# Phase-space Properties and Chemistry of the Sagittarius Stellar Stream Down
to
the Extremely Metal-poor ($\rm[Fe/H]\lesssim-3$) Regime

Guilherme Limberg Universidade de São Paulo, Instituto de Astronomia,
Geofísica e Ciências Atmosféricas, Departamento de Astronomia,
SP 05508-090, São Paulo, Brasil  Department of Astronomy & Astrophysics,
University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA  Kavli
Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637,
USA  Anna B. A. Queiroz Leibniz-Institut f$\ddot{u}$r Astrophysik Potsdam
(AIP), An der Sternwarte 16, 14482 Potsdam, Germany  Institut für Physik und
Astronomie, Universität Potsdam, Haus 28 Karl-Liebknecht-Str. 24/25, 14476
Golm, Germany  Hélio D. Perottoni Universidade de São Paulo, Instituto de
Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Astronomia,
SP 05508-090, São Paulo, Brasil  Institut de Ciències del Cosmos (ICCUB),
Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, E08028 Barcelona,
Spain  Silvia Rossi Universidade de São Paulo, Instituto de Astronomia,
Geofísica e Ciências Atmosféricas, Departamento de Astronomia,
SP 05508-090, São Paulo, Brasil  João A. S. Amarante Visiting Fellow at UCLan
Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB),
Martí i Franquès 1, E08028 Barcelona, Spain  Jeremiah Horrocks Institute,
University of Central Lancashire, Preston, PR1 2HE, UK  Rafael M. Santucci
Universidade Federal de Goiás, Instituto de Estudos Socioambientais,
Planetário, Goiânia, GO 74055-140, Brasil  Universidade Federal de Goiás,
Campus Samambaia, Instituto de Física, Goiânia, GO 74001-970, Brasil  Cristina
Chiappini Leibniz-Institut f$\ddot{u}$r Astrophysik Potsdam (AIP), An der
Sternwarte 16, 14482 Potsdam, Germany  Laboratório Interinstitucional de
e-Astronomia - LIneA, RJ 20921-400, Rio de Janeiro, Brasil  Angeles Pérez-
Villegas Instituto de Astronomía, Universidad Nacional Autónoma de México,
Apartado Postal 106, C. P. 22800, Ensenada, B. C., México  Young Sun Lee
Department of Astronomy and Space Science, Chungnam National University,
Daejeon 34134, Republic of Korea  Department of Physics and Astronomy and JINA
Center for the Evolution of the Elements, University of Notre Dame,
Notre Dame, IN 46556, USA

###### Abstract

In this work, we study the phase-space and chemical properties of Sagittarius
(Sgr) stream, the tidal tails produced by the ongoing destruction of Sgr dwarf
spheroidal (dSph) galaxy, focusing on its very metal-poor (VMP;
$\rm[Fe/H]<-2$) content. We combine spectroscopic and astrometric information
from SEGUE and Gaia EDR3, respectively, with data products from a new large-
scale run of StarHorse spectro-photometric code. Our selection criteria yields
${\sim}1600$ stream members, including ${>}200$ VMP stars. We find the leading
arm ($b>0^{\circ}$) of Sgr stream to be more metal-poor, by ${\sim}0.2$ dex,
than the trailing one ($b<0^{\circ}$). With a subsample of turnoff and
subgiant stars, we estimate this substructure’s stellar population to be
${\sim}1$ Gyr older than the thick disk’s. With the aid of an $N$-body model
of the Sgr system, we verify that simulated particles stripped earlier (${>}2$
Gyr ago) have present-day phase-space properties similar to lower-metallicity
stream stars. Conversely, those stripped more recently (${<}2$ Gyr) are
preferentially more akin to metal-rich ($\rm[Fe/H]>-1$) members of the stream.
Such correlation between kinematics and chemistry can be explained by the
existence of a dynamically hotter, less centrally-concentrated, and more
metal-poor population in Sgr dSph prior to its disruption, implying that this
galaxy was able to develop a metallicity gradient before its accretion.
Finally, we identified several carbon-enhanced metal-poor ($\rm[C/Fe]>+0.7$
and $\rm[Fe/H]\leq-1.5$) stars in Sgr stream, which might be in tension with
current observations of its remaining core where such objects are not found.

††software: corner (Foreman-Mackey, 2016), gala (Price-Whelan, 2017), jupyter
(Kluyver et al., 2016), matplotlib (Hunter, 2007), NumPy (van der Walt et al.,
2011), pandas (The pandas development team, 2020), SciPy (Virtanen et al.,
2020), scikit-learn (Pedregosa et al., 2012), TOPCAT (Taylor, 2005).

##  1 Introduction

The Galactic stellar halo is expected to be assembled through a succession of
merging events between the Milky Way and dwarf galaxies of various masses in
the context of the hierarchical formation paradigm (Searle & Zinn, 1978; White
& Frenk, 1991; Kauffmann et al., 1993; Springel et al., 2006). Upon
interacting with the Galactic gravitational potential well, the constituent
stars of these satellites become tidally unbound and, over time, phase-mixed
into a smooth halo (e.g., Helmi & White, 1999). The intermediate stage of this
process is characterized by the appearance of stellar streams, spatially
elongated structures produced by accreted debris that remains kinematically
cohesive (Johnston, 1998; Bullock & Johnston, 2005; Cooper et al., 2010, 2013;
Pillepich et al., 2015; Morinaga et al., 2019).

The magnificence of immense stellar streams can be appreciated both in
external massive galaxies (e.g., M31/Andromeda, NGC 5128/Centaurus A, and
M104/Sombrero; Ibata et al. 2001a, Crnojević et al. 2016, Martínez-Delgado et
al. 2021) as well as in the Milky Way itself (e.g., Belokurov et al. 2006).
The archetype of the above-described process is the Sagittarius (Sgr) stream
(e.g., Mateo et al., 1998), the tidal tails produced by the destruction of Sgr
dwarf spheroidal (dSph) galaxy (Ibata et al., 1994, 1995).

Over the past couple of decades, the Sgr stream has been mapped across ever
increasing areas of the sky (Mateo et al., 1996, 1998; Alard, 1996; Ibata et
al., 2001b; Newberg et al., 2003; Martínez-Delgado et al., 2004). Eventually,
wide-area photometric data allowed us to contemplate the grandiosity of Sgr
stream throughout both hemispheres (Majewski et al., 2003; Yanny et al.,
2009a). Furthermore, observations of distant halo tracers (e.g., RR Lyrae
stars; Vivas et al., 2005) and line-of-sight velocity ($v_{\rm los}$)
measurements (Majewski et al., 2004) served as constraints for an early
generation of $N$-body simulations that attempted to reproduce the phase-space
properties of the stream (Helmi & White, 2001; Helmi, 2004; Johnston et al.,
2005; Law et al., 2005; Fellhauer et al., 2006; Peñarrubia et al., 2010).
These works culminated in the landmark model of Law & Majewski (2010), which
was capable of reproducing most of Sgr stream’s features known at the time.

Thanks to the Gaia mission (Gaia Collaboration et al., 2016a, b, 2018, 2021),
precise astrometric data for more than a billion stars in the Milky Way are
now available, revolutionizing our views of the Milky Way and the knowledge
about Galactic stellar streams (e.g., Malhan et al., 2018; Price-Whelan &
Bonaca, 2018; Shipp et al., 2019; Riley & Strigari, 2020; Li et al., 2021).
For instance, it has allowed the blind detection of $\mathcal{O}(10^{5})$
high-probability members of Sgr stream (Antoja et al., 2020; Ibata et al.,
2020; Ramos et al., 2022), dramatically advancing our understanding of its
present-day kinematics. Moreover, a misalignment between the stream’s track
and the motion of its debris has been identified toward the leading arm
(Galactic latitude $b>0^{\circ}$) of Sgr (Vasiliev et al., 2021, hereafter
V21). Such observation can be reconciled with time-dependent perturbations
induced by the Large Magellanic Cloud (LMC; see Oria et al. 2022 and Wang et
al. 2022).

Despite these Gaia-led advances, a fundamental difficulty in studies of Sgr
stream continues to be the large heliocentric distances of its member stars
(${\gtrsim}10$ kpc as informed by, e.g., the aforementioned V21 model). This
challenge is usually tackled via the utilization of stellar standard candles
appropriate for the study of old stellar populations such as blue horizontal-
branch and RR Lyrae stars (e.g., Belokurov et al., 2014; Hernitschek et al.,
2017; Ramos et al., 2020), allowing us to identify Sgr stream in angular-
momentum space (Peñarrubia & Petersen, 2021, hereby PP21) or in integrals of
motion (Yang et al., 2019; Yuan et al., 2019, 2020a).

Although the usage of some specific halo tracers has been crucial for
advancing our knowledge of the dynamical status of Sgr stream, it comes with
the obvious caveat of limited sample sizes. One way to go about this is to
leverage both spectroscopic and photometric information from large-scale
surveys in order to obtain full spectro-photometric distance estimates
(Santiago et al., 2016; Coronado et al., 2018; McMillan et al., 2018; Queiroz
et al., 2018; Hogg et al., 2019; Leung & Bovy, 2019) for much larger stellar
samples.

Recently, Hayes et al. (2020) used spectro-photometric distances for stars
observed during the Apache Point Observatory Galactic Evolution Experiment
(APOGEE; Majewski et al., 2017) to investigate abundances in the Sgr system
(stream$+$remnant). Significant chemical differences between the leading and
trailing ($b<0^{\circ}$) arms were reported, with the latter being more metal-
rich (by ${\sim}0.3$ dex) than the former (see also Monaco et al. 2005, 2007,
Li et al. 2016, 2019, Carlin et al. 2018, and Ramos et al. 2022), as well as
$\rm[Fe/H]$ and [$\alpha$/Fe] gradients along the stream itself (e.g.,
Bellazzini et al. 2006, Chou et al. 2007, 2010, Keller et al. 2010, Shi et al.
2012, and Hyde et al. 2015). Moreover, Johnson et al. (2020, referred to as
J20) investigated the stellar population(s) of Sgr stream with data from the
Hectochelle in the Halo at High Resolution (H3; Conroy et al. 2019) survey and
spectro-photometric distances derived as in Cargile et al. (2020, see also ).
The extended metallicity range (reaching $\rm[Fe/H]\approx-3$) probed by H3,
in comparison to APOGEE ($\rm[Fe/H]\gtrsim-2$; see Limberg et al. 2022 for a
discussion), allowed these authors to uncover a metal-poor, dynamically hot,
and spatially diffuse component of Sgr stream, confirming a previous
suggestion by Gibbons et al. (2017).

In this contribution, we explore the phase-space and chemical properties of
Sgr stream, but focusing on its very metal-poor (VMP;
$\rm[Fe/H]<-2$)141414Following the convention of Beers & Christlieb (2005).
population. seeking to quantify the whole evolution of its kinematics as a
function of chemistry. For this task, we need a large enough sample of stars
covering a wide metallicity range. Therefore, our attention was drawn to low-
resolution ($\mathcal{R}\sim 1800$) spectroscopic data from the Sloan
Extension for Galactic Understanding and Exploration (SEGUE; Yanny et al.,
2009b; Rockosi et al., 2022) survey, a sub-project within the Sloan Digital
Sky Survey (SDSS; York et al., 2000). Atmospheric parameters provided by the
SEGUE Stellar Parameter Pipeline (SSPP; Allende Prieto et al., 2008; Lee et
al., 2008a, b, 2011; Smolinski et al., 2011) are combined with Gaia’s
parallaxes and broad-band photometry from various sources, similar to Queiroz
et al. (2020), to estimate spectro-photometric distances for ${\sim}175{,}000$
low-metallicity ($-3.5\lesssim\rm[Fe/H]\leq-0.5$) stars in the SEGUE catalog.
The complete description of this effort, including other spectroscopic
surveys, is reserved for an accompanying paper (Queiroz et al., submitted).

This work is organized as follows. Section 2 describes the observational data
analyzed throughout this work. Section 3 is dedicated to investigate the
chemodynamical properties of Sgr stream in SEGUE. Comparisons with the
$N$-body model of V21 are presented in Section 4. We explore $\alpha$-element
and carbon abundances in Section 5. Finally, Section 6 is reserved for a brief
discussion and our concluding remarks.

##  2 Data

###  2.1 SEGUE$+$Gaia and $\mathtt{StarHorse}$

SEGUE’s emphasis on the distant halo is suitable for studying Sgr (and other
streams; Newberg et al., 2010; Koposov et al., 2010) and has, indeed, been
extensively explored for this purpose (Yanny et al., 2009a; Belokurov et al.,
2014; de Boer et al., 2014, 2015; Gibbons et al., 2017; Chandra et al., 2022;
Thomas & Battaglia, 2022). The novelty is the availability of complete phase-
space information thanks to Gaia. Hence, we are in a position to construct a
larger sample of confident Sgr stream members than previous efforts.

Stellar atmospheric parameters, namely effective temperatures ($T_{\rm eff}$),
surface gravity ($\log g$), and metallicities (in the form of [Fe/H]), as well
as $\alpha$-element abundances ([$\alpha$/Fe]) and $v_{\rm los}$ values for
SEGUE stars were obtained via application of the SSPP151515Over the years, the
SSPP has also been expanded to deliver carbon (Carollo et al., 2012; Lee et
al., 2013, 2017, 2019; Arentsen et al., 2022), nitrogen (Kim et al., 2022),
and sodium (Koo et al., 2022) abundances (see Section 5.2). routines. The
final run of the SSPP to SEGUE spectra was presented alongside the ninth data
release (DR9) of SDSS (Ahn et al., 2012) and has been included, unchanged, in
all subsequent DRs. Recently, Rockosi et al. (2022) reevaluated the internal
precision of SSPP’s atmospheric parameters for DR9, which are no worse than 80
K, 0.35 dex, and 0.25 dex for $T_{\rm eff}$, $\log g$, and [Fe/H],
respectively, across the entire metallicity and color ranges explored. Unless
explicitly mentioned, we consider SEGUE’s as our fiducial stellar parameters
throughout the remainder of this paper. These also serve as input for the
Bayesian isochrone-fitting code StarHorse (Santiago et al., 2016; Queiroz et
al., 2018), which, in turn, provides ages and distances.

In this work, we only consider spectra with moderate signal-to-noise ratio
($S/N>20$ pixel-1). We keep only those stars within $4500<T_{\rm eff}/{\rm
K}<6500$, which is the optimal interval for the performance of SSPP. Moreover,
we limit our sample to low-metallicity stars ($\rm[Fe/H]\leq-0.5$), which
removes most of the contamination from the thin disk, but maintains the
majority of Sgr stream members; out of 166 stars analyzed by Hayes et al.
(2020), only 5 (3%) show $\rm[Fe/H]>-0.5$.

We cross-match the above-described SEGUE low-metallicity sample with Gaia’s
early DR3 (EDR3; Gaia Collaboration et al. 2021) using 1.5′′ search radius. In
order to ensure the good quality of the data at hand, we only retain those
stars whose renormalized unit weight errors are within the recommended range
($\texttt{ruwe}\leq 1.4$; Lindegren et al. 2021a). Parallax biases and error
inflation are handled following Lindegren et al. (2021b) and Fabricius et al.
(2021), taking into account magnitudes, colors, and on-sky positions. Stars
with largely negative parallax values ($\texttt{parallax}<-5$) are discarded.
Also, we emphasize that only those stars with an available parallax
measurement are considered to ensure good distance results. Those stars with
potentially spurious astrometric solutions are also removed
($\texttt{fidelity\\_v2}<0.5$; Rybizki et al. 2022).

Figure 1: Cartesian Galactocentric projections of the SEGUE/StarHorse low-
metallicity sample. Top: $(X,Y)$. Bottom: $(X,Z)$. Spatial bins are color-
coded by their mean [Fe/H] values. The attentive reader may notice the
footprint of Sgr stream as metal-rich trails at ${|Z|}\gtrsim 20\,{\rm kpc}$.

We applied StarHorse to this SEGUE$+$Gaia EDR3 sample in order to estimate
precise distances that would allow us to study the Sgr stream; at
${\geq}10\,{\rm kpc}$ from the Sun, our derived uncertainties are at the level
of ${\sim}13\%$. The medians of the derived posterior distributions are
adopted as our nominal values, while $16$th and $84$th percentiles are taken
as uncertainties. Further details regarding stellar-evolution models and
geometric priors can be found in Queiroz et al. (2018, 2020) and Anders et al.
(2019). See also Anders et al. (2022) for details regarding the compiled
photometric data.

With the StarHorse output at hand, we restrict our sample to stars with
moderate ($<$20%) fractional Gaussian uncertainties in their estimated
distance values. We refer to this catalog as the “SEGUE/StarHorse low-
metallicity sample” or close variations of that. We refer the interested
reader to Perottoni et al. (2022) for an initial application of these data.
Its coverage in a Cartesian Galactocentric projection can be appreciated in
Figure 1. By color-coding this plot with the mean [Fe/H] in spatial bins, the
footprint of Sgr stream is already perceptible as metal-rich trails at
${|Z|}\gtrsim 20\,{\rm kpc}$.

###  2.2 Kinematics and Dynamics

Positions ($\alpha$, $\delta$) and proper motions
($\mu_{\alpha}^{*}=\mu_{\alpha}\cos{\delta}$, $\mu_{\delta}$) on the sky,
$v_{\rm los}$ values from SEGUE, and StarHorse heliocentric distances are
converted to Galactocentric Cartesian phase-space coordinates using Astropy
Python tools (Astropy Collaboration et al., 2013, 2018). The adopted position
of the Sun with respect to the Galactic center is
$(X,Y,Z)_{\odot}=(-8.2,0.0,0.0208)\,{\rm kpc}$ (Bland-Hawthorn & Gerhard,
2016; Bennett & Bovy, 2019). The local circular velocity is $\mathbf{V_{\rm
circ}}=(0.0,232.8,0.0)\,{\rm km\,s^{-1}}$ (McMillan, 2017), while the Sun’s
peculiar motion with respect to $\mathbf{V_{\rm circ}}$ is
$(U,V,W)_{\odot}=(11.10,12.24,7.25)\,{\rm km\ s^{-1}}$ (Schönrich et al.,
2010).

For reference, we write, below, how each component of the total angular
momentum ($\boldsymbol{L}$) is calculated.

$\displaystyle L_{x}=YV_{z}-ZV_{y}$ (1) $\displaystyle L_{y}=ZV_{x}-XV_{z}$
$\displaystyle L_{z}=XV_{y}-YV_{x}{,}$

where $L=\sqrt{L_{x}^{2}+L_{y}^{2}+L_{z}^{2}}$. We recall that, although
$\boldsymbol{L}$ is not fully conserved in an axisymmetric potential, with the
exception of the $L_{z}$ component, it has been historically used for the
identification of substructure in the Galaxy as it preserves reasonable amount
of clumping over time (see Helmi 2020 for a review)

For the entire SEGUE/StarHorse low-metallicity sample, we also compute other
dynamical parameters, such as orbital energy ($E$) and actions
($\boldsymbol{J}=(J_{R},J_{\phi},J_{z})$ in cylindrical frame). The azimuthal
action is equivalent to the vertical component of angular momentum
($J_{\phi}\equiv L_{z}$) and we use these nomenclatures interchangeably. In
order to obtain these quantities, orbits are integrated for 10 Gyr forward
with the AGAMA package (Vasiliev, 2019) within the axisymmetric Galactic model
of McMillan (2017). A total of 100 initial conditions were generated for each
star with a Monte Carlo approach, accounting for uncertainties in proper
motions, $v_{\rm los}$, and distance. The final orbital parameters are taken
as the medians of the resulting distributions, with $16$th and $84$th
percentiles as uncertainties.

Figure 2: Upper row: $J_{z}>J_{R}$ (predominantly polar orbits). Bottom:
$J_{z}<J_{R}$ (radial/eccentric orbits). Background density maps are produced
with the full SEGUE/StarHorse low-metallicity sample. White dots are Galactic
GCs. Those associated with Sgr dSph/stream are displayed as yellow diamonds,
with M54 as the star symbol (see text). Left panels: $(L_{z},L_{y})$. Our Sgr
stream selection is shown as the yellow box. The gray dashed line exhibits the
J20 criterion. The yellow cross is the central location of Sgr in this space
according to PP21. Yellow dots represent Sgr stream members. Middle:
$(L_{z},E)$. Right: $(L_{z},J_{z})$.

##  3 Sgr Stream in SEGUE

###  3.1 Selection of Members

Given our goals, we seek to construct a sample of Sgr stream members that is
both ($i$) larger in size and ($ii$) with greater purity than previously
considered by J20, but ($iii$) with a similarly extended metallicity range,
reaching the extremely metal-poor ($\rm[Fe/H]<-3$) regime. J20 have shown that
stars from the Sgr stream can be selected to exquisite completeness in the
($L_{z},L_{y}$) plane, which exploits the polar nature of their orbits. We
reproduce their criterion in Figure 2 (left panels, dashed lines). However,
PP21 have recently argued that the J20’s criterion also includes
${\approx}21\%$ of interlopers.

We inspect the aforementioned ($L_{z},L_{y}$) plane, splitting it into
$J_{z}>J_{R}$ (predominantly polar orbits; Figure 2, top row) and
$J_{z}<J_{R}$ (radial/eccentric orbits; bottom row) as was done in Naidu et
al. (2020). In Figure 2, there exists an excess of stars toward negative
values of $L_{y}$ (top left panel), which is prograde (top middle), and with
$J_{z}\gtrsim 2000\,{\rm kpc\,km\,s^{-1}}$ (top right; Thomas & Battaglia,
2022), corresponding to the footprint of Sgr stream (see Malhan et al., 2022).
In the case where $J_{z}<J_{R}$, where Sgr stream completely vanishes, the
($L_{z},E$) space is dominated by the  Gaia Sausage/Enceladus (GSE; Belokurov
et al., 2018; Haywood et al., 2018, also Helmi et al. 2018).

Developing on the above-described facts, we quantify how useful the
$J_{z}>J_{R}$ condition is for eliminating potential GSE contaminants within
our Sgr stream members. We look at a suite of chemodynamical simulations of
Milky Way-mass galaxies with stellar halos produced by a single GSE-like
merger presented in Amarante et al. (2022). Within these models, the fraction
of GSE debris that end up (at redshift $z=0$) on orbits with $J_{z}>J_{R}$ is
always below 9%. Therefore, we incorporated this condition to our selection as
it should remove ${>}90\%$ of potential GSE stars.

Figure 3: Top row: metallicity (left) and age (right) distributions. In both
panels, blue and red histograms represent the leading and trailing arms of Sgr
stream, respectively. Filled and empty grayish histograms show the $\rm[Fe/H]$
distributions of Sgr’s core according to Hayes et al. (2020, updated to APOGEE
DR17) and Minelli et al. (2022), respectively. The complete SEGUE/StarHorse
low-metallicity sample is shown in black. Bottom row: configuration space in
the Galactic Cartesian coordinate system. Left: $(X,Z)$. Right: $(Y,Z)$. Blue
and red dots are stars associated with the leading and trailing arms,
respectively. The location of the M54 GC, which coincides with the center of
Sgr dSph, is shown as the yellow star symbol. The background Sgr model
(stream$+$surviving core) is from V21, where gray and pink dots are dark
matter and stellar particles, respectively. The Milky Way’s center and disk
(40 kpc diameter) are illustrated by the black circle and line, respectively.

Lastly, we restrict the kinematic locus occupied by Sgr stream in
($L_{z},L_{y}$) in comparison to J20 and consider only those stars at ${>}6$
kpc from the Sun, in conformity with the V21 model. In this work, the
conditions that a star must fulfill in order to be considered a genuine member
of Sgr stream are listed below:

  * •

$J_{z}>J_{R}$;

  * •

${\rm heliocentric\ distance}>6\,{\rm kpc}$;

  * •

$-10<L_{y}/(10^{3}\,{\rm kpc}\,{\rm km}\,{\rm s}^{-1})<-3$;

  * •

$-4<L_{z}/(10^{3}\,{\rm kpc}\,{\rm km}\,{\rm s}^{-1})<+1$.

This selection is delineated by the yellow box in the top left panel of Figure
2. It is clear that our criteria is more conservative than J20’s.
Nevertheless, the raw size of our final Sgr stream sample (${\sim}1600$ stars)
is twice as large as the one presented by these authors despite the sharp cut
at $\rm[Fe/H]<-0.5$. Moreover, the metallicity range covered reaches
$\rm[Fe/H]\sim-3$, with ${\gtrsim}200$ VMP stars in the sample (top left in
Figure 3). Finally, although these Sgr stream candidates were identified from
their locus in ($L_{z},L_{y}$), we found them to be spatially cohesive and in
agreement with the V21 model in configuration space (bottom row of Figure 3).
Even so, the potential contamination by other known polar streams (see Malhan
et al., 2021) is explored in Appendix A.

With this new set of selection criteria at hand, we verified which known
Galactic globular clusters (GCs) would be connected to the Sgr system.
Consequently, we examined the orbital properties of 170 GCs from the Gaia
EDR3-based catalog of Vasiliev & Baumgardt (2021). We found that a total of
seven GCs can be linked to this group, including NGC 6715/M54, Whiting1,
Koposov1, Terzan7, Arp2, Terzan8, and Pal12. We note that M54 has long been
recognized to be the nuclear star cluster of Sgr dSph (e.g., Bellazzini et
al., 2008). Furthermore, most of these other GCs had already been attributed
to Sgr by several authors (Massari et al., 2019; Bellazzini et al., 2020;
Forbes, 2020; Kruijssen et al., 2020; Callingham et al., 2022; Malhan et al.,
2022).

###  3.2 Leading and Trailing Arms

We begin our study of Sgr stream’s stellar populations by looking at the
metallicity distributions obtained for the leading and trailing arms and
differences between them. In Figure 3, the immediately perceptible feature is
the excess of VMP stars in the leading arm. On the contrary, the trailing arm
presents a significant contribution of metal-rich ($\rm[Fe/H]\gtrsim-1$)
stars. This property had already been noticed by several authors (e.g., Carlin
et al., 2018; Hayes et al., 2020) and is recovered despite the intentional
bias of the SEGUE catalog to low-metallicity stars (note the excess at
$\rm[Fe/H]\lesssim-1$ in the black/all-sample histogram; see Bonifacio et al.
2021 and Whitten et al. 2021 for discussions).

The final median [Fe/H] values we obtained for the leading and trailing arms
are $-1.46^{+0.02}_{-0.03}$ and $-1.28^{+0.03}_{-0.05}$, respectively, where
upper and lower limits represent bootstrapped ($10^{4}$ times) 95% confidence
intervals. These metallicity values derived from SEGUE are $\sim$0.3–0.4 dex
lower than the ones obtained from APOGEE data (Hayes et al., 2020; Limberg et
al., 2022), but we recall that this is due to SEGUE’s target selection
function (Rockosi et al., 2022).

We further notice that the location of these metallicity peaks for both arms
of the stream are well aligned with the secondary, more metal-poor,
$\rm[Fe/H]$ peak for stars in the core of Sgr (grayish histograms in Figure 3;
Hayes et al. 2020161616Updated with APOGEE DR17 (Abdurro’uf et al.,
2022)./APOGEE and Minelli et al. 2022). Although differences in metallicity
scales might be at play, this observation could be relevant for the evolution
of the Sgr system in the presence of the Milky Way and LMC.

From StarHorse’s output, we should also, in principle, be able to access
information regarding ages for individual stars as this parameter is a
byproduct of the isochrone-fitting procedure (e.g., Edvardsson et al. 1993,
Jørgensen & Lindegren 2005, and Sanders & Das 2018). However, there are some
caveats in this approach. First, it becomes increasingly difficult to
distinguish between isochrones of different ages toward both the cooler
regions of the main sequence as well as the upper portions of the red giant
branch (see figure 2 of Souza et al. 2020 for a didactic visualization).
However, it is still possible to go around this issue by looking at the
turnoff and subgiant areas where isochrones tend to be better segregated (see
discussion in Vickers et al., 2021). Second, even at these evolutionary
stages, variations in ages and metallicities have similar effects on the
color–magnitude diagram (e.g., Yi et al. 2001, Demarque et al. 2004,
Pietrinferni et al. 2004, 2006, and Dotter et al. 2008). Hence, spectroscopic
[Fe/H] values can be leveraged as informative priors to break this
age–metallicity degeneracy. Third, distant non-giant stars are quite faint,
which is the case for our Sgr stream sample. This is where SEGUE’s exquisite
depth, with targets as faint as $g=19.5$, where $g$ is SDSS broad band
centered at $4800$ Å (Fukugita et al., 1996), comes in handy.

In this spirit, we attempt to provide a first estimate of the typical ages for
stars in Sgr stream. Similar to recent efforts (Bonaca et al., 2020; Buder et
al., 2022; Xiang & Rix, 2022), we selected stars in the SEGUE/StarHorse low-
metallicity sample near the turnoff and subgiant stages. For the sake of
consistency, for this task, we utilized stellar parameters derived by
StarHorse itself during the isochrone-fitting process as these will be
directly correlated with the ages at hand. These turnoff and subgiant stars
are mostly contained within $4.5<\log g_{\rm SH}\lesssim 3.6$ and $T_{\rm
eff,SH}\gtrsim 5250\,{\rm K}$, where the subscript “SH” indicates values from
StarHorse instead of SSPP. A parallel paper describes in detail this
(sub)sample with reliable ages (Queiroz et al., submitted). In any case, for
the purpose of this work, we highlight that typical differences between
SEGUE’s atmospheric parameters and those obtained with StarHorse are at the
level of SSPP’s internal precision.

We found a total of 56 turnoff or subgiant stars in Sgr stream (31 in the
leading arm plus 25 in the trailing one) for which ages are most reliable (top
right panel of Figure 3). As expected, these are quite faint ($17.5<g<19.5$),
which reinforces the value of a deep spectroscopic survey such as SEGUE.
Members of Sgr stream (blue and red histograms representing leading and
trailing arms, respectively) appear to be older (11–12 Gyr) than the bulk of
our sample, which is mostly composed of thick-disk stars. It is reassuring
that the age distribution for the entire SEGUE/StarHorse low-metallicity
sample (black) peaks at 10–11 Gyr, which is, indeed, in agreement with ages
derived from asteroseismic data for the chemically-defined, i.e.,
high-$\alpha$, thick-disk population (Silva Aguirre et al., 2018; Miglio et
al., 2021). We quantify this visual interpretation with a kinematically-
selected thick-disk sample, following $100<|\mathbf{V}-\mathbf{V_{\rm
circ}|/({\rm km\,s^{-1}}})<180$ (check Venn et al., 2004; Bensby et al., 2014;
Li & Zhao, 2017; Posti et al., 2018; Koppelman et al., 2020), where
$\mathbf{V}=(V_{x},V_{y},V_{z})$ is the total velocity vector of a given star,
i.e., $V=\sqrt{V_{x}^{2}+V_{y}^{2}+V_{z}^{2}}$. Within the SEGUE/StarHorse
low-metallicity data (${\sim}7,800$ stars), we found a median age of 10.6 Gyr
for this population.

For Sgr stream specifically, the bootstrapped median age for the leading arm
is $11.6^{+0.4}_{-0.2}\,{\rm Gyr}$. For the trailing arm, we found
$11.8^{+0.3}_{-0.2}\,{\rm Gyr}$. This translates to $11.7^{+0.3}_{-0.2}\,{\rm
Gyr}$ considering all Sgr stream stars. Of course, uncertainties for
individual stars are still substantial, usually at the level of ${>}25\%$
(${\sim}3$ Gyr). Therefore, we hope that it will be possible to test this
scenario, that the Sgr stream is dominated by stars older (by ${\sim}1$ Gyr)
than those from the Galactic thick disk, with data provided by the upcoming
generation of spectroscopic surveys, such as 4MOST (de Jong et al., 2019),
SDSS-V (Kollmeier et al., 2017), and WEAVE (Dalton et al., 2016), and building
on the statistical isochrone-fitting framework of StarHorse.

###  3.3 Evolution of Velocity Dispersion with Metallicity

The original motivation for us to identify Sgr stream members in the
SEGUE/StarHorse catalog was to analyze the evolution of its kinematics
extending deeply into the VMP regime, similar to Gibbons et al. (2017) and
J20. The former was the first to propose the existence of two populations in
Sgr stream. Its main limitation was the lack of complete phase-space
information, which are now available thanks to Gaia. Regarding the latter, the
caveats were the small amount of (${\sim}50$) VMP stars in their sample (from
H3 survey) and potential contamination by Milky Way foreground stars ( PP21,
). Here, instead of splitting Sgr stream into two components, our approach is
to model its velocity distribution across different [Fe/H] intervals. The
results of this exercise can provide constraints to future chemodynamical
simulations attempting to reproduce the Sgr system as was recently done for
GSE (Amarante et al., 2022).

Figure 4 displays the distributions of total velocity ($V$) across different
metallicity ranges, from VMP (left) to metal-rich (right). The color scheme is
blue/red for leading/trailing arm as in Figure 3. From visual inspection, one
can notice that both histograms become broader at lower [Fe/H] values. In
order to quantify this effect of increasing velocity dispersion ($\sigma_{V}$)
with decreasing [Fe/H], we model these distributions, while also accounting
for uncertainties, using a Markov chain Monte Carlo (MCMC) method implemented
with the emcee Python package (Foreman-Mackey et al., 2013). As in Li et al.
(2017, 2018), the Gaussian $\log$-likelihood function is written as

$\log{\mathcal{L}}=-\dfrac{1}{2}\sum_{i=1}^{N}\left[\log{\left(\sigma^{2}_{V}+\sigma^{2}_{V,i}\right)}+\dfrac{\left(V_{i}-\langle
V\rangle\right)^{2}}{\left(\sigma^{2}_{V}+\sigma^{2}_{V,i}\right)}\right]{,}$
(2)

where $V_{i}$ and $\sigma_{V,i}$ are the total velocity and its respective
uncertainty for the $i$th star within a given [Fe/H] bin. We adopt only the
following uniform priors: $0<\langle V\rangle/({\rm km}\,{\rm s}^{-1})<500$
and $\sigma_{V}>0$. Lastly, we run the MCMC sampler for 500 steps with 50
walkers, including a burn-in stage of 100. Although some of the $V$ histograms
in Figure 4 show non-Gaussian tails, this exercise is sufficient for the
present purpose.

The results of our MCMC calculations are presented in Table 1. Upper and lower
limits are 16th and 84th percentiles, respectively, from the posterior
distributions. Between $-1.5<\rm[Fe/H]\leq-0.5$, we found no statistically-
significant (${<}1\sigma$) evidence for $\sigma_{V}$ variations. However, at
$\rm[Fe/H]\leq-1.5$, the $\sigma_{V}$ increases substantially for both arms.
According to present data, the VMP component of Sgr stream (left panel of
Figure 4) is dynamically hotter than its metal-rich counterpart at the
${\gtrsim}2\sigma$ level. We also verified that this effect is less prominent
(${\sim}1\sigma$) for GSE (green histograms in Figure 4; Table 1) even with a
not-so-pure (at least 18% contamination; Limberg et al. 2022) selection
(Feuillet et al., 2020), which is to be expected given the advanced stage of
phase-mixing of this substructure.

Figure 4: Distributions of $V=\sqrt{V_{x}^{2}+V_{y}^{2}+V_{z}^{2}}$ in intervals of [Fe/H]. From left to right, we move from the VMP to the metal-rich regime. Blue, red, and green histograms represent the leading arm, trailing arm, and GSE, respectively.  Table 1: Velocity Dispersion for the Leading and Trailing Arms of Sgr, as well as GSE, in bins of [Fe/H]  Substructure | $\sigma_{V}$ | $\sigma_{V}$ | $\sigma_{V}$ | $\sigma_{V}$
---|---|---|---|---
| (km s-1) | (km s-1) | (km s-1) | (km s-1)
| $\rm[Fe/H]\leq-2.0$ | $-2.0<\rm[Fe/H]\leq-1.5$ | $-1.5<\rm[Fe/H]\leq-1.0$ | $-1.0<\rm[Fe/H]\leq-0.5$
Leading |  $70^{+4}_{-4}\%$ (194) |  $62^{+3}_{-3}\%$ (284) |  $51^{+2}_{-2}\%$ (405) |  $53^{+5}_{-4}\%$ (94)
Trailing |  $44^{+6}_{-5}\%$ (62) |  $38^{+3}_{-3}\%$ (185) |  $32^{+2}_{-5}\%$ (319) |  $28^{+2}_{-2}\%$ (203)
GSE |  $87^{+2}_{-2}\%$ (1153) |  $86^{+1}_{-1}\%$ (4314) |  $83^{+1}_{-1}\%$ (8020) |  $82^{+2}_{-2}\%$ (1322)

Now, we put our results in context with those in the literature. With the
understanding that Sgr stream is comprised of two kinematically distinct
populations (J20), the increasing $\sigma_{V}$ as a function of decreasing
metallicity can be interpreted as larger fractions of the “diffuse” ( J20, )
component contributing to the low-[Fe/H] (dynamically hotter) bins. On the
contrary, the “main” component, which contains most of the stars of the
substructure, is preferentially associated with the high-[Fe/H] (dynamically
colder) intervals.

PP21 recently argued that the broad velocity distribution for metal-poor stars
in Sgr stream could be an artifact of Milky Way contamination in the J20 Sgr
stream data. However, this effect is still clearly present in our $2{\times}$
larger sample with more rigorous selection criteria. To summarize, in the low-
metallicity regime, there appears to be considerable contribution from both
ancient and recently formed wraps of the stream. On the other hand, at high
metallicities ($\rm[Fe/H]>-1.0$), only the newest wrap is represented.

Figure 5: Sgr stream in $(\Lambda_{\rm Sgr},v_{\rm los})$ space. As in Figure
3, blue and red dots are stars associated with the leading and trailing arms,
respectively. Dark matter and stellar particles from the V21 model are shown
as gray and colored dots, respectively. Green dots are attributed to the new
($t_{\rm strip}<2\,{\rm Gyr}$) and orange ones to the old ($t_{\rm
strip}>2\,{\rm Gyr}$) wraps. Black dots remain bound to the progenitor until
the present day (redshift $z=0$), i.e., the end of the simulation. From top to
bottom, we move from the VMP to the metal-rich regime following the same
[Fe/H] ranges of Figure 4 and Table 1.

##  4 Model Comparisons

In this section, we interpret the phase-space properties of Sgr stream and how
they correlate with chemistry via the comparison of our Sgr sample with the
V21 model.

###  4.1 Model Properties, Assumptions, and Limitations

V21’s is a tailored $N$-body model of the Sgr system designed to match several
properties of its tidal tails. In particular, in order to mimic the
aforementioned misalignment between the stream track and its proper motions in
the leading arm, the authors invoke the presence an LMC with a total mass of
$1.5\times 10^{11}\,M_{\odot}$, compatible with Erkal et al. (2019), Shipp et
al. (2021), and Koposov et al. (2022). The initial conditions are set to
reproduce the present-day positions and velocities of both Sgr and LMC
building on earlier results (Vasiliev & Belokurov, 2020). However, unlike the
LMC and Sgr, the Milky Way is not modeled in a live $N$-body scheme. Hence, it
comes with the limitation that V21 depend on the Chandrasekhar analytical
prescription for dynamical friction (e.g., Mo et al., 2010). See Ramos et al.
(2022) for a discussion on how this approximation might influence the
stripping history of the stream.

In the fiducial model, the initial stellar mass of Sgr dSph is $2\times
10^{8}\,M_{\odot}$ and follows a spherical King density profile (King, 1962).
Moreover, the system is embedded in an, also spherical, extended dark matter
halo of $3.6\times 10^{9}\,M_{\odot}$. Other key features of V21’s work is the
capability of recovering crucial kinematic and structural features of Sgr’s
remnant (as in Vasiliev & Belokurov, 2020), accounting for perturbations
introduced by the gravitational field of LMC (Garavito-Camargo et al., 2019,
2021; Cunningham et al., 2020; Petersen & Peñarrubia, 2020, 2021; Erkal et
al., 2021), and properly following mass loss suffered by the system.

Despite the close match between observations and the V21 model, there are a
few limitations that could affect their results. For instance, the model does
not account for the gaseous component , which may be relevant for the
distribution of the debris as discussed in Wang et al. (2022) and references
therein. An additional caveat is the lack of bifurcations in the modeled
stream, as originally observed by Belokurov et al. (2006) and Koposov et al.
(2012, see discussions by ). Finally, Sgr likely experienced at least one
pericentric passage $\gtrsim$6 Gyr ago as can be inferred from dynamical
perturbations in the Galactic disk (Binney & Schönrich, 2018; Laporte et al.,
2018, 2019; Bland-Hawthorn & Tepper-García, 2021; McMillan et al., 2022, and
see Antoja et al. 2018) as well as the star-formation histories of both the
Milky Way (Ruiz-Lara et al., 2020) and Sgr itself (Siegel et al., 2007; de
Boer et al., 2015). Hence, the V21 simulation, which starts only 3 Gyr in the
past, is unable to cover this earlier interaction.

###  4.2 New and Old Wraps

Figure 5 shows observational and simulation data in $(\Lambda_{\rm Sgr},v_{\rm
los})$, where $\Lambda_{\rm Sgr}$ is the stream longitude coordinate as
defined by Majewski et al. (2003) based on Sgr’s orbital plane.
Leading/trailing arm stars are blue/red dots. These are overlaid to the V21
model, where gray and colored points are dark matter and stellar particles,
respectively. We split these simulated particles according to their stripping
time ($t_{\rm strip}$171717Formally, $t_{\rm strip}$ is defined as the most
recent time when a particle left a 5 kpc-radius sphere around the progenitor (
V21, ).). For the remainder of this paper, we refer to the portion of the
(simulated) stream formed more recently ($t_{\rm strip}<2\,{\rm Gyr}$) as the
“new” wrap (green). The more ancient ($t_{\rm strip}>2\,{\rm Gyr}$) component
is henceforth the “old” wrap (orange). Stellar particles that are still bound
to the progenitor by the end of the simulation (redshift $z=0$) are colored
black.

We divide our Sgr stream data in the same metallicity intervals as Figure
4/Table 1. Essentially, our selected members of Sgr stream share all regions
of phase space with the V21 model particles. Notwithstanding, the bottom-most
panel of Figure 5 reveals a first interesting feature. Metal-rich stars in the
sample are almost exclusively associated with the new wrap, though this is
more difficult to immediately assert for the leading arm because of the
overlap between new and old portions within $180\degree\lesssim\Lambda_{\rm
Sgr}<300\degree$.

As we move toward lower-metallicity (upper) panels of Figure 5, we see larger
fractions of observed Sgr stream stars coinciding with the old wrap in phase
space. At the same time, the dense groups of stars overlapping with the new
wrap fade away as we reach the VMP regime (top panel). As a direct
consequence, stream members are more spread along the $v_{\rm los}$ axis in
Figure 5, which, then, translates into the higher $\sigma_{V}$ discussed in
Section 3.3 for metal-poor/VMP stars. In general, the new wrap is
preferentially associated with metal-rich stars, but also extends into the VMP
realm. Conversely, the old component contains exclusively metal-poor
($\rm[Fe/H]\lesssim-1$) stars. Therefore, these suggest that, at low
metallicities, Sgr stream is composed of a mixture between old and new wraps
and this phenomenon drives the increasing $\sigma_{V}$ quantified in Table 1.

Figure 6: Left: distributions of $t_{\rm strip}$ for dark matter (gray) and
stellar (pink) particles in the V21 model of Sgr (stream$+$dSph) system. The
orbital trajectory of Sgr in the form of Galactocentric distance is presented
as the overlapping blue line and circles. Middle: dark matter and stellar
(colored dots) particles in configuration space, where $(X,Y)_{\rm Sgr,0}$ are
spatial coordinates in a Sgr-centered sytem in the initial snapshot of the
same V21 model (see text). Right: cumulative distribution functions of
galactocentric radii ($r_{\rm Sgr,0}$) of the same model particles, also
centered around Sgr in the initial snapshot. Vertical dashed lines mark the
positions containing 90% of the stars of each component. In all panels, the
color scheme is the same as Figure 5, where orange represents stars that end
up as the old wrap of the stream ($t_{\rm strip}>2$ Gyr), green is for the new
wrap ($t_{\rm strip}<2$ Gyr), and black are those particles that remain bound
to Sgr dSph until present-day/end of the simulation ($t_{\rm strip}=0$).

###  4.3 Sgr dSph Before its Disruption

The dichotomy between metal-rich/cold and metal-poor/hot portions of Sgr
stream has been suggested, by J20, to be linked to the existence of a stellar
halo-like structure in Sgr dSph prior to its infall. This stellar halo would
have larger velocity dispersion, be spatially more extended, and have lower
metallicity than the rest of the Sgr galaxy. As a consequence of its
kinematics, this component would be stripped at earlier times. Indeed, we
verified that the old wrap of Sgr stream, stripped ${>}2\,{\rm Gyr}$ ago in
V21’s model, is mainly associated with metal-poor stars (Figure 5), in
conformity with J20’s hypothesis. Meanwhile, the majority of the most metal-
rich stars can be attributed to the new wrap. In order to check how the
present-day properties of Sgr stream are connected to those of its dSph
progenitor, hence testing other conjectures of J20, we now look at the initial
snapshot of V21’s simulation, including the satellite’s orbit and disruption
history.

Simply to comprehend the assembly of the stream over time according to the V21
model, we plot the distribution of $t_{\rm strip}$ in the left panel of Figure
6. The excess at $t_{\rm strip}=0$ is due to $N$-body particles that remain
bound to the progenitor. On top of these histograms, we add the trajectory of
Sgr dSph in the simulation (blue line and dots) in terms of its Galactocentric
distance. With this visualization, it is clear how intense episodes of
material being stripped (at both $2.0<t_{\rm strip}/{\rm Gyr}\lesssim 2.7$ and
$0.5\lesssim t_{\rm strip}/{\rm Gyr}\lesssim 1.5$) are intrinsically related
to close encounters between Sgr and the Milky Way (at ${\sim}2.5$ and
${\sim}1.2$ Gyr ago), which originates the new and old wraps discussed in
Section 4.2. Also, note how most of the material is associated with the
recently formed component (new wrap) of the stream.

In order to test J20’s conjecture that the stripped portion of Sgr dSph
associated with the formation of the old wrap was already dynamically hotter
than the new one prior to the galaxy’s disruption, we check the $\sigma_{V}$,
with respect to Sgr, of these components in the initial snapshot of V21’s
simulation, which starts 3 Gyr in the past (redshift $z\sim 0.25$ in Planck
Collaboration et al. 2020 cosmology). Indeed, the $\sigma_{V}$ of stars that
end up forming the old wrap, i.e., stripped at earlier times, is higher
(${\sim}18$ km s-1) in comparison to the $\sigma_{V}$ of stars from the new
component (${\sim}14$ km s-1).

In the middle panel of Figure 6, the initial snapshot is presented in
configuration space as $(X,Y)_{\rm Sgr,0}$, a Sgr-centered frame. The orange
dots ($t_{\rm strip}>2$ Gyr/old wrap) in this plot are less centrally
concentrated (90% of stellar particles within $\sim$4 kpc) than the green ones
($t_{\rm strip}<2$ Gyr/new wrap; 90% within 3 kpc). This behavior is clear
from the right panel of the same figure that shows the cumulative
distributions of galactocentric radii ($r_{\rm Sgr,0}$) in the same system.
Also, stars that remain bound until redshift $z=0$ have even lower
$\sigma_{V}$ (${\sim}11$ km s-1) and are spatially more concentrated (90%
within ${<}2$ kpc) than the other components.

From the above-described properties of the V21 model, we can infer that the
periphery of the simulated Sgr dSph contains a larger fraction of stars that
end up as the old wrap (stripped earlier) in comparison to its central
regions. Therefore, with the understanding that the old wrap is essentially
composed of low-metallicity stars), we reach the conclusion that the core
regions of Sgr dSph were more metal-rich than its outskirts prior to its
accretion. We recall that, indeed, previous works reported evidence for a
metallicity gradient in the Sgr remnant (Bellazzini et al., 1999; Layden &
Sarajedini, 2000; Siegel et al., 2007; McDonald et al., 2013; Mucciarelli et
al., 2017; Vitali et al., 2022). Nevertheless, fully understanding how these
stellar-population variations in the Sgr system relate to its interaction with
the Milky Way remains to be seem (for example, via induced star-formation
bursts; Hasselquist et al. 2021).

Although our interpretation favors a scenario where Sgr dSph had enough time
to develop a metallicity gradient before its disruption, quantifying this
effect is difficult. One way to approach this would be painting the model with
ad hoc metallicity gradients and, then, comparing with, for instance, the
present-day [Fe/H] variations observed across the Sgr stream (Hayes et al.
2020 and references therein). We defer this exploration to a forthcoming
paper.

##  5 Chemical Abundances

###  5.1 $\alpha$ Elements

Apart from $T_{\rm eff}$, $\log g$, and $\rm[Fe/H]$, the SSPP also estimates
$\alpha$-element abundances based on the wavelength range of
$4500\leq\lambda/{\rm\textup{\AA}}\leq 5500$ (Lee et al., 2011), which
contains several Ti I and Ti II lines as well as the Mg I triplet
(${\sim}5200$ Å). de Boer et al. (2014) utilized $[\alpha/{\rm Fe}]$ values
made available by SEGUE for stars in Sgr stream to argue that a “knee” existed
at $\rm[Fe/H]\lesssim-1.3$ in the [$\alpha$/Fe]–[Fe/H] diagram (Wallerstein,
1962; Tinsley, 1979) for this substructure. However, this result is not
supported by contemporaneous high-resolution spectroscopic data, specially
from APOGEE (Hayes et al., 2020; Horta et al., 2022; Limberg et al., 2022),
also H3 (Johnson et al., 2020; Naidu et al., 2020). If the position of Sgr’s
$\alpha$ knee was truly located at such high [Fe/H], it would imply that it
should be even more massive than GSE under standard chemical-evolution
prescriptions (e.g., Matteucci & Brocato, 1990).

Here, we revisit the $\alpha$ abundances for Sgr stream using SEGUE, but with
a larger sample with lower contamination. In the left panel of Figure 7, we
see the continuous decrease of [$\alpha$/Fe] as a function of increasing
metallicity for both the Sgr stream and GSE. Most important, at a given value
of [Fe/H], the median [$\alpha$/Fe] of Sgr stream (both leading and trailing
arms) is lower than GSE’s. This difference becomes more prominent at
$\rm[Fe/H]\gtrsim-1.5$, in agreement with the aforementioned high-resolution
spectroscopy results from both H3 and APOGEE. Despite that, the low
accuracy/precision of [$\alpha$/Fe] in SEGUE still makes it difficult to
attribute stars to certain populations on an individual basis.

Figure 7: Left: [$\alpha$/Fe]–[Fe/H]. Green line is the running median of
GSE’s [$\alpha$/Fe] values in bins of 0.2 dex in [Fe/H], with the shaded area
covering 16th and 84th percentiles. Blue and red lines and shaded regions are
the same, but for the leading and trailing arms of Sgr stream, respectively.
Middle: [C/Fe]–[Fe/H]. The yellow rectangle marks the locus of CEMP stars.
Blue/red symbols are leading/trailing arm stars. Candidate ($3\sigma$; see
text) CEMP stars are shown as star symbols. Right: $\rm[Fe/H]_{\rm
L13}$–$\rm[Fe/H]_{\rm DR9}$, where the “L13”and “DR9” subscripts refer to
[Fe/H] values either from Lee et al. (2013) or SEGUE’s standard catalog from
SDSS DR9. Background density maps represent the full SEGUE/StarHorse low-
metallicity sample.

###  5.2 Carbon

With the SEGUE low-metallicity data at hand, we also explore carbon
abundances. In particular, we are interested in finding carbon-enhanced metal-
poor (CEMP; $\rm[C/Fe]>+0.7$ and $\rm[Fe/H]<-1$; see Beers & Christlieb 2005,
Aoki et al. 2007, and Placco et al. 2014) stars in Sgr stream. The reasoning
for that being the recent results by Chiti et al. (2020, also  and ) where
these authors found no CEMP star in their sample of Sgr dSph members within
$-3.1<\rm[Fe/H]\lesssim-1.5$. Moreover, we utilize observations of Sgr stream
as a shortcut to check for potential differences in CEMP fractions between a
dwarf galaxy and the Milky Way’s stellar halo (see Venn et al., 2012; Kirby et
al., 2015; Salvadori et al., 2015; Chiti et al., 2018) in a homogeneous
setting. Given that the CEMP phenomenon, specially at $\rm[Fe/H]\lesssim-2.5$,
is connected to nucleosynthesis events associated with the first generations
of stars, perhaps Population III (e.g., Nomoto et al., 2013; Yoon et al.,
2016; Chiaki et al., 2017), identifying such objects provide clues about the
first chemical-enrichment processes that happened in a galaxy.

Throughout this section, we consider carbon abundances obtained for SEGUE
spectra by Lee et al. (2013, see also , , and ). Inconveniently, this catalog
also comes with slight variations of the stellar atmospheric parameters in
comparison with the public SEGUE DR9 release. Therefore, in order to
confidently identify CEMP stars, we first select candidates using only Lee et
al. (2013) [C/Fe] and [Fe/H] (subscripts “L13” in Figure 7). Then, we compare
$\rm[Fe/H]_{\rm L13}$ with [Fe/H] values from our standard DR9 sample
($\rm[Fe/H]_{\rm DR9}$; right panel of Figure 7) to confirm their low-
metallicity nature.

The middle panel of Figure 7 ([C/Fe]–[Fe/H]) exhibits our selection of CEMP
candidates (yellow box). Note that we take only those stars at $\rm[Fe/H]_{\rm
L13}<-1.5$, for consistency with the metallicity range covered by Chiti et al.
(2020). Expanding this boundary to $\rm[Fe/H]_{\rm L13}<-1$ would only include
a couple of additional CEMP candidates. We discovered a total of 39 likely-
CEMP stars (33 at $\rm[Fe/H]_{\rm L13}<-2$). With this sample at hand, we
looked for those candidates confidently ($3\sigma$ in $\rm[C/Fe]_{\rm L13}$)
encompassed by the CEMP criteria. We found 7 such objects, shown as star
symbols in Figure 7. Although two of these CEMP stars have discrepant
metallicity determinations ($\rm[Fe/H]_{\rm L13}$ vs. $\rm[Fe/H]_{\rm DR9}$;
right panel of Figure 7), we can still confidently assert that there exist
CEMP stars in Sgr stream.

A possible explanation for the lack of CEMP stars in Chiti et al.’s (2020)
sample could be their photometric target selection, which was based on
SkyMapper DR1 (Wolf et al., 2018). The excess of carbon, hence the exquisite
strength of the CH $G$-band, is capable of depressing the continuum extending
to the wavelength region of the Ca II K/H lines, close to the center of
SkyMapper’s $v$ filter ($3825\textup{\AA}$; see Da Costa et al. 2019 and
references therein), a phenomenon referred to as “carbon veiling” (Yoon et
al., 2020). A scenario where, if confirmed, the surviving core of Sgr dSph has
a lower CEMP fraction than its outskirts/stream at a given metallicity could
be similar to what potentially happens to the Milky Way’s bulge and halo
(Arentsen et al., 2021). Either way, the unbiased discovery of additional VMP
stars in Sgr as well as other dSph satellites (e.g., Skúladóttir et al., 2021)
will be paramount for us to advance our understanding about the earliest
stages of chemical enrichment in these systems.

Finally, we also calculate the fraction of CEMP stars in Sgr stream and
compare it with the Milky Way. Arentsen et al. (2022) has recently
demonstrated that various observational efforts focused on the discovery and
analysis of metal-poor stars via low/medium-resolution (up to $\mathcal{R}\sim
3000$) spectroscopy report inconsistent CEMP fractions among them (Lee et al.,
2013; Placco et al., 2018, 2019; Aguado et al., 2019; Arentsen et al., 2020;
Yuan et al., 2020b; Limberg et al., 2021a; Shank et al., 2022). However, we
reinforce that it is not our goal to provide absolute CEMP fractions (e.g.,
Rossi et al., 2005; Lucatello et al., 2006; Yoon et al., 2018), but rather use
the SEGUE/StarHorse low-metallicity sample to make a homogeneous comparison.
For this reason, we do not perform any evolutionary corrections (as in Placco
et al. 2014) to the carbon abundances of Lee et al. (2013). The overall
fraction of CEMP stars in the whole sample at $\rm[Fe/H]<-2$, but excluding
Sgr, is $19\pm 1\%$181818Uncertainties for fractions are given by Wilson score
confidence intervals (Wilson, 1927). See Limberg et al. (2021a) for details.
within the same $\log g$ range. For the whole Sgr stream, leading and trailing
arms altogether, this number is $16\pm 5\%$. Limiting our analysis to only
giants ($T_{\rm eff}<5800$ K and $\log g<4$), we find 12% for both the stream
and full sample. Therefore, we conclude the SEGUE carbon-abundance data does
not provide evidence for variations in the CEMP frequency between Sgr (stream)
and the Milky Way.

##  6 Conclusions

In this work, we performed a chemodynamical study of Sgr stream, the tidal
tails produced by the ongoing disruption of Sgr dSph galaxy. Because of recent
literature results, we were particularly interested in exploring the VMP
regime of this substructure. Our main goals were to quantify the kinematic
properties of this population as well as search for CEMP stars. For the task,
we leveraged low-resolution spectroscopic and astrometric data from SEGUE DR9
and Gaia EDR3, respectively. Moreover, this catalog was combined with broad-
band photometry from various sources in order to deliver precise distances for
${\sim}175,000$ low-metallicity ($\rm[Fe/H]\leq-0.5$) stars via Bayesian
isochrone-fitting in a new StarHorse run (Figure 1), an effort that is fully
described in an accompanying paper (Queiroz et al., submitted). Our main
conclusions can be summarized as follows.

  * •

We delineated a new set of selection criteria for the Sgr stream based on
angular momenta and actions (Figure 2). Despite being more conservative than
previous works (e.g., J20 and Naidu et al. 2020), we identify ${\sim}1600$
members of Sgr stream, which is twice as many as these authors. Out of these,
there are ${>}200$ VMP stars as well as 7 GCs.

  * •

Reassuringly, although the SEGUE target selection inflates the number of
metal-poor stars ($\rm[Fe/H]<-1$; Figure 3), we found the leading arm to be
more metal-poor, by ${\sim}0.2$ dex, than the trailing one. This is in
agreement with many previous works (notably Hayes et al., 2020).

  * •

We provided the first age estimates for individual stars in Sgr stream. For
the task, we constructed a subsample of 56 turnoff/subgiant stars in this
substructure, for which StarHorse ages are most reliable. We found an overall
median age of $11.7^{+0.3}_{-0.2}\,{\rm Gyr}$, which is ${\sim}1$ Gyr older
than the bulk of thick-disk stars according both to our own SEGUE/StarHorse
data as well as asteroseismic estimates (Miglio et al., 2021).

  * •

We found ($2\sigma$) evidence for increasing velocity dispersion in Sgr stream
between its metal-rich and VMP populations (Figure 4/Table 1). Similar
findings were presented by J20, but were contested by PP21. Now, we reassert
the former’s findings with a $2{\times}$ larger sample and more rigorously-
selected Sgr stream members (Figure 4/Table 1).

  * •

With the $N$-body model of V21, we found that the new wrap (composed of stars
recently stripped; $t_{\rm strip}<2\,{\rm Gyr}$) of Sgr stream preferentially
contains metal-rich ($\rm[Fe/H]>-1.0$) stars. Conversely, the old wrap
($t_{\rm strip}>2\,{\rm Gyr}$) is exclusively associated with metal-poor stars
($\rm[Fe/H]<-1.0$) in phase space. Hence, the increasing velocity dispersion
with decreasing [Fe/H] is driven by the mixture between these components,
i.e., larger fractions of the old wrap are found at lower metallicities, while
the metal-rich population is only representative of the new wrap (Figure 5).

  * •

Looking at the initial snapshot of the V21 simulation, we found that stars
that end up forming the old wrap are dynamically hotter and less centrally
concentrated than those that compose the new wrap. With the understanding that
the old wrap contains stars of lower metallicities, this implies that the
outskirts of Sgr dSph, prior to disruption, were more metal-poor than is core
regions, i.e., internal [Fe/H] variations in the galaxy.

  * •

On the chemical-abundance front, SEGUE data allowed us to verify that the
[$\alpha$/Fe] of Sgr stream decreases with increasing [Fe/H]. Most important,
at a given metallicity, we ascertained that the median [$\alpha$/Fe] of Sgr
stream is lower than GSE’s, in conformity with other recent efforts
(Hasselquist et al., 2021; Horta et al., 2022; Limberg et al., 2022).

  * •

We confidently (${>}3\sigma$) identify CEMP stars in Sgr stream. Also, its
CEMP fraction is compatible ($1\sigma$) with the overall SEGUE catalog. Hence,
we argue that the apparent lack of CEMP stars in Sgr dSph (Chiti et al., 2020,
and references therein) could be associated with target-selection effects
and/or small sample sizes.

This paper emphasizes how powerful the synergy between deep spectroscopy and
astrometric data can be in our quest to unravel the outer Galactic halo. It
also shows how crucial the fully Bayesian approach of StarHorse is for the
task of deriving precise parameters (mainly distances) even for faint stars.
In fact, the SEGUE/StarHorse catalog provides a glimpse of the scientific
potential that will be unlocked by the next generation of wide-field surveys
such as 4MOST, SDSS-V, and WEAVE. Finally, we reinforce the importance of
tailored $N$-body models as fundamental tools for interpreting of the complex
debris left behind by disrupted dwarf galaxies in the Milky Way’s halo.

The authors thank the referee for a timely and constructive review which has
contributed to this work. G.L. is indebted to Alex Ji, Ani Chiti, Felipe
Almeida-Fernandes, Ting Li, and Vini Placco for discussions and suggestions
that contributed to the original manuscript as well as Anke Arentsen who
provided feedback on a preprint version of it. G.L. also thanks several
authors who provided observational or simulation data, namely Alice Minelli,
Amina Helmi, Emma Dodd, Khyati Malhan, Sergey Koposov, and Zhen Yuan. G.L. is
particularly grateful toward Eugene Vasiliev, who readily provided the initial
snapshot of the V21 simulation as well as assistance with the model. Finally,
G.L. thanks all those authors who made their observational and/or simulation
data publicly available and are referenced throughout this work. G.L., H.D.P.,
S.R., J.A., and R.M.S. extend heartfelt thanks to all involved with the
“Brazilian Milky Way group meeting”, namely Eduardo Machado-Pereira, Fabrícia
O. Barbosa, Hélio J. Rocha-Pinto, Lais Borbolato, Leandro Beraldo e Silva, and
Yuri Abuchaim. G.L. acknowledges FAPESP (procs. 2021/10429-0 and
2022/07301-5). H.D.P. also thanks FAPESP (procs. 2018/21250-9 and
2022/04079-0). S.R. thanks support from FAPESP (procs. 2014/18100-4 and
2015/50374-0), CAPES, and CNPq. J.A. acknowledges funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation program (grant agreement No. 852839). R.M.S. acknowledges CNPq
(Proc. 306667/2020-7). A.P.-V. acknowledges the DGAPA-PAPIIT grant IA103122.
Y.S.L. acknowledges support from the National Research Foundation (NRF) of
Korea grant funded by the Ministry of Science and ICT (NRF-2021R1A2C1008679).
Y.S.L. also gratefully acknowledges partial support for his visit to the
University of Notre Dame from OISE-1927130: The International Research Network
for Nuclear Astrophysics (IReNA), awarded by the US National Science
Foundation. 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.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for
the Participating Institutions of the SDSS Collaboration.

This research has made use of the VizieR catalogue access tool, CDS,
Strasbourg, France (https://cds.u-strasbg.fr). The original description of the
VizieR service was published in Ochsenbein et al. (2000).

##  Appendix A Other Dwarf-galaxy Polar Streams

In order to test if our Sgr stream selection is robust against the presence of
other known dwarf-galaxy polar stellar streams (see Malhan et al., 2021), we
assembled literature data for Cetus (Yuan et al., 2019, originally found by
Newberg et al. 2009), Orphan (Koposov et al., 2019, first described by
Belokurov et al. 2006, 2007), LMS-1/Wukong (Yuan et al., 2020a, also Naidu et
al. 2020), and Helmi streams (O’Hare et al., 2020, discovered by Helmi et al.
1999). In this process, we made an effort to compile only members of streams
found with automatic algorithms (Myeong et al., 2018a, b; Yuan et al., 2018).
The only exception is Orphan, whose members were selected based on the
stream’s track on the sky as well as proper motions. Note that, originally,
Yuan et al. (2020a) dubbed the LMS-1/Wukong substructure as “low-mass stellar-
debris stream”, hence the acronym. Almost at the same time, Naidu et al.
(2020) identified a very similar dynamical group of stars in $(L_{z},E)$ with
the H3 survey and referred to it as “Wukong”. For now, we keep both
nomenclatures, similar to what several authors adopt for GSE. Apart from the
$J_{z}>J_{R}$ condition, we followed Naidu et al. (2022) and Limberg et al.
(2021b, which builds on , , and ) to apply further constraints to both Orphan
and Helmi streams, respectively, in order to guarantee better purity for these
samples.

The kinematic/dynamical locus occupied by the polar streams is shown in Figure
8. Crucially, they do not overlap the box in $(L_{z},L_{y})$ defined for Sgr
(yellow region in the left panel). However, note how the J20 criteria actually
encompasses the bulk of Orphan stream stars, which emphasizes the importance
of our more rigorous selection. Helmi stream stars are the ones that reach the
closest to our Sgr boundary in angular-momentum space. Although no stars from
this substructure actually fulfill our entire set of selection criteria for
Sgr, it is difficult to assert that Helmi stream interlopers are nonexistent
in our Sgr sample. One way to quantify the cross-contamination between halo
substructures would be to explore $N$-body models, similar to what has been
recently done by Sharpe et al. (2022). For the time being, even without such a
dedicated effort, we highlight that our criteria achieves several benchmarks,
such as eliminating ${>}90\%$ of potential GSE stars, removing low-$J_{z}$
contaminants from the Galactic disk(s), and excluding most stars from other
well-known dwarf-galaxy streams.

Figure 8: Similar to the top row of Figure 2 ($J_{z}>J_{R}$), but including
literature data for dwarf-galaxy polar streams. Left: $(L_{z},L_{y})$. The
dashed line shows the J20 criterion for selecting Sgr members. The yellow box
exhibits our criteria. Colored dots represent stars from Sgr (yellow), Cetus
(red), Orphan (white), LMS-1/Wukong (blue), and Helmi (green) streams (see
text). Middle: $(L_{z},E)$. Right: $(L_{z},J_{z})$ In all panels, density maps
represent the full SEGUE/StarHorse low-metallicity sample.

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