# The metal-weak Milky Way stellar disk hidden in the Gaia-Sausage-Enceladus
debris: the APOGEE DR17 view.

Sofia Feltzing Lund Observatory, Department of Astronomy and Theoretical
Physics, Box 43, SE-221 00 Lund, Sweden  Lund Observatory, Department of
Geology, Sölvegatan 12, SE-223 62 Lund, Sweden  Diane Feuillet Lund
Observatory, Department of Astronomy and Theoretical Physics, Box 43, SE-221
00 Lund, Sweden  Lund Observatory, Department of Geology, Sölvegatan 12,
SE-223 62 Lund, Sweden

(Received March 1, 2023; Revised June 18, 2023; Accepted June 20, 2023)

###### Abstract

We have for the first time identified the early stellar disk in the Milky Way
by using a combination of elemental abundances and kinematics. Using data from
APOGEE DR17 and Gaia we select stars in the Mg-Mn-Al-Fe plane with elemental
abundances indicative of accreted origin and find stars with both halo-like
and disk-like kinematics. The stars with halo-like kinematics lie along a
lower sequence in [Mg/Fe], while the stars with disk-like kinematics lie along
a higher sequence. Through with asteroseismic observations, we determine the
stars with halo-like kinematics are old, 9–11 Gyr and that the more evolved
stellar disk is about 1–2 Gyr younger.

We show that the in situ fraction of stars on deeply bound orbits is not
small, in fact the inner Galaxy likely harbours a genuine in-situ population
together with an accreted one.

In addition, we show that the selection of Gaia-Sausage-Enceladus in the
$E_{\rm n}-L_{\rm z}$-plane is not very robust. In fact, radically different
selection criteria give almost identical elemental abundance signatures for
the accreted stars.

Milky Way stellar halo(1060) – Milky Way formation(1053) – Galactic
Archaeology (2178)

††facilities: Gaia††software: astropy (Astropy Collaboration et al., 2013,
2018), galpy (Bovy, 2015, http://github.com/jobovy/galpy)

##  1 Introduction

The formation and evolution of the Milky Way can be studied via the ages,
elemental abundances and kinematics of its stars (Freeman & Bland-Hawthorn,
2002). The stars present in the stellar components of the Galaxy are thought
to have formed via two main processes: in situ formation and accretion. In
situ stars would have formed in the body of the main progenitor of the galaxy
and the accreted stars fin the galaxies that later merged with the main
progenitor. The accreted stars would have chemical signatures different from
those formed in situ since they have formed in shallower potential wells.
However, some of the oldest stars formed in a Milky Way-like progenitor may
occupy the same elemental abundance space as the accreted stars (Horta et al.,
2022).

The Milky Way halo is thought to comprise stars formed in the early Milky Way
as well as stars formed in nearby low-mass dwarf galaxies that have been
accreted over time (Di Matteo et al., 2019; Helmi, 2020; Forbes, 2020; Hammer
et al., 2023). Historically, these accreted stellar populations have been
identified as spatial overdensities or kinematically associated stars (Helmi
et al., 1999; Belokurov et al., 2006; Belokurov, 2013; Helmi, 2020) and have
mainly been limited to mergers that have not yet dissolved into the Milky Way
field populations. Following Gaia Data Release 1 (DR1, Gaia Collaboration et
al., 2016a) and Data Release 2 (DR2, Gaia Collaboration et al., 2018a),
substantial accreted material was identified in the Milky Way.

The most prominent, newly discovered stellar population is the Gaia-Sausage-
Enceladus (Helmi et al., 2018; Belokurov et al., 2018; Myeong et al., 2019;
Naidu et al., 2020). Apart from the Gaia-Sausage-Enceladus, several other
debris have been identified using Gaia data (e.g. Myeong et al., 2019;
Koppelman et al., 2019; Naidu et al., 2020). Most of these newly identified
populations generally have metallicities lower than those of the Milky Way
disk and bulge (see e.g. Malhan et al., 2022, Fig. 7 for some examples).

On a larger scale, it was found that the high velocity Milky Way halo has a
dual sequence in the colour-magnitude diagram (Gaia Collaboration et al.,
2018b). Helmi et al. (2018); Haywood et al. (2018); Sahlholdt et al. (2019a);
Gallart et al. (2019) show that for stars with large transversal velocities
(defined as $V_{T}>200$ km s-1), these two populations show different
metallicity distribution functions, tentatively different elemental abundance
trends, and different ages pointing to different origins, potentially we are
seeing an in situ population (the red sequence) and an accreted population
(the blue sequence). In addition, Belokurov et al. (2020) identified a
structure they dubbed the Splash, which they take to be the result of the
merger of the Gaia-Sausage-Enceladus. This merger perturbed stars in the
existing stellar disk creating a heated component. Belokurov et al. (2020)
identify the Splash as stars with $|V_{\theta}|<100$ km s-1 and [Fe/H] $>-0.8$
dex.

Di Matteo et al. (2019) argue that there is no in situ halo just an accreted
one. In this interpretation, the two sequences in the halo colour-magnitude
diagram are the cumulative accreted populations and the heated early disk.
However, Amarante et al. (2020) provide simulations that show that it is
feasible to create something akin to the Splash without any merger taking
place. They argue for a formation of stars in a heated medium. It appears that
observational data has not yet been sufficient to distinguish between
different formation scenarios.

Although many accreted stellar populations have been identified in the Milky
Way halo through their kinematics, the main criteria distinguishing stars as
having formed outside the Milky Way is a difference in the elemental
abundances. The elemental abundance ratios measured in the atmospheres of low-
mass stars have long been used as a tool to probe the evolutionary history of
galaxies. Not only does the abundance of individual elements increase over
time as evolved stars contribute enriched material to the interstellar medium,
but the star forming conditions of a given galaxy will affect the elemental
abundance trends measured in its stellar populations.

Theoretically, it is well understood that the enrichment of $\alpha$-elements
is dependent on the star formation rate (Matteucci, 2012). This is confirmed
in observations of Local Group dwarf galaxies where star formation proceeds
more slowly (Tolstoy et al., 2009). However, recently other elements have
empirically been found to show significant differences in stars formed in
high-mass or low-mass stellar systems. The APOGEE survey (Majewski et al.,
2017) has provided aluminum abundance measurements for $\sim 570,000$ stars in
the Milky Way and nearby dwarf galaxies. From this dataset, it has been shown
that the accreted Gaia-Sausage-Enceladus stellar population and nearby dwarf
galaxies have [Al/Fe] abundance ratios $\sim 0.5-1.0$ dex lower than the Milky
Way disk across a large [Fe/H] range (e.g. Hasselquist et al., 2021; Horta et
al., 2022).

Hawkins et al. (2015) and Das et al. (2020) suggest that the Mg-Mn-Al-Fe-plane
could have high diagnostic power for identifying accreted populations in the
Milky Way. Observational studies have found that many of the kinematically
identified accreted stellar populations in the Milky Way lie within the
proposed accreted region of this Mg-Mn-Al-Fe-plane (e.g. Feuillet et al.,
2021; Horta et al., 2022). Initial attempts to understand this plane using
chemical evolution models have found a difference in the expected distribution
of low-mass Gaia-Sausage-Enceladus-like galaxies, present day dwarf galaxies
and Milky Way-like galaxies. Horta et al. (2021); Fernandes et al. (2023)
provide chemical evolution models in the Mg-Mn-Al-Fe-plane for these different
types of galaxies.

In this paper we use the latest APOGEE dataset combined with astrometry from
Gaia and the Mg-Mn-Al-Fe-plane to explore a subset of stars that have
elemental abundances indicative of accreted or early Milky Way origin.

This paper is organised as follows: Section 2 describes our selection of data
from APOGEE DR17 and Gaia. Section 4 discusses the chemical signatures of
accreted populations, in particular the Mg-Mn-Al-Fe-plane and potential
problems using this plane related to our shortcomings in deriving elemental
abundances reliably. Section 3 defines our samples using the Mg-Mn-Al-Fe-plane
while Sect. 5 explores the kinematic and chemical properties of specific
samples. Section 6 attempts to date the different samples using ages available
in the literature while Sect. 7 provides a discussion. The paper concludes
with a summary in Sect. 8.

##  2 Data

Figure 1: Elemental abundance distribution for our full sample selected from
APOGEE DR17. a) [Mg/Fe] vs [Fe/H] and b) [Al/Fe] vs [Fe/H]. Details of the
selection of data can be found in Sect. 2 and Table 1 provides an overview of
the flags used in the selections from the main catalogues of APOGEE DR17 and
Gaia. The labels A, B, C are inserted to help the reader to identify the three
main components seen in this plot in relation to the description given in
Sect. 2: A – classical thick disk, B – classical thin disk, C – additional
low-$\alpha$ component.

We use data from the 17th Data Release (DR17) of the high-resolution
spectroscopic SDSS APOGEE survey (Majewski et al., 2017; Abdurro’uf et al.,
2022)111The data was retrieved from the SDSS-IV archive at
https://www.sdss4.org/dr17/irspec/spectro_data/. combined with the Gaia Early
Data Release 3 (Gaia EDR3, Gaia Collaboration et al., 2016b, 2021) astrometric
data222For the purpose of the analysis present in this paper there is no
difference between using EDR3 and DR3 for Gaia as the astrometric solution is
the same. Gaia parameters additional to those provided by APOGEE were queried
via the ESA archive https://gea.esac.esa.int/archive/. To ensure robust
stellar parameters, elemental abundances, and kinematic measurements, we
impose the selection criteria listed in Table 1.

Table 1: Selection criteria used to select data from APOGEE DR17 and Gaia.
Further details can be found in Sect. 2. APOGEE DR17
---
Flag | Criterium
SNREV | $>$ | 80
TEFF | $<$ | 6000
TEFF | $>$ | 4000
LOGG | $<$ | 2.8
FE_H_FLAG | = | 0
MG_FE_FLAG | = | 0
MN_FE_FLAG | = | 0
AL_FE_FLAG | = | 0
STARFLAG | $\neq$ | VERY_BRIGHT_NEIGHBOR or PERSIST_HIGH
ASPCAPFLAG | $\neq$ |  STAR_BAD, CHI2_BAD, M_H_BAD, or CHI2_WARN
EXTRATARG | $\neq$ | DUPLICATE
Gaia
Property | Criterium
$\sigma_{\pi}/\pi$ | $<$ | 0.2
Additional selection for sample with no RC stars
Property | Criterium
LOGG | $<$ | 2
LOGG | $>$ | 1

The sample is limited to giants to avoid an apparently anomalous feature in
the [Al/Fe] vs [Fe/H] distribution of metal-rich dwarf stars. Although we
focus mainly on lower metallicity stars in this work, aluminum is one of the
four diagnostic elements used in our analysis and high data quality is
important. The limits on effective temperature ensure only giants with
reliable elemental abundance measurements are included. For more details on
the APOGEE DR17 data quality see the SDSS DR17 documentation available on the
web333https://www.sdss.org/dr17/ and a detailed discussion of DR16 in Jönsson
et al. (2020). In addition, the sample is cleaned of stars in fields targeting
known star clusters and dwarf galaxies. A full list of the field and program
names removed can be found in App. A.1. This constitutes our full sample. In
what follows we, following Weinberg et al. (2019), often limit the data set
further to exclude red clump stars, i.e. $1<\log g<2$.

The [Mg/Fe] and [Al/Fe] abundance distributions as a function of [Fe/H] of the
full sample are shown in Fig. 1. In Fig. 1 we have indicated the classical
thick disk sequence with a A in red and the classical thin with a B in blue.
An additional low-[Mg/Fe] component can be seen at the lower metallicities,
which has been identified by previous studies as a signature of an accreted
population (Nissen & Schuster, 2010; Hayes et al., 2018; Haywood et al., 2018;
Helmi et al., 2018). In Fig. 1 we indicate the position of this sequence with
a C in yellow. These stars also have [Al/Fe] lower than the Milky Way disk,
another potential signature of an accreted origin (Hawkins et al., 2015; Horta
et al., 2021; Feuillet et al., 2021).

Full kinematics and 3D positions are calculated for the sample using Astropy
(Astropy Collaboration et al., 2013, 2018) and galpy (Bovy, 2015). Input data
used are Gaia astrometric measurements and magnitudes, photogeometric
distances derived by Bailer-Jones et al. (2021), and APOGEE spectroscopic
radial velocity measurements. We use the actionAngleStaeckel approximation
(Bovy & Rix, 2013; Binney, 2012) with the MWPotential14 Milky Way potential
(Bovy & Rix, 2013), delta of 0.4, and default values for all other parameters.

We estimated the uncertainties in the kinematics through a Monte Carlo
analysis using 10 000 iterations. For each iteration, full kinematics were
calculated using parameters drawn from an uncertainty distribution. A Gaussian
distribution was used for the distance and radial velocity. For the RA proper
motion and Dec proper motion, a multivariate Gaussian distribution was used
accounting for the Gaia covariance in RA proper motion, Dec proper motion, and
parallax as well as the uncertainty in the individual parameter. The
uncertainty in the kinematic parameters for each star were taken to be the
standard deviation in each parameter over the 10 000 iterations.

As the main focus of this paper in on a few subsamples, we calculate kinematic
uncertainties for all of Sample I (see below) and a representative selection
of Sample III. We find the largest kinematic uncertainties in stars on high-
energy, low-$L_{z}$ orbits as these stars tend to be at larger distances.
However, the typical uncertainties are less than 10% in all kinematic
parameters and do not affect our conclusions. Effects of select kinematics are
discussed where relevant in the text and the distributions of kinematic
uncertainties are shown in Appendix B.

##  3 Defining and naming stellar samples selected in the Mg-Mn-Al-Fe-plane

In this section we make an empirical definition of the samples we wish to
study. These definitions are based on the appearance of the data in the Mg-Mn-
Al-Fe-plane. In Sect. 4 we will ascertained that the division of Milky Way
stars into two samples using the Mg-Mn-Al-Fe-plane is robust against
shortcomings in the elemental abundance analysis . We thus proceed with a
discussion of how to best define and name our samples.

Figure 2: a) Full sample, showing definition of the diagonal cut, which
results in Sample I and II. b) Histogram of the [Mg/Mn] values for stars
belonging to Sample II. The histogram identifies a suitable cut to define
Sample III and IV. c) Shows the two cuts used and the position of Sample I,
III, and IV in the Mg-Mn-Al-Fe-plane. The exact definitions of the cuts are
summarised in Table 2.

Figure 2 a) empirically defines our cut in the Mg-Mn-Al-Fe-plane, splitting
the sample into two (Sample I and Sample II). The validity of the diagonal cut
is extensively discussed in Sect. 4. Figure 2 b) shows a histogram of [Mg/Mn]
for the stars in Sample II. We see a clear dip in the number counts (also
visible in the 2D histogram in panel a). We define a cut such that stars with
[Mg/Mn] $>$ 0.32 is one sample (Sample III) and stars with [Mg/Mn] $<$ 0.22
another (Sample IV). Table 2 summarises our empirical definitions of the
samples. The current study is mainly concerned with Sample I and to some
extent Sample III. We plan to return to the full Sample II and also Sample IV
in other studies, but we show the full sample selection here for completeness.
We are thus left with four different samples, where Sample III and IV are
subsets of Sample II. Sample Ia and Ib are defined in Sect. 5.1.

Naming these samples is somewhat problematic. One option would be to call them
halo, thick and thin disk or accreted and in-situ populations. However, it is
likely that the thick disk (and halo) overlap to some larger or smaller extent
with the Splash (Belokurov et al., 2020). Another option would be to follow
Horta et al. (2021) and refer to the stars to the left of the diagonal cut as
accreted stars. We are quite certain we will find some accreted stars there,
but are all stars accreted?

Our aim is to investigate how these samples interact and how the Milky Way was
assembled. By giving the samples names we may inadvertently guide our
thinking. To avoid this we have opted to simply refer to the samples defined
in the Mg-Mn-Al-Fe-plane as Sample I, II, III and IV (compare Fig. 2). If sub-
samples are defined to these major samples, for example by imposing a
kinematic constraint, they will be given a letter in addition to identify them
(e.g. Sample Ia). The median uncertainty in $L_{z}/J_{tot}$ for Sample I is
0.06. We note that we have left a substantial gap in the selection of Sample
Ia and Ib.

Table 2: Stellar sub-samples used in this work. The selection criteria for stars to be included in each of the four main samples are given on the first line for each sample (compare Fig. 2). Criteria listed for each sub-sample (e.g., Sample Ia) lists the criterion added to the main criterion (e.g. adding a kinematic criterion to the elemental abundance criterion). Name | Selection criteria
---|---
Sample I: |
S I | [Mg/Mn] $>0.65+1.6\ast$[Al/Fe]
S Ia |  plus $|L_{z}/J_{\rm tot}|<0.25$
S Ib |  plus $L_{z}/J_{\rm tot}>0.6$
Sample II: |
S II | [Mg/Mn] $<0.35+1.6\ast$[Al/Fe]
Sample III: |
S III | [Mg/Mn] $<0.35+1.6\ast$[Al/Fe]
|  and [Mg/Mn] $>$0.32
Sample IV: |
S IV | [Mg/Mn] $<0.35+1.6\ast$[Al/Fe]
|  and [Mg/Mn] $<$0.22

##  4 Chemical signatures of accreted stellar populations

It has long been understood that the elemental abundance ratios as observed in
the stellar atmospheres of long-lived stars hold information about the
conditions in the gas from which the stars formed (Lambert, 1989; McWilliam,
1997). By analysing the spectra of such stars we can trace the chemical
evolution of a stellar population over time or we can use the abundance ratios
as indications of the relative stellar ages. Different elements are released
to the inter-stellar medium by stars with different masses and therefore on
different timescales (see e.g. Arnett, 1996; Nomoto et al., 1997; Kobayashi et
al., 2020). Comparing the elemental abundances therefore gives a timing of the
events.

Stellar systems of different mass and gas densities will evolve on different
timescales. This means that smaller galaxies, like the Magellanic Clouds and
the dwarf spheroidal (dSph) galaxies, are expected to show different elemental
abundance trend. This is born out by observations (see e.g. Tolstoy et al.,
2009; Hasselquist et al., 2021). This in turn means that stellar populations
accreted to the Milky Way should show elemental abundance trends that differ
from those seen for stars formed in the main body of the Milky Way. Hereafter,
we will refer to those stars as “in situ” stars while stars now present in the
Milky Way that formed in (smaller) systems that have been accreted at some
point onto the main body of the Milky Way will be referred to as “accreted”.

It is interesting to consider which elements will give us the best
possibilities to identify accreted stellar populations. The best elements to
use will depend on several factors, beyond those of purely chemical evolution
concern, such as availability of atomic lines of sufficient strength (but not
too strong), our ability to model the strengths of lines in the stellar
spectra as a function of the elemental abundance, e.g., due to deviation from
local thermal equilibrium.

Much focus has been attached to the $\alpha$-elements as it was early
understood that they should show different trends depending on the star
formation rate in the system (McWilliam, 1997, and references therein) and
since such elements have atomic lines of good strength across the optical
spectrum. Another focus has been the neutron-capture elements as they show
distinct patterns for very metal-poor stars and for metal-poor stars in
present day dSph galaxies (Bonifacio et al., 2009; Koch et al., 2013; Roederer
et al., 2016). The neutron-capture elements are, however, difficult to study
as in many stars the available lines are weak. Several of the spectral lines
arising from these elements also have complex structures including hyper-fine-
splitting and NLTE effects (see e.g. Battistini & Bensby, 2016, and references
therein) making them difficult to analyse.

Here we follow upon the work of Hawkins et al. (2015) and explore the
possibilities to use the elemental abundances of magnesium, manganese,
aluminum and iron to identify accreted stars.

###  4.1 Exploring the Mg-Mn-Al-Fe-plane

Figure 3: The Mg-Mn-Al-Fe-plane. a) This figure shows the placement of the
APOGEE DR17 data in the Mg-Mn-Al-Fe-plane. Two chemical evolution models
presented in Horta et al. (2021) are also shown. The black $+$-signs indicate
when the model has reached a metallicity of $-0.8$ dex. The blue arrows show
the sizes and directions of 3D+NLTE effects discussed in Sect. 4.2. b) This
figure illustrates the placement of six different galaxies in the Mg-Mn-Al-Fe-
plane using APOGEE DR17 data. Each of the five dwarf galaxies are shown as a
box centered on the mean values of the data for all red giant stars in that
galaxy and the size is simply half of the full width at half maximum. The
Milky Way disk is shown as a grey area. c) This figure shows the individual
stellar data for three of the dwarf galaxies in panel b). In addition, the
division between traditional halo and disk used in this paper are shown as two
lines (compare Fig. 2). d) This figure reproduces the division of the Mg-Mn-
Al-Fe-plane as used in Horta et al. (2021) and the cuts used in this work to
define Sample I, II, III and IV (see also Fig. 2). The Milky Way disk sample
from figure b) is reproduced as a faint grey area.

Hawkins et al. (2015) and later Das et al. (2020) proposed to use the Mg-Mn-
Al-Fe-plane to identify stellar populations formed in smaller systems and
later accreted onto the main body of the Milky Way. Later works show that this
works well for example in identifying the Gaia-Sausage-Enceladus members
(Feuillet et al., 2021). To the best of our understanding, the works by
Hawkins et al. (2015) and Das et al. (2020) were essentially empirical,
inspired by the large and high quality dataset from APOGEE DR14. Horta et al.
(2021) made a first theoretical illustration of how this plane can work to
identify different stellar population. For completeness and because of the
importance of these findings for our work we here repeat some of the arguments
from Horta et al. (2021) for and against using the Mg-Mn-Al-Fe-plane to
identify accreted stellar populations in the Milky Way.

We start by exploring the Mg-Mn-Al-Fe-plane. Figure 3 a) shows the density map
in this plane of the data selected in Sect. 2. We note that the stars are not
evenly distributed. We see a lighter, round concentration centered at
([Al/Fe],[Mg/Mn]) = (–0.3,+0.5) dex and a more elongated structure to the
right. In between these structures there is a clear depression in the number
densities. We will, Hawkins et al. (2015) and Das et al. (2020) did, use this
lack of stars as a natural place to separate traditional halo and disk stars.
The stars in the structure to the right may also show two rather than a single
structure with one round concentration at (0.3,0.45) and a more elongated
structure below. We will return to these features in more detail in future
studies.

The figure also shows evolutionary tracks for two different systems; the Milky
Way and the Gaia-Sausage-Enceladus. The trends shown are replications from
Horta et al. (2021), their Fig. 1. Horta et al. (2021) uses the Milky Way
solar neighborhood chemical evolution model as their fiducial model (shown
here in red) that is representative of in situ chemical evolution. The model
shown in blue is tailored to represent the Gaia-Sausage-Enceladus progenitor.
The latter then shows what an accreted stellar population may look like. For
each model the following time stamps are indicated by filled circles: 300 Myr,
1 Gyr, and 5 Gyr. In addition the point when each model has reached a chemical
enrichment of –0.8 dex is indicated. Further details on the model parameters
can be found in Andrews et al. (2017) and Horta et al. (2021). As can be
understood from these model predictions, the region to the left will
inevitably include both accreted stars as well as in situ stars if the in situ
population has a reasonably large amount of metal-poor stars. On the other
hand if the in situ population mainly forms from gas that is already enriched
then the region to the left will essentially be void of in situ stars.

Figure 3 b) shows where stars in different known systems fall. The Milky Way
disk is shown by using the APOGEE DR17 data selected as disk stars for this
study (shown as contours, see Fig. 4). In addition, data from APOGEE DR17 for
the Large Magellanic Cloud (LMC), the Small Magellanic Cloud (SMC), the core
and tidal stream of the Sagittarius (Sgr) dwarf spheroidal galaxy, and the
Draco and Ursa Minor dSph galaxies are shown as coloured boxes. The selection
of the stars in these galaxies are described in Appendix A.2. The centres of
the boxes are the mean values of [Mg/Mn] and [Al/Fe] for the data for each
galaxy and the size of the boxes is simply half of the standard deviation for
each data set around their mean values. As can be seen, the Milky Way stellar
disk (the heaviest system) has the highest [Al/Fe] values whilst lighter
systems have lower [Al/Fe] values. Specifically, the SMC is lower in [Al/Fe]
than the LMC. The Milky Way disk spans a large range in [Mg/Mn] while the
other systems have a somewhat smaller range.

The smaller systems all have [Al/Fe] systematically lower than the Milky Way
disk, indicating that it is not unreasonable to assume that stars from a
systems that has formed in relative isolation and then accreted onto the main
body of the Milky Way will be possible to identify thanks to their low
[Al/Fe]. This is further supported by the models from Horta et al. (2021) and
Fernandes et al. (2023) that show that a lighter system will reach a maximum
[Al/Fe] value that is smaller than the main body of the Milky Way disk. See
also Fernandes et al. (2023) for a full characterization of low-mass systems
in APOGEE.

Figure 3 c) shows the full data-set used to calculate the boxes in Fig. 3 b)
for SMC, and the Draco and Ursa Minor dSph galaxies. As can be seen scatter is
relatively high for the two dSph galaxies whilst the data is more compactly
distributed for SMC. The two lines illustrate the cut that we use to separate
traditional halo from disk (Fig. 2). Dwarf galaxies surviving to this day are
clearly on the left-hand side of these cuts and illustrate that we may
reasonably assume to find accreted stars in those regions.

Figure 3 d) replicates the cuts used by Horta et al. (2021) to divide the
plane into Accreted and In situ high- and low-$\alpha$ stars (their
nomenclature). We also show the cuts used in this study defined in Sect. 3.
The main difference is that we divide the sample not considering any selection
based on other elemental abundances (i.e. $\alpha$). The near vertical cut
that separate the samples differ somewhat between the two studies but the
general idea is the same. In our selection, we also leave a gap in order to
provide clean samples, while Horta et al. (2021) prefers a single cut with no
gap. Horta et al. (2021) discuss how, based on their models, a Milky Way-sized
galaxy will inevitably create some stars with high [Mg/Mn] and low [Al/Fe]
that will contaminate any accreted population identified in the Mg-Mn-Al-Fe-
plane (compare Fig. 3 a).

###  4.2 Comments on NLTE and 3D effects on the elemental abundances

In the vast majority of studies of stellar elemental abundances the abundances
are derived under assumption of Local Thermal Equilibrium (LTE). Our
understanding of how to treat departures from LTE (NLTE) has been growing for
a long time and is now commonly implemented in small studies as well as in
large spectroscopic surveys. Departures from LTE can have a significant
effects, in particular when studying stars which span a wide range of
[Fe/H]-values (see e.g. Bergemann et al., 2012; Lind et al., 2012). The stars
in the samples we are studying are giant stars. For the most evolved stars,
the assumption of plane parallel model atmospheres is also under question
(Heiter & Eriksson, 2006) as well as the possibility that the stellar
atmosphere is not homogenous but instead a full 3D modeling is necessary.

In large spectroscopic surveys it is difficult to take full account of NLTE
and 3D effects, mainly because the calculation of these effects are time
consuming. However, recently first instances of including e.g. departure from
the LTE assumption have been performed in the 2nd and 3rd data release from
the GALAH survey (Buder et al., 2018, 2021). In the future, more surveys will
undoubtedly do so.

In APOGEE DR17, NLTE corrections have been applied to the magnesium abundance
measurements following Osorio et al. (2020), but not for aluminum, iron, or
manganese. This means that it is important for us to check whether the
abundance measurements used in our study may be effected by NLTE and/or 3D
effects to such a degree that our conclusions fail. Below we discuss possible
effects on the two elemental abundance ratios that we consider in this work.

####  4.2.1 NLTE and 3D effects on [Al/Fe]

Nordlander & Lind (2017) studies NLTE and 3D effects on the derivation of
[Al/Fe] in late type stars. They show that corrections can be substantial for
some stars whilst for others the corrections are minor. In addition, the
corrections vary significantly for a given star depending on which atomic
lines are being used.

APOGEE uses three near-infrared Al I lines to derive the aluminum abundances.
The lines in the APOGEE linelist by Shetrone et al. (2015); Smith et al.
(2021) are listed as 16723.5, 16755, and 16768. Å. These are given as measured
in vacuum, whilst the lines listed as APOGEE lines in Nordlander & Lind (2017)
are given as 16718.9, 16750.5, and 16763.3 Å, which are measured in air. The
line at 16750.5 Å (air) also has hyperfine splitting. This leads Nordlander &
Lind (2017) to recommend that this line should not be used in derivation of
aluminum abundances for metal-poor cool giant stars such as Arcturus.

For Arcturus, a red giant, with ($T_{\rm eff}/\log g$/[Fe/H]) =
(4247/1.59/–0.52), Nordlander & Lind (2017) find that average 3D and NLTE
together gives a correction of about (–0.2,–0.3, -0.1 ) dex for the three
lines used in APOGEE (as read from their Fig. 10). This should be compared to
an average using all available lines across the optical and near-infrared
stellar spectrum which give a difference of –0.13 dex (their Table 1). They
also analyse HD 122563, another metal-poor giant, ($T_{\rm eff}/\log
g$/[Fe/H]) = (4608/1.61/–2.64). In this star the Al I lines are weak because
the star is so metal-poor and they can therefore only analyse the lines at
16718.9 and 16750.5 Å (air). They find excellent agreement between the [Al/Fe]
abundance in HD 122563 derived from these two lines and the blue UV line at
3961 Å, as well as an average difference of +0.09 dex in the sense 1D LTE - 3D
NLTE (i.e. the value should be added to the 1D LTE value to achieve the
corrected value).

Arcturus and HD 122563 span the full range of [Fe/H] for our sample and have
$\log g$ and $T_{\rm eff}$-values that are representative of our sample. The
size of a 3D plus NLTE correction to [Al/H] abundance in Arcturus derived from
near-infrared lines should be negative and the size about 0.2 dex. For HD
122563, which is much more metal-poor, the correction is also in the negative
sense but less substantial, around 0.1 dex.

Although we do not have the possibility to apply line-by-line NLTE and 3D
corrections to the data from APOGEE DR17 the discussion in the preceding text
leads us to conclude that for the full sample the maximum corrections to
[Al/H] from NLTE and 3D is no more than 0.2 dex (perhaps slightly more) and
not less than 0.1 dex.

For optical spectra it is found that NLTE and 3D effects on derived iron
abundances are small or negligible for stars around –1 dex and with surface
gravities close to 1–2 (Bergemann et al., 2012; Lind et al., 2012; Amarsi et
al., 2016). However, more recent studies indicate that the corrections could
be larger than previously perceived (Amarsi et al., 2022). For iron lines in
the wavelength region covered by APOGEE there exists no full 3D-NLTE
calculation that can be trusted (Masseron et al., 2021). NLTE caclulation are
readily available and show to be essentially non-existent for the stellar
parameter range we are interested in. Taking these aspects into account we
find that there is no need to consider NLTE-3D effects for iron for our
sample. Hence, the effects for [Al/Fe] are the same as for [Al/H].

####  4.2.2 NLTE and 3D effects on [Mg/Mn]

For magnesium, we make use of the calculations by Bergemann et al. (2017) and
Zhang et al. (2017) to estimate the size of the effects of departures from
LTE, as well as 3D effects. Alexeeva et al. (2018) also study departures from
LTE for magnesium but they do not include the near-infrared lines used in
APOGEE DR17.

Zhang et al. (2017) study NLTE effects on derived magnesium abundances based
on Mg I lines in the H-band. Their Table 3 shows that the maximum correction
for 1D NLTE for red giant stars is 0.35 dex for [Mg/Fe]. Table 5 in Bergemann
et al. (2017) shows that the difference between 1D LTE and $<$3D$>$ NLTE in
[Mg/H] from NIR Mg lines is of the order zero.

Departures from 1D LTE for Mn was studied by Bergemann et al. (2019), who
found that 3D NLTE Mn abundances derived from the Mn i lines used in APOGEE
are, on average, significantly higher than those calculated in 1D LTE: for
stars with ($T_{\rm eff},\log g,$[Fe/H]) = (4500/2.0/–1) and (4500/2.0/–2.0)
they find a correction of +0.3 and +0.35 dex, respectively (top panel in Fig.
17 in Bergemann et al., 2019).

Combining this information, we conclude that the [Mg/Mn] elemental abundances
derived from the NIR Mn i lines used in APOGEE has a negative correction of up
to 0.35 dex.

####  4.2.3 Summary: How well can stellar populations be separated in the Mg-
Mn-Al-Fe-plane?

Based on the literature review provided in Sects. 4.2.1 and 4.2.2 we find that
for a typical giant star in our sample the NLTE combined with 3D corrections
amount to about –0.1 to –0.2 dex in [Al/Fe] and –0.35 dex in [Mg/Mn]. This
implies a movement down and to the left in the Mg-Mn-Al-Fe-plane. The slope of
the correction is roughly aligned with the empirical, diagonal cut we adopt to
split our sample into two (see Fig. 3 and 2). This implies that although stars
would collectively move within the diagram if the NLTE and 3D corrections were
applied, in fact the gap between the two populations would remain.

We conclude that, in the case of the data selected in this study from APOGEE
DR17, we can indeed make use of the Mg-Mn-Al-Fe-plane to separate accreted
stars from those formed in the main body of the Galaxy. For individual stars
there might be differences but for the populations as such it is sufficient to
use the uncorrect elemental abundances from APOGEE DR17.

It is important to remember that this statement is valid for the stars
selected for this study, i.e. stars on the Red Giant Branch (compare Table 1).
Stars in other evolutionary stages may not be as readily separable and a fresh
assessment should be made for each study taking exact atomic lines used in the
derivation of the elemental abundances into account.

##  5 Kinematic properties and elemental abundances for Sample I and III

Figure 4: $V_{\phi}-$[Fe/H] plane for the full sample from APOGEE DR17 used in
this study.

Figure 4 shows the density plot of $V_{\phi}$ as a function of [Fe/H] for our
full sample. We see that the majority of the stars have a velocity compatible
with that of the stellar disk (Bland-Hawthorn & Gerhard, 2016). There is also
a prominent downward trend at [Fe/H] of about $-0.7$ dex as well as
substructure at lower metallicities with kinematics typical of the stellar
halo (Bland-Hawthorn & Gerhard, 2016).

In this section we first analyse the kinematical properties of the full sample
as well as the chemically defined sub-samples. Secondly, we combine selection
in elemental abundance space with the kinematic properties and identify the
stellar disk.

###  5.1 Kinematics of Sample I and III

Figure 5:  $V_{\phi}$ as a function of $V_{R}$ for the full sample and the
samples defined via cuts in the Mg-Mn-Al-Fe-plane. See Fig. 2 and Table 2 for
the definition of the samples. Median value for $V_{\phi}$ for the full sample
shown as a thick grey line, repeated in all four panels. a) Full sample. b)
Sample IV. c) Sample I. Median value of $V_{\phi}$ for this sample shown as a
light-blue dash-dotted line. d) Sample III. Median value of $V_{\phi}$ for
this sample shown as a red dash-dotted line.  Figure 6: Action diamonds for
Sample I and III. a) Action diamond for Sample I for stars with $1<\log g<2$.
b) Action diamond for Sample III for stars with $1<\log g<2$. c) Action
diamond for Sample I for stars with $1<\log g<2$ colour coded by [Mg/Fe]. d)
Action diamond for Sample III for stars with $1<\log g<2$ colour coded by
[Mg/Fe]. e) 2D histogram action diamond for the full Sample I. f) 2D histogram
action diamond for the full Sample III.

There are several kinematic spaces used in the literature to analyse the
stellar content of the Milky Way halo. The Toomre diagram has been extensively
used to make a separation of stellar disk and halo stars (examples include
Helmi et al., 2018; Bensby et al., 2014; Nissen & Schuster, 2010). A simple
plot of $V_{\phi}$ as a function of $V_{R}$ can help to study the connection
between disk and halo (Belokurov et al., 2020). Other quantities such as
angular momenta or actions are (near) preserved and can be used to identify,
e.g., streams (Helmi et al., 1999).

We start by studying our stellar samples defined in the Mg-Mn-Al-Fe-plane in
various kinematic spaces. Figure 5 shows $V_{\phi}$ as a function of $V_{R}$
for the full sample and for Sample I, III, and IV as defined in Fig. 2. In
each panel the median value for $V_{\phi}$ of the full sample is shown as a
grey line, whilst the median of the selected sample is shown as a coloured,
dashed line. For Sample IV the grey and the coloured lines have the same
value. Sample I shows an elongated structure centred at $V_{\phi}=0$ and an
extension of stars to higher (pro-grade) $V_{\phi}$-values which is centred at
$V_{R}=0$. Sample IV is, as already noted, very similar to the bulk of the
full sample, whilst Sample III has a distinctly lower mean $V_{\phi}$-value as
well as an extension towards $V_{\phi}=0$ and even negative values (retro-
grade).

To summarize, the main sample is well concentrated around ($V_{R}$,
$V_{\phi}$) = (0, $\sim 200$) km s-1. When divided into sub-samples using the
Mg-Mn-Al-Fe-plane we find that one sample takes up the bulk of the stars
centred at the same values as the main sample whilst the other two samples
contain the stars making up the down-ward flow of stars towards $V_{\phi}=0$
as well as flaring out to larger (pos/neg) values of $V_{R}$. The three
samples are distinct in the ($V_{R}$, $V_{\phi}$)-plane.

Recently, another depiction of the stellar kinematics has been used – the
action diamond (Vasiliev, 2019; Myeong et al., 2019; Lane et al., 2022). The
diamond is constructed from the actions and angular momenta of the stellar
orbits. On the $x$-axis is $L_{z}/J_{\rm tot}$ and on the $y$-axis
$(J_{z}-J_{R})/J_{\rm tot}$. As explained in Lane et al. (2022) this space is
particularly intuitive to interpret; the left- and right-hand corners occur
when the angular momentum in the $z$-direction and the total action are equal,
i.e. a pro- or retro-grade orbit in the plane. The bottom corner contains the
stars on purely radial orbits while the top corner gathers the stars on polar
orbits.

Figure 6 a) and c) show the action diamonds of Sample I for the full sample
and for only stars with $1<\log g<2$ , respectively. In both cases, the sample
is mainly concentrated to the bottom corner. The bottom corner of the action
diamond is associated with radial orbits (see Sect. 4.1.1 in Lane et al.,
2022). However, the figures also show that there is a smaller concentration of
stars in the right hand corner. This corner is associated with pro-grade disk-
like orbits. Figure 6 b) and d), show the action diamonds of Sample III for
the full sample and for only stars with $1<\log g<2$, respectively. Sample III
populates the right-hand corner of the action diamond associated with disk-
like orbits (Lane et al., 2022). Fig. 6 e) and f) show the action diamonds of
Sample I and III for stars with $1<\log g<2$, colour-coded according to the
[Mg/Fe]-ratios of the stars. Sample I shows mainly low(er) [Mg/Fe]-ratio than
Sample III. However, the stars in the left- and right-hand corners of the
action diamond for Sample I have high-[Mg/Fe] ratios suggesting there may be
two stellar populations in Sample I.

Figure 7: Four kinematic spaces showing the properties of the stars selected
for Sample I (first column) and Sample III (third column) using the Mg-Mn-Al-
Fe-plane (Fig 2). Only stars with $1<\log g<2$ are included (plots look very
similar with all stars included). The middle column shows the two sub-samples
of Sample I defined using the action diamond: Sample Ia (red) are stars with
$-0.25<L_{z}/J_{tot}<0.25$ and Sample Ib (blue) stars with
$L_{z}/J_{tot}>0.6$. The number of stars in each sample are indicated in the
panels in the top-row.

To ensure that our interpretation of the properties of Sample I as seen in the
action diamond actually implicates two stellar populations with different
kinematical status we show four commonly used kinematic planes. We define two
sub-samples in Sample I based on the stars’ $L_{z}/J_{tot}$. Sample Ia is
defined as stars with $-0.25<L_{z}/J_{tot}<0.25$ and Sample Ib stars with
$L_{z}/J_{tot}>0.6$. Figure 7 shows the four kinematic spaces for the two new
Sample Ia (red) and Ib (blue), as well as Sample I and III. For all samples,
only stars with $1<\log g<2$ are shown444We note that for the orbital
calculations with galpy we have used the MWPotential2014 in Bovy & Rix (2013);
Bovy (2015). To be compatible with other studies we also present the same
plots using the McMillan (2017) potential in Appendix B. The conclusions
remain, the main difference being the values of $E_{\rm n}$, which are
shifted..

We observe that the kinematical properties of Sample I and III are distinct.
Remember that these selections are only based on elemental abundances (Fig 2).
Sample I has mainly radial orbits of the type associated with the halo and
Sample III can best be described as a somewhat heated disk, with most stars on
prograde orbits. Sample Ia and Ib indeed show the expected dichotomy – Sample
Ia has a radial orbit (as per design) while Sample Ib clearly is picking up
essentially all the disk-like stars in Sample I. Note that there will be a gap
between the samples as per the selection.

To summarise, Sample I contains two stellar samples identified in the action
diamond, one on radial orbits and one on disk-like pro-grade orbits. Sample
III contains an essentially disk, pro-grade stellar sample.

###  5.2 Chemical properties of Sample I and Sample III

Figure 8: [Mg/Fe] as a function of [Fe/H] for Sample I, Ia, Ib, and III.
Samples are restricted to stars with $1<\log g<2$. a) [Mg/Fe] as a function of
[Fe/H] for Sample I. b) [Mg/Fe] as a function of [Fe/H] for Sample III. c)
[Mg/Fe] as a function of [Fe/H] for Sample I colour-coded by $L_{z}/J_{\rm
tot}$. Values as indicated by the colour bar. d) [Mg/Fe] as a function of
[Fe/H] for Sample Ia. e) [Mg/Fe] as a function of [Fe/H] for Sample Ib. The
same plots but for [Ni/Fe] can be found in App. C.

We now turn to the chemical properties of Sample I, Ia, Ib, and III. We start
by noting that Fig. 6 e) and f) show that Sample I and Sample III have
distinct chemical properties where Sample III contains almost exclusively
stars with [Mg/Fe] $>$0.25. In Sample I, stars with [Mg/Fe] $<$0.2 are mainly
concentrated towards the bottom corner of the action diamond. The right- and
left-hand corners are dominated by stars with [Mg/Fe] $>$0.25 There are also
some stars spread into the rest of the action diamond with high
[Mg/Fe]-ratios.

To summarise, it appears that the two kinematical sub-samples in Sample I
identified in Sect. 5.1 have distinct chemical signatures with the stars on
disk-like orbits being elevated in [Mg/Fe] in comparison to the stars with
radial, halo-like orbits.

Fig.ure 8 a) and b) show [Mg/Fe] as a function of [Fe/H] for Sample I and III.
These are clearly distinct with Sample III being more metal-rich (median
[Fe/H] = –0.55) and showing high [Mg/Fe] for all stars. Sample I has lower
[Fe/H] (median [Fe/H] = –1.33) and a downward trend for [Mg/Fe], starting from
the highest values and continuing down to about 0.0 dex.

Figure 8c) shows the stars in Sample I colour-coded according to $L_{z}/J_{\rm
tot}$. Here we find that almost all stars with positive $L_{z}/J_{\rm tot}$
have high [Mg/Fe]-ratios, while stars with $L_{z}/J_{\rm tot}$ around zero
follow the down-ward trend. To more easily see this, Fig. 8 d) and e) show
Sample Ia and Ib, i.e. $-0.25<L_{z}/J_{\rm tot}<0.25$ and $L_{z}/J_{\rm
tot}>0.6$, respectively. Sample Ib has a high [Mg/Fe]-ratio with only a
sprinkle of stars with lower ratios. The sample also stops quite abruptly at
[Fe/H] about –1.1 dex. We note that Sample III starts roughly at the same iron
abundance as Sample Ib stops, suggesting Sample III could be a later stage
evolution of Sample Ib. Figure 19 shows that [Ni/Fe] behaves in the same way
as [Mg/Fe]. In fact, the picture is even a bit clearer when using [Ni/Fe].

###  5.3 Potential selection effects

Figure 9: Galactocentric radius ($R$) as a function of height above and below
the Galactic plane ($z$). Only stars with $1<\log g<2$ are included. The
number of stars in each panel are indicated, for the top row in the left-hand
bottom corner and for middle and bottom rows in the upper right-hand corner.
The top-row is colour-coded by $L_{z}/J_{\rm tot}$ according to the colour-bar
to the right of the plots. a) Full sample. b) Sample I. c) Sample III. d) Full
sample, only stars with $-0.25<L_{z}/J_{\rm tot}<0.25$. e) Sample I, only
stars with $-0.25<L_{z}/J_{\rm tot}<0.25$, i.e. Sample Ia. f) Sample III, only
stars with $-0.25<L_{z}/J_{\rm tot}<0.25$. g) Full sample, only stars with
$0.6<L_{z}/J_{\rm tot}$. h) Sample I, only stars with $0.6<L_{z}/J_{\rm tot}$,
i.e. Sample Ib. i) Sample III, only stars with $0.6<L_{z}/J_{\rm tot}$.

With large spectroscopic surveys, inevitably the selection function of the
survey may influence the perceived properties of a stellar population (Mints &
Hekker, 2019; Stonkutė et al., 2016). Preferably it should be possible to
correct for the introduced biases or model their effect on the data in order
to capture the underlying truth. This, however, can be more or less difficult
to do and the examples in the literature are few. In the present work we are
foremost concerned with identifying and characterising stellar components with
the help of elemental abundance trends. The interpretation of such data does
not need a complete sample but it is important to understand if certain parts
of the Galaxy or parameter space have been excluded thanks to the selection
function of the original survey or via a too vigorous down selection of
objects in the study itself.

To ensure that our conclusions are robust we have looked at the spatial
properties of our samples and also at what effects the original APOGEE
selection function may have on the phase space data we are using.

##### Spatial properties of our samples

The top-row of Fig. 9 shows the $R$-$z$-plane for our full sample, Sample I
and III, colour-coded by $L_{z}/J_{\rm tot}$. Visual inspection shows that
Sample I covers the full extent in $z$ of the full sample, that it also covers
a fair portion of the $R$, but that there is a lack of stars with these
chemical signatures in the disk beyond the solar position (Fig. 9 b). Sample
III is more confined to the plane ($z<4$ kpc, Fig. 9c) and covers the disk
better than Sample I.

Rows two and three further divide the data into $-0.25<L_{z}/J_{\rm tot}<0.25$
(i.e. halo-like orbits) and $0.6<L_{z}/J_{\rm tot}$ (i.e. disk-like orbits).
In all three cases this division shows that stars with halo-like orbits occupy
the full space spanned by all stars (potentially with some lack of stars
outside the solar orbit in the plane) and stars with disk-like orbits are more
confined to the plane.

As we observe the same behavior for the full sample and for Sample I and III,
we conclude that there is no direct indication that our results should not be
valid for the whole Galaxy, i.e. the properties of the stellar populations we
observe are not just a local, but a global phenomenon.

##### Selection effects showing up in the $E_{\rm n}-L_{\rm z}$ plane

Figure 10: a) $E_{\rm n}$ as a function of $L_{\rm z}$ for stars in our full
sample selected at different galactocentric radii, as indicated in the legend.
b) Cumulative distribution functions for our full sample, stars with z $<$1
kpc, and Sample I. c) $E_{\rm n}$ as a function of $L_{\rm z}$ for stars in
two galactocentric bins ($<4$, blue, and $8-10$ kpc, red). Stars with $|z|<1$
kpc are shown in bright colours while stars with $|z|>1$ kpc are shown with
more transparent colours (see legend). d) $E_{\rm n}$ as a function of $L_{\rm
z}$ for stars in our Sample I selected at different galactocentric radii as
indicated in the legend in panel a).

Figures 9 and 10 highlights an underlying selection effect from the original
APOGEE DR17 sample. In Fig. 10 a) our sample stars are shown colour-coded
according to their galactocentric distances. Stars in the plane at a given
distance in a galactic potential follow a certain parabola in the $E_{\rm
n}-L_{\rm z}$ plane (see Fig. 5 in Lane et al., 2022). As expected, stars at a
certain radius follow a parabola. The upward scatter in each sample is due to
the sampling of stars at different heights above the Galactic plane. This is
illustrated in panel c) for two radial bins ($<4$ and $8-10$ kpc) where stars
with $|z|>1$ kpc are shown in a fainter colour. At a given $L_{\rm z}$ these
stars are more spread in $E_{\rm n}$ than stars at lower $z$.

In Fig. 10 d) we show the data for our Sample I. Remember that this sample is
simply selected based on the elemental abundances of the stars (Table 2). The
$E_{\rm n}-L_{\rm z}$ plane shows a clear lack of stars for $E_{\rm
n}\simeq-2\cdot 10^{5}$ to $-1.8\cdot 10^{5}$. Is this gap real or part of a
selection effect? In panels a) and d) of Fig. 10 we have colour coded the
stars according to their galactocentric distances. We can see that the
energies for the gap corresponds to radial distances of about 5 kpc. As
discussed in Lane et al. (2022) the observing strategy of APOGEE (for DR16 but
also for DR17) includes some extra deep fields towards the Galactic bulge.
These result in an excess of stars observed closer to the Galactic center, at
a lower $E_{\rm n}$ than the nominal disk survey (their Fig. 6) If we refer to
Fig. 9, we can see that the galactocentric distance of 5 kpc is less populated
than other radii thanks to the placement of the two deep pointings at low
latitude while the main survey observed at high latitudes reaching well above
the Galactic plane. This survey strategy has left a clear gap in stellar
distribution seen edge-on. This gap is present in all our samples and is thus
not a feature of the selection in the Mg-Mn-Al-Fe-plane.

We can thus assume that our results are not biased, however, we are missing
objects around 5 kpc (compare Fig. 10 b). There is no reason to assume these
objects do not exist but will be found in future surveys.

##  6 Dating the stellar components

It would be interesting to date the Sample Ia and Ib to further understand
their role in the formation of the Milky Way. We are using RGB stars for our
studies and hence it is not feasible to obtain good ages for individual stars
using isochrone fitting (Soderblom, 2010; Sahlholdt et al., 2019b). However,
asteroseismology offers an alternative possibility to derive ages for RGB
stars (see e.g. Miglio et al., 2017, 2021). We searched the literature for
ages derived from asteroseismological observations for stars with similar
characteristics to those we find in Sample I and found two studies: Montalbán
et al. (2021) and Borre et al. (2022). Although these are relatively small
studies they can still give us some first hints as to the nature of the ages
of our samples and also point to which specific studies would help to better
constrain our observations.

We first took a look at the overlap between the two datasets and how many of
the stars in the two studies would fall into our Sample I. We found that the
overlap is, for the objective of our study and focus on Sample I, sufficiently
large that nothing is gained by using both samples and we thus selected Borre
et al. (2022) as being the sample with more stars falling in Sample I.

###  6.1 Data

Figure 11: Elemental abundances from APOGEE DR17 for the stars with ages from
Borre et al. (2022). Purple symbols refer to stars that fulfill our quality
criteria for APOGEE DR17 and Gaia DR3, while pink symbols do not fulfill those
criteria. Filled symbols indicate stars that we would associate with Sample I.
a) The Mg-Mn-Al-Fe-plane. The grey 2D histogram shows our full sample and the
coloured lines our selection criteria for the different samples as defined in
Fig. 2. b) [Mg/Fe] as a function of [Fe/H]. Grey dots indicate our Sample I.

Borre et al. (2022) studied a sample compiled from a cross-match between
asteroseismic data from the Kepler mission, astrometric data from the Gaia
mission, elemental abundances from APOGEE DR16, and the Two Micron All Sky
Survey (2MASS). For references and details of the selection of stellar data,
final target assembly, and calculation of stellar ages and space motions we
refer the reader to Sect. 2 in Borre et al. (2022).

In total, Borre et al. (2022) provide ages for 70 stars based on photometric,
asterometric, and asteroseismic data (individual frequencies or $\nu_{\rm
max}$ and $\Delta\nu$). Here we are interested in the ages provided by this
study and less with their target selection. However, it is worth noting that
they start from a kinematic selection (defined in $L_{\rm z}$). This results
in a large range of [Fe/H] values.

Borre et al. (2022) used elemental abundances from APOGEE 16 (Ahumada et al.,
2020). In our work we are using APOGEE DR17 (Abdurro’uf et al., 2022). The
exact values of [Fe/H] as well as [$\alpha$/Fe] will to some extent influence
the derived stellar ages. Figure 10 in Borre et al. (2022) provide a
comparison of [Fe/H] values used in their study and in Montalbán et al.
(2021), who use APOGEE DR14, showing offsets ranging from 0 to about 0.2 dex.
In the same figure there is also a comparison of the ages derived for the
stars which shows the ages to have small differences (from 0 to about 2 Gyr).
In all cases, the ages derived in the two studies agree well within the error
bars. We conclude that the small offsets in [Fe/H] between APOGEE DR16 used to
derived the ages and APOGEE DR17 used in our elemental abundance selection are
negligible, and that the choice of Borre et al. (2022) ages over Montalbán et
al. (2021) will not influence our conclusions.

The elemental abundances for this sample are shown in Fig.11.

###  6.2 Age of the stars in Sample I

Table 3: Stars from Borre et al. (2022) that fulfill our quality criteria, Table 1, and fall in our Sample I region in the Mg-Mn-Al-Fe-plane based on elemental abundances from APOGEE DR17. Ages are from Borre et al. (2022), while [Fe/H] and [Mg/Fe] are taken from APOGEE DR17. The last column indicate if the stars falls in Sample Ia. No star falls in Sample Ib. Gaia ID | [Fe/H] | [Mg/Fe] | Age | Age error | $L_{\rm z}/J_{\rm tot}$ | Ia
---|---|---|---|---|---|---
53635139275591040 | –1.38 | 0.20 | 11.69 | +2.57/–2.82 | +0.038 | ✓
2099659187162016512 | –1.37 | 0.34 | 11.75 | +1.91/–1.20 | –0.113 | ✓
2126445115779806976 | –1.43 | 0.24 | 5.54 | +1.88/–3.18 | –0.252 | –
2127447522484965504 | –1.50 | 0.36 | 10.51 | +2.18/–1.82 | –0.480 | –
2133314619611880448 | –1.56 | 0.27 | 10.27 | +1.96/–2.50 | +0.092 | ✓
2538202737087917184 | –0.87 | 0.13 | 9.85 | +3.40/–3.45 | +0.170 | ✓
2626567188077168896 | –0.77 | 0.09 | 4.59 | +4.23/–2.19 | –0.026 | ✓

In Table 3, we list those stars that fulfill our quality criteria and fall in
Sample I (see Table 1 and 2). We note that our quality criteria are more
restrictive than those applied in Borre et al. (2022), this is likely partly
due to different versions of APOGEE being used. We also consider those stars
that would be selected based on their elemental abundances if we disregarded
the quality flags we applied.

We find an average of $9.2\pm 2.7$ Gyr for the 7 stars that fall in the Sample
I region in the Mg-Mn-Al-Fe-plane and fulfill our quality cuts. Two of the
stars have young ages, typical of the stellar disk. If those are excluded the
age is $10.8\pm 0.8$ Gyr. If we use our cut in $L_{\rm z}/J_{\rm tot}$ to
consider the stars in Sample Ia (see Sect. 5.1), we are left with five stars
that have a mean age of $9.6\pm 2.6$ Gyr. If the young star is excluded we
obtain a mean age of $10.9\pm 0.8$ Gyr.

We can conclude that the stars that fall in Sample I or Sample Ia and fulfill
our quality criteria for the elemental abundances have an old age. There are
two stars that have young ages. Such stars have been found also in other
studies and are sometimes referred to as young $\alpha$-rich stars (Chiappini
et al., 2015). One explanation for the presence of such stars is that they are
in fact blue stragglers (Jofré et al., 2016).

None of the stars in the seismic sample that fall in the Sample I region in
the Mg-Mn-Al-Fe-plane have $L_{\rm z}/J_{\rm tot}>0.6$, i.e. stars in Sample
Ib. This means that although we can put an age on Sample Ia we are unable from
the presently available stellar ages to derive an age for Sample Ib, i.e. the
disk.

We undertake the same analysis for Sample III as we did for Sample I, see
Table 8. From this we derive an age of $8.8\pm 2.8$ Gyr for Sample III using
the ages from Borre et al. (2022). Thus with this dataset, we find that the
stars in Sample I have a mean-age about 1–2 Gyr older than those in Sample
III.

##  7 Discussion

Table 4: List of selection criteria used to select the Gaia-Sausage-Enceladus for Fig. 12 and 13. The letter in the first column refers to the panel labels in those figures. The studies are ordered according to publication year. Panel | Study | Selection ctriteria | Units
---|---|---|---
i) | “Sausage” | $-100$ | $<$ | $V_{\phi}$ | $<$ | $100$ | km s-1
f) | Helmi et al. (2018) | $-1500$ | $<$ | $L_{\rm z}$ | $<$ | $150$ | kpc km s-1
|  | $-1.8\cdot 10^{5}$ | $<$ | $E_{\rm n}$ |  |  | km2 s-1
c) | Myeong et al. (2019) |  |  | $|J_{\phi}/J_{\rm tot}|$ | $<$ | $0.07$ |
|  |  |  | $\frac{(J_{\rm z}-J_{\rm z})}{J_{\rm tot}}$ | $<$ | $-0.3$ |
h) | Feuillet et al. (2020) | 30 | $<$ | $\sqrt{(}J_{\rm r})$ | $<$ | $50$ | (kpc km s-1)1/2
|  | $-500$ | $<$ | $L_{\rm z}$ | $<$ | 500 | kpc km s-1
b) | Horta et al. (2022) |  |  | $|L_{\rm z}|$ | $<$ | $0.15\cdot 10^{3}$ | kpc km s-1
|  | $-1.6\cdot 10^{5}$ | $<$ | $E_{\rm n}$ | $<$ | $-1.1\cdot 10^{5}$ | km2 s-1
e) | Naidu et al. (2022) | $-1.5\cdot 10^{5}$ | $<$ | $E_{\rm n}$ |  |  | km2 s-1
|  | 0.7 | $<$ | $eccentricity$ |  |  |
|  | 5 | $<$ | $R_{\rm galcentre}$ | kpc
|  | $0.25$ | $<$ | [Mg/Mn] |  |  |
|  | $0.55$ | $<$ | [Mg/Mn] $-4.25\cdot$[Al/Fe] |

Following the work by Hawkins et al. (2015) and Das et al. (2020) we have
explored the ability of the Mg-Mn-Al-Fe-plane to distinguish stars from
different stellar populations in the Milky Way. By further combining the
elemental abundance data with kinematical properties of the stars we have
found that the region with low [Al/Fe]-values (our Sample I) contains stellar
populations with kinematical properties associated with the stellar halo and
with the stellar disk. Furthermore, we find that those samples differ in their
[Mg/Fe] and [Ni/Fe] abundance trends, indicating different origins.

###  7.1 Gaia-Sausage-Enceladus

When the astrometric data from the ESA Gaia satellite are combined with radial
velocities it is possible to study the halo kinematics in great detail. Using
different techniques, research teams have found stellar populations, accreted
galaxies, and stellar streams.

The Gaia-Sausage-Enceladus and other discreet stellar populations have been
found thanks to the astrometric data from the ESA Gaia satellite (Helmi et
al., 2018; Belokurov et al., 2018; Helmi, 2020; Naidu et al., 2022; Horta et
al., 2022).

In Table 4 we have, from the literature, collected five different ways of
selecting Gaia-Sausage-Enceladus stars. We also include a kind of trivial
definition of the Sausage, i.e. $-100<V_{\phi}<100$ km s-1. Figure 12 a) shows
a 2D histogram of the $E_{\rm n}-L_{\rm z}$ plane for our full sample. In all
remaining panels, our Sample I is shown in cyan for comparison. Our Sample Ia
and Ib are shown in panels d) and g). In the other panels we show the
resulting distributions in the $E_{\rm n}-L_{\rm z}$ plane when we select
stars from our main sample according to the six Gaia-Sausage-Enceladus
criteria listed in Table 4. We show two selections for each sample. Grey
points indicate stars selected from our catalogue only using the criterium
listed in Table 4 and the number of selected stars indicated in grey in the
lower left-hand corner of each panel. Black points indicate stars that also
fall into our Sample I (Table 2) and the number of such stars is indicated in
black in the lower left-hand corner of each panel. In the upper right-hand
corner of the six Gaia-Sausage-Enceladus panels, the average $L_{\rm z}$ and
associated $\sigma$ are shown.

It is interesting to note that the five definitions of Gaia-Sausage-Enceladus
taken from the literature show distinctly different distributions in the
$E_{\rm n}-L_{\rm z}$ plane. In all cases, imposing our selection criterium in
the Mg-Mn-Al-Fe plane lowers the number of stars but it does not seem to
change the distribution in the $E_{\rm n}-L_{\rm z}$ plane much apart from for
the trivial definition shown in panel i), where we can see that the $E_{\rm
n}$ gap is less prominent in the grey points than in the black ones. A similar
effect is suggested in panel c) using the criterium from Myeong et al. (2019).

It is immediately obvious that our Sample Ib bears little resemblance in the
$E_{\rm n}-L_{\rm z}$ plane to any of the definitions of the Gaia-Sausage-
Enceladus. This is not surprising given that we find it has disk-like
kinematics. Our Sample Ia on the other hand occupies many of the same spaces
in $E_{\rm n}-L_{\rm z}$ as the six definitions. The distribution based on
selection by Myeong et al. (2019) is the one most similar to our Sample Ia. In
general though the literature definitions avoid the lower energies included in
Sample Ia. These are only present in the trivial definition and in Myeong et
al. (2019). Feuillet et al. (2020) and Horta et al. (2022) have quite similar
distributions while Naidu et al. (2022) has a much wider distribution in
$L_{\rm z}$ than the other two. It also reaches higher energies. Finally, we
note that the selection criteria defined by Helmi et al. (2018) creates an
essential retrograde population, which reaches to quite low energies.

Fig. 13 presents the associated distribution of [Mg/Fe] as a function of
[Fe/H] for Sample I, Ia, Ib, and all six definitions of Gaia-Sausage-
Enceladus. Colour-coding is the same as in Fig. 12, but here we only print the
number of stars fulfilling both the literature criteria and our selection in
Mg-Mn-Al-Fe-plane. In addition, each panel shows the average [Fe/H] and
[Mg/Fe] for the black points.

There are three immediate observations to be made from these plots: 1)
Regardless of selection criteria all selections result in a down-going trend
for [Mg/Fe] with increasing [Fe/H]. The trend coincides with our Sample I and
even more clearly with Sample Ia. 2) In all cases adding our selection in the
Mg-Mn-Al-Fe-plane removes the high [Mg/Fe] stars at higher [Fe/H], i.e. the
disk. 3) In all but the trivial case there are stars more enhanced in [Mg/Fe]
at a given [Fe/H] in Sample I (cyan). These stars are deselected in all but
the trivial case and overlap with our Sample Ib in this plane.

Figure 12: $E_{\rm n}$ as a function of $L_{\rm z}$. In all plots the data are
restricted to stars with $1<\log g<2$. a) 2D histogram for our full sample. b)
– i) Samples as indicated on the top of each panel. Cyan symbols always refer
to our Sample I. Black symbols refer to stars which fulfill both the selection
criteria from the study indicated on the top as well as our own selection
criteria for Sample I. Grey symbols refer to stars that are selected by the
criteria in the indicated study but falls outside our Sample I. The number of
stars in each sample is given in the lower left-hand corner of each plot. In
the upper right hand-corners are the mean $L_{\rm z}$ for each sample
indicated in black shown. Table 4 shows the selection criteria for used for
each of the studies.  Figure 13: [Mg/Fe] as a function of [Fe/H]. In all plots
the data are restricted to stars with $1<\log g<2$. a) Sample I. b) – i)
Samples as indicated on the top of each panel. Cyan symbols always refer to
our Sample I. Black symbols refer to stars which fulfill both the selection
criteria from the study indicated on the top as well as our own selection
criteria for Sample I. Grey symbols refer to stars that are selected by the
criteria in the indicated study but falls outside our Sample I. The number of
black points in each sample is given in the upper right-hand corner of each
plot. In the lower left-hand corners are the mean [Fe/H] and [Mg/Fe] for the
black, blue and red points shown. Table 4 shows the selection criteria for
used for each of the studies.

Various investigations have used kinematic criteria and/or various clustering
algorithms to identify groups of stars that likely come from a single accreted
progenitor. We find that the Mg-Mn-Al-Fe-plane is suitable for identifying
stars with halo kinematics and likely accreted origin, but we find that the
same region also includes stars with typical disk kinematics. When we study
the elemental abundance trends, we find that, regardless of selection method,
samples that can be associated with the Gaia-Sausage-Enceladus progenitor show
remarkably similar elemental abundance trends but not always the same
kinematic characteristics. In particular, the accreted stars appear to be able
to have both pro- and retro-grade orbits. It appears remarkable that
regardless of criterium used, we recreate the same downward [Mg/Fe] trend
first observed by Nissen & Schuster (1997, 2010). Thus it appears that the
stars from this merger are well-mixed in kinematics but better distinguished
in elemental abundance space.

The Hestia simulations (Libeskind et al., 2020; Khoperskov et al., 2022a, b,
c) follow three Local Group pairings of galaxies and their respective merger
histories. One important aspect of these simulations is that the galactic
potential evolves in the cosmological context. This means that after a smaller
galaxy merges with the main progenitor the potential gets deeper with time.
The effect is that, regardless of time of merger, all of the major mergers
have roughly the same energy today. This means that the $E_{\rm n}$ – $L_{\rm
z}$ plane is partly degenerate when it comes to picking up individual merger
debris. Another important information gleaned from the inspection of the
$E_{\rm n}$ – $L_{\rm z}$ diagrams for the mergers in the Hestia simulations
is the fact that almost all mergers show stars on both pro- and retro-grade
orbits. This is very similar to what we find when we are looking at the stars
that, in various ways, could be associated with the Gaia-Sausage-Enceladus.

Massari et al. (2019) studied the globular cluster system in the Milky Way and
defined the Main Progenitor as the properties traced by globular clusters
formed in situ in the stellar disk or the Galactic Bulge. The left panel of
Fig. 2 in Massari et al. (2019) shows the $E_{\rm n}$ – $L_{\rm z}$ plane of
Milky Way globular clusters. It is interesting to note that the clusters
associated with the Main Progenitor have a distribution in the $E_{\rm n}$ –
$L_{\rm z}$ plane that is strongly reminiscent of our Sample Ib. Kruijssen et
al. (2019), in a similar manner, used globular clusters to trace early merger
events in the Milky Way and identified what they claim to be one such event;
the deeply bound Kraken galaxy. We have tentatively looked at the deeply bound
portions of our samples, compare also the trivial definition of the Gaia-
Sausage-Enceladus presented earlier. We find some similarities in elemental
abundance space with our Sample Ib and a Kraken sample.

A recent critique of the practice of using the globular clusters to trace the
formation and assembly history of a galaxy can be found in Pagnini et al.
(2023). They study the accretion of galaxies and associated globular clusters
onto a galaxy where the potential is allowed to change as the main galaxy
grows via mergers over cosmic time. In agreement with the main findings of the
Hestia simulations, they show that the globular clusters from the merged
galaxy do not end up in the same part of the $E_{\rm n}$ – $L_{\rm z}$ plane
as stars from their host galaxy. Only for small galaxies may there remain some
similarities in kinematic properties between the field stars accreted from the
smaller galaxy and its globular clusters.

###  7.2 The chemically unevolved stellar disk

Figure 14: a) Normalized cumulative distribution of [Mg/Mn] for Sample I, Ia,
and Ib as indicated in the legend. b) Normalized cumulative distribution of
[Mg/Mn] for Sample I, Ia, and Ib as indicated in the legend in panel a). c)
[Mg/Mn] as function of [Al/Fe] showing the positions of the median values for
Sample I, Ia and Ib as indicated in the legend. The two models from Horta et
al. (2022) are also shown. d) 2D histogram [Mg/Mn] as function of [Al/Fe] for
the whole sample (grey) and Sample Ia (red). e) 2D histogram [Mg/Mn] as
function of [Al/Fe] for the whole sample (grey) and Sample Ib (blue). f) 2D
histogram [Mg/Mn] as function of [Al/Fe] for the whole sample where the colour
indicated the median eccentricity ($ecc.$) for the stars in each bin as
indicated by the colour-bar.

Earlier (Sect.5.1) we found evidence that Sample Ib is part of the disk of the
Milky Way and not the halo even though the stars fall in the region of the Mg-
Mn-Al-Fe-plane thought to (mainly) harbour halo and/or accreted stars. Figure
14 a) and b) shows the cumulative distributions of [Mn/Mg] and [Al/Fe],
respectively, for Sample I, Ia and Ib. It is immediately clear that the
kinematically defined sub-samples differ. Sample Ib is more enhanced in both
[Mg/Mn] and [A/Fe]. In Fig. 14 c) we compare the median values of the
elemental abundances for our three samples with the two chemical evolution
models by Horta et al. (2022). Sample Ib lies close to the evolutionary track
of the Milky Way model, while the full sample as well as Sample Ia tend more
towards the GSE model thus giving further support to our interpretation that
Sample Ib really is the (chemical) beginning of the Milky Way disk.

In Fig. 14 d) and e) we look at the distributions of the data for Sample Ia
and Ib in the Mg-Mn-Al-Fe-plane using a 2D histogram. We find that not only do
their median values differ, but also the distribution of the stars in this
plane. Sample Ia shows an elongated, more or less vertical distribution, while
Sample Ib shows a horizontal distribution and is a more chemically enriched
population. The two kinematically defined sub-samples in Sample I clearly
occupy two chemically distinct populations – one seemingly following a
trajectory that could describe an accreted dwarf galaxy and the other a
trajectory that would connect well to the chemical evolution of the main body
of the Milky Way when compared with chemical evolution models.

Finally, we look at some of the kinematic information for our whole sample in
Fig. 14 where we show all stars in the Mg-Mn-Al-Fe-Plane binned into a 2D
histogram where the colour represents the median eccentricity of the stars in
each bin. There are several things to note from this plot. The first one is
that the distribution of eccentricity changes between different regions of the
plane.

In particular, stars that fall virtually in the same place as Sample Ia have a
mean eccentricity of 0.90 (with a $\sigma$=0.10 and median eccentricity
uncertainty of 0.03), i.e. radial orbits. Stars in the region occupied by
Sample Ib show a lower mean eccentricity of 0.37 (with a $\sigma$=0.16 and
median eccentricity uncertainty of 0.01). This carries over into the region
where Sample III sits with mean a eccentricity of 0.38 (with a $\sigma$=0.21
and a median eccentricity uncertainty $<0.01$) and then flows down towards
lower [Mg/Mn], decreasing in eccentricity such that Sample IV is almost
entirely on circular orbits with a mean eccentricity of 0.15 (with a
$\sigma$=0.09).

This figure is a nice illustration that the stars on eccentric orbits, i.e.
accreted stars, are found in a particular region of the Mg-Mn-Al-Fe-plane, but
that they do not occupy the whole area that is normally assigned to the
accreted region. Instead only a specific region is occupied. This shows that
although we originally divided our Sample I into two extremes, as concerns
their kinematics, we still picked up the major accreted component – presumably
the Gaia-Sausage-Enceladus. The stars with disk kinematics in Sample I on the
other hand connect kinematically quite well to Sample III which harbours the
stars we ordinarily associate with the thick disk, and possibly with the
Splash to some extent.

We summarise that the stellar disk extends into the regions in the Mg-Mn-Al-
Fe-plane associated with merger debris. The kinematics of the whole plane
shows that this part of the stellar disk, the chemically unevolved disk,
smoothly connects to the hotter part of the disk that is also significantly
chemically enriched.

###  7.3 Estimating the accreted fraction of stars

Figure 15: Accreted fraction of stars in APOGEE DR17 based on selection of
Sample I in the Mg-Mn-Al-Fe-plane, Table 2. The colour-coding indicates how
much of the population should be considered accreted (log of fractional
contribution indicated by the colour bar). Pixels with two or fewer stars have
been removed. a) $\sqrt{J_{\rm R}}$ as a function of $L_{\rm z}$. b)
$V_{\phi}$ as a function of $V_{\rm R}$. c) Toomre diagram. d) $E_{\rm n}$ as
a function of $L_{\rm z}$. Units as indicated on the axes. Figure 16: Action
diamond showing the accreted fraction of stars in APOGEE DR17 based on
selection of Sample I in the Mg-Mn-Al-Fe-plane, Table 2. The colour-coding
indicates how much of the population should be considered accreted (log of
fractional contribution indicated by the colour bar). Pixels with two or fewer
stars have been removed. Units as indicated on the axes.

If we want to understand how galaxies form and evolve we would like to know
how much of the stellar mass has formed in the galaxy itself and how much has
been accreted. If stars formed in smaller galaxies have elemental abundance
signatures that make them stand out from those stars that have formed in the
galaxy itself that would be one way of estimating how many of the stars in a
galaxy today have actually formed in other galaxies and this would then give
us constraints on galaxy formation in general.

As we have discussed, the Mg-Mn-Al-Fe-plane is a good place to identify stars
formed in other galaxies. But, we have also shown that the area associated
with the signatures of smaller stellar systems in the Mg-Mn-Al-Fe-plane also
contains stars belonging to the (old) disk. This is not unexpected given the
modeling results by Horta et al. (2022). However, we think it is still of
interest to obtain an upper limit to the number of accreted stars in our
sample as well as obtaining maps that show us where the majority of accreted
and in situ stars are situated.

Here we use Sample I in its entirety to represent accreted stars. This thus
gives us an over estimate of the fraction of accreted stars as Sample I
includes stars on disk orbits. The accreted fraction of stars with a kinematic
signature is simply the number of stars in Sample I divided by the total
number of stars. Fig. 15 shows our results in four kinematic spaces. In these
plots pixels with two or fewer stars have been removed. Figure 16 shows the
same type of data but now presented in the action diamond.

We see that the kinematic region associated with the Gaia-Sausage-Enceladus
shows up as dark blue regions in all four spaces in Fig. 15 (compare e.g.
Feuillet et al., 2021, and Fig. 12) but the action diamond appears to be a lot
less sensitive to pick out the accreted stars (see Fig. 16). In Fig. 15 d) we
see that for low energies, i.e. tightly bound orbits below $\sim-0.7\cdot
10^{5}$ km2 s-1, the fraction of accreted stars is about 10–30% for stars on
orbits with $L_{\rm z}$ close to zero. This is interesting as it is indicating
that based on the stellar chemical make-up we are seeing stars that have
formed in the main galaxy here, i.e. there is not just accreted stars but we
are seeing evidence for the main progenitor.

Thus, even though the central parts of the Milky Way may harbor accreted
components there is a substantial portion of in situ formed stars that should
belong to the initial galaxy. This would agree with our finding that Sample Ib
is a disk-like population.

##  8 Conclusions

We have for the first time identified the early stellar disk in the Milky Way
by using a combination of elemental abundances and kinematics.

Stars accreted on to the Milky Way by other (smaller) galaxies merging with
our Galaxy can be difficult to find. In particular kinematic signatures may be
erasade more quickly and completely than previously though when the evolving
Galactic potential is taken into account. Instead, we turn our attention
initially to the elemental abundances in the stars.

Hawkins et al. (2015) and Das et al. (2020) empirically found that the
elemental abundance plane spanned by [Mg/Mn] and [Al/Fe] could be used to
identify accreted stars. Horta et al. (2021) further discussed this
possibility underpinning their arguments with chemical evolution models. We
re-address the validity of the Mg-Mn-Al-Fe-plane for identifying accreted
debris and find that it is useful also when taking issues related to the
derivation of elemental abundance, such as departures from LTE, into account.
As illustrated in Fig. 3, the selection of clumps of stars in the Mg-Mn-Al-Fe
plane is robust against departures from NLTE and 3D for the red giant branch
stars used in this study.

We proceed to use this abundance plane to identify the accreted/halo component
solely using elemental abundances, which we refer to as Sample I. The
kinematical properties of the stars in Sample I contains, as expected, stars
with all the kinematic hallmarks of being accreted, but we also find stars on
clear disk-like orbits. We also find that the spatial distribution of the
stars differ. Stars with disk-like kinematics are (more) confined to the
Galactic plane.

We further analyse the properties of the two sub-samples and identify the
accreted stars (mainly) with the Gaia-Sausage-Enceladus whilst the disk stars
are the start of the main body of the Milky Way disk (as predicted by chemical
evolution models). The stars in Sample I with disk-like orbits have higher
[Mg/Fe] as a given [Fe/H] than the stars in Sample I with halo-like orbits,
see Fig. 8, similar to a thick disk population.

We have thus for the first time identified the early stellar disk by using a
combination of elemental abundances and kinematics.

In addition, we show that the selection of Gaia-Sausage-Enceladus in the
$E_{\rm n}-L_{\rm z}$-plane is not very robust. This is in line with recent
numerical simluations which indicate that merger signatures are erased also in
this plane (Khoperskov et al., 2022b; Pagnini et al., 2023).

Our study shows the need to carefully combine both elemental abundances and
kinematics to make progress understanding the mass accretion and early history
of the Milky Way. The latest Gaia data release, as well as the new and
upcoming massive spectroscopic surveys (WEAVE, GALAH, APOGEE, SDSS-V, DESI,
LAMOST, 4MOST), will provide the necessary data.

SF and DF were supported by Swedish Research Council grant 2016-03412 and by a
project grant from the Knut and Alice Wallenberg foundation (KAW 2020.0061
Galactic Time Machine). 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. This work has made use
of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. Funding for the Sloan
Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the
U.S. Department of Energy Office of Science, and the Participating
Institutions. SDSS-IV acknowledges support and resources from the Center for
High Performance Computing at the University of Utah. The SDSS website is
www.sdss4.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, Center for Astrophysics — Harvard & Smithsonian, the
Chilean Participation Group, the French Participation Group, Instituto de
Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the
Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the
Korean Participation Group, 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
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatário 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.

##  Appendix A Additional information on the selection of stars from APOGEE
DR17

###  A.1 APOGEE fields and programs excluded

Table 5: APOGEE fields removed from consideration when construcitng our sample. The strings listed correspond to the APOGEE DR17 parameter FIELD. Stars labelled with these strings were removed from our final catalogue. The asterisk ($\ast$) is used as a wild card character, indicating multiple possible names.  `47TUC` | `ANDR*` | `BOOTES1` | `Berkeley*` | `CARINA` | `COL261`
---|---|---|---|---|---
`CygnusX*` | `DRACO` | `FL_2020` | `FORNAX` | `GD1-*` | `IC342_NGA`
`IC348*` | `INTCL_N*` | `JHelum*` | `LAMBDAORI-*` | `LMC*` | `M10`
`M107` | `M12-N` | `M12-S` | `M13` | `M15` | `M2`
`M22` | `M3` | `M3-RV` | `M33` | `M35N2158` | `M35N2158_btx`
`M4` | `M5` | `M53` | `M54SGRC*` | `M55` | `M5PAL5`
`M67*` | `M68` | `M71*` | `M79` | `M92` | `N1333*`
`N1851` | `N188*` | `N2204` | `N2243*` | `N2264` | `N2298`
`N2420` | `N2808` | `N288` | `N3201*` | `N362` | `N4147`
`N5466` | `N5634SGR2` | `N5634SGR2-RV_btx` | `N6229` | `N6388` | `N6397`
`N6441` | `N6752` | `N6791` | `N6819*` | `N752_btx` | `N7789`
`NGC188_btx` | `NGC2420_btx` | `NGC2632_btx` | `NGC6791*` | `NGC7789*` | `ORION*`
`ORPHAN-*` | `Omegacen*` | `PAL*` | `PLEIADES*` | `SCULPTOR` | `SEXTANS`
`SGR*` | `SMC*` | `Sgr*` | `TAUL*` | `TRIAND-*` | `TRUMP20`
`Tombaugh2` | `URMINOR` | `moving_groups` | `ruprecht147` | `sgr_tidal*` |
Table 6: APOGEE programs removed from consideration. The strings listed correspond to the APOGEE DR17 parameter PROGRAMNAME. Stars labelled with these strings were removed from our final cataligue. We list only unique programs but some stars belong to multiple programs.  `Drout_18b` | `Fernandez_20a` | `Geisler_18a` | `beaton_18a` | `cluster_gc` | `cluster_gc1` |  |
---|---|---|---|---|---|---|---
`cluster_gc2` | `cluster_oc` | `clusters_gc2` | `clusters_gc3` | `geisler_18a` | `geisler_19a` |  |
`geisler_19b` | `geisler_20a` | `halo2_stream` | `halo_dsph` | `halo_stream` | `kollmeier_19b` |  |
`magclouds` | `monachesi_19b` | `sgr` | `sgr_tidal` | `stream_halo` | `stutz_18a` |  |
`stutz_18b` | `stutz_19a` |  |  |  |  |  |

When creating our catalogue from APOGEE DR17 we de-selected observations
beloning to specific objects or programs. In particular we removed open and
globular clusters as well as the Magellanic Clouds and other dwarf galaxies in
the Local Group. In addition, we removed those programs that targetted
specific stellar streams. Tables 5 and 6 list the values of the APOGEE DR17
FIELD and PROGRAMNAME parameters that were excluded when selecting the sample
of Milky Way field stars used in our study.

###  A.2 Dwarf Galaxy membership selection

Below we detail the selection of the member stars for the five dwarf galaxies
used in Fig. 3. We require a minimum SNR of 10 for all dwarf galaxy members.
We used the 876 Sagittarius core and stream members reported in Hayes et al.
(2020) and cross-matched them with APOGEE DR17 to get the updated elemental
abundances. Other members of dwarf galaxies were selected using the APOGEE
FIELD parameter. A further selection was done based on a combination of radial
velocity (RV) and proper motion using limits empirically found to contain the
main distribution of member stars. The RV was taken from APOGEE DR17. The
proper motions (PMRA, PMDEC) are from Gaia EDR3 as provided in APOGEE DR17.
The limits used for LMC and SMC as well as for the Draco and Ursa Minor dSph
galaxies are given in Table 7. In the last column in the table we indicate the
number of stars selected for each galaxy.

Table 7: Selection criteria used to find stars that belong to various Local Group dwarf galaxies as indicated by their name. The asterisk ($\ast$) is used as a wild card character, indicating multiple possible names.  Galaxy | FIELD | RV | PMRA | PMDEC | N Stars
---|---|---|---|---|---
LMC | `LMC*` | $>160$ | [1.0, 2.3] | [-1.0, 2.0] | 5847
SMC | `SMC*` | $>90$ | [0.2, 1.6] | [-1.7, -0.9] | 1739
Draco | `DRACO` | $[-310,-260]$ | – | – | 19
Ursa Minor | `URMINOR` | – | $[-0.6,0.2]$ | $[-0.2,0.4]$ | 29

##  Appendix B Addition kinematic spaces and uncertainties

Figure 17: Four kinematic spaces showing the properties of the stars selected
for Sample I (first column) and Sample III (third column) using the Mg-Mn-Al-
Fe-plane (Fig 2). These plots use the McMillan (2017) potential. Only stars
with $1<\log g<2$ are included (plots look very similar with all stars
included). The middle column shows the two sub-samples of Sample I defined
using the action diamond: Sample Ia (red) are stars with
$-0.25<L_{z}/J_{tot}<0.25$ and Sample Ib (blue) stars with
$L_{z}/J_{tot}>0.6$. The number of stars in each sample are indicated in the
panels in the top-row.

In the first part of our analysis we use the MWPotential2014 in Bovy & Rix
(2013); Bovy (2015) to calculate orbital parameters for the stars. Later we
also use the McMillan (2017) potential in order to be able to apply the same
cuts in for example $E_{n}$ as used in some other studies. For completeness we
here show the orbital parameter spaces calculated using the McMillan (2017)
potential. Comparing Fig. 17 with those calculated with the MWPotential2014 in
Bovy & Rix (2013); Bovy (2015) (Fig. 7) there are hardly any differences apart
from the expected shift in $E_{\rm n}$. We conclude that our results are
robust against whichever commonly used potential is being implemented.

Figure 18: Distributions of kinematic uncertainties of stars in Sample Ia (red
points) and Sample Ib (blue points). Uncertainties in each kinematic parameter
are shown as a function of the given parameter. The calculation of
uncertainties is described in Section 2. The horizontal lines indicate the
median uncertainty in each sample.

We also calculated uncertainties in the kinematic parameters as described in
Section 2. Here we show the distribution of these uncertainties as a function
of the given kinematic parameter for Sample Ia (red) and Ib (blue), Fig. 18.
We note that Sample Ia represents the largest kinematic uncertainties as this
sample is, on average, more distant. The median uncertainty in each parameter
for each sample is indicted by the horizontal lines. The median uncertainties
in all of Sample I are also shown as the black line. We note that although
some individual stars have large uncertainties, the median uncertainties are
low, typically $<10$%.

##  Appendix C Additional elemental abundance plots

Figure 19: [Ni/Fe] as a function of [Fe/H] for Sample I, Ia, Ib, and III.
Samples are restricted to stars with $1<\log g<2$. a) [Ni/Fe] as a function of
[Fe/H] Sample I. b) [Ni/Fe] as a function of [Fe/H] Sample III. c) [Ni/Fe] as
a function of [Fe/H] Sample I colour-coded by $L_{z}/J_{\rm tot}$. Values as
indicated by the colour bar. d) [Ni/Fe] as a function of [Fe/H] for Sample Ia.
e) [Ni/Fe] as a function of [Fe/H] for Sample Ib.

Apart from the $\alpha$-elements, nickel also shows the downward trend
characteristic of Gaia-Sausage-Enceladus, as already demonstrated in Nissen &
Schuster (1997, 2010). Fig. 19 shows the same elemental abundance plots as
shown for [Mg/Fe] in Fig. 8 but for [Ni/Fe]. As can be seen, the resemblance
is striking, further indicating that our analysis and conclusions are robust.

##  Appendix D The age of Sample III based on asteroseismic data

Table 8 provides the date for stars from Borre et al. (2022) that fall in our
Sample III and fullfill the quaility criteria we apply (Table 1). The ages are
from Borre et al. (2022) while the elemental abundances are taken from APOGEE
DR17. We list the KIC/EPIC ID as given in Borre et al. (2022) and provde a
cross-match to the Gaia DR3 IDs.

Table 8: Stars from Borre et al. (2022) that fulfill our quality criteria, Table 1, and fall in our Sample III region in the Mg-Mn-Al-Fe-plane based on elemental abundances from APOGEE DR17. Ages are from Borre et al. (2022), while [Fe/H] and [Mg/Fe] are taken from APOGEE DR17. The KIC/EPIC labelare taken from Borre et al. (2022). KIC/EPIC |  Gaia ID | [Fe/H] | [Mg/Fe] | Age | Age error
---|---|---|---|---|---
KIC 2571323 | 2051107025724208256 | –0.77 | 0.34 | 9.81 | 2.87 /–0.96
KIC 2165615 | 2051825277390535552 | –0.73 | 0.36 | 2.45 | 0.67/–0.38
KIC 2301577 | 2052544465376348416 | –0.45 | 0.31 | 3.67 | 0.74/–0.33
KIC 5371173 | 2076546151381304448 | –0.51 | 0.33 | 9.43 | 0.45/–1.12
KIC 7908109 | 2078761117553102208 | –0.75 | 0.35 | 9.80 | 1.50/–0.23
KIC 11774651 | 2087261373224223616 | –0.43 | 0.32 | 13.18 | 0.71/–1.62
KIC 5698156 | 2101432149662610816 | –1.27 | 0.31 | 12.80 | 1.52/–2.15
KIC 5446927 | 2101503690937150464 | –0.74 | 0.13 | 4.90 | 7.37 -3.25
KIC 6267115 | 2104059540072830336 | –0.35 | 0.31 | 8.12 | 1.80 -1.86
KIC 7502070 | 2104862900816530432 | –0.59 | 0.33 | 9.25 | 2.68 -1.43
KIC 7946809 | 2105698602672618752 | –0.54 | 0.33 | 7.04 | 2.88 -2.55
KIC 8544630 | 2106715341689368320 | –0.58 | 0.32 | 8.32 | 1.43 -0.55
KIC 10207078 | 2129106380594661248 | –0.31 | 0.33 | 9.40 | 0.66 -1.10
KIC 12109442 | 2130163625443203328 | –0.54 | 0.38 | 12.05 | 1.76 -2.94
KIC 10398120 | 2130915214660138624 | –0.99 | 0.34 | 8.59 | 1.35 -1.52
KIC 12506245 | 2133443541646852864 | –0.71 | 0.31 | 12.75 | 0.78 -2.86
EPIC 220387868 | 2551830805756981248 | –1.07 | 0.36 | 8.20 | 1.70 -1.88
EPIC 220269276 | 2559320399792228096 | –0.31 | 0.29 | 4.33 | 2.87 -1.53
EPIC 205997746 | 2596851370212990720 | –1.06 | 0.32 | 11.29 | 2.10 -1.90
EPIC 205972576 | 2598768815412715776 | –0.35 | 0.26 | 11.62 | 2.30 -2.66
EPIC 251512185 | 3684177626014911360 | –0.67 | 0.37 | 9.18 | 3.92 -4.38
EPIC 204785972 | 4127168730546419072 | –0.46 | 0.30 | 7.34 | 4.39 -4.25
EPIC 204298932 | 6050297413148822656 | –0.68 | 0.35 | 9.24 | 3.91 -3.11
EPIC 205083494 | 6245695266654085888 | –1.01 | 0.36 | 8.17 | 1.80 -1.80
EPIC 212297999 | 6293687295639821824 | –0.57 | 0.33 | 7.69 | 4.28 -3.30
EPIC 213463719 | 6758726460165845248 | –0.07 | 0.22 | 13.19 | 1.40 -3.65
EPIC 213523425 | 6759483817516180352 | –0.37 | 0.30 | 13.18 | 0.71 -2.35
EPIC 213632986 | 6759511374026333568 | –0.57 | 0.38 | 6.98 | 5.01 -3.53
EPIC 213853964 | 6759619023088186496 | –0.70 | 0.29 | 7.81 | 3.18 -1.98
EPIC 213764390 | 6759773577490110464 | –0.36 | 0.25 | 5.32 | 1.66 -1.41

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