# APOGEE Chemical Abundance Patterns of the Massive Milky Way Satellites

Sten Hasselquist11affiliation: Department of Physics & Astronomy, University
of Utah, Salt Lake City, UT, 84112, USA<EMAIL_ADDRESS>$\dagger$$\dagger$affiliation: NSF Astronomy and Astrophysics Postdoctoral
Fellow , Christian R. Hayes2525affiliation: Department of Astronomy,
University of Washington, Seattle, WA, 98195, USA , Jianhui Lian11affiliation:
Department of Physics & Astronomy, University of Utah, Salt Lake City, UT,
84112, USA<EMAIL_ADDRESS>, David H.
Weinberg1919affiliation: Department of Astronomy, The Ohio State University,
140 W. 18th Ave., Columbus, OH 43210, USA 3737affiliation: Department of
Astronomy and Center for Cosmology and AstroParticle Physics, The Ohio State
University, 140 W. 18th Ave, Columbus, OH, 43210, USA , Gail
Zasowski11affiliation: Department of Physics & Astronomy, University of Utah,
Salt Lake City, UT, 84112, USA<EMAIL_ADDRESS>, Danny
Horta2323affiliation: Astrophysics Research Institute, Liverpool John Moores
University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF,
UK , Rachael Beaton66affiliation: Department of Astrophysical Sciences,
Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA , Diane K.
Feuillet33affiliation: Lund Observatory, Department of Astronomy and
Theoretical Physics, Box 43, SE-221 00 Lund, Sweden , Elisa R.
Garro77affiliation: Departamento de Ciencias Físicas, Facultad de Ciencias
Exactas, Universidad Andres Bello, Fernández Concha 700, Las Condes, Santiago,
Chile , Carme Gallart3434affiliation: Instituto de Astrofísica de Canarias
(IAC), E-38205 La Laguna, Tenerife, Spain 3535affiliation: Universidad de La
Laguna (ULL), Departamento de Astrofísica, E-38206 La Laguna, Tenerife, Spain
, Verne V. Smith2424affiliation: National Optical Astronomy Observatory, 950
North Cherry Ave, Tucson, AZ 85719 , Jon A. Holtzman1818affiliation:
Department of Astronomy, New Mexico State University, Las Cruces, NM 88003,
USA , Dante Minniti77affiliation: Departamento de Ciencias Físicas, Facultad
de Ciencias Exactas, Universidad Andres Bello, Fernández Concha 700, Las
Condes, Santiago, Chile 88affiliation: Vatican Observatory, Vatican City
State, V-00120, Italy , Ivan Lacerna1212affiliation: Instituto de Astronomía,
Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile
1313affiliation: Millennium Institute of Astrophysics, Nuncio Monsenor Sotero
Sanz 100, Of. 104, Providencia, Santiago, Chile , Matthew
Shetrone2929affiliation: Lick Observatory , Henrik Jönsson3636affiliation:
Materials Science and Applied Mathematics, Malmö University, SE-205 06 Malmö,
Sweden , Maria-Rosa L. Cioni2626affiliation: Leibniz-Institut für Astrophysik
Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany , Sean P.
Fillingham2525affiliation: Department of Astronomy, University of Washington,
Seattle, WA, 98195, USA , Katia Cunha1010affiliation: Steward Observatory, The
University of Arizona, Tucson, AZ, 85719, USA 1111affiliation: Observatório
Nacional, 20921-400 So Cristóvao, Rio de Janeiro, RJ, Brazil , Robert
OĆonnell22affiliation: Department of Astronomy, University of Virginia,
Charlottesville, VA, 22904, USA , José G. Fernández-Trincado1212affiliation:
Instituto de Astronomía, Universidad Católica del Norte, Av. Angamos 0610,
Antofagasta, Chile 4040affiliation: Instituto de Astronomía y Ciencias
Planetarias, Universidad de Atacama, Copayapu 485, Copiapó, Chile , Ricardo R.
Muñoz3939affiliation: Departamento de Astronomía, Universidad de Chile, Camino
El Observatorio 1515, Las Condes, Santiago, Chile , Ricardo
Schiavon2323affiliation: Astrophysics Research Institute, Liverpool John
Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool
L3 5RF, UK , Andres Almeida1616affiliation: Instituto de Investigación
Multidisciplinario en Ciencia y Tecnología, Universidad de La Serena. Avenida
Raúl Bitrán S/N, La Serena, Chile , Borja Anguiano22affiliation: Department of
Astronomy, University of Virginia, Charlottesville, VA, 22904, USA , Timothy
C. Beers99affiliation: Department of Physics and JINA Center for the Evolution
of the Elements, University of Notre Dame, Notre Dame, IN 46556, USA , Dmitry
Bizyaev3030affiliation: Apache Point Observatory and New Mexico State
University, Sunspot, NM 88349 3131affiliation: Sternberg Astronomical
Institute, Moscow State University, Moscow, 119992, Russia , Joel R.
Brownstein11affiliation: Department of Physics & Astronomy, University of
Utah, Salt Lake City, UT, 84112, USA<EMAIL_ADDRESS>, Roger
E. Cohen3838affiliation: Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD 21218, USA , Peter Frinchaboy3333affiliation: Department
of Physics & Astronomy, Texas Christian University, Fort Worth, TX 76129, USA
, D. A. García-Hernández3434affiliation: Instituto de Astrofísica de Canarias
(IAC), E-38205 La Laguna, Tenerife, Spain 3535affiliation: Universidad de La
Laguna (ULL), Departamento de Astrofísica, E-38206 La Laguna, Tenerife, Spain
, Doug Geisler1515affiliation: Departamento de Astronomía, Casilla 160-C,
Universidad de Concepcion, Chile 1616affiliation: Instituto de Investigación
Multidisciplinario en Ciencia y Tecnología, Universidad de La Serena. Avenida
Raúl Bitrán S/N, La Serena, Chile 1717affiliation: Departamento de Física y
Astronomía, Facultad de Ciencias, Universidad de La Serena. Av. Juan Cisternas
1200, La Serena, Chile , Richard R. Lane2020affiliation: Centro de
Investigación en Astronomía, Universidad Bernardo O’Higgins, Avenida Viel
1497, Santiago, Chile 1212affiliation: Instituto de Astronomía, Universidad
Católica del Norte, Av. Angamos 0610, Antofagasta, Chile , Steven R.
Majewski22affiliation: Department of Astronomy, University of Virginia,
Charlottesville, VA, 22904, USA , David L. Nidever44affiliation: Department of
Physics, Montana State University, P.O. Box 173840, Bozeman, MT 59717-3840
<EMAIL_ADDRESS>, Christian Nitschelm2222affiliation: Centro de
Astronomía (CITEVA), Universidad de Antofagasta, Avenida Angamos 601,
Antofagasta 1270300, Chile , Joshua Povick44affiliation: Department of
Physics, Montana State University, P.O. Box 173840, Bozeman, MT 59717-3840
<EMAIL_ADDRESS>, Adrian Price-Whelan2727affiliation: Center for
Computational Astrophysics, Flatiron Institute, 162 5th Ave., New York, NY
10010, U.S.A. , Alexandre Roman-Lopes1717affiliation: Departamento de Física y
Astronomía, Facultad de Ciencias, Universidad de La Serena. Av. Juan Cisternas
1200, La Serena, Chile , Margarita Rosado2828affiliation: Instituto de
Astronomía, Universidad Nacional Autónoma de México, A.P. 70-264, 04510,
Mexico, D.F., México , Jennifer Sobeck2525affiliation: Department of
Astronomy, University of Washington, Seattle, WA, 98195, USA , Guy
Stringfellow3232affiliation: Center for Astrophysics and Space Astronomy,
Department of Astrophysical and Planetary Sciences, University of Colorado,
Boulder, CO 80309 , Octavio Valenzuela2828affiliation: Instituto de
Astronomía, Universidad Nacional Autónoma de México, A.P. 70-264, 04510,
Mexico, D.F., México Sandro Villanova1515affiliation: Departamento de
Astronomía, Casilla 160-C, Universidad de Concepcion, Chile , Fiorenzo
Vincenzo1919affiliation: Department of Astronomy, The Ohio State University,
140 W. 18th Ave., Columbus, OH 43210, USA

###### Abstract

The SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE)
survey has obtained high-resolution spectra for thousands of red giant stars
distributed among the massive satellite galaxies of the Milky Way (MW): the
Large and Small Magellanic Clouds (LMC/SMC), the Sagittarius Dwarf (Sgr),
Fornax (Fnx), and the now fully disrupted _Gaia_ Sausage/Enceladus (GSE)
system. We present and analyze the APOGEE chemical abundance patterns of each
galaxy to draw robust conclusions about their star formation histories, by
quantifying the relative abundance trends of multiple elements (C, N, O, Mg,
Al, Si, Ca, Fe, Ni, and Ce), as well as by fitting chemical evolution models
to the [$\alpha$/Fe]-[Fe/H] abundance plane for each galaxy. Results show that
the chemical signatures of the starburst in the MCs observed by Nidever et al.
in the $\alpha$-element abundances extend to C+N, Al, and Ni, with the major
burst in the SMC occurring some 3-4 Gyr before the burst in the LMC. We find
that Sgr and Fnx also exhibit chemical abundance patterns suggestive of
secondary star formation epochs, but these events were weaker and earlier
($\sim$ 5-7 Gyr ago) than those observed in the MCs. There is no chemical
evidence of a second starburst in GSE, but this galaxy shows the strongest
initial star formation as compared to the other four galaxies. All dwarf
galaxies had greater relative contributions of AGB stars to their enrichment
than the MW. Comparing and contrasting these chemical patterns highlight the
importance of galaxy environment on its chemical evolution.

##  1\. Introduction

Galaxies are ubiquitous structures in the Universe. While we have made
tremendous strides in describing and understanding the patterns seen in
galaxies on global or coarsely resolved scales (e.g., mass-metallicity
relation, galaxy color-magnitude diagram), our understanding of how these
patterns reflect finer details of formation and evolution is severely limited.
This is largely due to the fact that only a few galaxies outside of our own
Milky Way (MW) can be studied at the spatial resolution of individual stars,
which is required to precisely analyze the galactic star formation histories
(SFHs). Fortunately, the Local Group consists of three main massive galaxies
(MW, M31, and M33) along with their vast populations of dwarf galaxies, which
themselves span a large range in mass, morphology, and environment (e.g.,
Hodge 1971, 1989; Mateo 1998; Tolstoy et al. 2009; McConnachie 2012; Ibata et
al. 2013; Weisz et al. 2014; Simon 2019). In principle, detailed SFHs built
from photometric or even spectroscopic observations can be constructed for
each of these galaxies, allowing for an understanding of the effects that halo
mass, formation environment, and interaction history have on a galaxy’s SFH.

In practice, the large distance to these galaxies combined with their often
large angular size means that fully spatially resolved SFH studies remain
observationally costly. Moreover, systematic differences between methods of
determining star formation histories can complicate comparisons across
multiple galaxies. Weisz et al. (2014) performed a SFH analysis of 40 Local
Group dwarf galaxies using photometry from the _Hubble Space Telescope_ ,
deriving SFHs from the color-magnitude diagram (CMD). Although these data did
consist of photometry of varying depths (see e.g., Ruiz-Lara et al. 2018 for
effects of photometric depth on SFH determination), the data were all analyzed
in a uniform way, and the authors were able to draw reasonably robust
conclusions on mass/environmental effects on galaxy evolution. In particular,
they found that in comparison to the more massive galaxies, less massive dwarf
galaxies generally formed a larger fraction of their stars in the first 2-3
Gyr of their existence.

The authors also found measurable scatter in SFHs at fixed mass, suggesting
where the galaxy formed in relation to other galaxies (i.e., its formation
environment) likely has a strong effect on evolution (also see Gallart et al.
2015). Many other works find similar SFH scatter at fixed mass (e.g., Mateo
1998; Grebel 1999), with some galaxies such as Carina experiencing distinct
bursts (e.g., de Boer et al. 2014; Santana et al. 2016). Simulations have
proven valuable for understanding exactly how environment affects SFH (e.g.,
Wetzel et al. 2016; Revaz & Jablonka 2018; Miyoshi & Chiba 2020), but the
extent to which external effects dominate over effects from a galaxy’s
intrinsic properties is still largely unknown (e.g, Kirby et al. 2011, 2013;
Hendricks et al. 2014; Escala et al. 2018; Wheeler et al. 2019).

While photometric studies have done much to characterize the star formation
rate of Local Group galaxies as a function of time, additional details can be
probed with spectroscopic observations from which detailed chemical abundance
patterns of individual stars can be obtained. Early star formation
efficiencies can be estimated from the “knee” in the $\alpha$-element
abundance trend (e.g., Tinsley 1979; Kobayashi et al. 2006; Shetrone et al.
2003; Nidever et al. 2014; Kirby et al. 2020), which has revealed that there
is likely a dependence on both galaxy mass and environment on star formation
history (e.g., Nidever et al. 2020). Additional star formation details, such
as variations in the initial mass function (IMF, e.g., McWilliam et al. 2013;
Hasselquist et al. 2017; Carlin et al. 2018) or amount of pollution from
asymptotic giant branch (AGB) stars (e.g., Bonifacio et al. 2000; Venn et al.
2004; Sbordone et al. 2007; Hansen et al. 2018; Skúladóttir et al. 2019;
Reichert et al. 2020; Fernández-Trincado et al. 2020) can be probed by close
examination of the abundance patterns of hydrostatic/explosive element
abundance ratios and $r$-/$s$-process element contributions, respectively.
However, the extent to which the abundance patterns can be precisely mapped to
parameters that govern star formation (e.g., inflow/outflow, IMF) largely
depends on the accuracy of yield tables, which are uncertain for some
elements, as well as inherent degeneracies in the predicted model abundance
tracks. Moreover, spectroscopic surveys are observationally expensive, and the
analysis techniques to extract abundances are susceptible to a range of
systematic uncertainties (e.g., using 3D and/or NLTE atmospheres vs. 1D plane-
parallel ones). Historically, this has meant that comparative spectroscopic
SFH studies have required using heterogeneous data from multiple literature
sources.

Fortunately, the SDSS-III/IV Apache Point Observatory Galactic Evolution
Experiment (APOGEE, Majewski et al. 2017) has obtained spectra of stars beyond
just the Milky Way, including the five most massive MW satellites: Large
Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), Sagittarius Dwarf Galaxy
(Sgr), Fornax (Fnx), and the _Gaia_ Sausage/Enceladus (GSE). The latter is no
longer a coherent structure separated from the Milky Way, but its distinct
remnant orbit structure means its stars can be relatively easily selected out
from the MW (e.g., Belokurov et al. 2018; Deason et al. 2018; Helmi et al.
2018; Myeong et al. 2018; Gallart et al. 2019; Mackereth et al. 2019; Feuillet
et al. 2020; Horta et al. 2021), thus serving as a distinct dwarf galaxy for
the purposes of this work. These galaxies span two orders of magnitude in
mass, and represent a wide range of formation environments, with GSE having
merged early with the MW (e.g., Gallart et al. 2019; Mackereth et al. 2019),
Sgr in the process of merging (e.g., Ibata et al. 2001; Majewski et al. 2003;
Belokurov et al. 2006; Ruiz-Lara et al. 2020a), Fnx in relative isolation now
but with some signatures of major mergers in recent times (e.g., Amorisco &
Evans 2012; del Pino et al. 2015, 2017), and the MCs falling into the MW for
the first time (e.g., Besla et al. 2007; Kallivayalil et al. 2013), while
clearly interacting with each other (e.g., Harris & Zaritsky 2009; Nidever et
al. 2010; Besla et al. 2016). Using APOGEE observations, we can now perform a
detailed, homogeneous comparison of the SFHs of these galaxies from the
_spectroscopic_ perspective.

In this work we present the detailed chemical abundance patterns of 10
elements for each of these five galaxies. We quantify the relative differences
in the median abundance patterns of these galaxies, allowing for more robust
conclusions about their relative star formation efficiencies and SFHs, and
more generally about the nucleosynthesis of different elements in these
disparate galaxies. We then use two chemical evolution models to interpret
these differences as actual physical differences in SFH parameters. Our
observations and data reduction are described in §2, and the sample selection
is described in §3. Chemical Abundance results are shown and compared in §4.
We fit chemical evolution models to the abundance results in §5, and these
results are discussed and compared to previous star formation history studies
in §6. Our conclusions are presented in §7.

##  2\. Observations and Data Reduction/Analysis

Observations were taken as part of APOGEE (Majewski et al., 2017), part of the
third and fourth iteration of the Sloan Digital Sky Survey (SDSS-III and SDSS-
IV; Eisenstein et al. 2011 and Blanton et al. 2017, respectively). The APOGEE
instruments are high-resolution (R $\sim$ 22,000), near-infrared ($H$-band)
spectrographs (Wilson et al., 2019) observing from both the Northern
Hemisphere at Apache Point Observatory (APO) using the SDSS 2.5m telescope
(Gunn et al., 2006), and the Southern Hemisphere at Las Campanas Observatory
(LCO) using the 2.5m du Pont telescope (Bowen & Vaughan, 1973). To date, the
dual APOGEE instruments have observed some 700,000 stars across the MW and
nearby systems, targeting these stars with selections described in Zasowski et
al. (2013) and Zasowski et al. (2017), with updates to the targeting plan
described in Santana et al. (2021) and Beaton et al. (2021).

We use APOGEE results from the 17th Data Release of SDSS (DR17, Masters et al.
in prep). Spectra are reduced as described in Nidever et al. (2015) (with
updates described in Holtzman et al. in prep) and analyzed using the APOGEE
Stellar Parameters and Chemical Abundance Pipeline (ASPCAP, García Pérez et
al. 2016), which uses the FERRE code (Allende Prieto et al., 2006) to
interpolate in a grid of model synthetic spectra (Zamora et al., 2015) to find
the best-fit stellar parameters and abundances. Updates to the DR17 chemical
abundance analysis include cerium abundances using lines characterized in
Cunha et al. (2017), as well as NLTE corrections for Na, Mg, K, and Ca (Osorio
et al., 2020). Validation of the APOGEE abundance results can be found in
Jönsson et al. (2018), Nidever et al. (2020), and Holtzman et al. in prep.

##  3\. Sample Selection

In this work we analyze five dwarf galaxy stellar samples (LMC, SMC, GSE, Sgr,
and Fnx) along with a comparison Milky Way sample, for a total of six stellar
samples. For each sample, we start with the following cuts:

  * •

Median S/N per pixel $>$ 70 (except for Fornax, see §A.4) to ensure precise
abundances.

  * •

No STAR_BAD bit set in the ASPCAPFLAG111See DR17 web documentation. to remove
problematic/suspect abundance determinations.

  * •

[Fe/H] $<$ 0.0 to remove obvious MW contamination from the dwarf galaxy
samples.

  * •

Remove duplicate observations of a single target that have bit 4 of EXTRATARG
set222See DR17 web documentation for a full description of this flag.
https://www.sdss.org/dr16/algorithms/bitmasks/.

Sample selection is then made through a mix of spatial, kinematic, and simple
chemical selection criteria. We briefly describe the selection for each sample
below, but refer the reader to Appendix A for more detailed plots and
descriptions.

The criteria used to select each sample are summarized in Table 1, and the
APOGEE IDs for each sample are in Table 2. To reproduce the results of this
paper, one can match Table 2 to the APOGEE allStar
catalog333https://data.sdss.org/datamodel/files/APOGEE_ASPCAP/APRED_VERS/ASPCAP_VERS/allStar.html.
Figure 1 shows the spatial distribution of each galaxy. The APOGEE
observations cover much of the spatial extent of these galaxies, including
nearly continuous coverage of the Sgr core and stream.

Table 1Galaxy Selection  System | Center ($\alpha$, $\delta$) | Dproj |  $V_{\rm helio}$ (km/s) |  $\mu_{\alpha}$ (mas/yr) |  $\mu_{\delta}$ (mas/yr) | Photometry | N∗ | Section
---|---|---|---|---|---|---|---|---
LMC | (80.894∘,-69.756∘) |  $<$ 12∘ | 161 $<$ $V_{\rm helio}$ $<$ 370 | 1.01 $<$ $\mu_{\alpha}$ $<$ 2.62 | -1.15 $<$ $\mu_{\delta}$ $<$ 1.70 | (J-Ks) $<$ 1.3; RGB444RGB tip, described in §A.1 | 3,909 |  3.1;A.1
SMC | (13.187∘,-72.829∘) |  $<$ 8∘ | 66 $<$ $V_{\rm helio}$ $<$ 235 | 0.05 $<$ $\mu_{\alpha}$ $<$ 1.51 | -1.57 $<$ $\mu_{\delta}$ $<$ -0.94 | (J-Ks) $<$ 1.3; RGB | 1,146 |  3.1;A.1
GSE555Primarily orbital selections | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | 972 |  3.2;A.2
Sgr666Primarily kinematic selections in Sgr coordinate frame | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | 946 |  3.3;A.3
Fnx | (39.748∘, -34.376∘) |  $<0.9^{\circ}$777Single APOGEE plug plate | 17 $<$ $V_{\rm helio}$ $<$ 89 | 0.17 $<$ $\mu_{\alpha}$ $<$ 0.60 | -0.71 $<$ $\mu_{\delta}$ $<$ -0.05 | $-$ | 192 |  3.4;A.4
Table 2Galaxy Selection  APOGEE ID | System
---|---
2M03141881-7642442 | LMC
2M03173277-7702254 | LMC
2M03174293-7712511 | LMC
…888full version online |
Figure 1.— Right ascension ($\alpha$) and declination ($\delta$) maps of four
galaxies: LMC (red, upper-left), SMC (blue, upper-right), Sgr (orange, lower-
left), Fnx (purple, lower-right). Spatial density bins are plotted except
where the bin count is below 5 stars. Black crosses mark the photometric
centers of these galaxies, and are noted in Table 1. The dashed circle in the
lower-left panel highlights the Sgr “main body” region, the coverage of which
is shown in the inset. About 2/3 of our Sgr targets reside in this main body
region.

###  3.1. Magellanic Clouds

The Magellanic Clouds have been extensively observed by APOGEE-2S, with many
programs targeting stars across a wide range of evolutionary type (see Nidever
et al. 2020 and Santana et al. 2021), including red giant branch (RGB) stars,
oxygen-rich asymptotic giant branch (O-AGB) stars, C-rich AGB stars (C-AGB),
and massive (M $\gtrsim$ 3 M⊙) red supergiant (RSG) stars. To select our MC
sample we use a combination of spatial, kinematical, color, magnitude, and
metallicity cuts, described in detail in §A.1. Because only the RGB stars have
well-vetted stellar parameters and abundances from APOGEE, we remove the
O-AGB, C-AGB, and RSG stars by only selecting stars that are below the Red
Giant Branch (RGB) tip (as defined by Hoyt et al. 2018). However, because the
stars above the RGB tip are generally the more massive stars in the MCs,
removing these stars means that we are biasing our sample against the youngest
(age $\lesssim$ 1 Gyr) MC stars. These cuts result in samples of $\sim$3,900
stars for the LMC and $\sim$1,100 stars for the SMC. This sample is largely
comprised of RGB stars, but likely still contains AGB stars that are below the
RGB tip. These stars span a large spatial extent of the MCs, as shown in the
top row of Figure 1.

The log(g)-Teff distribution of these stars are shown in the left two panels
of Figure 3. While most of the MC stars that pass these cuts have log(g) and
Teff consistent with being upper giant branch stars, the LMC contains three
groups of stars that have different stellar parameters than the majority of
the sample: (1) the clump of log(g) $<$ 0 stars in the LMC panel of Figure 3,
(2) the cool, higher gravity stars (log(g) $>$ 1.5 & Teff $<$ 4200 K, and (3)
stars at Teff $>$ 5000 K. After analyzing these stars and comparing to other
surveys, we have determined that (1) are thermally pulsating asymptotic giant
branch stars (TP-AGB), enhanced in C+N, (2) are likely mass-transfer binaries,
enhanced in [Ce/Fe], and (3) are identified as Delta Cep pulsators by
Soszynski et al. (2008). We do not explicitly remove these stars, and present
their chemical results in §5.3.

###  3.2. Gaia Sausage/Enceladus (GSE)

In this work, we treat the accreted halo stars, defined below, as originating
from one progenitor, the GSE, that has since merged with the MW. However, when
treating the GSE as one entity, we assume that we have selected stars in a way
that is not chemically biased. A compact remnant for GSE has not yet been
confirmed. Should this remnant exist and be absent from our selection, then it
is possible we are missing the most chemically evolved GSE stars in our
sample. Furthermore, like other studies, we are assuming the stars come from
one progenitor rather than multiple. We are also only explicitly removing
stars in known globular clusters, but should GSE contain dissolved GC stars,
then we might expect our sample to contain stars that show GC-like abundance
pattern variations. However, these stars are likely to comprise only a small
fraction of our GSE sample, and will not significantly impact our
interpretations of the median abundance trends.

There are now a wide range of literature works that show how GSE stars can be
selected by applying various kinematical and dynamical selection criteria. In
this work, we follow Feuillet et al. (2020) and select stars in
$\sqrt{J_{R}}$-Lz space, with these quantities provided in the
astroNN999https://www.sdss.org/dr16/data_access/value-added-
catalogs/?vac_id=the-astronn-catalog-of-abundances,-distances,-and-ages-for-
apogee-dr16-stars APOGEE DR17 value-added catalog(Leung & Bovy, 2019). These
selections result in some contamination from the high-$\alpha$ MW disk, so we
perform a chemical cut in [(C+N)/Fe] for stars with [Fe/H] $>$ -1.05 to remove
the obvious high-$\alpha$ MW stars, which are $\sim$ 0.2-0.3 dex enhanced in
[(C+N)/Fe] as compared to GSE. Selecting GSE members is described in more
detail in §A.2, and our final sample consists of $\sim$ 1000 stars. Figure 2
shows that our GSE sample studied here primarily comes from stars near the
solar radius, at $\pm$5 kpc from the plane of the MW, although some stars do
come from much further away. To make these maps we use distances from DR17
astroNN (Leung & Bovy, 2019).

Figure 2.— Map of the GSE members (green) studied in this work using astroNN
distances (Leung & Bovy, 2019). Left: Rectangular X and Y Galactic
coordinates, where the position of the Sun is notated by a red cross. Right:
vertical height above/below the plane plotted as a function of Galactic
cylindrical radius. The grey-scale density map shows the location of APOGEE MW
stars.

###  3.3. Sagittarius

To select Sgr members, we take a similar approach to that of Hayes et al.
(2020). We first only consider stars with [Fe/H] $<$ 0.0, heliocentric
distance greater than 10 kpc, and within $\pm$30∘ of the plane of the Sgr
stream (Majewski et al., 2003). Then, we make an initial selection in $V_{\rm
zs}$ \- $L_{\rm zs}$ plane, where $V_{\rm zs}$ and $L_{\rm zs}$ are the
vertical velocity and angular momenta in the Sagittarius Galactocentric
coordinate system, as derived and described in Majewski et al. (2003). We then
make further selections in the $\phi_{\rm vel,s}$-$\Lambda_{\rm s}$ plane,
where $\phi_{\rm vel,s}$ is the velocity direction in the X and Y directions
of the Sgr coordinate system and $\Lambda_{\rm s}$ is the longitude along the
Sgr stream (Majewski et al. 2003; Hayes et al. 2020), to remove stars that are
moving perpendicular to the stream. We describe the selection process in more
detail in §A.3. The final Sgr sample consists of $\sim$1,000 stars, $\sim$ 2/3
of which are in the main body of Sgr (within 12∘ of the center of Sgr). See
$\S$ A.3 for details on the coverage of the Sgr main body.

###  3.4. Fornax

The APOGEE Fornax field was designed specifically to observe likely members
based on radial velocities, proper motions, and/or CMD (see Zasowski et al.
2017 and Santana et al. 2021). Therefore, most targets in this field are
likely Fornax members, but we re-analyze the APOGEE RVs and _Gaia_ proper
motions to remove any contamination. We adopt a lower cut of S/N $>$ 40 for
the Fornax sample to include a meaningful number of stars to compare to the
other galaxies. This lower S/N cut means that the individual abundance
uncertainties are generally larger for Fnx stars than the stars in other
galaxies. The final selection cuts we used are shown in Table 1, and the
process is described in more detail in §A.4.

###  3.5. MW Comparison Sample

While the APOGEE pipeline has had several improvements to eliminate Teff and
log(g) systematics in abundance determination (Jönsson et al., 2020), recent
work by Griffith et al. (2020) shows that some elemental abundances still
exhibit some small systematic trends in abundance with Teff and log(g) (e.g.,
Al and Si). Thus, to minimize these effects on our interpretations of the
abundance trends, we compare each galaxy to a MW sample of roughly similar
stellar parameters. For each galaxy, we select a Teff range corresponding to
$\pm 2\sigma$ from the median Teff values of each galaxy, as shown in Figure
3.

Figure 3.— HR Diagram for the five different galaxy samples (monochromatic
density maps and circles where bins contain fewer than 5 stars) plotted with
the HR diagram of the Teff-matched MW stars (grayscale density). Horizontal
lines indicate the 2$\sigma$ Teff range adopted to select out the MW
comparison samples.

For the MCs, Sgr, and Fnx, we are primarily analyzing the abundance patterns
of luminous giants (log(g) $\lesssim$ 1.5). While we do not make specific
spatial selections for the MW stars, the MW comparison sample for the MCs,
Sgr, and Fnx, covers much of MW disk and bulge region. The GSE sample spans
much of the giant branch (0.5 $<$ log(g) $<$ 3.0), so the MW comparison sample
contains a larger fraction of intrinsically less-luminous stars, resulting in
a MW sample that is primarily located spatially within 1-2 kpc from the Sun.
Weinberg et al. (2019) show that the median trends of APOGEE elemental
abundance ratios are nearly independent of location in the disk provided one
separates the low-$\alpha$ and high-$\alpha$ populations, so we do not expect
geometrical selection effects within the MW to have an effect on our
comparison.

##  4\. Chemical Abundance Results

In this section, we present the elemental abundances for C+N, the
$\alpha$-elements (O, Mg, Si, Ca), Al, Ni, and Ce. We select these elements
because they are among the most precise APOGEE abundances across the full
parameter space covered here, and are among the most accurate when comparing
to optical studies (see e.g., Jönsson et al. 2018, 2020). We combine C and N
because stars will change their [C/Fe] and [N/Fe] abundances during dredge up
ascending to and along the giant branch, but these processes occur in such a
way that the [(C+N)/Fe] abundance is largely constant before and after these
mixing processes (see e.g., Gratton et al. 2000). We compare the abundance
patterns of each galaxy to the abundance pattern of the MW in this section, as
well as compare the abundance patterns of the dwarf galaxies to each other.

Throughout these sections, we describe various aspects of the abundance
patterns of each galaxy, linking certain features to physical drivers of SFH,
such as early star formation efficiency or presence/strength of a secondary
star burst. We provide an example schematic diagram of how we interpret
abundance patterns in Figure 4. In the top row of Figure 4 we show flexCE
(described in detail in Andrews et al. 2017, §5.1, and §B) chemical evolution
model tracks (left) with mock observations of the tracks (right) to show what
the abundance patterns of two galaxies (labeled as “Dwarf Galaxy Model” and
“MW Model” in the Figure) with different initial star formation efficiencies
look like in the [Si/Fe]-[Fe/H] abundance space. The combination of the star
formation efficiency (SFE $\equiv$ $\dot{\rm M}_{*}/{\rm M}_{\rm gas}$) and
the gas supply (${\rm M}_{\rm gas}(t)$) determines the star formation rate
(SFR$(t)=\dot{\rm M}_{*}(t)$). The gas supply in turn depends on the gas
accretion history, and is further regulated by star formation and outflows
(which deplete ${\rm M}_{\rm gas}$) and recycling from evolved stars (which
replenishes ${\rm M}_{\rm gas}$).

Figure 4.— Chemical evolution model tracks of the [Si/Fe]-[Fe/H] abundance
plane (left column) along with mock observations sampled from these tracks
with 0.05 dex abundance uncertainties (right column). The top row compares two
galaxy model tracks with different early star formation efficiency, and the
bottom row compares two galaxy model tracks with identical early star
formation efficiencies, but one with a secondary burst of star formation.

The top row of Figure 4 shows that the [Si/Fe]-[Fe/H] abundance pattern of the
lower SFE dwarf galaxy model (red) begins to decrease with increasing [Fe/H]
at much lower [Fe/H] values than the higher SFE MW model (black). In both
galaxies, the [Si/Fe] abundance decreases after Type Ia SNe begin to
substantially contribute to the chemical evolution of these galaxies, which is
thought to occur some time after star formation begins (see e.g., Tinsley
1979). Type Ia SNe produce Fe without producing much Si (which is primarily
produced in Type II SNe), resulting in a decrease of the [Si/Fe] abundance as
the Type Ia/Type II SNe ratio increases. Because the delay time at which Type
Ia SNe begin to contribute to the chemical enrichment of these galaxies is
assumed to be the same, the metallicity at which [Si/Fe] begins to decrease
(sometimes referred to as the $\alpha$-element abundance “knee”) probes the
early SFE of a galaxy, with more metal-poor knees indicating a galaxy
experienced fewer Type II SNe events contributing to its enrichment before the
delayed Ia SNe started to contribute. Therefore, from these abundance
patterns, we would conclude that the dwarf galaxy experienced lower efficiency
SF at early times than the MW.

The bottom row of Figure 4 compares two dwarf galaxies with the same early
star formation efficiency, but the red track emphasizes how a starburst
influences the [Si/Fe]-[Fe/H] track. The red model track was used in Nidever
et al. (2020) to explain the rising [$\alpha$/Fe] abundance pattern observed
in the APOGEE LMC data. We would therefore conclude that the red dwarf galaxy
experienced some secondary star formation epoch whereas the black dwarf galaxy
did not. In this example, the starburst is induced by temporarily increasing
the star formation efficiency while maintaining the same gas accretion history
(see §5.1). Many more examples of the influence of star formation and outflow
parameters on evolutionary tracks can be found in Andrews et al. (2017) and
Weinberg et al. (2017), and a systematic exploration of chemical evolution
tracks with starbursts can be found in Johnson & Weinberg (2020).

APOGEE abundance results of each dwarf galaxy as compared to their respective
MW comparison samples are shown in Figures 5 and 6. Figure 5 shows the
“traditional” abundance patterns using Fe as the reference element
([X/Fe]-[Fe/H]), whereas Figure 6 shows the abundance patterns using Mg as a
reference element ([X/Mg]-[Mg/H]) to analyze abundance patterns as a function
of Type II SNe ejecta alone, following Weinberg et al. (2019). Each row of
these Figures shows a different elemental abundance ratio ([X/Fe] or [X/Mg])
plotted against a “metallicity indicator”, represented by [Fe/H] or [Mg/H].
Each column shows how a given dwarf galaxy’s abundances compare to that of its
respective MW comparison sample. The MW comparison samples are nearly
identical for the LMC, SMC, Sgr and Fnx panels, but the MW comparison sample
for GSE contains a much larger fraction of lower luminosity stars. The
chemical abundance pattern for each sample is plotted as a density map except
for where the pixel contains fewer than 5 stars, where the individual
measurements are displayed as circles instead.

Figure 5.— Chemical abundance patterns of select elements for each of the
dwarf galaxies as compared to the MW. Over-plotted for each galaxy are 2D
density histograms except for bins where the density falls below 5 stars. The
dashed black line in the [Al/Fe], [Ni/Fe], and [Ce/Fe] panels indicate the
grid edges, below which the APOGEE spectra grids do not extend. Representative
median individual uncertainties in the abundances for each dwarf galaxy are
shown in black in the bottom of each panel. Figure 6.— Same as in Figure 5,
but using Mg as the reference element instead of Fe.

To compare the chemical tracks of the dwarf galaxies with each other, we also
show the median abundance tracks for the dwarf galaxies all in one panel per
chemical element in Figure 7, with [X/Fe]-[Fe/H] plotted on the left column
and [X/Mg]-[Mg/H] plotted on the right column. Running medians are calculated
in bins of 30 stars. Because GSE sampled a much larger section of the giant
branch than the other dwarf galaxies, we only include stars with 3600 K $<$
T${}_{\rm eff}<4200$ K to make for a more systematic-free comparison. We also
select a comparison MW sample to now only cover 3600 K $<$ T${}_{\rm
eff}<4200$ K.

Figure 7.— Median abundance tracks (solid colored lines) and associated $\pm$1
$\sigma$ uncertainties on the median track (colored shaded regions) for each
galaxy in moving bins of 30 stars. The MW sample is plotted as a grayscale
density image. We have removed all GSE and MW stars with $T_{\rm eff}>$ 4200 K
to make for relatively systematic-free comparison across all galaxies. Note
that vertical axis ranges vary from panel to panel, but grey dot-dashed
horizontal lines are spaced at 0.20 dex in all panels so they can be used as a
visual reference for comparing the strength of metallicity trends across
elements.

In the following subsections, we describe the chemical abundance patterns of
each galaxy, regularly referring to Figures 5, 6, and 7.

###  4.1. LMC

The left columns of Figures 5 and 6 show the abundance patterns for the LMC.
The APOGEE LMC sample contains stars across a wide range of metallicities,
-2.2 $<$ [Fe/H] $<$ -0.3, making it currently one of the most metal-rich MW
satellite galaxies (compare the median abundance tracks in Figure 7). Such a
wide metallicity range implies an extended star formation history, the
complexity of which is highlighted in the [X/Fe] and [X/Mg] abundance
patterns, as described in detail below.

####  4.1.1 O, Mg, Si, and Ca

The $\alpha$-elements, O, Mg, Si, and Ca, are primarily produced in massive
stars and released to the ISM via Type II SNe, with Si and Ca having non-
negligible contributions from Type Ia SNe in the MW disk (e.g., Weinberg et
al. 2019). As already shown by Nidever et al. (2020), and again presented in
the left columns of Figures 5 and 7, the APOGEE LMC sample exhibits an
[$\alpha$/Fe]-[Fe/H] abundance pattern that decreases over the metallicity
range -2.2 $<$ [Fe/H] $<$ -1.2 to sub-solar [$\alpha$/Fe] values, before
increasing to intersect with the MW low-$\alpha$ disk trend. Nidever et al.
(2020) interpreted this pattern as very weak (i.e., low efficiency) early star
formation, followed by a strong burst in star formation that occurred in more
recent times, when many Type II SNe drove up the $\alpha$-element abundance.
This picture is qualitatively consistent with photometric studies of the LMC
(e.g., Harris & Zaritsky 2009; Monteagudo et al. 2018; Ruiz-Lara et al.
2020b), but is only somewhat consistent with other spectroscopic studies. Many
spectroscopic abundance studies (e.g., Smith et al. 2002; Lapenna et al. 2012;
Van der Swaelmen et al. 2013) find that the more metal-poor LMC stars are
deficient in the $\alpha$ elements relative to the MW, but only the Mg
abundances of Lapenna et al. (2012) show a flat or slightly increasing [Mg/Fe]
abundance with metallicity at [Fe/H] $>$ -1.5. We refer the reader to Nidever
et al. (2020) for a more detailed discussion of the comparison samples, but
note here that the APOGEE sample studied in this work is a factor of $\sim$40
larger than other high-resolution abundance studies. Moreover, the APOGEE
random uncertainties of individual abundance measurements are $\sim$1/4 those
presented in other studies.

While the pattern of low early SF followed by a major burst is seen across all
$\alpha$-elements, the extent to which the metal-rich LMC stars overlap the MW
disk sample varies. The [O/Fe] and [Mg/Fe] abundance patterns reach the MW
low-$\alpha$ disk trend, whereas the [Si/Fe] and [Ca/Fe] actually rise above
the MW low-$\alpha$ disk trend (perhaps best seen in the left column of Figure
7). The [O/Mg], [Si/Mg], [Ca/Mg] abundances all slightly decrease with
increasing [Mg/H], with [Ca/Mg] remaining $\sim$0.05 dex above the MW trend at
[Mg/H] = -0.4.

Compared to the other dwarf galaxies (Figure 7), only Sgr extends to as high
metallicities as the LMC. However, the metal-poor LMC stars have lower
[$\alpha$/Fe] (by $\sim$ 0.05-0.1 dex) than the Sgr stars until [Fe/H] = -1.0,
at which point the LMC increases its [$\alpha$/Fe] abundance, whereas the
[$\alpha$/Fe]-[Fe/H] abundance track of Sgr continues to decrease before
becoming mostly flat. Over the metallicity range -1.5 $<$ [Fe/H] $<$ -1.0, the
LMC is $\sim$ 0.2 dex deficient across all $\alpha$ elements compared to GSE.
Despite these differences in the [$\alpha$/Fe]-[Fe/H] tracks, most galaxies
show similar decreasing [$\alpha$/Mg] abundances with increasing [Mg/H], the
exception being Fornax in [Ca/Mg] (discussed more in §4.5).

####  4.1.2 Carbon and Nitrogen

Carbon and nitrogen are elements that are thought to be produced in great
quantities in type II SNe, with nitrogen yields expected to have some
dependence on progenitor metallicity (e.g., Kobayashi et al. 2006). Both
elements are also thought to be produced in appreciable amounts by AGB stars
(e.g., Nomoto et al. 2013; Karakas & Lattanzio 2014; Andrews et al. 2017;
Rybizki et al. 2017). Throughout this work, we analyze the sum of these
abundances, [(C+N)/Fe] and [(C+N)/Mg], as red giant stars undergo dredge up
processes that mix the surface abundances with material produced as a
consequence of nuclear reactions deeper in the star. This mixing operates in a
way such that the star’s birth C+N abundance is largely conserved (e.g., Iben
1964; Gratton et al. 2000; Salaris et al. 2015; Vincenzo et al. 2021).

The [(C+N)/Fe] abundance pattern of the LMC shows a slight decrease from -0.1
to $\sim$ -0.3 dex over the range -2.2 $<$ [Fe/H] $<$ -1.2. At [Fe/H] $>$
-1.2, the [(C+N)/Fe] is flat at 0.3 dex below the MW abundance trend before
rapidly increasing to almost intersect with the MW low-$\alpha$ “thin” disk
trend at [Fe/H] = -0.3. In the [(C+N)/Mg]-[Mg/H] abundance plane shown in
Figure 6 and in the right column of Figure 7, both the LMC and the MW
high-$\alpha$ “thick” disk stars show similar trends of slightly increasing
[(C+N)/Mg] with [Mg/H] in their region of overlap, with the LMC pattern being
enhanced by $\sim$ 0.1 dex. Over the wide metallicity range (-1.7 $<$ [Mg/H]
$<$ -0.5) the LMC [(C+N)/Mg] trend is flat to within $\sim$ 0.05 dex, implying
that (C+N) production tracks Mg production at these metallicities.

As shown in Figure 7, only Sgr appears to show a similar increase in
[(C+N)/Fe] as the LMC at [Fe/H] $>$ -0.7, although this increase is not as
steep as the increase in the LMC. Most other galaxies show a similar slight
decrease of [(C+N)/Fe] from [Fe/H] = -2.0 to [Fe/H] = -1.0, although both Fnx
and GSE have enhanced [(C+N)/Fe] over this metallicity range as compared to
the LMC by $\sim$0.15 dex. However, the [(C+N)/Mg]-[Mg/H] abundance patterns
show that Fnx is enhanced as compared to the LMC, and GSE is actually slightly
deficient.

####  4.1.3 Aluminum and Nickel

Aluminum is an element thought to be produced by massive stars and released to
the ISM solely via Type II SNe with some dependence on progenitor metallicity
(e.g., Weinberg et al. 2019), whereas Nickel is an element produced in both
Type II and Type Ia SNe. The [Al/Fe]-[Fe/H] abundance pattern of the LMC
appears qualitatively consistent with the starburst scenario (flat, then
increasing abundance at point of star burst). The [Al/Mg] plot shown in the
left column of Figure 6 shows that the [Al/Mg] ratio is still about 0.2 dex
below the MW trend at the same [Mg/H]. The [Al/Mg]-[Mg/H] abundance tracks are
similar across all of the dwarf galaxies (right column of Figure 7), showing a
steady rise from [Al/Mg] $\simeq$ -0.6 at [Mg/H] $\simeq$ -1.7 to [Al/Mg]
$\simeq$ -0.25 at [Mg/H] $\simeq$, which suggests that Type II Al yields
increase steadily over this metallicity range.

The LMC Ni abundance trends, for both [Ni/Fe] and [Ni/Mg], are similar to the
$\alpha$-element abundance trends, being most similar to [Si/Fe] and [Si/Mg].
However, [Ni/Fe] remains below the MW low-$\alpha$ disk trend whereas the
$\alpha$ elements reach the same level as the MW low-$\alpha$ disk trend at
the highest LMC metallicities. The decline of [Ni/Mg] with increasing [Mg/H]
is also steeper than that of [Si/Mg], probably because of a larger Type Ia SNe
contribution. The [Ni/Mg] of the metal-rich LMC is slightly deficient as
compared to the metal-rich Sgr stars, with the LMC stars lying in between the
two MW sequences, and Sgr lying closer to the MW low-$\alpha$ sequence.

####  4.1.4 Cerium

The heavy $s$-process element cerium is one of the elements whose abundances
are presented in DR17 and is based upon Ce II lines as described in Cunha et
al. (2017). The astrophysical source of the s-process elements, such as Ce, is
dominated by thermally-pulsing (TP) AGB stars, with the probable neutron
source being 13C($\alpha$,n)16O (e.g., Karakas & Lugaro 2016; Prantzos et al.
2018; Kobayashi et al. 2020). This particular neutron source is important, as
it takes place in the inter-shell region (between shell He-burning
triple-$\alpha$ and shell H-burning via CN-cycle reactions) between thermal
pulses (e.g., Karakas & Lattanzio 2014) and is a primary neutron source (i.e.,
independent of the star’s birth metallicity), driven by the mixing of protons
into 12C-rich regions (from triple-alpha) resulting in
12C(p,$\gamma$)13N($\beta^{+}$,$\nu$)13C. Cerium is a sensitive diagnostic of
TP-AGB chemical enrichment, which continues to take place over relatively long
timescales (of order several Gyr), and provides information on nucleosynthesis
and chemical evolution that complements that provided by the $\alpha$-elements
(massive stars and Type II SNe), the Fe-peak (Type Ia SNe), or the $r$-process
(merging neutron stars).

The LMC [Ce/Fe] pattern increases with [Fe/H] across nearly the entire
metallicity range, with the most metal-rich MW stars having slightly enhanced
[Ce/Fe] as compared to the MW disk. The rise of [Ce/Fe] with [Fe/H] is similar
to what was found by Pompéia et al. (2008) in a sample of LMC red giants for
the s-process element barium, which will behave similarly to Ce. There is also
a small clump of stars at [Fe/H] $\simeq$ -0.7 that are $\sim$ 0.2 dex more
enhanced than the rest of the LMC stars, which pulls the median up in Figure 7
to be slightly above the [Ce/Fe] abundance pattern of Sgr.

The LMC [Ce/Mg]-[Mg/H] abundance pattern also shows an increasing [Ce/Mg] with
[Mg/H], however, the lower-left panel of Figure 6 and the lower-right panel of
Figure 7 shows that the [Ce/Mg] increases more slowly with [Mg/H] at [Mg/H]
$>$ -1.0. In the regime of $-1.8<$ [Mg/H] $<-0.7$, the rise of [Ce/H] with
[Mg/H] is well-fit by a slope of 1.4, while in the range of -0.7 $<$ [Mg/H]
$<$ -0.2 the slope drops to $\sim$0.9. The different behavior from [Ce/Fe]
arises because [Mg/Fe] itself is rising over this interval, probably because
of a burst in star formation. This burst evidently boosts Mg more rapidly than
Ce, which is as expected if Ce production is dominated by less massive stars.
Such a change in slope is less evident in the [Ce/Mg]-[Mg/H] abundance
patterns of Sgr, which has a flat [Mg/Fe] trend at high metallicity.

####  4.1.5 LMC Interpretations

The metal-poor $\alpha$-element abundance patterns show that, compared to GSE,
Sgr and the MW, the LMC enriched to a much lower [Fe/H] before Type Ia SNe
began to contribute to its enrichment, suggesting much lower early star
formation efficiency. We interpret the increasing $\alpha$-element abundance
patterns at higher metallicity, along with the increases of both [(C+N)/Fe]
and [Al/Fe] with increasing [Fe/H], as results of a major starburst in the LMC
that occurred at [Fe/H] $\simeq$ -0.8 (see §5.3 for quantitative modeling).
The [Ni/Fe]-[Fe/H] abundance pattern of the LMC is qualitatively similar to
the $\alpha$-element abundance tracks (slight decrease at the metal-poor end
followed by a slight increase from the burst), but [Ni/Fe] in the LMC remains
below the MW trend at [Fe/H] $>$ -0.7, whereas the $\alpha$ elements all reach
the MW low-$\alpha$ disk trend. Because the [Ni/Mg] ratio at this point in the
LMC’s evolution is closer to that of the high-$\alpha$ MW disk (e.g., the
“pure” Type II SNe [Ni/Mg] abundance), the expectation is that the [Ni/Fe]
should be closer to the abundance of the high-$\alpha$ MW disk. The [Ni/Fe]
deficiency is therefore plausibly a result of the LMC lacking more metal-rich
Type Ia SNe contributing its chemical evolution, if the production of Ni in
Type Ia SNe is indeed metallicity-dependent (see e.g., Woosley & Weaver 1995;
Chieffi & Limongi 2004; Seitenzahl et al. 2013; Andrews et al. 2017; Rybizki
et al. 2017).

While the trend of increasing [Al/Mg] with increasing [Mg/H] in all dwarf
galaxies can be explained by metallicity-dependent Type II SNe yields, the
slight deficiency in [Al/Mg] for the most metal-rich LMC and Sgr stars
relative to MW stars is a bit difficult to explain given that Al and Mg are
both pure type II SNe products (e.g., Weinberg et al. 2019). One plausible
explanation is that the low star formation efficiencies in the dwarfs cause a
stronger “metallicity lookback” effect – e.g., when the metallicity of the ISM
(and newly forming stars) is -0.5, the average metallicities of the stars that
enriched the ISM is still significantly lower than -0.5, with consequently
lower Al production. This could also be an explanation for the Ni abundance
patterns if Ni production is metallicity-dependent in both Type Ia and Type II
SNe.

[O/Mg] and [Si/Mg] for the LMC, and other dwarf galaxies, slowly decrease (by
about 0.1 dex) over the range -1.3 $<$ [Mg/H] $<$ -0.5, with both the LMC and
Sgr joining the MW trends at [Mg/H] $>$ -0.5. This is either a result of
metallicity-dependent Type II SNe yields for these elements (e.g., more Si and
O relative to the MW at low metallicity), or a result of a slowly increasing
Type II/Type Ia SNe fraction, as star formation was extended after the initial
SF epoch. The [Fe/Mg] suggests the latter scenario is plausible, at least from
-0.8 $<$ [Mg/H] $<$ -0.4, over which the [Fe/Mg] ratio slowly decreases as
more Type II SNe contribute. The slightly enhanced [Ca/Mg] for the LMC and Sgr
at these metallicities as compared to the MW stars is a result of Type Ia
contribution to Ca, which is still substantial even with the starburst
injecting many more Type II SNe products than at lower metallicities. These
results suggest that Ca has a higher contribution from Type Ia SNe than Si
(also see e.g., Tsujimoto et al. 1995; Hayes et al. 2018).

We interpret the slightly increasing [(C+N)/Mg] with [Mg/H] as metallicity-
dependent C+N yields in Type II SNe (since the MW high-$\alpha$ stars also
show this trend), combined with some contribution of C+N from another source,
such as AGB stars, which results in the LMC (and Sgr) trend being slightly
elevated from the MW high-$\alpha$ sequence. However, this is a small effect,
with [(C+N)/Mg] varying by only $\pm$0.05 dex over the metallicity range -1.7
$<$ [Mg/H] $<$ -0.3. The enhanced [Ce/Fe] and [Ce/Mg] both suggest that the
LMC and Sgr experienced significant contributions to their evolution from the
$s$-process (likely from AGB stars), with the most metal-rich stars enhancing
to similar levels of [Ce/Mg] as the more metal-rich MW low-$\alpha$ sequence.
The slight change in slope observed in the [Ce/Mg]-[Mg/H] abundance pattern of
the LMC is likely due to the starburst polluting the ISM with much more Mg
from Type II SNe.

###  4.2. SMC

The second column of Figures 5 and 6 show the abundance patterns of the SMC,
and the median abundance tracks (blue) are compared to the other galaxies in
Figure 7. The SMC only gets as metal-rich as [Fe/H] $\simeq$ -0.6 and [Mg/H]
$\simeq$ -0.7, $\sim$ 0.3-0.4 dex less than the LMC. This is an expectation
from the established mass-metallicity relation in Local Group dwarf galaxies
(e.g., Kirby et al. 2010), where the more massive galaxies tend to be more
metal-rich. However, the most metal-rich stars of the SMC are still $\sim$ 0.5
dex more metal poor than the most metal-rich stars in Sgr.

####  4.2.1 O, Mg, Si, and Ca

The $\alpha$-elements of the APOGEE SMC sample were first explored in Nidever
et al. (2020), where it was noted that the SMC also experienced very weak (low
efficiency) early SF. This is shown in the O, Mg, Si, and Ca panels of Figure
5, where the SMC shows a declining $\alpha$-element abundance ratio from -2.2
$<$ [Fe/H] $<$ -1.5. The [$\alpha$/Fe] abundances for the SMC over this range
are $\sim$ 0.05 dex lower than the LMC [$\alpha$/Fe] abundances. When using Mg
as a reference element, this slightly deficient [$\alpha$/Fe]-[Fe/H] abundance
pattern manifests as a slightly enhanced [Fe/Mg]-[Mg/H] abundance pattern from
-2.0 $<$ [Mg/H] $<$ -1.0.

The [Mg/Fe]-[Fe/H] abundance pattern is similar to the LMC in that there is a
slight increase in [Mg/Fe] beginning at [Fe/H] $\simeq$ -1.3, with a peak at
[Fe/H] $\simeq$ -1.0, followed by a slight decrease. The [O/Fe], [Si/Fe], and
[Ca/Fe] abundance patterns are flat over this range. The [$\alpha$/Mg]-[Mg/H]
abundance patterns are nearly identical to the LMC, with the SMC only
extending to [Mg/H] $\simeq$ -0.8, $\sim$0.4 dex lower than the metal-rich
extent of the LMC.

####  4.2.2 Carbon and Nitrogen

Both the [(C+N)/Fe]-[Fe/H] and [(C+N)/Mg]-[Mg/H] abundance patterns of the SMC
are similar to those of the LMC. At [Fe/H] $>$ -0.8, the LMC [(C+N)/Fe]
abundance begins to increase with increasing [Fe/H] whereas the SMC appears to
remain flat before ending $\sim$ 0.3-0.4 dex below the MW trend. Because the
[(C+N)/Mg]-[Mg/H] abundance of the SMC follows that of the LMC, the slight
difference at the metal-rich end of the [(C+N)/Fe]-[Fe/H] abundance pattern is
likely due to different amount of Fe from Type Ia SNe between the two
galaxies.

####  4.2.3 Aluminum and Nickel

The Al and Ni abundance patterns of the SMC again are very similar to those of
the LMC. The SMC shows slight deficiencies in [Al/Fe] and [Ni/Fe] as compared
to the LMC at [Fe/H] $<$ -1.5, as well as at [Fe/H] $>$ -0.8. However, the
[Ni/Mg] and [Al/Mg] abundance patterns show that like for the other elements,
this difference is driven by a difference in Fe.

####  4.2.4 Cerium

The [Ce/Fe]-[Fe/H] and [Ce/Mg]-[Mg/H] patterns of the SMC are similar to those
of the LMC, including the apparent change in increase of [Ce/Mg] abundance. In
the case of the SMC, the respective slopes of the [Ce/Mg] increases are 1.6
and 0.9, with the break in the slope occurring at [Mg/H]$\sim$-1.3.

####  4.2.5 SMC Interpretations

The similarities between the SMC and LMC abundance patterns show that they
indeed had a similar chemical evolution history, with the LMC enriching to
higher metallicities than the SMC by $\sim$ 0.4 dex, potentially a consequence
of its larger mass. However, there are two subtle differences between the two.
First, the SMC had slightly weaker early star formation efficiency, as shown
by its slightly lower $\alpha$-element abundance for the metal-poor stars (or
enhanced [Fe/Mg]). Second, while the small rise of [Mg/Fe] at [Fe/H] $\simeq$
-1.0, and the change in slope of the [Ce/Mg]-[Mg/H] abundance pattern all
suggest the SMC experienced an increase of Type II SNe, this increase was
weaker than that in the LMC. We quantify the relative strengths and timing of
these star formation events in the galaxies in §5.3.

###  4.3. GSE

The middle columns of Figures 5 and 6 show the abundance pattern of GSE, and
the median tracks are plotted in green in Figure 7. The abundance patterns of
this dwarf were studied in detail before it was even confirmed to be a
separate entity (e.g., Nissen & Schuster 2010; Schuster et al. 2012; Hawkins
et al. 2015; Fernández-Alvar et al. 2018; Hayes et al. 2018). The
characteristic abundance pattern of this galaxy is the declining [$\alpha$/Fe]
abundance pattern with increasing [Fe/H] that occurs at lower [Fe/H] values
than the MW (-1.2 $\lesssim$ [Fe/H] $\lesssim$ -0.7), resulting in a
“separate” sequence from the MW disk sequences. There have been some recent
works that have fit chemical evolution models to this abundance pattern,
finding one major star formation epoch that was cut off some 10 Gyr ago,
presumably by its in-fall onto the MW environment (e.g., Fernández-Alvar et
al. 2018; Gallart et al. 2019; Vincenzo et al. 2019).

####  4.3.1 O, Mg, Si, and Ca

The $\alpha$-element abundance patterns of the GSE look like a more metal-poor
MW high-$\alpha$ disk track. The $\alpha$ elements are relatively flat at
[Fe/H] $<$ -1.3, but decline at [Fe/H] $>$ -1.2, with the most metal-rich GSE
stars reaching solar [$\alpha$/Fe] abundances. Compared to the other dwarf
galaxies, GSE is enhanced in [$\alpha$/Fe] over the metallicity range -1.5 $<$
[Fe/H] $<$ -0.7, but still $\sim$ 0.10-0.15 dex below the MW high-$\alpha$
sequence. The difference in Fe abundance at fixed [Mg/H] is highlighted in the
[Fe/Mg]-[Mg/H] panel of Figure 7, where the GSE abundance pattern lies much
closer to the MW high-$\alpha$ sequence (low-Fe) than that of the other dwarf
galaxies.

The [O/Mg], [Si/Mg], and [Ca/Mg] abundances of GSE are all within $\sim$ 0.05
dex of solar over its full metallicity range, consistent with production by a
population of massive stars that is similar to the MW’s. Relative to the other
dwarf galaxies, [O/Mg] and [Si/Mg] are nearly indistinguishable, but [Ca/Mg]
is slightly depressed, perhaps because Ca has a larger Type Ia SNe
contribution and the Type Ia enrichment of GSE is lower as shown by its
depressed [Fe/Mg].

####  4.3.2 Carbon and Nitrogen

Unlike the MCs, the [(C+N)/Fe] abundances of the majority of GSE stars are
flat across nearly the entire metallicity range, with some of the more metal-
poor stars scattering to higher values of [(C+N)/Fe]. The [(C+N)/Mg]-[Mg/H]
abundance pattern of GSE is a metal-poor extension of the MW high-$\alpha$
sequence (perhaps best seen in the upper-right panel of Figure 7), with the
GSE abundance pattern perhaps being slightly enhanced by $\sim$ 0.05 dex, but
still deficient as compared to the other dwarf galaxies.

####  4.3.3 Aluminum and Nickel

Aluminum is one of the elements that literature works have often used to
select out what were then referred to as “accreted halo” stars from MW samples
(e.g., Hawkins et al. 2015), and the [Al/Fe]-[Fe/H] abundance patterns of GSE
presented here show that the GSE stars with [Fe/H] $>$ -1.2 are $\sim$ 0.2-0.3
dex deficient from the MW. This deficiency is shared by the other dwarf
galaxies, although the [Al/Fe]-[Fe/H] abundance patterns of the dwarf galaxies
differ slightly in shape from each other. However, the [Al/Mg]-[Mg/H]
abundance patterns emphasize that the differences among the dwarfs are again
driven by differences in Fe rather than differences in Al, as nearly all dwarf
galaxies share the same [Al/Mg] abundance pattern. Their trends remain
substantially below an extension of the MW [Al/Mg] trend.

Similar to the $\alpha$ elements, the [Ni/Fe]-[Fe/H] abundance pattern is
slightly deficient ($\sim$ 0.05 dex from the most metal-rich stars) as
compared to the MW abundance pattern, but still enhanced as compared to the
other dwarf galaxies ($\sim$ 0.05 dex). The [Ni/Mg] abundance of GSE is closer
to the pure Type II abundance ratio of the MW high-$\alpha$ disk, slightly
below that of the other dwarf galaxies.

####  4.3.4 Cerium

The [Ce/Fe]-[Fe/H] abundance pattern of GSE is similar to the other dwarf
galaxies. However, the [Ce/Mg]-[Mg/H] abundance plots show that at fixed
[Mg/H], GSE is slightly deficient in [Ce/Mg] ($\sim$ 0.10-0.15 dex) as
compared to the other dwarf galaxies.

####  4.3.5 GSE Interpretations

The relatively simple $\alpha$-element abundance patterns can be explained by
Type II SNe dominating at low metallicities, before Type Ia SNe exploding
after some time delay, diluting the $\alpha$ elements as Fe is added to the
ISM in large quantities (e.g., Tinsley 1979). Whatever extended star formation
GSE might have had was cutoff by its proximity to the MW. As such, we see no
sign of flat or increasing $\alpha$-element abundance patterns suggesting a
starburst like the MCs, or any extended SFH. However, the fact that GSE was
$\alpha$-element enhanced until [Fe/H] $\sim$ -1.2 shows that the early SF of
this galaxy was much more efficient than the early SF of the MCs, which were
$\alpha$-element enhanced until [Fe/H] $\sim$ -2.2. This difference in star
formation history also results in slightly enhanced [Al/Fe]-[Fe/H] and
[Ni/Fe]-[Fe/H] abundance patterns as compared to the other dwarf galaxies, but
these differences are largely driven by the “extra” Fe from the increased
relative contribution from Type Ia SNe in the other dwarf galaxies.

The slight deficiencies observed in [Ce/Mg] and [(C+N)/Mg] observed for GSE
suggest that GSE had slightly lower contributions from AGB stars to its
evolution as compared to these galaxies. This is expected if GSE only evolved
over the course of 2-4 Gyr, before large amounts of AGB stars could contribute
to its evolution.

###  4.4. Sgr

The chemistry of the Sgr dwarf has been studied by numerous authors (e.g.,
Chou et al. 2007; Sbordone et al. 2007; McWilliam et al. 2013; Hasselquist et
al. 2017; Carlin et al. 2018; Hansen et al. 2018), with Hayes et al. (2020)
analyzing the largest sample of core and stream stars using APOGEE DR16. In
general, these analyses all find the [X/Fe] abundances of the more metal-rich
stars in the Sgr core to be below the MW abundance trends. Interpretations of
such sub-solar abundance ratios range from high Type Ia/Type II SNe ratio to
top-light IMF. Here we analyze a sample of stars that is essentially an
expanded sample of Hayes et al. (2020).

While a detailed analysis of the spatial dependence of the chemical abundance
patterns of Sgr is beyond the scope of this work, we find that the Sgr stream
sample is $\sim$ 0.5 dex more metal-poor than the main body sample (see e.g.,
Hayes et al. 2020). However, we verify that stars with similar metallicities
between the two samples have near-identical chemical abundance patterns (see
§A.3 for more details).

####  4.4.1 O, Mg, Si, and Ca

The $\alpha$-elements in Sgr smoothly decline from -2.5 $<$ [Fe/H] $<$ -0.9,
going from the MW “halo” high-$\alpha$ plateau at the metal-poor end to below
the MW low-$\alpha$ “thin” disk trend at [Fe/H] = -0.9. Sgr begins this
decline at a slightly higher metallicity than the MCs, but a lower metallicity
than GSE. At [Fe/H] $>$ -0.9, the [O/Fe], [Si/Fe] and [Ca/Fe] abundances are
nearly flat at solar or slightly sub-solar values, but the [Mg/Fe] abundance
shows a slight increase followed by a decrease, as also observed in the SMC.
The [$\alpha$/Fe] abundance of Sgr at [Fe/H] $>$ -0.9 remains $\sim$ 0.1 dex
below the LMC trend and MW low-$\alpha$ sequence.

While Sgr extends to slightly higher values of [Fe/H] than the LMC, both
galaxies enriched to nearly the same level of [Mg/H], with the Sgr abundance
trend being deficient in [Fe/Mg] as compared to the MCs at [Fe/H] $>$ -1.0,
but enhanced at [Fe/H] $>$ -1.0. The Sgr stars with [Mg/H] $>$ -0.5 are very
slightly enhanced in [Ca/Mg] as compared to the LMC, but otherwise the
[Ca/Mg], [O/Mg], and [Si/Mg] patterns are nearly identical to those of the
LMC.

####  4.4.2 Carbon and Nitrogen

The [(C+N)/Fe]-[Fe/H] abundance pattern of Sgr is similar to that of the LMC.
The increase in [(C+N)/Fe] occurs at [Fe/H] $\simeq$ -0.8 for both galaxies,
but the slope of the increase with [Fe/H] is shallower in Sgr than the LMC, so
the sequences diverge at higher [Fe/H].

At [Mg/H] $>$ -0.7, the Sgr [(C+N)/Mg] abundance trend is $\sim$ 0.05 dex
above the LMC trend, with the most metal-rich Sgr stars intersecting the MW
low-$\alpha$ trend, showing that at these metallicities Sgr formed stars with
an AGB/Type II SNe ratio that was closer to that of the MW low-$\alpha$ disk.

####  4.4.3 Aluminum and Nickel

The [Al/Fe] abundance pattern of Sgr is $\sim$ 0.4 dex below the MW trend at
[Fe/H] $>$ -0.8. This is even more deficient than the other galaxies mentioned
thus far. However, as shown in the [Al/Mg] abundance plane in Figure 6 and in
Figure 7, the Sgr [Al/Mg]-[Mg/H] abundance pattern is nearly indistinguishable
from the other dwarf galaxies, with both the LMC and Sgr remaining noticeably
deficient ($\sim$ 0.2 dex) compare to the MW in [Al/Mg] at [Mg/H] $>$ -0.7.

The [Ni/Fe]-[Fe/H] pattern of Sgr largely follows that of the LMC, but it
continues to decline at [Fe/H] $>$ -0.9, at which point the LMC [Ni/Fe]-[Fe/H]
abundance patterns becomes flat/slightly increasing. The [Ni/Mg]-[Mg/H]
pattern of Sgr at [Mg/H] $>$ -0.8 lies in between the MW low-$\alpha$ sequence
and the LMC. The [Ni/Mg] differences follow the [Fe/Mg] differences, which
suggests that they are driven by differing levels of Type Ia SNe enrichment.

####  4.4.4 Cerium

The [Ce/Fe]-[Fe/H] abundance pattern of Sgr is similar to those of the other
galaxies, with the most metal-rich Sgr stars being enhanced in [Ce/Fe] as
compared to the MW stars. The median tracks in Figure 7 show that the most
metal-rich Sgr stars are slightly enhanced in [Ce/Mg] as compared to the LMC,
and moderately enhanced ($\sim$ 0.2 dex) as compared to the MW.

####  4.4.5 Sgr Interpretations

The $\alpha$-element abundance patterns show that early on in its evolution,
Sgr experienced relatively weak star formation as compared to the MW and GSE,
but stronger than the MCs and Fnx. Sgr then evolved to a much higher Type
Ia/Type II SNe ratio than the other dwarf galaxies, with a [Fe/Mg] ratio that
is enhanced over the MCs and MW low-$\alpha$ sequence at [Mg/H] $>$ -1.0.
Despite this clear difference in early star formation efficiency, Sgr and LMC
enrich to nearly the same levels of [Fe/H], with Sgr extending to
metallicities that are $\sim$ 0.2 dex higher than the LMC. The increased early
SFE and enhanced enrichment is unexpected in the paradigm of the mass-
metallicity relationship (Kirby et al., 2011), as the Sgr dwarf was thought to
be much less massive than the LMC. However, the two galaxies do enrich to the
same level of [Mg/H], implying the tension is somewhat reduced if [Mg/H] is
used to track metallicity instead of [Fe/H]. To more accurately analyze where
these two galaxies lie on the mass-metallicity relationship, we would need to
better account for selection biases, which is beyond the scope of this work.
Both the final metallicity and the early SFE seem to show Sgr behaving as
though it were a fairly massive dwarf galaxy.

The flat, or near-flat, in the case of Mg, [$\alpha$/Fe]-[Fe/H] abundance
patterns at [Fe/H] $>$ -0.9 imply that Sgr did experience some extended SF,
with an increase in Mg from Type II SNe preventing the [Fe/Mg] abundance from
rising further. This extended star formation event could have been started as
Sgr began falling into the MW. As shown in Hayes et al. (2020), the Sgr stream
does not contain stars with [Fe/H] $\gtrsim$ -0.50, but the Sgr [$\alpha$/Fe]
abundance becomes flat with increasing [Fe/H] at [Fe/H] $\sim$ -0.9. So the
extended star formation occurred before some stars were stripped as well as
after, plausibly corresponding with pericenter passages through the disk of
the MW (see also Ruiz-Lara et al. 2020a).

The low [Ni/Fe] in Sgr was interpreted as evidence for a top-light IMF in some
literature works (e.g., Hasselquist et al. 2017). However, analyses of MW
median abundance trends implies that Type II SNe contribute a larger fraction
of Ni than of Fe (Weinberg et al., 2019), so this deficiency could also arise
from differences in the Type Ia/Type II SNe ratios. Both the [Ni/Fe] and
[Al/Fe] abundance patterns can largely be attributed to Sgr evolving to a
higher Ia/II ratio than the MW and MCs, increasing the amount of Fe in Sgr.
However, Sgr shares the peculiar deficiency relative to the MW in [Al/Mg] at
[Mg/H] $>$ -0.5, which is plausibly explained by more metal-poor Type II SNe
contributing to the enrichment than the metallicity of those SNe that
contributed to the Al enrichment in Sgr, perhaps because of its lower SFE.

The [(C+N)/Mg] and [Ce/Mg] abundance patterns imply that Sgr had more
contribution from AGB stars to its enrichment than the LMC and the MW. This is
perhaps an expectation given the higher Type Ia/Type II SNe ratio in Sgr, as
implied by the other abundance patterns, allowing for a stronger AGB
contribution as well.

###  4.5. Fnx

The abundances of Fnx have been studied in a variety of literature studies,
some of which are comparable in number to what we have in APOGEE. In general,
these studies find that Fnx exhibits a relatively metal-poor $\alpha$-element
abundance “knee” (e.g., Hendricks et al. 2014), with sub-MW [$\alpha$/Fe]
abundance ratios at [Fe/H] $>$ -1.5 (e.g., Letarte et al. 2010; Hendricks et
al. 2014). These studies suggest Fnx underwent some extended SFH and formed
stars from gas with a larger Type Ia/Type II SNe ratio than the MW at similar
metallicity. The APOGEE data, shown in the right columns of Figure 5 and 6,
contains Fnx stars with -2.2 $<$ [Fe/H] $<$ -0.5. However, because the Fnx
sample is generally lower in S/N as compared to the other galaxies, most of
our analysis is focused on the Fnx stars with [Fe/H] $>-1.2$, as the stars
more metal poor than this have larger abundance uncertainties. The APOGEE Fnx
sample is also relatively sparse at low-metallicity, consisting of $\sim$20
stars with -2.2 $<$ [Fe/H] $<$ -1.2.

####  4.5.1 O, Mg, Si, and Ca

While it is difficult to analyze the metal-poor “knee” of Fnx using this
APOGEE sample, the $\alpha$-element abundances decline from -2.2 $<$ [Fe/H]
$<$ -1.2. This is a similar range of decrease as the MCs, although Fnx reaches
a much more deficient [$\alpha$/Fe] abundance at [Fe/H] = -1.2 than the MCs
($\sim$ 0.2 dex deficient). At [Fe/H] $>$ -1.2, there is a slight increase in
the $\alpha$-element abundances, with the most metal-rich Fnx stars reaching
the same [$\alpha$/Fe] abundance of the Sgr stars at [Fe/H] $>$ -0.8.

The exceptionally low [Mg/Fe]-[Fe/H] manifests as an exceptionally enhanced
[Fe/Mg]-[Mg/H] abundance pattern, where for fixed [Mg/H], Fnx is $\sim$0.2 dex
enhanced in Fe from the MCs, $\sim$0.3 dex enhanced from GSE, and $\sim$0.4
dex enhanced over the MW high-$\alpha$ sequence. Fnx is also enhanced in
[Ca/Mg] relative to the other galaxies at [Mg/H] $<$ -1.0, but is nearly
identical to the other galaxies in [O/Mg] and [Si/Mg].

####  4.5.2 Carbon and Nitrogen

Like the other galaxies, Fnx shows a slight increase in [(C+N)/Fe] with [Fe/H]
at [Fe/H] $>$ -1.0, but even the most metal-rich Fnx stars remain $\sim$ 0.3
dex below the MW trend. At fixed [Mg/H], Fnx is the most enhanced galaxy in
[(C+N)/Mg], with an abundance that is $\sim$ 0.1 dex above the MCs and Sgr
over the range -1.5 $<$ [Mg/H] $<$ -1.0.

####  4.5.3 Aluminum and Nickel

Despite having the most deficient [Al/Fe]-[Fe/H] pattern of all of the
galaxies, the Fnx [Al/Mg] is nearly identical to the other dwarf galaxies. Fnx
is also most deficient in [Ni/Fe], with [Ni/Fe] $\simeq$ -0.1 dex across much
of the metallicity range, $\sim$ 0.1 dex below the MCs and Sgr, although the
most metal-rich Sgr stars reach nearly this low [Ni/Fe] abundance. The [Ni/Mg]
abundance of Fnx is enhanced compared to GSE and the high-$\alpha$ MW
sequence, but about the same as the MCs and Sgr, at least at [Mg/H] $>$ -1.5.

####  4.5.4 Cerium

The [Ce/Fe]-[Fe/H] abundance pattern of Fnx largely traces those of the other
galaxies, although Ce is only measurable for $\sim$ 40% of the Fnx sample. At
-1.4 $<$ [Mg/H] $<$ -1.0, Fornax is 0.2-0.4 dex enhanced in [Ce/Mg] relative
to the other dwarf galaxies, and 0.5 dex enhanced relative to the MW
high-$\alpha$ sequence. This level of enhancement in Fnx at [Mg/H] = -1.0 is
similar to that of the MW low-$\alpha$ sequence at [Mg/H] $\sim$ -0.2.

####  4.5.5 Fnx Interpretations

Fnx is the most striking outlier among the five dwarf galaxies, in [O/Fe],
[Mg/Fe], [Si/Fe], [Ni/Fe], [(C+N)/Mg], [Ca/Mg], and to a lesser extend,
[Ce/Mg]. Possibly these differences could imply different IMF-averaged yields
from Fnx stars, e.g., Type II SNe that produced more Fe relative to
$\alpha$-elements. Another possibility is winds that preferentially ejected
Type II SNe products. Or, Fnx could simply have a SFH that led to an
exceptionally high ratio of Type Ia/Type II SNe enrichment. A high relative
contribution of Type Ia SNe could explain most of these anomalies, and a
similarly high contribution of AGB enrichment could explain high [(C+N)/Mg]
and [Ce/Mg] ratios.

###  4.6. [C/N] as an Age Indicator

As has now been shown in many works (e.g., Masseron & Gilmore 2015; Martig et
al. 2016; Ness et al. 2016; Hasselquist et al. 2019), we can use the APOGEE
[C/N] abundance ratio as a mass/age indicator for APOGEE red giant stars. More
massive stars mix a larger amount of CNO-processed material into their
convective envelopes when ascending the red giant branch, which lowers their
[C/N] abundance ratio because C is depleted and N is enhanced during CNO
burning. However, the [C/N] abundance is only a reliable mass indicator at
[Fe/H] $\gtrsim$ -0.6, below which some extra mixing occurs to further alter
the [C/N] abundance (see e.g., Shetrone et al. 2019). We therefore limit the
following [C/N]-age analysis to these metallicities, meaning that we only
study the [C/N] abundance patterns of the more metal-rich LMC and Sgr stars.

In Figure 8 we show how the [C/N] abundance tracks of these two galaxies as
compared to those of the MW, again selecting a MW comparison sample of 3600 K
$<$ Teff $<$ 4200 K to remove the effects of potential Teff systematic
uncertainties on abundance determination. As was done in Figure 7, we
calculate medians in bins of 30 stars, and plot those medians as well as the
standard deviations.

Figure 8.— [C/N] as compared to the MW just for Sgr (orange) and LMC (red).
Running medians of 30 stars per bin are shown for the dwarf galaxies, along
with the standard deviation in each bin. The MW sample is plotted as a
grayscale density image.

From Figure 8 we see that the Sgr stars show a [C/N] abundance pattern that
falls in the same region of this abundance space as the MW low-$\alpha$ or
“thin” disk stars ([C/N] $\simeq$ -0.3). This suggests a median age of the
stars at these [Fe/H] of 3-6 Gyr (e.g., Bensby et al. 2014; Martig et al.
2016; Ness et al. 2016). This age estimate of the metal-rich Sgr stars is
qualitatively consistent with the “intermediate age metal-rich population”
described in Alfaro-Cuello et al. (2019), who found that the stars in their
sample corresponding to metal-rich Sgr stars had a mean metallicity of [Fe/H]
= 0.29 $\pm$ 0.16 and mean age of 4.28 $\pm$ 1.16 Gyr. The LMC stars, on the
other hand, have median [C/N] abundances that are below the Sgr trend by
0.2-0.3 dex across the entire metallicity range. This implies an age of these
stars of $<$ 3 Gyr. However, the larger standard deviation in these bins
implies an age range at fixed metallicity, one that is potentially spatially
dependent.

While we do not explicitly map to age in this work, Hasselquist et al. (2020)
derived ages for a few of these metal-rich stars and found a median age of the
LMC stars of 2 Gyr, and a median age of the Sgr stars of 5 Gyr. Additionally,
Povick et al. in prep derive ages for these stars and find that most stars
with [Fe/H] $>$ -0.5 are younger than 2 Gyr. This is consistent with the
results of the $\alpha$-element abundances presented above and in Nidever et
al. (2020), which highlight that the metal-rich LMC stars likely formed in a
recent burst of star formation. This picture is also consistent with
literature studies of the SFH of the LMC (e.g., Harris & Zaritsky 2009; Weisz
et al. 2013; Monteagudo et al. 2018; Ruiz-Lara et al. 2020b; Nidever et al.
2021). Our interpretation presumes that the birth [C/N] ratios of the metal-
rich Sgr, LMC, and low-$\alpha$ MW sequence are similar such that these
differences in [C/N] reflect differences in dredge-up materials that in turn
reflect differences in stellar mass.

###  4.7. Chemical Abundance Summary

The $\alpha$ elements, O, Mg, Si, and Ca, show that out of all these dwarf
galaxies, GSE had the highest early star formation efficiency, followed by
Sgr, then the MCs. Our Fnx sample does not contain enough metal-poor stars to
precisely place its early star formation efficiency in comparison to the other
galaxies, but we do find that Fnx evolved to the highest Type Ia/Type II SNe
ratio, with a [Mg/Fe] abundance that is $\sim$0.15 dex below the MCs and Sgr
at [Fe/H] = -1.2. All galaxies except for GSE show a flattening or even
increase in their $\alpha$-element abundance pattern ([$\alpha$/Fe]),
suggesting an extended star formation event that polluted the ISM with many
more Type II SNe. The LMC had the strongest second star formation event, which
actually slightly enhanced the [$\alpha$/Fe] abundance patterns. The [C/N]
abundance patterns suggest that this strong second star formation event
occurred at more recent times than the second star formation epoch in Sgr.

All of the dwarf galaxies are deficient in [Ni/Fe] to some level as compared
to the MW, with GSE being slightly deficient ($\sim$ 0.1 dex at most) and Fnx
being the most deficient ($\sim$ 0.35 dex at most). However, the fact that the
[Ni/Mg] abundances of these galaxies are below the MW low-$\alpha$ sequence
suggests that there is some metallicity dependence on the production of Ni,
since the enhanced Type Ia/Type II SNe ratio implied by the $\alpha$-element
abundance pattern does not not result in an enhanced [Ni/Mg] abundance.
Another plausible explanation of deficient [Ni/Fe] is the contribution of sub-
Chandrasekhar Type Ia SNe to the chemical enrichment of a galaxy (e.g.,
McWilliam et al. 2018; Hill et al. 2019; Kirby et al. 2019), although Kirby et
al. (2019) finds minimal evidence for this in the dwarf galaxies that had
extended star formation histories (e.g., Fornax), favoring the metallicity-
dependent production of Ni as the explanation for the abundance patterns
presented here.

More metal-poor SNe is also a plausible explanation for the deficient [Al/Mg]
abundances of the dwarf galaxies, with the stars forming at [Mg/H] $>$ -0.7
forming from gas that was polluted preferentially bye lower metallicity SNe
than the MW sequences, which evolved much quicker.

The [(C+N)/Mg] and [Ce/Mg] abundance patterns show that all dwarf galaxies had
higher contributions to their evolution from AGB stars than the MW
high-$\alpha$ sequence. Compared to each other over the metallicity range
-1.5, $<$ [Mg/H] $<$ -1.0, GSE had the weakest contribution from AGB stars,
followed by Sgr, then the MCs, and finally Fnx. Only the LMC and Sgr evolved
substantially past [Mg/H] = -1.0, at which point the relative AGB contribution
to their chemical enrichment diverged, with the LMC experiencing an increase
in Mg from the strong starburst.

From these chemical abundance comparisons, we find evidence that galaxies in
denser environments undergo high-efficiency formation events early on in their
histories. Conversely, more isolated galaxies have very low-efficiency star
formation events early on, and form apparently large fractions of their stars
as a result of interactions: Sgr with the MW (e.g., Ruiz-Lara et al. 2020a),
MCs interacting with each other, and Fnx with a small merger (e.g., Coleman et
al. 2005; Leung et al. 2020 ).

##  5\. Chemical Evolution Modeling

In this section, we implement chemical evolution models to infer physical
parameters of the star formation histories of these galaxies. Note that we are
using these tools to estimate the star formation histories of these galaxies
using the APOGEE chemistry alone. This allows us to quantify the relative
strengths of the starbursts of the LMC and SMC, for example. While we do
compare these star formation histories to photometric studies in §6.2, a much
more quantitative and robust analysis of these data can be done in which the
photometry is combined with the spectroscopic abundance data, resulting in
much tighter constraints of the star formation histories. This analysis is
beyond the scope of this work.

To extract parameters of the SFHs of each galaxy, we adopt two chemical
evolution codes: flexCE (Andrews et al., 2017) and the model described in Lian
et al. (2018) and Lian et al. (2020b), hereafter referred to as “the Lian
model”.

While the models are similar at a fundamental level, there are several
distinct differences (explained in detail in Appendix B) that make the
inclusion of both of them valuable. First, the flexCE model was tuned in its
yields and fiducial parameters to match the APOGEE [O/Fe]-[Fe/H] abundance
pattern (which tracks very closely to [Si/Fe]; see Andrews et al. 2017). O is
an $\alpha$-element with nucleosynthetic yields that are thought to be well
understood (e.g., Kobayashi et al. 2006). However, the APOGEE O abundances are
not as well-measured across the HR diagram as Si abundances are. Therefore, we
only fit flexCE model tracks to [Si/Fe]-[Fe/H] abundances. The Lian model, on
the other hand, has been tuned to fit the APOGEE [Mg/Fe]-[Fe/H] abundance
plane.

The model codes are also parameterized differently, which we describe both
below and in §B. Results of the modeled star formation histories are shown and
discussed in §5.3. In all cases where we consider bursts of star formation, we
implement them as time-localized changes to the star formation efficiency,
with a smooth gas accretion history. The effects of efficiency-driven
starbursts and accretion-driven starbursts on chemical evolution are somewhat
different (see e.g., Johnson & Weinberg 2020). For satellite galaxies,
efficiency-driven bursts caused by dynamical interactions seem the somewhat
more natural choice, as the smaller gravitational potential of lower-mass
satellite galaxies reduces their chance of accretion-driven starbursts.

###  5.1. FlexCE Modeling

FlexCE is a one-zone, open-box, chemical evolution modeling code that is
broadly described in Andrews et al. (2016), which also provides a fiducial
model designed to fit the MW’s [O/Fe]-[Fe/H] chemical abundance pattern for
stars in the solar neighborhood. Naturally dwarf galaxies are expected to have
different SFHs than the MW, so many of these parameters must be changed to
produce appropriate dwarf galaxy chemical evolution models. However, we have
kept some of the fiducial parameters, because they are thought to vary less
from galaxy to galaxy or to be driven by stellar evolution rather than
galactic evolution.

For example, we retain the fiducial parameters for the chemical abundance
yields, Type Ia supernova delay-time distribution (which appears to be
constant across massive galaxies at least, Walcher et al., 2016), and the
initial mass function (IMF). Andrews et al. (2016) use a Kroupa IMF (Kroupa,
2001) for their MW model. While some past studies have speculated that
individual dwarf galaxies may have had a more top-light IMF (e.g., Carlin et
al., 2018), other studies have refuted these claims when observing lower
metallicity stars (Hansen et al., 2018). Any parameters not mentioned below or
given in Tables 3 and 4 use the fiducial values from Andrews et al. (2016).

There are two general modifications we make to the fiducial flexCE model. 1)
We use a delayed tau model for the gas inflow of our chemical evolution models
(motivated by cosmological simulation; e.g., Simha et al., 2014), allowing the
gas inflow to ramp up at early times in the universe before peaking and
falling off at later times. 2) We add a formulation for a time variable SFE to
flexCE, that scales the SFE up or down in a Gaussian shaped deviation from a
constant SFE. This addition allows us to temporarily cut off star formation or
produce a burst of star formation in our models. More information about these
modifications and how they were implemented can be found in Section B.0.1 and
B.0.2 for the inflow and SFE, respectively.

With these modifications we model the chemical abundances of our five
galaxies. Because there are many parameters that can produce variation in
chemical evolution models, we have chosen to vary only the parameters that
most strongly impact the chemistry (other than yields), and we use slightly
different strategies for different galaxies. For simplicity of modeling each
system we limit the number of variable parameters to four and fix the
remaining parameters at the values shown in Table 3.

For each system we allow the SFE and outflow mass loading factor to differ,
which control much of the global chemical abundance patterns that are
produced. The flexCE outflow parameterization assumes that enriched ISM gas is
ejected proportionally to the the star formation rate, with the mass loading
factor, $\eta$, as the constant of proportionality (Andrews et al., 2016).
This is a relatively simple form for outflow, but allows the model to
generally track gas outflows due to stellar sources, such as stellar winds,
supernovae, stellar radiation pressure, etc. In addition to these parameters
we add a time variable SFE for all galaxies except GSE, since we don’t see any
complex features in its chemistry.

For the LMC and SMC, because we see a bump or rise in the chemical abundance
patterns that we believe is due to a recent burst of star formation, we fit
these systems by adding an increase in star formation that has a variable
timing and strength, with a fixed duration of $\sigma_{b}=750$ Myr, roughly
the duration of the increase in SFR modeled for the LMC in Nidever et al.
(2020).

Some literature works found that Sgr and Fnx have had a generally bursty star
formation history, with periods of star formation broken up by periods where
there is very little star formation (see e.g., Siegel et al. 2011 for Sgr and
e.g., Hendricks et al. 2014 for Fnx). To reproduce this type of variable star
formation we model these systems with a decrease in SFE to 1% of its baseline
value, with the time and duration of this decrease as free parameters.

For all five galaxies we fix the initial gas mass and inflow mass scale and
use the same values across all galaxies. While these galaxies do not have the
same masses, the overall mass scale (i.e., total mass) does not impact the
chemistry, and only the ratio of initial-to-inflow mass impacts the chemistry.
However, the initial gas mass has a minor effect that is largely degenerate
with other parameters we vary, so we have held this ratio constant for all
galaxies.

We also fix the inflow timescale of each galaxies’ model, which has some
impact on the chemistry, particularly the shape of the $\alpha$-knee, but we
consider this a secondary effect, and defer it to future study. For GSE, the
SMC, and the LMC, the timescale has been fixed to a value that roughly fits
the shape of the $\alpha$-knee and is early enough so that most of the
accretion happens before the range of starburst timings probed in the SMC and
LMC. Similarly for Sgr and Fnx we use a slightly earlier inflow timescale so
that most gas is accreted before the range of timescales for the stalls in
star formation that we fit.

Then for each galaxy, we produce a grid of chemical evolution models with the
variable parameters mentioned above. We initially test a broad ranges of
parameters before narrowing to the final grids used here. At a minimum we
require five grid steps in each dimension, but have expanded the initial grids
in dimensions where the best fit value lay near a grid edge to confirm the
validity of the best fit results. The values of the grid points and their
spacings are listed in Table 4, and parameters that are not varied are marked
by “$-$” with values listed in Table 3.

Table 3flexCE Fixed Parameters (§5.1 and §B) System | Initial Gas Mass | Inflow Mass Scale | Inflow Timescale | Burst Duration | Burst Strength
---|---|---|---|---|---
Name |  ${\rm M}_{0}$ (${\rm M}_{\odot}$) |  ${\rm M}_{\rm i}$ (${\rm M}_{\odot}$) |  $\tau_{\rm i}$ (Gyr) |  $\sigma_{\rm b}$ (Gyr) | $\rm F_{\rm b}$
LMC | $3\times 10^{9}$ | $6\times 10^{10}$ | 2 | 0.75 | $-$
SMC | $3\times 10^{9}$ | $6\times 10^{10}$ | 2 | 0.75 | $-$
Sgr | $3\times 10^{9}$ | $6\times 10^{10}$ | 1 | $-$ | 0.01
GSE | $3\times 10^{9}$ | $6\times 10^{10}$ | 2.5 | $-$ | $-$
Fnx | $3\times 10^{9}$ | $6\times 10^{10}$ | 1 | $-$ | 0.01

To fit our models, we compute the $\chi^{2}$ of each model’s resulting
[Si/Fe]-[Fe/H] track relative to the data for each system. As previously
mentioned, Si is used for this fitting, because it is both precisely measured
by APOGEE (Jönsson et al., 2020) and has well understood nucleosynthetic
yields that can match MW chemical abundance patterns (Andrews et al., 2016).
To obtain the $\chi^{2}$ of each model we first calculate the model $\chi^{2}$
using the distance of each observed star from the model track in
[Si/Fe]-[Fe/H] space and the magnitude of the star’s [Si/Fe] and [Fe/H]
uncertainties in that direction. We then also penalize models that evolve past
the maximum metallicity of each system with an extra term to the model
$\chi^{2}$ that is the distance of each model time step from the high
metallicity end of each galaxy scaled by the typical abundance uncertainties
at those metallcities. We only turn off this penalization for GSE because we
know that its star formation was cutoff after some time (which we use as a
check on our chemical evolution model for GSE), and for the last 1 Gyr of
evolution in the remaining galaxies, because we wouldn’t expect to observe RGB
stars of such young age.

To find the optimal solution for each of our fit parameters, we then take the
model with the minimum $\chi^{2}$ as our best fit. The best fit values of each
parameter can be found in Table 4 for our five galaxies.

Table 4flexCE Variable Parameters’ Model Grid Ranges (§5.1 and §B) System | SFE | Outflow | Burst Time | Burst Duration | Burst Strength
---|---|---|---|---|---
Name | (Gyr-1) | $\eta_{\rm wind}$ |  $\tau_{\rm b}$ (Gyr) |  $\sigma_{\rm b}$ (Gyr) | $\rm F_{\rm b}$
Model Grid
LMC | 0.01$-$0.03 ($\Delta=0.005$) | 2$-$10 ($\Delta=2$) | 8$-$12 ($\Delta=1$) | $-$ | 4$-$8 ($\Delta=1$)
SMC | 0.006$-$0.01 ($\Delta=0.001$) | 5$-$25 ($\Delta=5$) | 6$-$11 ($\Delta=1$) | $-$ | 2$-$10 ($\Delta=2$)
Sgr | 0.02$-$0.06 ($\Delta=0.01$) | 12.5$-$22.5 ($\Delta=2.5$) | 4$-$8 ($\Delta=1$) | 0.25$-$1.25 ($\Delta=0.25$) | $-$
GSE | 0.08$-$0.2 ($\Delta=0.01$) | 1$-$11 ($\Delta=1$) | $-$ | $-$ | $-$
Fornax | 0.01$-$0.05 ($\Delta=0.01$) | 20$-$120 ($\Delta=20$) | 2$-$8 ($\Delta=1$) | 1$-$6 ($\Delta=1$) | $-$
Best Fit
LMC | 0.015 | $\ \,\ \,2$ | 11 | $-$ | 6
SMC | 0.008 | $\ \,10$ | $\ \,7$ | $-$ | 4
Sgr | $0.03\ \,$ | $\ \,\ \,\ 17.5$ | $\ \,5$ | $\ \,\ 0.5$ | $-$
GSE | $0.14\ \,$ | $\ \,\ \,6$ | $\ \,-$ | $-$ | $-$
Fornax | $0.03\ \,$ | 100 | $\ \,6$ | 5 | $-$

###  5.2. Lian Modeling

The Lian chemical evolution model is a one-zone open-box model that considers
the metal production and depletion by star formation, gas accretion and
galactic winds. The star formation rate is determined from the gas mass
following the form of the Kennicutt-Schmidt star formation law (SFL, Kennicutt
1998), assuming a Kroupa IMF (Kroupa, 2001). The SFE is thus regulated by the
coefficient of the SFL; we assume a constant coefficient ($C_{\rm initial}$)
unless a starburst event occurs. A different version of this model with more
flexible gas accretion and star formation histories has been successfully
applied to interpret the stellar chemistry observations in various components
of the Milky Way, including the bulge (Lian et al., 2020c), inner disk (Lian
et al., 2020a), and outer disk (Lian et al., 2020b). For more details about
the nucleosynthesis prescription and development of the basic model, we refer
the reader to Lian et al. (2018) and Lian et al. (2020b).

We include here two major modifications of the Lian et al. (2018) and Lian et
al. (2020b) models. First, the gas inflow parameterization is simpler, with
our approach assuming gas accretion to decline exponentially (compare to
§5.1): $A(t)=A_{\rm initial}e^{-t/\tau_{\rm acc}}$, where $A_{\rm initial}$ is
the initial gas accretion rate and $\tau_{\rm acc}$ is the declining
timescale. In this way, the burst event is described by three parameters: the
timescale ($\tau_{\rm burst}$), start time ($t_{\rm start}$) and duration
($\Delta t$) of the SFE increase. After the burst, the coefficient of the SFL
is set to decrease exponentially. Since this paper mainly focuses on the burst
event, for simplicity, we fix this decreasing timescale to be 0.2 Gyr.

The outflow is characterized as in flexCE, with the strength regulated by the
mass loading factor, $\lambda$. As stronger outflows remove more gas from the
galaxy, to keep the present-day stellar mass predicted by various models
fixed, we set the initial gas accretion rate to scale with the outflow
strength, i.e. $A_{\rm initial}\propto(1+\lambda)$.

We have six free parameters in total: two parameters characterizing the
initial gas accretion and star formation histories ($\tau_{\rm acc}$ and
$C_{\rm initial}$), three parameters describing the starburst event
($\tau_{\rm burst}$, $t_{\rm start}$, and $\Delta t$), and one parameter
determining the strength of gas outflow ($\lambda$), shown in Table 5.

We build a grid of models with each chemical evolution code and find the best-
fit model through chi-squared minimization. As in flexCE, we fit only to the
chemical evolution tracks and not to the density.

Table 5Lian Variable Parameters’ Model Grid Ranges (§5.2 and §B.0.4) System | Gas Inflow | Outflow | Star Burst
---|---|---|---
Name | $\tau_{acc}$ | Cinitial | $\lambda_{\rm wind}$ | $\tau_{\rm burst}$ | $t_{\rm start}$ |  $\Delta$ t
Grid
| 2, 10 | 0.001$-$0.1($\Delta$log = 0.5) | 0$-$20($\Delta$ = 5) | -0.5$-$-8($\Delta$log = 0.3) | 4$-$12($\Delta$ = 2) | 1$-$6($\Delta$=1)
Best Fit
LMC | 10 | 0.01 | $\ \,15$ | -2 | $\ \,10$ | 3
SMC | 10 | 0.01 |  20 |  -1 | $\ \,8$ | 1
Sgr | 2 |  $0.01\ \,$ |  10 |  -4 |  6 | 4
GSE | 2 |  $0.01\ \,$ | $\ \,5$ |  -2 |  - | 2
Fornax | 2 |  0.032 |  20 | -1 |  6 | 1

###  5.3. Chemical Evolution Modeling Results

Chemical evolution modeling results are shown in Figure 9 for flexCE and
Figure 10 for the Lian model. As before, each column shows a different dwarf
galaxy. The top row shows the best-fit model chemical track through the
abundance pattern, the middle row shows the star formation history of that
chemical track, and the bottom row shows the metallicity evolution as a
function of time. We describe the results in the following subsections, and
compare and contrast the model results in §5.4. Because the models are only
parameterized with a single burst in SF after the initial SF epoch, the models
are likely fitting to the most significant “burst” in a galaxy’s SFH that
provided the most stars with the ages that we probe with APOGEE.

Figure 9.— Top row: [Si/Fe]-[Fe/H] abundance space for each of the five dwarf
galaxies, along with their best-fit chemical evolution track as inferred from
the flexCE code (Andrews et al., 2017) over-plotted in black. Middle row: star
formation histories of each galaxy, normalized by the peak star formation
rate. Vertical dotted lines indicate the time of peak SF. Bottom row:
metallicity evolution with time for each dwarf galaxy. Horizontal dotted lines
indicate the [Fe/H] at the peak of the SFH. Figure 10.— Same as in Figure 9,
but with the Lian models that are fit to [Mg/Fe]-[Fe/H] instead of
[Si/Fe]-[Fe/H].

####  5.3.1 Magellanic Clouds

The flexCE results show that strong bursts are favored to match the abundance
patterns of both the LMC and SMC, although the burst in the SMC is somewhat
weaker, and occurred $\sim$ 4 Gyr earlier than the burst in the LMC. The burst
results in quick metallicity evolution, with the LMC enriching from [Fe/H]
$\simeq$ -0.8 to [Fe/H] $\simeq$ -0.3 in the last 2-3 Gyr. The SMC experienced
similar swift enrichment, but over a period of 5-8 Gyr ago, with the evolution
much slower in the last 2-3 Gyr.

The Lian results also favor bursts in the MCs, although the bursts are more
similar in relative strength between the two galaxies than the flexCE results.
The Lian models also predict a “dip” in star formation that reached a minimum
at 10 Gyr for the LMC and at 8 Gyr for the SMC, and show that the duration of
the burst is shorter for the SMC than the LMC. Like the flexCE results, the
Lian model results favor a scenario in which the SMC experienced a peak star
burst $\sim$ 4 Gyr before the LMC. Also like the flexCE models, the Lian
models show that the bursts result in rapid metallicity evolution, although
the metallicity evolution is more rapid than the flexCE results, and begins at
[Fe/H] = -1.3 rather than at [Fe/H] = -0.8. This is at least partially due to
the difference in how the two models are parameterized.

The flexCE models predict that all LMC stars with [Fe/H] $\gtrsim$ -0.7 should
be younger than 3-4 Gyr, and the Lian models predict the same age for stars
with [Fe/H] $\gtrsim$ -1.2. The [C/N] results in §4.6 suggest that the LMC
stars at [Fe/H] $>$ -0.6 are significantly younger than the MW thin disk stars
at the same metallicity, which is qualitatively consistent with these
predictions.

####  5.3.2 GSE

Both models find a SFH for GSE that peaks at early times and declines. Because
the gas inflow is treated differently in the two models, the flexCE models
show a broader SF peak located at a slightly later time, than the Lian model.
While the model tracks extend to present day, GSE reaches [Fe/H] = -0.5
(maximum observed metallicity) $\sim$ 5 Gyr into its evolution in the flexCE
models and 8-9 Gyr into its evolution in the Lian models, although the Lian
models show very slow GSE metallicity enrichment beginning at $\sim$5 Gyr into
its evolution. This is consistent with the picture that GSE merged with the MW
some 8-10 Gyr ago, thus cutting off this late evolution. Our results prefer a
merger some 7-9 Gyr ago.

In the flexCE models we adopt similar inflow timescales for GSE and the MCs
(2.5 Gyr vs. 2 Gyr), and the fit leads to a much higher (factor 10-20) SFE and
thus to a SFH that peaks at much earlier times. This result is driven by the
higher metallicity of the “knee” in the [Si/Fe]-[Fe/H] diagram. According to
the flexCE SFH, by 5 Gyr into its evolution, GSE achieved [Fe/H] = -0.5, as
compared to -1.2 and -1.5 for the LMC and SMC, respectively. The Lian models
show a similar result, with GSE enriching to [Fe/H] = -0.8 5 Gyr into its
evolution as compared to -1.4 and -1.55 for the LMC and SMC, respectively.
Here the SFE is similar between the MCs and GSE, and the strong early SF peak
in GSE arises from a short inflow timescale. In the flexCE model, it took the
LMC 10 Gyr to enrich to [Fe/H] = -0.7, which is about where GSE enriched to
before merging with the MW. In the Lian model, the LMC only attained GSE
metallicities at recent times, although GSE took $\sim$6 Gyr to reach [Fe/H] =
-0.7 instead of $\sim$4 Gyr in the flexCE model.

####  5.3.3 Sgr

As described in §5.3, the relatively flat $\alpha$-element abundance patterns
at [Fe/H] $>$ -0.8 suggest some kind of extended SFH. Both models find that a
second star formation epoch, beginning some 5-6 Gyr into its evolution and
rising above the declining trend from earlier times, is required in Sgr to
produce the flatter or “hooked” abundance $\alpha$-element abundance pattern.
Without such a secondary peak, the chemical evolution tracks show
monotonically decreasing [Si/Fe] or [Mg/Fe] with increasing [Fe/H], rather
than the slight flattening of the observations. In the flexCE model, the sharp
minimum of star formation at 5 Gyr produces the kink in the [Si/Fe]-[Fe/H]
abundance track, slightly improving the fit to the data. In both models, this
second SF epoch is not as strong relative to the earlier epoch, in contrast to
the MCs, and as such, the [$\alpha$/Fe] ratio is not enhanced like it is in
the MCs.

The early chemical enrichment of Sgr was in between GSE and the MCs in both
models (e.g., intermediate SFE), with Sgr enriching to [Fe/H] = -0.7 and -1.0
5 Gyr into its evolution for the flexCE model and the Lian model,
respectively. After this point, the flexCE model favor a shorter, stronger
burst, compared to a more sustained, weaker burst for the Lian model. In both
models, Sgr effectively stops forming stars 10 Gyr into its evolution, which
is consistent with observations of Sgr that show few or no young (age $<$ 2-3
Gyr) stars (e.g., Siegel et al. 2007), as well as the [C/N] inferences shown
in §4.6.

####  5.3.4 Fnx

As was the case for Sgr, both the flexCE and Lian models find support for a
second epoch of star formation in Fnx, although this second “burst” was much
weaker than the initial SF peak ($\sim$ 3 times weaker for the flexCE results
and $\sim$ 9 times weaker for the Lian model results). Even though Fnx has a
much lower stellar mass than the other galaxies, both models suggest that Fnx
enriched to nearly the same [Fe/H] as the SMC 5 Gyr into its evolution.

Like the MCs, Fnx is one of the galaxies where the [Mg/Fe]-[Fe/H] and
[Si/Fe]-[Fe/H] patterns differ most strongly from each other, which is likely
a source of at least some of the differences in results between the two
chemical evolution codes.

###  5.4. Summary and Model Comparison

In Figure 11 we show the SFHs of each galaxy for the flexCE results and Lian
model results, comparing the SFR (top row) and the cumulative star formation
(bottom row). The top row of Figure 11 is useful to compare the relative
shapes of the SFHs of the galaxies, but because the mass scale of the models
has not been adjusted such that the final stellar mass of the model matches
the observed stellar masses of each galaxy (see §5.1), the
normalization/scaling of the SFR of each galaxy is inaccurate.

The final stellar mass of each system in the flexCE models, for example, do,
however, match the mass ordering that observations suggest, with the final
stellar masses of $7.3\times 10^{9}$ M⊙ for the LMC, $2.3\times 10^{9}$ M⊙ for
the SMC, and $3.7\times 10^{8}$ M⊙ for Fnx. The final stellar masses of the
flexCE models for Sgr, $2.0\times 10^{9}$ M⊙, and GSE, $2.9\times 10^{9}$ M⊙
after 5 Gyr of evolution, are also consistent in suggesting that Sgr and GSE
may have been similar in mass to the SMC prior to their respective disruption
(see the discussion in §6.1). Nonetheless we remark that the resulting final
stellar masses are $\sim 5-10\times$ too high compared to observational
estimates (see §6.1 for observed masses; but note again as mentioned in §5.1,
the total mass scale does not impact the final chemical tracks). Therefore, a
better way to compare SFHs across galaxies from the models is to use the
cumulative star formation histories (CSFH), shown in the bottom row of Figure
11.

Both sets of models show weaker early SFH for the MCs as compared to the other
galaxies, and both models show that the MCs experienced peaks in SF that
occurred much later than the SF peaks in the other galaxies, with the most
significant period of enhanced SF in the SMC occurring $\sim$ 4 Gyr before the
LMC.

Figure 11.— Comparison of the derived SFHs for the two different model sets,
flexCE on the left and Lian on the right. The top rows shows the SFR as a
function of time, and the bottom rows shows the cumulative star formation over
time.

The model SFHs differ in the relative strengths of the bursts, with the SMC,
Sgr, and Fnx all showing weaker bursts in the Lian results than the flexCE
results. The Lian models also imply that GSE and Sgr each formed about 70% of
their stars in the first 4 Gyr of evolution, whereas the flexCE models show
Sgr forming 60% of its stars prior to this point, and GSE 40%. However, both
models predict GSE evolution continuing beyond the observed tracks, and
stopping them at the maximum observed [Fe/H] $\simeq$ -0.5 implies truncating
star formation at $t\simeq$ 5 Gyr in the flexCE model and $t\simeq$ 10 Gyr in
the Lian model, a plausible result of disruption or ram pressure stripping by
the MW. The substantially weaker burst for Fnx in the Lian models also results
in nearly all stars in Fnx forming by 6 Gyr into its evolution, whereas the
flexCE models find only 70% of the stars to have formed at this point.

##  6\. Discussion

In the following section we discuss what these SFHs mean in the greater
context of galaxy formation and evolution. We also compare our SFH results
from chemistry alone to those derived in the literature primarily through
photometry, as well as discuss future prospects.

###  6.1. Mass and Environmental Effects on Galaxy Evolution

The chemical abundance patterns and inferred SFHs highlight the importance of
galaxy environment for chemical evolution. McConnachie (2012) and references
therein tabulate the following stellar masses for the galaxies in our sample:
LMC = $1.5\times 10^{9}M_{\odot}$, SMC = $4.6\times 10^{8}M_{\odot}$, Sgr
(main body) = $2.1\times 10^{7}M_{\odot}$, and Fnx = $2.0\times
10^{7}M_{\odot}$. Sgr was much more massive in the past, with some studies
finding masses as high as $6.4\times 10^{8}M_{\odot}$ (e.g., Niederste-Ostholt
et al. 2010). Estimates for the stellar mass of GSE are generally in the range
$3-10\times 10^{8}M_{\odot}$ (e.g., Mackereth et al. 2019).

The LMC, GSE, SMC, and Sgr span about an order of magnitude in stellar mass,
with the LMC being the most massive. Fnx is at least another order of
magnitude less massive even than the SMC/GSE/Sgr. Despite its relatively low
present-day mass compared to the other galaxies, Sgr is the most enriched
dwarf galaxy, reaching slightly higher metallicities than the LMC. The SMC,
GSE, and Fnx have all enriched to nearly the same metallicity, despite their
vastly different stellar masses. What is very different across these dwarfs is
the environments in which they formed and evolved.

Currently, these galaxies are all well inside the MW environment, or have
already been accreted by the MW. However, GSE is thought to have formed close
to the MW and was accreted at early times (e.g., Gallart et al. 2019;
Mackereth et al. 2019), Sgr and Fnx at more intermediate times (e.g., Rocha et
al. 2012; Fillingham et al. 2019), and the MCs are only falling in recently,
having likely evolved in near isolation until now (e.g., Besla et al. 2016).
In the paradigm of Gallart et al. (2015), in which dwarfs galaxies are
assigned to two groups according to their SFH, we could consider the MCs to be
“slow dwarfs”, forming the bulk of their stars more recently, as compared to
the “fast dwarfs” (e.g., Sgr, GSE, and Fnx), that started their evolution with
a dominant early star formation event (see e.g., Shi et al. 2020 for similar
simulation results). However, even the MCs became “faster” dwarfs when they
began to interact with each other driving up the $\alpha$-element abundances.
This suggests that proximity to any galaxy, not just a more massive Milky Way,
can be important drivers in star formation history. Had the MCs not interacted
with each other, they would likely have a lot of gas, still, but contain far
fewer stars. The inferred SFH presented here suggests that without the
interactions between them, the MCs would have enriched to [Fe/H] $\simeq$ -0.7
for the LMC and [Fe/H] $\simeq$ \- 1.5 for the SMC.

There is good agreement in the literature that the MW and M31 environments
have strong effects on the quenching times of in-falling satellite galaxies,
with many low-mass galaxies (M∗ $<$ $10^{8}M_{\odot}$) quenching within
$\sim$2 Gyr of passing through the virial radii of the host galaxies (e.g.,
Rocha et al. 2012; Slater & Bell 2014; Fillingham et al. 2015; Weisz et al.
2015; Wetzel et al. 2015; Akins et al. 2021). This is likely a consequence of
ram pressure stripping effectively removing gas from these galaxies,
preventing further star formation (see e.g., Hester 2006; Bekki 2014;
Fillingham et al. 2016). Sgr was likely just massive enough to avoid fast
quenching from ram pressure stripping (e.g., Niederste-Ostholt et al. 2010),
but the mass of Fnx is low enough (M∗ $\sim 10^{7}M_{\odot}$, e.g.,
McConnachie 2012) such that it should have been quickly quenched when entering
the environment of the MW. However, the extended SFH of Fnx inferred from both
the APOGEE data presented here and other literature studies can be reconciled
with its low mass if the environmental quenching timescale also depends on
satellite orbit. Recent studies have found that not all of these low-mass
dwarfs are quenched, with the galaxies on more circular orbits and larger
pericenter passages (such as Fnx) having much longer quenching timescales
(e.g., Fillingham et al. 2019). Such “fortuitous” orbits have been found to
enhance star formation in some simulations (e.g., Di Cintio et al. 2021), and
observational evidence exists of Sgr and the MW undergoing enhanced SF epochs,
coincident with Sgr pericenter passages (Ruiz-Lara et al., 2020a)).

In addition to environment, the mass of a galaxy can also play an important
role in its evolution. The less massive dwarf spheroidal galaxies, such as
Sculptor, Draco, and Ursa Minor, have formed very few stars in recent times,
and have only enriched to [Fe/H] $\sim$ -1.0 or lower. Moreover, there is an
established mass-_mean_ metallicity relationship in the literature described
in Kirby et al. (2011), with more massive galaxies enriching to a higher mean
metallicity, plausibly because they are able to retain some of their gas that
is ejected from SNe. Because of APOGEE selection biases, it is difficult to
use the APOGEE mean metallicities to accurately place these galaxies on the
mass-metallicity relationship. However, Sgr likely has a much higher
metallicity for its present-day mass as compared to the SMC, and maybe even as
compared to the LMC. Fornax also likely has a mean metallicity that is closer
to the SMC than perhaps it should be for its mass. Conversely, another way to
view the discrepancy is that the MCs, having evolved in relative isolation
until recent times, are too metal-poor for their large stellar masses. While
works such as Reichert et al. (2020) and Hendricks et al. (2014) have shown
that Local Group galaxies tend to exhibit correlations between their
$\alpha$-element enrichment and luminosity, the MCs would also be an exception
to this correlation (see also Nidever et al. (2020)).

Geha et al. (2012) find that nearly all field galaxies with a stellar mass $<$
$10^{9}M_{\odot}$ are still forming stars today. Perhaps mass is the primary
fundamental driver for how enriched a given galaxy is, but galaxy-galaxy
interactions can push galaxies off of this relation, either by merging and
increasing the mass without too much extra star formation, or by falling into
the potential of a massive galaxy, where star formation is momentarily kick
started before the galaxy is disrupted or quenched.

###  6.2. Comparison to Photometric Star Formation Histories

This work is far from the first to derive star formation histories for these
galaxies. However, this is among the first work to derive/estimate star
formation histories from the chemical abundance patterns of multiple galaxies,
applying the same model frameworks to observations from nearly identical
setups. In the following section we compare the star formation histories we
measure above to those measured in the literature. Throughout this section we
use “photometric star formation histories (SFHs)” to refer to star formation
histories derived from color-magnitude diagrams. As described in greater
detail below, these photometric SFHs can vary in precision depending on
whether or not the photometry is deep enough to reach the old main sequence
turn-off (oMST, e.g., Ruiz-Lara et al. 2018). Moreover, most of the literature
photometric studies for these galaxies are small, pencil-beam patches of the
galaxies (typically the central regions) as compared to our samples, which
cover large fractions of the entire spatial extent of these galaxies.

####  6.2.1 The Magellanic Clouds

There have been many photometric studies of the SFHs of the MCs. In this
section we compare the MC chemical SFHs to the photometric studies of Weisz
(Weisz et al. 2013, 2014, Figure 12), Harris and Zartitsky (HZ, Harris &
Zaritsky 2004, 2009, Figure 13), and more recent SFHs derived from the Survey
of the MAgellanic Stellar History (SMASH, Nidever et al. 2017, 2021, Figure
13). The HZ work is ground-based, so is typically shallower photometry but
covers much of the same spatial regions of the MCs as our data. The Weisz work
is much deeper photometry from HST, but is of the central regions of the MCs.
The SMASH work is both deep and covers large spatial regions of the MCs.

Figure 12.— Comparison between the SFHs derived in this work and the SFHs
derived in Weisz et al. (2013) (LMC and SMC, top row) and Weisz et al. (2014)
(Fnx and Sgr, bottom row).  Figure 13.— Comparison of our inferred cumulative
SFHs to those of Harris & Zaritsky (2009), Harris & Zaritsky (2004), and SMASH
(Nidever et al., 2021) for the LMC (left) and SMC (right).

We find reasonable agreement between the various photometric SFHs of the LMC
and what we infer from the chemical evolution models fit to the APOGEE data.
In the upper-left panel of Figure 12, we find that the Weisz cumulative SFH
falls between what is derived for the two models from this work for the LMC at
older ages, but all 3 results are in agreement with the LMC forming $\sim$20%
of its stars in the last 2 Gyr. This is similar to the SFHs from HZ and SMASH
(shown in the left panel of Figure 12), although the SMASH SFHs suggest that
the LMC formed $\sim$40% of its stars by 4 Gyr into its evolution, which is
slightly higher than Weisz, and much higher than the $\sim$10% found in the HZ
work. This discrepancy is possibly due to the fact that the HZ work was not
deep enough to capture the oMST, resulting in more uncertain SFRs at early
times. The Lian model agrees well with the SMASH LMC SFH, and the flexCE
agrees well with the Harris & Zaritsky (2009) LMC SFH.

The SFH results for the LMC derived by Monteagudo et al. (2018) are
qualitatively similar to what is shown here. They find some spatial dependence
of the SFH, with the bar region of the LMC forming a higher fraction of total
stars at more recent times than the disk. Specifically, they find that the
disk regions of the LMC formed half of their stars 7-8 Gyr into its evolution,
whereas the bar had not formed half of their stars until 9-10 Gyr into the
galaxy’s evolution. Meschin et al. (2014) find similar results, and also that
the trend of larger fraction of stars formed at earlier times extends to the
outer regions of the LMC. A detailed comparison of the spatial dependence of
the SFH is beyond the scope of this work.

For the SMC, we find worse agreement in our inferred SFHs compared to the
Weisz SFH than we do for the LMC (upper-right panel of Figure 12).
Specifically, both models find a much larger fraction of SMC stars forming at
earlier times than the Weisz et al. (2013) work. This could be in part due to
the difference in spatial coverage, which is why there is slightly better
agreement with the SMASH work shown in the right panel of Figure 13, where the
flexCE, Lian, and SMASH CSFHs all show that the SMC formed $\sim$70-80% of its
stars in the first 8 Gyr of its evolution. A recent study by Rubele et al.
(2018) suggests significant enhancement of SF took place in the SMC beginning
100 Myr ago. Our sample selection cuts nearly all of these stars out (see
§A.1), but these stars still represent a small fraction of total stars formed
in the SMC. Future analysis confirming the reliability of results for massive
supergiants in APOGEE will allow for a chemical exploration of these more
massive, younger stars.

####  6.2.2 Sgr and Fnx

We compare the Weisz Sgr and Fnx SFHs to those that we infer in the bottom row
or Figure 12. The flexCE Fnx model reproduces a cumulative star formation
history that is very much like what is derived in Weisz et al. (2014), with
Fnx forming 20% of its stars in the last $\sim$ 4 Gyr. The Lian model, with
the much weaker secondary SF epoch, implies Fnx formed the vast majority of
its stars by 6 Gyr ago. Support for a recent burst in Fnx can be found
throughout the literature, including the recent work of Rusakov et al. (2021),
who find that Fnx underwent a strong starburst some 4-5 Gyr ago, one that was
close to or even exceeded the strength of the early SF event. This is more
consistent with our flexCE results, which shows a nearly equal strength second
burst in Fnx that peaked 4-5 Gyr ago. Hendricks et al. (2014) find chemical
evidence for a starburst in Fnx, like we do here in this work, but they
suggest the burst occurred at much earlier times than either the flexCE or
Lian models suggest. The more spatially-extended SFH work of de Boer et al.
(2012) shows Fnx underwent a more gradual enrichment from 3-8 Gyr ago,
enriching from [Fe/H] = -1.5 to [Fe/H] = -0.5, which is an enrichment rate
that is more consistent with the flexCE results.

The Sgr comparison is shown in the bottom-right panel of Figure 12. Neither
model matches well with the Weisz et al. (2014) SFH of Sgr, though they agree
well with each other. This could be due to the fact that our Sgr sample
contains many stream stars, whereas Weisz et al. (2014) was looking at the
main body of the galaxy, where the tidal interactions have preferentially
removed many metal-poor stars, including into the streams. However, all of the
star formation histories agree that Sgr formed nearly all of its stars by 3-4
Gyr ago. This is mostly in line with other photometric SFH studies, such as
Siegel et al. (2007), although we do not find the metal-rich youngest
populations that they find in the core. de Boer et al. (2015) find that the
Sgr stream stars exhibit a tight age-metallicity relation, enriching to [Fe/H]
= -0.7 by 5-7 Gyr ago, again consistent with both model results (see the
bottom row of Figures 9 and 10). Our SFH here also qualitatively agrees with
recent work by Garro et al. (2021), who analyzed the ages and metallicities of
the globular cluster population of Sgr, including 12 new clusters discovered
by Minniti et al. (2021). They find that Sgr formed its metal-rich (-0.9 $<$
[Fe/H] $<$ -0.3) globular clusters some 6-8 Gyr ago.

###  6.3. Future Prospects

We have restricted the parameter space of our chemical evolution models in
part for computational practicality in this exploratory study, but also
because we are constraining them with a single observable, the [Si/Fe]-[Fe/H]
or [Mg/Fe]-[Fe/H] track. In future work, we can allow greater model
flexibility by simultaneously employing these observables (including more than
just two chemical elements) and the photometric star formation histories
illustrated in Figures 12 and 13, and we can test or further constrain these
models using metallicity distribution functions (MDFs). Computing MDFs from
the metallicity distribution of observed APOGEE stars requires correcting for
selection biases; alternatively, one can incorporate selection effects into
the model and directly predict the observed distributions. For completeness,
we show and discuss the uncorrected MDFs in §C.

One natural route for such an investigation is to take the photometrically-
inferred star formation histories as a starting point, then derive the gas
accretion history that produces this star formation for given assumptions
about star formation efficiency. Fitting the evolutionary tracks will restrict
the model parameters, and model variations that predict different enrichment
vs. time will predict different MDFs. As our exploratory results already
suggest, chemical evolution constraints may make it possible to detect bursts
or other variations in the star formation history. Joint modeling can test the
need for more radical differences among the galaxies being considered, such as
different IMFs, different Type Ia SNe populations, different AGB yields that
could arise from systematic differences in stellar rotation, or differences in
outflow physics such as preferential ejection of Type II SNe products relative
to Type Ia SNe or AGB products.

##  7\. Conclusions

We have presented the APOGEE chemical abundance patterns for five MW dwarf
galaxies that span a range in mass and evolution environments. Our major
conclusions are summarized as follows:

  * •

The chemical abundance patterns of these five dwarf galaxies show very
different early star formation efficiencies, with GSE having had the
strongest, followed by Sgr, then the MCs. Fnx plausibly had an early star
formation efficiency similar to Sgr, but exhibits the lowest $\alpha$-element
abundance at [Fe/H] = -1.2, suggesting either a rapidly declining SFH or
outflows that preferentially ejected Type II SNe products.

  * •

All dwarf galaxies except for GSE show chemical signs of extended star
formation periods after the initial star formation epochs, with the LMC
showing an increasing [$\alpha$/Fe]-[Fe/H] abundance pattern, suggestive of a
more intense starburst compared to the other galaxies. The lower [C/N]
abundances of the metal-rich LMC stars suggest that they were formed at more
recent times than the Sgr and MW low-$\alpha$ sequence stars at the same
metallicity.

  * •

In median abundance trends, [X/Fe]-[Fe/H] and [X/Mg]-[Mg/H], Fnx is the
strongest outlier among these five dwarfs, followed by GSE. Tracks for the MCs
and Sgr are fairly similar except for low-metallicity [$\alpha$/Fe]
differences driven by star formation efficiency, and high-metallicity
[$\alpha$/Fe] differences driven by late star formation.

  * •

The C+N and Ce abundance patterns show that all galaxies had greater
contribution of AGB enrichment (relative to SNe contributions) to their
evolution as compared to the MW high-$\alpha$ sequence, with Fnx showing the
highest relative contributions and GSE showing the lowest at [Mg/H] $<$ -0.8.
However, the most metal-rich Sgr stars have the highest [Ce/Mg] abundances of
any galaxy, and therefore have had the largest relative contribution of AGB
stars to their enrichment.

  * •

The deficient [Al/Mg] abundances of the dwarf galaxies relative to the MW is
plausibly a result of the overall lower metallicity Type II SNe that occurred
in the dwarf galaxies as compared to the MW. Lower star formation efficiency
may lead to a great “lag” between the metallicity of the ISM and the
metallicity of the stars that enriched the ISM.

  * •

The deficient [Ni/Fe] abundances of the dwarf galaxies relative to both MW
sequences combined with the deficient [Ni/Mg] relative to the MW low-$\alpha$
sequence can be explained if the production of Ni is dependent on the
metallicity of the supernova progenitor.

We also use chemical evolution models to quantify some aspects of these
chemical abundance patterns, finding that the SMC also experienced a recent
enhancement of star formation, but this enhancement was weaker than the burst
in the LMC by a factor of $\sim$2-3, and occurring 2-4 Gyr before the burst in
the LMC. While not found to be coincident in the chemical evolution models, it
is likely that the increased star formation epochs in both galaxies are
results of their mutual interactions.

From the models, we infer similar extended star formation events occurring in
Sgr and Fnx some 3-6 Gyr ago, but these increases in star formation are small
compared to the initial bursts. Future works that are able to properly account
for selection biases can combine the photometric constraints on the SFHs with
the chemical abundance patterns and metallicity distribution functions to
investigate further details of the SFHs of these galaxies (e.g., IMF
variation, different AGB yields, etc.).

This comparative chemical abundance analysis highlights the role galactic
environment has on shaping a galaxy’s chemical evolution. The most isolated
galaxies, the MCs, had the weakest early star formation efficiency whereas Sgr
and GSE enriched to much higher metallicities before Type Ia SNe began to
significantly contribute to their chemical enrichment histories, likely due to
their proximity to the MW. The less-massive Sgr was able to continue forming
stars upon beginning its merger with the MW whereas the evolution of GSE was
likely cut short as it merged, perhaps because of its larger mass and more
radial infall trajectory. The MCs evolved slowly in isolation, before
interacting with each other at more recent times to drive up their star
formation. Fnx was apparently not quenched when it fell into the MW
environment, showing chemical signatures of a star formation history that was
extended by either a merger, or a pericenter passage around the MW.

SH is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship
under award AST-1801940. JL is supported by the National Science Foundation
under Grant No. 2009993. DW acknowledges support of NSF grant AST-1909841. MRC
acknowledges funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (grant
agreement no. 682115). DM is supported by the BASAL Center for Astrophysics
and Associated Technologies (CATA) through grant AFB-170002, and by FONDECYT
Regular grant No. 1170121. CG acknowledges support from the State Research
Agency (AEI) of the Spanish Ministry of Science, Innovation and Universities
(MCIU) and the European Regional Development Fund (FEDER) under grant
AYA2017-89076-P. DAGH acknowledges support from the State Research Agency
(AEI) of the Spanish Ministry of Science, Innovation and Universities (MCIU)
and the European Regional Development Fund (FEDER) under grant
AYA2017-88254-P. R.R.M. acknowledges partial support from project BASAL
AFB-$170002$. D.G. gratefully acknowledges support from the Chilean Centro de
Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL grant AFB-170002.
D.G. also acknowledges financial support from the Dirección de Investigación y
Desarrollo de la Universidad de La Serena through the Programa de Incentivo a
la Investigación de Académicos (PIA-DIDULS). MR acknowledges funding from
UNAM-DGAPA PAPIIT IN109919, CONACyT CF-2019-86367, and CY-253085. T.C.B.
acknowledges partial support for this work from grant PHY 14-30152: Physics
Frontier Center / JINA Center for the Evolution of the Elements (JINA-CEE),
awarded by the US National Science Foundation. 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 web site is
www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for
the Participating Institutions of the SDSS Collaboration including the
Brazilian Participation Group, the Carnegie Institution for Science, Carnegie
Mellon University, the Chilean Participation Group, the French Participation
Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica
de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and
Mathematics of the Universe (IPMU) / University of Tokyo, Lawrence Berkeley