APOGEE. We also thank
the staff of the Keck Observatory, especially Jim Lyke, Randy Campbell, Gary
Puniwai, Heather Hershey, Hien Tran, Scott Dahm, Jason McIlroy, Joel Hicock,
and Terry Stickel, for all their help in obtaining the new observations.

The W. M. Keck Observatory is operated as a scientific partnership among the
California Institute of Technology, the University of California, and the
National Aeronautics and Space Administration. The authors wish to recognize
that the summit of Maunakea has always held a very significant cultural role
for the indigenous Hawaiian community. We are most fortunate to have the
opportunity to observe from this mountain. The Observatory was made possible
by the generous financial support of the W. M. Keck Foundation.

Support for this work was provided by NSF AAG grant NSF AAG AST-1909554.

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##  8 Appendices

In the appendices, we describe in greater detail the experiments to estimate
systematic uncertainties in the full-spectral fitting method. Section 8.1
describes the comparison of the BOSZ and PHOENIX spectral grids. Section 8.3
describes the robustness of fitting surface gravity and improvements that can
be made by using log $g$ estimates from photometry. Section 8.4 describes the
uncertainty introduced by interpolation between spectra at different points in
the spectral grid. Section 8.2 examines correlated uncertainties between the
different physical parameters. Section 8.5 describes our experiments with
masking selected portions of our spectra based on several criteria to test if
masking can reduced the systematic uncertainties due to template mismatch.
Section 8.6 is our experiments with fitting spectra at a lower resolution.
Section 8.7 describes the relationship between signal-to-noise of the spectra
and the statistical uncertainties in the fitted parameters. Section 8.8
contains the individual spectra and best fits for the stars in this work.

###  8.1 PHOENIX and BOSZ grid comparison.

Figure 9: We test the PHOENIX and BOSZ spectral grids by comparing the best
fit parameters using these grids with their best fit values from the APOGEE
survey. We find that in general the BOSZ grid has smaller offsets and scatter
(blue) compared to the PHOENIX grid (orange) for log g (first panel),
[$\alpha/$Fe] (second panel), $T_{eff}$ (3rd panel), and [M/H] (4th panel).
This indicates that fits with the BOSZ grid are better able to reproduce the
known properties of the calibrator stars. The red points in the bottom panel
are the $\chi^{2}$ value with the BOSZ model set at the APOGEE values, showing
that the best-fit parameters from StarKit are better matches to our spectra
compared to the best-fit APOGEE values evaluated using the BOSZ and PHOENIX
grids.

Here, we discuss the results of our experiment comparing the results of
fitting the PHOENIX and BOSZ grids with full-spectrum fitting, and potential
sources of the systematic uncertainties arising from the particular grids.

We fit the spectra of calibrator stars in open clusters with both grids and
compared them to the APOGEE DR16 values in order to determine which grid gives
more robust results. These stars are also used as calibrators for the APOGEE
pipelines and we use the APOGEE DR16 values (Ahumada et al. (2019) as the
ground truth physical parameter values. The offsets between the measured
values and APOGEE DR16 were calculated for each calibrator star along with the
$\chi^{2}$ values for each fit for both grids (Figure 9). The BOSZ grid result
in similar or better agreement with the APOGEE values than the PHOENIX grid.
The fits from using the BOSZ also show smaller scatter in their offsets.

The BOSZ fit also shows smaller residuals than the fit using the PHOENIX grid
for all calibrator stars (Figure 10). The relatively smaller residuals from
the fits using the BOSZ grid is reflected in the $\chi^{2}$ values as well
(Figure 9).

The scatter in the best-fit parameters for the BOSZ grid fits are similar or
slightly larger than the APOGEE systematic uncertainties, except for surface
gravity (Mészáros et al., 2013). The standard deviations in the offsets
between the best-fit BOSZ grid values and APOGEE DR16 with all parameters
fitted were found to be $\sigma_{T_{eff}}$=180K, $\sigma_{[M/H]}$=0.09,
$\sigma_{[\alpha/Fe]}$=0.15, $\sigma_{\log g}=0.5$ (5). Mészáros et al. (2013)
stated the precision of the APOGEE values of these parameters as
$\sigma_{T_{eff}}$=50 - 100K, $\sigma_{[M/H]}$=0.09,
$\sigma_{[\alpha/Fe]}$=0.07, and $\sigma_{\log g}=0.17$. StarKit measurements
with the BOSZ grid has similar scatter compared to the APOGEE Mészáros et al.
(2013) results for [$M/H$], and has about twice the scatter for $T_{eff}$ and
[$\alpha/Fe$]. We will discuss the $\log g$ measurements further in Section
8.3. Overall, our methodology can produce similar precision in metallicity and
alpha-abundance using K-band spectra as APOGEE can in the H-band for these
calibrators.

To test that our best-fit parameters produced the lowest residuals between the
observed spectra and grid, the BOSZ model spectrum was evaluated at the APOGEE
physical values for each calibrator, and the reduced $\chi^{2}$ calculated.
The BOSZ model set to the best-fit parameters produced the smallest reduced
$\chi^{2}$, as seen in Figure 4. These lower reduced $\chi^{2}$ values showed
the APOGEE values were not the best match for our K-band spectra, and the
StarKit fitting was not getting caught in a local reduced $\chi^{2}$ minimum.

Figure 10: Comparison of the best-fit spectrum from BOSZ (blue) and PHOENIX
(orange) grid to the observed spectrum (black) of one of our calibrators
(2M19205338+3748282). The bottom shows the residuals of the data minus the
best-fit model; the black dashed line is $\pm$5$\%$ residual. The BOSZ grid
produces smaller fitting residuals compared to the PHOENIX grid.

There likely multiple reasons why the BOSZ grid results in better fits than
the PHOENIX grid. One explanation is that the PHOENIX grid uses older atomic
data than BOSZ, which may have more updated transition probabilities (Husser
et al., 2013; Bohlin et al., 2017). Different atmospheric assumptions in the
calculations of line shapes and strengths could again introduce another source
of error in the best-fit values. Our best-fitting models with PHOENIX appeared
to have issues matching both strong and weak lines, as can be seen in Figure
10 with the Si line at 21970. BOSZ also has issues matching some lines, such
as the Na line at 22090Å in Figure 10, although there are fewer mismatches,
and they typically are not as large as the PHOENIX mismatches. Improvements in
the grid template will have the greatest impact on our ability to measure
abundances accurately.

###  8.2 Testing for correlations between physical parameters and offsets

We fit the relationship between the the BOSZ grid offset for each parameter
($T_{eff}$, log $g$, [$M/H$], and [$\alpha/Fe$]) from the calibration stars
and their APOGEE values to examine correlations. To test for correlations, we
use an F-test comparing a linear fit to the offsets to a constant fit; if the
linear fit is a statistically better fit, then it is likely there is a
correlation. We compute the F-statistic for the linear and constant fits at
the 5$\%$ levels. If the F-statistic was lower than this critical value, we
cannot reject the constant (uncorrelated fit) for the linear fit. The constant
fit passes the F-test for all cases. There is a marginal correlation between
the [$M/H$] offset and $\log$ $g$ offset, which was above the critical value
for the model at a 10$\%$ significance level (Figure 11).

Figure 11: We find log g does not have a very strong dependence on the
physical parameters [M/H] and [$\alpha$/Fe] until it is offset by more than
0.4 dex. The figure shows the dependence of the offset between the reference
APOGEE values for calibrator stars and the best-fit values using the BOSZ grid
as a function of offset in log g from the APOGEE values ($\alpha$/Fe],
$T_{eff}$, and [M/H]). We also compute the F-statistics and critical values
are listed for each offset plot. If the F-statistic meets or exceeds 5$\%$
critical value, then there is at least a 5$\%$ significance to the
correlation. There is a weak correlation between [$M/H$] and log $g$, but no
significant correlations for the other parameters.

###  8.3 Systematic Uncertainties in Surface Gravity

We find that using photometry or other methods to estimate $\log g$ to be
helpful to improve the accuracy of the abundance measurements in K-band. In
Section 8.1, we found that the surface gravity, log $g$, has the largest
offset between the best-fit value and the published APOGEE values for the
calibrators; $\log g$ also shows slightly correlation with [$M/H$] offset
(Section 8.2). The average offset is log $g$ = -0.09$\pm$0.45 for the BOSZ
grid. This is within the APOGEE log $g$ precision of 0.17 dex from Mészáros et
al. (2013), but the standard deviation of our log $g$ offsets are larger at
0.9 dex. Like the BOSZ grid, the PHOENIX grids physical parameter with the
largest mean offset is the surface gravity. The average offset in log $g$ is
-1.22$\pm$1.07 for the PHOENIX grid. We find that an offset of $\Delta$log $g$
= 0.4 dex is needed to change [$M/H$] and [$\alpha/Fe$] by greater than 0.1
dex, or within the systematic uncertainties for these parameters with log $g$
at the APOGEE or MIST isochrone values. $T_{eff}$ also remained within its
systematic uncertainty at this offset.

The large offsets in the surface gravity suggests that the majority of the
features in the section of K-band considered here are not very sensitive to
surface gravity. We therefore use photometry and other sources of information
to narrow the possible range of log $g$ for our fits. For the APOGEE stars, we
fix the surface gravity to the best fit APOGEE DR16 values before fitting the
K-band spectra. The surface gravity values for the Galactic center stars were
determined using stellar evolutionary models for stars with similar ages and
metallicities as the Galactic center. MIST evolutionary models (Choi et al.,
2016) with merged atmosphere models (more details on merged atmosphere models
in Hosek et al., 2020) for [$M/H$]=0.5 and [$M/H$]=-1.0, at ages of 10 Gyr and
5 Gyr suggested log $g$=0.6 for NE1-1-003 and log $g$=0.9 for N2-1-002 would
be appropriate for both the subsolar and supersolar metallicity populations at
the two stars’ respective magnitudes. A sample isochrone used is shown in
Figure 12. For more details on the cluster modeling, see Chen et al. (in
prep).

By estimating the surface gravity to values from photometry, we can reduce
this source of systematic uncertain below that of the spectral grid (see
Section 4).

Figure 12: The MIST isochrone (Choi et al., 2016) with an [$Fe/H$] = -1.0 and
an age of 5 Gyr is well matched to the photometry and temperature data for the
two stars at the Galactic center (red stars). We use this isochrone to measure
the surface gravity for NE1-1-003 (log $g$ = 0.6) and N2-1-002 (log $g$ = 0.9)
using their $T_{eff}$ measurement and $K_{s}$ photometry.

###  8.4 Interpolation Uncertainty

Spectral grids are sampled at discreet values of physical parameters, and so
in order to produce models at arbitrary parameter values, we must interpolate
between grid points. This interpolation can introduce an additional source of
uncertainty. To investigate how much the interpolation was contributing to the
error, we remove a grid point, and then interpolated the spectrum at the
parameters of the removed point. This is repeated at every point in the grid,
and the value and wavelength of the maximum residual between the removed grid
spectrum and the interpolated spectrum are recorded. This allows us examine
the interpolation accuracy of different portions of the spectral grid. Our
maps show that the worst interpolated regions were at the lower bounds of the
grid’s $T_{eff}$, log $g$, and [$\alpha/Fe$] ranges, and at the upper bounds
of the grid’s [$M/H$] range. For example, the maximum interpolation residual
at a grid point decreased as $T_{eff}$ increased from the lower bound.
Overall, the interpolation errors are very small. Within the NIRPEC wavelength
range used in this paper, the maximum interpolation residuals is $\lesssim
0.5\%$.

Overall, our interpolation tests suggest that interpolation is not a major
source of systematic uncertainty. The interpolated spectra generated when the
grid points were removed were fitted with the BOSZ grid, and offsets between
the best-fit parameter values and the actual grid point parameters were
calculated. This gave us estimates of the maximum errors introduced by
interpolation. These fits showed that the mean offsets and scatter in best-fit
values about the grid points were $\Delta T_{eff}$ = -6$\pm$38, $\Delta$ log
$g$ = 0.1$\pm$0.1, $\Delta$ [$M/H$] = -0.01$\pm$0.03 $\Delta[\alpha/Fe$] =
-0.01$\pm$0.02. These additional sources of error were added in quadrature to
the systematic and statistical errors.

###  8.5 Masking and Abundance Sensitivities

We performed several experiments to examine whether including only regions
where the lines are sensitive to changes in the physical parameters would
produce more accurate fits. Overall, masking different portions of the spectra
did not have a significant effect on the parameter estimates.

One way to determine the changes in the line strengths is to measure how the
flux scales with changes in the physical parameters at each wavelength. We
measure this by fitting a linear trend to flux changes by varying one
parameter at time by $\pm 0.1$ dex, while fixing the others. We vary the
parameters around the best-fit values for the spectra from 7 calibrator stars.
We mask all points that do not vary by more than 5$\%$ when varying [$M/H$] by
0.1 dex, [$\alpha/Fe$] by 0.1 dex, or $T_{eff}$ by 400K, and re-fit these
spectra. The best-fit values from this masking method did not change
significantly compared to their non-masked best-fit values.

The next masking method tested used a parameter called the sensitivity
function $S_{\lambda}$, described in Sheminova & Cowley (2014). $S_{\lambda}$
is a parameter that describes how much the flux at a given wavelength changes
as a physical parameter (in this case [$M/H$]) is increased and decreased by a
specified increment. The expression for $S_{\lambda}$ is:

$S_{\lambda}=100\frac{R_{\lambda}(A+\Delta A)-R_{\lambda}(A-\Delta
A)}{R_{\lambda}(A))},R_{\lambda}=1-F$ (5)

with A representing our physical parameter, and F our normalized flux. The
$S_{\lambda}$ value at each wavelength was evaluated for changes of $\pm$0.1
dex about the unmasked best-fit [$M/H$], and regions with $S_{\lambda}$ less
than a specified cut-off value were excluded from the fit. When $S_{\lambda}$
was compared to the model spectrum, the regions of highest $S_{\lambda}$ (or
regions with the strongest response to physical parameter changes) were
typically located in the wings of stronger lines, and in center of weaker
lines. This is consistent with where Sheminova & Cowley (2014) found the
greatest $S_{\lambda}$ values. Figure 13 shows an example of how masking is
applied with the spectrum of calibrator star 2M19205338+3748282.

Figure 13: An example of masking regions of a spectrum (2M19205338+3748282,
black line) which respond the least to changes in physical parameters, as
quantified by the $S_{\lambda}$ parameter from Sheminova & Cowley (2014). We
compute $S_{\lambda}$ (green line) and then mask values below 0.024 (dashed
horizontal black line) . Red dots show masked datapoints which are not used in
the fit. Vertical grey lines are spectral lines. We find that masking using
this method does not significantly improve the quality of our fits.

We run fits with different constraints on the cut-off value, and find that
there is no significant improvement on fits with a fixed log $g$. We run fits
with with $S_{\lambda}$ cutoff between 1 and 400 and log $g$ fixed to the
reference value. The fraction of the data that is masked, and as a result
excluded from the fits, ranges from 0$\%$ for the lowest $S_{\lambda}=1$
cutoff to 99$\%$ for the highest cutoff $S_{\lambda}=400$. We find no
particular cut-off values significantly change the parameter estimates across
all the calibrators (Figure 14). When log $g$ is allowed to be free, masking
improves the estimation of log $g$ by reducing the scatter in the offsets from
the reference values by 0.15 dex at a cut-off of $S_{\lambda}$=2.0 and higher.
The quality of fits for [$M/H$], [$\alpha/Fe$], and $T_{eff}$ are not affected
by masking. This indicates that $S_{\lambda}$-based masking may be helpful to
explore if log $g$ values are important to derive from spectra in the future.

Figure 14: The best-fit physical parameters for all calibrator stars for
various threshold values of $S_{\lambda}$ used to mask and remove data points
from the spectra before fitting. Higher thresholds of $S_{\lambda}$ remove
more data points. log $g$ is fixed to the APOGEE DR16 value in these fits.
Connected blue points are fits for the same calibrator star. Their is very
little variance in the best-fit values for different $S_{\lambda}$ cutoffs,
and no particular value improves the fit compared to no masking.

For the final masking method, the model was evaluated at the best-fit unmasked
values, and the residuals between the observed spectrum and the unmasked model
were found. The data points with residuals higher than a specified cut-off
value were then masked. Nine residual cut-off values were tested, ranging from
17.5$\%$ to 2$\%$. The quality of the fits does not improve with this masking
method.

###  8.6 Fitting with spectra convolved to a lower resolution

In order to ensure that the StarKit fitting produces similar best-fit
parameters at different spectral resolutions, the calibrator star spectra are
convolved with a Gaussian filter to R = 4,000, from R $\sim$ 24,000. The
lower-resolution spectra is fit again with the BOSZ grid, and the results of
the R = 4,000 calibrator star fits are compared with the R $\sim$ 24,000 fits
to check for consistency. The lower-resolution fits are consistent to within
1$\sigma$ of the higher-resolution fits using the BOSZ grid, as seen in Figure
15.

Figure 15: We examine whether the best-fit physical parameters are biased at
lower spectral resolution by convolving the R=24,000 NIRSPEC spectra to
R=4,000. These mean offset and scatter at medium resolution (green) is similar
to the mean and scatter at high resolution (blue). This indicates that medium
resolution spectra and high resolution spectra have consistent results with
out fitting method.

R$\sim$2,000 spectra from the SPEX stellar spectra library (Rayner et al.,
2009) are fit in the same manner as the NIRSPAO spectra, and offsets from the
physical parameters from Cesetti et al. (2013) are calculated to provide an
additional check for consistency at lower resolution. The offset plots for
$T_{eff}$, log $g$, and [$M/H$] are shown in Figure 16. The mean offsets and
scatter for $\Delta T_{eff}$ = -250$\pm$280 K, $\Delta\log g$ = -0.22$\pm$0.73
dex, and [$\Delta M/H$] = -0.14$\pm$0.25 dex. The offset means are similar to
what was found for the R $\sim$ 24,000 offsets, although with greater scatter.
In summary, our fitting routine produces similar best-fit values at lower
spectral resolution as at high spectral resolution, but with increasing
scatter, suggesting there are larger systematic uncertainties at lower
spectral resolution.

Figure 16: We examine how well StarKit and the BOSZ grid fit stars at R 2,000
using the sample from Rayner et al. (2009). The fits at low resolution produce
mean physical parameter offsets similar to the high resolution NIRSPEC sample,
but with a factor of 2-3 times larger scatter. Reference physical values taken
from Cesetti et al. (2013).

###  8.7 Fit robustness at different signal-to-noise ratios

We find that the StarKit fits are robust at a signal-to-noise ratio (SNR)
greater than $\sim 10$. To determine this threshold, we performed a series of
Monte Carlo simulations by adding artificial noise until the best-fit
parameters become systematically different than without the extra noise. We
added noise to the 11 calibrator spectra to reduce their SNR to between 2 and
25, and fit the new spectra with fixed log $g$, and the BOSZ grid. We find
that the offsets do not diverge from the best-fit value without extra noise at
SNR above 10 (Figure 17).

Figure 17: We examine how the best-fit physical parameters from StarKit vary at lower SN ratios by artificially lowering the SN ratio by adding noise. We find that the scatter in the offsets from the values (individual offsets are transparent blue points, mean offsets are opaque blue points) without additional noise does not reach the scale of the systematic error until SN 10, indicating our fits are robust to a SN ratio of 10. Table 7: Mean offsets and standard deviations for fitting experiments Experiment | Grid | $T_{eff}$ | log $g$ | [$M/H$] | [$\alpha/Fe$]
---|---|---|---|---|---
|  | K |  |  |
$v_{rad}$, log $g$ fixed | BOSZ | -117.0$\pm$180.0 | 0.0$\pm$0.0 | -0.16$\pm$0.09 | -0.2$\pm$0.15
log $g$ fixed | BOSZ | -129.0$\pm$158.0 | 0.0$\pm$0.0 | -0.15$\pm$0.1 | -0.18$\pm$0.16
$v_{rad}$ fixed | BOSZ | -172.0$\pm$149.0 | -0.27$\pm$0.67 | -0.21$\pm$0.16 | -0.19$\pm$0.15
R fixed | BOSZ | -145.0$\pm$178.0 | -0.09$\pm$0.45 | -0.18$\pm$0.16 | -0.18$\pm$0.18
R=4000 convolution | BOSZ | -103.0$\pm$91.0 | 0.16$\pm$0.54 | -0.03$\pm$0.15 | -0.19$\pm$0.18
SN$\sim$12 | BOSZ | -93.0$\pm$120.0 | -0.08$\pm$0.61 | -0.04$\pm$0.2 | -0.16$\pm$0.16
$S_{\lambda}$ mask | BOSZ | -90.0$\pm$120.0 | -0.11$\pm$0.5 | -0.07$\pm$0.19 | -0.16$\pm$0.15
APOGEE spectrum | BOSZ | -130.0$\pm$139.0 | -0.09$\pm$0.68 | -0.2$\pm$0.32 | -0.15$\pm$0.16
R fixed | PHOENIX | -147.0$\pm$250.0 | -1.22$\pm$1.07 | -0.2$\pm$0.29 | 0.19$\pm$0.24
APOGEE spectrum | PHOENIX | -22.0$\pm$252.0 | -0.9$\pm$1.03 | -0.22$\pm$0.27 | 0.22$\pm$0.21

###  8.8 Spectral Atlas

An example of the observed and best fit spectra for the Galactic center
sources and all calibrations in each of the NIRSPAO orders is shown in Figure
18. See online journal for the complete spectral atlas.

Fig. Set18. The complete spectral atlas figure set (39 images) is available in
the online journal

Figure 18: Best-fit model (log $g$ fixed, BOSZ grid) compared to observed
spectrum, with residuals.