11institutetext: Lund Observatory, Department of Geology, Sölvegatan 12,
SE-223 62 Lund, Sweden 22institutetext: Dipartimento di Fisica e Astronomia,
Universitá degli Studi di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino,
Italy

# Gaia-Sausage-Enceladus star formation history as revealed by detailed
elemental abundances

An archival study using SAGA data

H. Ernandes<EMAIL_ADDRESS>11 D. Feuillet 11 S. Feltzing 11 Á.
Skúladóttir 22

(Received XXXX; accepted YYYY)

###### Abstract

Context. The Gaia-Sausage-Enceladus merger was a major event in the history of
the Milky Way. Debris from this merger has been extensively studied with full
kinematic data from the Gaia mission. Understanding the star formation history
of the progenitor galaxy aids in our understanding of the evolution of the
Milky Way and galaxy formation in general.

Aims. We aim to constrain the star formation history of the Gaia-Sausage-
Enceladus progenitor galaxy using elemental abundances of member stars.
Previous studies on Milky Way satellite dwarf galaxies show that key elemental
abundance patterns, which probe different nucleosynthetic channels, reflect
the host galaxy’s star formation history.

Methods. We gather Mg, Fe, Ba, and Eu abundance measurements for Gaia-Sausage-
Enceladus stars from the SAGA database. Gaia-Sausage-Enceladus members are
selected kinematically. Inspired by previous studies, we use [Fe/Mg], [Ba/Mg],
[Eu/Mg], and [Eu/Ba], as a function of [Fe/H] to constrain the star formation
history of Gaia-Sausage-Enceladus. We use the known star formation histories
and elemental abundance patterns of the Sculptor and Fornax dwarf spheroidal
galaxies as comparison.

Results. The elemental abundance ratios of [Fe/Mg], [Ba/Mg], [Eu/Mg], and
[Eu/Ba] all increase with [Fe/H] in Gaia-Sausage-Enceladus. The [Eu/Mg] begins
to increase at [Fe/H] $\sim-2.0$ and continues steadily, contrasting with the
Sculptor dSph galaxy. The [Eu/Ba] increases and remains high across the [Fe/H]
range, contrasting with that of the Sculptor dSph galaxy and deviating from
the Fornax dSph galaxy at high [Fe/H]. The [Ba/Mg] is higher than those of the
Sculptor dSph galaxy at the lowest [Fe/H] and gradually increases, similar to
the Fornax dSph galaxy. We constrain three main properties of the Gaia-
Sausage-Enceladus star formation history: 1) star formation started gradually,
2) it extended for over 2 Gyr, and 3) it was quenched around [Fe/H] of $-0.5$,
likely when it fell into the Milky Way.

Conclusions. We show that the elemental abundance ratios [Fe/Mg], [Ba/Mg],
[Eu/Mg], and [Eu/Ba] can be used to trace the star formation history of a
disrupted galaxy when these measurements are available over an [Fe/H] range
that is representative of the progenitor galaxy’s stellar population.

###### Key Words.:

Stars: abundances – Nuclear reactions, nucleosynthesis, abundances – Galaxies:
individual: Gaia-Sausage-Enceladus – Galaxies: evolution

##  1 Introduction

Recently, using astrometric data from ESA’s Gaia satellite, the presence of a
large galaxy that merged with the Milky Way about 10 billion years ago was
confirmed and dubbed the Gaia-Sausage-Enceladus population (e.g., Helmi et
al., 2018; Belokurov et al., 2018). Indications of such a population had been
noted in the literature as early as Nissen & Schuster (2010). With larger
spectroscopic and astrometric datasets available, several studies have now
looked into how to select the stars that came with that galaxy using
kinematics and/or chemical composition (see Belokurov et al., 2018; Feuillet
et al., 2021; Carrillo et al., 2024, and references therein).

To first order, the surface composition of stars reflects the gas composition
from which they formed. The relative abundance of individual elements in the
gas is strongly dependent on the history of the host galaxy as different
elements are deposited into the interstellar medium on different timescales.
The $\alpha$-elements (e.g. O and Mg) are all (mainly) released from ccSN
(Woosley & Weaver, 1995). This process will enrich the interstellar medium on
short timescales ($10^{7-8}$ Gyr), tracking the star formation. The iron-peak
elements on the other hand, are mainly produced by type Ia SN (SNIa), which
happens on longer timescales ($10^{8-9}$ Gyr).

Elements heavier than Zn ($Z>30$) are created through neutron-capture
nucleosynthesis. This process can be divided into subcategories depending on
the flux of neutrons required to create them. These subcategories are the slow
($s$), intermediate ($i$), and rapid ($r$) processes. The $s$-process takes
place when the neutron flux is lower than the time of the $\beta$-decay (with
which the nucleus moves towards higher proton numbers). Thus it is feasible
for this process to occur in Asymptotic Giant Branch (AGB) stars on long
timescales ($10^{8-10}$ Gyr). The $s$-process is the main nucleosynthetic site
of elements such as Ba. The $r$-process on the other hand requires a faster
neutron capture. The exact site for this process is still a matter of debate.
The $r$-process elements, such as Eu, likely have more than one source and
have been found to contribute to the chemical enrichment of a stellar
population both on long and short time-scales (Skúladóttir & Salvadori, 2020).

The abundance of a given elements over time in the interstellar medium of a
galaxy will depend on the timescale of the contributing stellar source(s) and
how many stars have been formed. The star formation history of a given (dwarf)
galaxy will, therefore, leave a unique imprint in the stellar elemental
abundances. Several studies show that the Gaia-Sausage-Enceladus galaxy has an
elemental abundance pattern for the $\alpha$-elements that differs from that
of the rest of the Milky Way halo and the metal-weak thick disk at the same
metallicities (see, e.g. Nissen & Schuster, 2010; Nissen et al., 2024; Helmi
et al., 2018). This provides strong evidence that stars belonging to the Gaia-
Sausage-Enceladus population formed in a galaxy outside the Milky Way.

While the $\alpha$-element pattern and overall metallicity distribution
function of the Gaia-Sausage-Enceladus have been well characterised (e.g.
Helmi et al., 2018; Feuillet et al., 2020, 2021; Naidu et al., 2020), studies
of elemental abundance trends beyond the $\alpha$-elements are few and, most
importantly, do not cover the full metallicity range (Aguado et al., 2021;
Matsuno et al., 2021, 2022; Monty et al., 2020). This makes it difficult to
exploit the elemental abundances from different nucleosynthetic channels in
order to constrain the star formation history of the Gaia-Sausage-Enceladus
galaxy. In this work, we build on Skúladóttir & Salvadori (2020) to do just
that.

Skúladóttir & Salvadori (2020) use a combination of star formation histories
for different dwarf spheroidal (dSph) galaxies together with elemental
abundance patterns to put constraints on the timescales of the $r$-process
sites. Inspired by this result, we find that if we have elemental abundances
measured for stars in Gaia-Sausage-Enceladus, we can add the known
nucleosynthesis timescales to interpret the features we observed in the
abundance trends as constraints to its star formation history.

In this paper, we take advantage of the availability of a large body of data
from the literature as compiled in the SAGA database (Suda et al., 2008),
which provides us with data for halo (and disk) stars. Using the best criteria
for selecting the stars, we proceed to trace the star formation history of the
Gaia-Sausage-Enceladus galaxy using these data. We use star formation
histories and elemental abundance patterns from the literature of the dSph
galaxies Fornax and Sculptor as comparisons to aid our interpretation.
Critically, the abundance measurements of Ba and Eu over a large range in
[Fe/H] allow us to constrain the star formation history of Gaia-Sausage-
Enceladus in detail.

##  2 Data

Figure 1: Number of [Eu/Fe] measurements (n[Eu/Fe]) for the stars in our SAGA
catalogue as a function of the median [Fe/H]. Colour coding shows the number
of available [Fe/H] measurements (n[Fe/H]).

Figure 2: Properties of the stars in our final sample with SAGA and Gaia data,
with three 10 Gyr PARSEC isochrones overlaid, metallicity as indicated in the
legends: a) Kiel diagram, colour-coded by the median [Fe/H]; b) Colour-
magnitude diagram, colour-coded by the number of [Fe/H] measurements
available.  Table 1: Gaia ID, SAGA ID, median SAGA stellar parameters,
elemental abundances, photometric $T_{\rm eff}$ (only for dwarf stars), median
age with 16 and 84 percentile, and $r$-II flag for stars selected according to
Feuillet et al. (2021) scheme.

Gaia DR3 ID | SAGA ID | $T_{\rm eff}$ | log$g$ | [Fe/H] | [Mg/Fe] | [Eu/Fe] | [Ba/Fe] | $T_{\rm eff}$ | a16 | Age | a84 |  $r$-II
---|---|---|---|---|---|---|---|---|---|---|---|---
|  | [K] |  |  |  |  |  | [K] | [Gyr] | [Gyr] | [Gyr] |
|  | SAGA |  |  |  |  |  | Photo |  | Median |  | flag
1458016709798909952 | G165-39 | 6220 | 3.96 |  $-$1.99 | +0.22 | +0.48 |  $-$0.04 | 6354 | 13.6 | 14.6 | 15.8 | No
689795494613436160 | G9-36 | 5788 | 4.35 |  $-$1.14 | +0.29 | +0.49 | +0.11 | 5739 | — | — | — | No
2077681190974623744 | KIC6611219 | 4652 | 1.74 |  $-$1.32 | +0.26 | +0.92 | +0.20 | — | — | — | — | Yes
$\cdots$

###  2.1 Chemical abundances in SAGA

The goal of this paper is to derive the Gaia-Sausage-Enceladus star formation
history using key elemental abundance trends across the full range of [Fe/H],
$\rm-2.2<[Fe/H]<-0.5$. We are in particular interested in the neutron capture
elements. To our knowledge, no study has so far studied the elemental
abundance trends for $r$\- and $s$-process elements across the full
metallicity range of the Gaia-Sausage-Enceladus galaxy.

In order to gather the largest sample possible with measurements of neutron
capture elements across a large range of metallicity, we chose to utilise a
compilation of data from the literature, the SAGA database. The SAGA database
(Suda et al., 2008) gathers elemental abundance measurements from the
literature provided by papers in the CDS111Centre de Données astronomiques de
Strasbourg database. The SAGA database was originally designed to provide a
catalogue of metal-poor stars. However, recently studies of more metal-rich
stars have been included. The database is categorised into catalogues of
several dwarf galaxy and the Milky Way. We selected stars from the latter
catalogue as described below. The version of the database used here was last
updated on April 10, 2023.

Using the SAGA plotting interface222http://sagadatabase.jp/, we selected stars
within the iron (Fe) abundance range we expect for Gaia-Sausage-Enceladus
stars (Feuillet et al., 2021). We selected stars meeting the following
criteria:

  * i)

$-2.2<$ [Fe/H] $<-0.5$,

  * ii)

measurements available for both [Eu/Fe] and [Fe/H].

This selection resulted in a sample of 804 stars, however, we note that after
searching for Gaia DR3 IDs for this sample, we find that not all of these
stars are unique, see Sec. 2.2 for details. For these stars, we added [Mg/Fe]
and [Ba/Fe] measurements from the SAGA database when available. We remove from
our sample so called Ba stars, which have surface Ba abundances that reflect
their binary evolution and not the chemical evolution of the host system, see
App. A for details.

The resulting catalogue provides for every star a unique row for each
literature source contributing a reported [Fe/H], [Eu/Fe], [Mg/Fe], and
[Ba/Fe]. This means that every star can have multiple entries, and each
elemental abundance measurement may come from a different study. Some
literature studies only derive elemental abundances and use stellar
parameters, including [Fe/H], from other sources. Therefore, the stellar
parameters of effective temperature ($T_{\rm eff}$), surface gravity ($\log
g$), and [Fe/H] may be neither unique nor homogeneous for each reported
elemental abundance of a single star. Fig. 1 illustrates the number of [Eu/Fe]
and [Fe/H] measurements available for stars in our catalogue.

The potential for multiple reported elemental abundances for a single star
means that we needed to make choices about how to combine the elemental
abundances available. When multiple abundance values are reported for a single
element in the same star, we use the median of all values. The systematic
uncertainties from each literature study were not considered in this analysis.
In section 3.3, we discuss the uncertainty in our results due to element
abundance dispersion between multiple studies and how this is indicated in
later figures.

Fig. 2a shows the Kiel diagram for the final sample of 654 stars from the SAGA
database that also have Gaia parameters (see discussion in Section 2.2). As
was done with the elemental abundances, we take the median $T_{\rm eff}$ and
log$g$ values of all reported literature values for a given star. The colour
of each point indicates the median [Fe/H] of each star. We note the metal-rich
giant branch stars are cooler than the majority of stars in the sample. These
stars, which all come from Tautvaišienė et al. (2021), are considerably more
metal-rich ($\rm[Fe/H]>-0.7$) than the other giant branch stars, therefore the
separation is expected. The metallicity distribution of our final sample is
shown in grey in Fig. 3.

###  2.2 Astrometric data and kinematics

We use Gaia astrometric parameters to determine the kinematics of the stars in
our sample. To do this, we first query for the Gaia DR3 IDs using the
capabilities of the astroquery.simbad (Ginsburg et al., 2019; Wenger et al.,
2000) package in Python. In this process, we find that 13 stars from Li et al.
(2022), which are in our SAGA sample, are not in the SIMBAD database under the
ID provided by SAGA. Through personal communication with Haining Li, we
received the Gaia DR3 ID for these 13 stars. This results in a sample of 680
unique stars from SAGA with Gaia DR3 IDs.

We then query the Gaia archive333https://gea.esac.esa.int/archive/ for the
Gaia DR3 parameters (Gaia Collaboration et al., 2021), finding that 654 stars
have Gaia astrometric and Radial Velocity Spectrometer (RVS) data available.

Fig. 2b shows the colour-magnitude diagram of the final sample of 654 stars.
The absolute magnitude ($M_{G}$) was calculated according to

$\centering M_{G}=G-5*\log(100/\pi),\@add@centering$ (1)

where $G$ is the Gaia $G$-band magnitude and $\pi$ is the parallax. We assume
zero extinction for all stars because the majority of stars in this sample do
not have an entry for ag_gspphot. The mean extinction for our sample, when
available, is below 0.2 and only a few have ag_gspphot up to 1. As we focus on
Gaia-Sausage-Enceladus, which is primarily found in the halo, the effects of
extinction and reddening are not expected to be large.

We calculate the full kinematics and orbital parameters of the stars in the
sample using the Python packages astropy (Astropy Collaboration et al., 2013,
2018, 2022) and galpy (Bovy, 2015). When determining the actions, we assume
the actionAngleStaeckel approximation (Binney, 2012; Bovy & Rix, 2013) using a
delta of 0.4. We calculate actions and kinematics using both the MWPotential14
(Bovy & Rix, 2013) and McMillan (2017) models for the Milky Way potential as
this is important when comparing different Gaia-Sausage-Enceladus selection
schemes reported in the literature. We adopted the geometric distances
provided in Bailer-Jones et al. (2021).

We use the spectroscopic radial velocity measurement from the SAGA database
when available. In the case that SAGA provided multiple RV entries for the
same target, we decided to adopt the value from the newest reference as the
deviation between different literature values for the radial velocity is
small. When radial velocity is not available in SAGA, we used the Gaia RVS
radial velocity. The kinematics are used to select the Gaia-Sausage-Enceladus
samples, see Sect. 3.1.

##  3 Analysis

###  3.1 Selecting the Gaia-Sausage-Enceladus stars

Figure 3:  Metallicity distribution for the stars in our final catalogue with
SAGA and Gaia data (grey outline). The stars in our primary Gaia-Sausage-
Enceladus sample are also shown, dwarf stars in blue (29 stars) and giant
stars in red (44 stars). The latter two are stacked.

Several schemes for selecting Gaia-Sausage-Enceladus members have been
described in the literature. Some of these selection schemes use only
kinematics, whilst others also place constraints on metallicity and/or
elemental abundance ratios. In particular, some of the proposed schemes
include a limit on [Mg/Mn] and [Al/Fe]. However, after an inspection of the
SAGA database we found that the availability of Al and Mn abundances is rather
limited for our sample. We thus decided not to include any selection scheme
that uses elemental abundances (e.g. Naidu et al., 2022).

Table 2 summarises the selection schemes which we consider here. For each
scheme, we use kinematics calculated using the same potential as the original
authors. We select three to investigate in detail: a simple “Sauage”-like
selection, Myeong et al. (2019), and Feuillet et al. (2021). We test a very
simple scheme that takes all stars with a rotational velocity typical of the
halo encompassing the sausage-like overdensity, $-100<V_{\phi}<100$ km s-1.
This leads to a large number of stars that might belong to a high-velocity
tail of the Milky Way stellar disk (Nissen & Schuster, 2010; Belokurov et al.,
2020). In contrast, the scheme proposed by Myeong et al. (2019) is very
conservative and picks stars in a narrow range of the “action diamond”.

As our primary selection scheme we choose that of Feuillet et al. (2021),
since it has been shown to be relatively pure, while not being too restricting
in regards to the number of Gaia-Sausage-Enceladus member stars (Carrillo et
al., 2024). Table 2 also gives the number of stars selected from our full SAGA
sample using each selection schemes. Using the Feuillet et al. (2021)
selection scheme, we have 73 stars with both Fe and Eu measurements. Of these,
70 stars have [Ba/Fe] measured, 61 stars have [Mg/Fe] measured, and 59 have
both [Ba/Fe] and [Mg/Fe]. Fig. 3 shows the metallicity distribution for our
primary Gaia-Sausage-Enceladus sample, separated into dwarf and giant stars
(see Fig. 2a for separation). We note that the giant and dwarf stars do not
show the same [Fe/H] distribution, at higher metallicities there are only
dwarf stars. This lack of higher metallicity giant stars is likely a
reflection of an inherent incompleteness of the SAGA database.

We do not include the selection schemes of Helmi et al. (2018), Naidu et al.
(2020), and Horta et al. (2023) in our primary elemental abundance analysis,
but they are shown in App. C. Horta et al. (2023) is sufficiently similar to
the scheme by Feuillet et al. (2021), while Naidu et al. (2020) is similar to
the “Sausage”. Therefore, they do not give any additional insights into the
properties of Gaia-Sausage-Enceladus. Although Helmi et al. (2018) present the
original selection scheme for the Gaia-Sausage-Enceladus, it produces a
predominantly retrograde sample while more recent studies suggest that the
Gaia-Sausage-Enceladus population includes stars on both retrograde and
prograde orbits. The Helmi et al. (2018) selection scheme could therefore
potentially distort the view of the chemistry of the Gaia-Sausage-Enceladus.
We find that our conclusions are not affected by our choice of selection
schemes.

Table 2:  The selection schemes for Gaia-Sausage-Enceladus stars, including references. Also listed are the total number of member stars in our SAGA catalogue and the number of stars with each elemental abundance available.  Reference | Selection criteria | Unit | Selected number of stars
---|---|---|---
|  |  | Total | n[Eu/Fe] | n[Ba/Fe] | n[Mg/Fe]
“Sausage” |  $-$100$<V_{t}<$100 | km s-1 | 299 | 299 | 286 | 250
Helmi et al. (2018) |  $-$1500$<L_{z}<$150 | kpc km s-1 | 178 | 178 | 171 | 147
$E_{n}>-1.8\times 10^{5}$ | km2 s-2
Myeong et al. (2019) |  $-$0.07$<J_{\phi}/J_{tot}<$0.07 |  |  42 | 42 | 41 | 31
$(J_{z}-J_{R})/J_{tot}<$ $-$0.3 |
Naidu et al. (2020) | e ¿0.7 |  | 264 | 264 | 254 | 217
Horta et al. (2023) |  $-$500$<L_{z}<$500 | kpc km s-1 |  86 | 86 | 83 | 70
$-1.6\times 10^{5}<E_{n}<-1.1\times 10^{5}$ | km2 s-2
Feuillet et al. (2021) |  $-$500$\leq L_{z}\leq$500 | kpc km s-1 |  73 |  73 |  70 |  61
30$\leq\sqrt{J_{r}}\leq$55 | (kpc km s-1)1/2

###  3.2 $r$-II stars

Stars significantly enhanced in $r$-process elements were first described by
Hill et al. (2002) and Sneden et al. (2003), then categorised as $r$-II stars
in Beers & Christlieb (2005). Several definitions have been suggested, but we
here use the recent definition by Holmbeck et al. (2020), which defines an
$r$-II star as having $\rm[Eu/Ba]>0.0$ and $\rm[Eu/Fe]>+0.7$. In our primary
sample of 73 Gaia-Sausage-Enceladus stars we have 10 $r$-II stars.

###  3.3 Uncertainties

Figure 4:  Median [Fe/H] for each star in our primary Gaia-Sausage-Enceladus
sample that have two or more measurements reported in SAGA. The number of
available measurements is indicated with a colour, as indicated on the colour-
bar. The MAD is shown as an error-bar (see Sect. 3.3).  Figure 5:  Median
[Eu/Fe] for stars in our primary Gaia-Sausage-Enceladus sample, which have two
or more measurements reported in SAGA. The number of available measurements is
indicated with a colour, as indicated on the colour-bar. The MAD is shown as
an error-bar (see Sect. 3.3).

We are using a database that compiles results from different studies. Not all
studies give a detailed error analysis and it is beyond the scope of this
study to attempt to put all data onto the same scale and determine proper,
homogeneously derived errors. Instead, we opt for a simple but reproducible
scheme. For those stars with more than one entry in the SAGA database we
decided to take as the final stellar parameters the median value for each
parameter. The uncertainties for these values are then calculated as the
Median Absolute Deviation (MAD).

For the elemental abundance plots we will display the MAD as an error-bar. For
the majority of the stars, we have only a single measurement of [Fe/H] and
[Eu/Fe] (see Figs. 4 and 5). When only one measurement is available, we show
no error-bar. For elemental abundance ratios that we construct, e.g. [Eu/Ba],
we calculate the error-bar by adding the MADs for the two values in
quadrature. Thus we wish to alert the reader to the fact that no error-bar
means a single measurement, while a substantial error-bar indicates very
differing results in the literature.

###  3.4 Stellar ages

We estimate ages for the dwarf stars in our sample following the methodology
outlined by Sahlholdt et al. (2019); Sahlholdt & Lindegren (2021). The method
calculates a two-dimensional age-metallicity probability distribution function
as described in Howes et al. (2019). This method is based on a Bayesian
isochrone fitting methodology and produces a joint marginal likelihood
$\mathcal{G}(\tau,\zeta|\textbf{x})$ of age ($\tau$) and metallicity
($\zeta$), given a set of input observables (x) in comparison with a set of
model isochrones. We use a grid of isochrones from PARSEC (Bressan et al.,
2012), where each isochrone point is described by its initial mass ($m$), age
($\tau$), metallicity ($\zeta$), and distance modulus ($\mu$). The likelihood
for each model is calculated as

$L(m,\tau,\zeta,\mu|\textbf{x})=\exp\left[-\frac{1}{2}\sum_{i}\left(\frac{x_{i}-X_{i}(m,\tau,\zeta,\mu)}{\sigma_{i}}\right)^{2}\right],$
(2)

where $X_{i}$ are the isochrone parameters at a given point, which is compared
to the observable parameters of a given star $x_{i}$ with uncertainty
$\sigma_{i}$.

For each star, $\mathcal{G}(\tau,\zeta|\textbf{x})$ is the marginalisation
over the mass and distance modulus, using priors $\xi(m)$ and $\psi(\mu)$,
respectively, and calculated as

$\mathcal{G}(\tau,\zeta|\textbf{x})=\int_{\mu}\int_{m}\xi(m)\psi(\mu)L(m,\tau,\zeta,\mu|\textbf{x})\,dm\,d\mu.$
(3)

We use a Salpeter initial mass function (Salpeter, 1955) for $\xi(m)$ and a
flat prior on distance modulus. As our sample is too small to consider the
two-dimensional age-metallicity probability distribution, we calculate the
one-dimensional $\mathcal{G}(\tau|\textbf{x})$ by marginalising over the
metallicity assuming a flat prior.

The observable input parameters used for each star are the $T_{\rm eff}$,
apparent magnitude, parallax, and [Fe/H]. The apparent magnitude is taken as
the Gaia $G$-band magnitude. The uncertainties on Gaia $G$ are very small,
$\sim$ 0.001, however, as discussed in Sect. 2, we assume zero extinction for
this sample. To account for that uncertainty, we use a standard uncertainty of
0.1 mag in Gaia $G$ for our age analysis. The parallax is from Gaia DR3 and
corrected for the zero-point offset following the prescription provided by
Lindegren et al. (2021). We use the SAGA [Fe/H] values and do not calculate
any [Fe/H] adjustment for a possible $\alpha$-enhancement. The $T_{\rm eff}$
values were determined from the BP-RP colour indices, utilising the
calibration established by Mucciarelli et al. (2021). In accordance with their
evaluation, we assume an uncertainty of $\sigma_{T_{\rm eff}}$ = 61 K. We
opted to use the photometric $T_{\rm eff}$, for our dwarf stars, instead of
$T_{\rm eff}$ from Gaia RVS or the literature $T_{\rm eff}$ reported in the
SAGA database. This choice is detailed in App. B.1.

Depending on the exact location of a dwarf star in the HR-diagram, the derived
probability distribution for its age may not be well-behaved. For some stars,
the distribution may be almost flat, for others there may be two or more peaks
(compare Sahlholdt et al., 2019). We selected those stars that have well-
behaved peaks. The results for these 13 dwarf stars meeting the criteria in
the Feuillet et al. (2021) selection scheme are shown in Fig. 6 (see also App.
B.2). The 13 stars all have a median age larger than 12 Gyr.

Figure 6: Age probability distribution functions for 13 dwarf stars in our
primary Gaia-Sausage-Enceladus sample. The remaining 16 dwarf stars have less
well behaved probability distribution functions (see App. B.2).

##  4 Results – Elemental abundances trends

Figure 7:  Gaia-Sausage-Enceladus stars selected from the SAGA database (Sect.
2). Panels show elemental abundance ratios as a function of [Fe/H]: a)
[Fe/Mg]; b) [Ba/Mg]; c) [Eu/Mg]; and d) [Eu/Ba]. Different colours are dwarf
(purple) and giant (blue) stars and x-symbols are $r$-II stars. Median trends
are shown with pink lines.  Figure 8:  Median abundance trends for Gaia-
Sausage-Enceladus stars as derived in Fig. 7 (pink), including the selection
schemes of “Sausage” (cyan) and Myeong et al. (2019, green). Panels show
trends with [Fe/H] for: a) [Fe/Mg]; b) [Ba/Mg]; c) [Eu/Mg]; and d) [Eu/Ba].

In Fig. 7, we inspect four key elemental abundance ratios for the 73 stars
selected using the scheme by Feuillet et al. (2021): [Fe/Mg], [Ba/Mg],
[Eu/Mg], and [Eu/Ba]. We highlight both dwarf and giant stars (see Fig. 2a for
the division), as well as $r$-II stars. The trends seen in the dwarf and giant
stars are not significantly different. We note that the $r$-II stars appear to
follow the median trends in a similar fashion to the other stars, apart from
their high Eu abundances, in accordance with their definition (Sect. 3.2). We
calculate the median abundance trends, for a more straight-forward comparison
between different selection schemes. The median trend lines were calculated as
the running median in 0.25 dex bins of [Fe/H], moving in steps of 0.15 dex.
Only the data-points are taken into account, not the error-bars (for a
discussion of the error-bars the reader is referred to Sect. 3.3).

For all four abundance ratios, [Fe/Mg], [Ba/Mg], [Eu/Mg], and [Eu/Ba], we see
overall rising trends with increasing [Fe/H]. However, for two of them,
[Eu/Mg] and [Eu/Ba], the trends appear to be more complex and not
monotonically increasing. The [Fe/Mg] distribution has the lowest scatter
around the median trend line. In contrast, the abundance ratio distributions
that include Eu have higher star-to-star scatter, with some stars quite far
from the median trend. As Fig. 5 shows, [Eu/Fe] measurements from different
studies can be very different from one another. As most of the stars selected
from the SAGA database only have one Eu measurement in the literature, it is
not possible to robustly assess if the large scatter in Fig. 7 c and d) is due
to large systematic differences between studies or if the Eu abundance in the
stars is truly different. The [Ba/Mg] distribution generally has smaller
scatter than Eu, with larger scatter at the lowest [Fe/H] end.

In order to test our decision to only analyse the elemental abundance trends
of the Gaia-Sausage-Enceladus population selected following Feuillet et al.
(2021), we also investigate the trends resulting from the “Sausage” and Myeong
et al. (2019) selection schemes, see Fig. 8. Overall, these trends are quite
similar. However, the trends resulting from the “Sausage” selection scheme
deviate in [Fe/Mg] and [Ba/Mg] $\rm[Fe/H]\gtrsim-1$. In [Eu/Ba] and [Eu/Mg],
similar differences appear already at $\rm[Fe/H]\approx-1.5$. These deviations
at higher [Fe/H] are likely due to the inclusion of kinematically hot, disk-
like Milky Way stars in the sample, which have preferentially higher [Fe/H].

Stars selected as Gaia-Sausage-Enceladus members by Myeong et al. (2019) have
very similar abundance trends to those selected by Feuillet et al. (2021), but
with higher Eu abundances at $\rm[Fe/H]\gtrsim-1.5$. This may suggest that the
Myeong et al. (2019) selection scheme results in fewer Milky Way stars;
however, because the sample selected following Feuillet et al. (2021) has
twice the number of stars and the resulting trends are very similar, we
proceed with our analysis considering only the sample selected with the scheme
by Feuillet et al. (2021). As described in Sect. 3.1, the selection scheme of
Feuillet et al. (2021) is found to be the most pure by Carrillo et al. (2024)
based on an analysis of a cosmological simulation of a Milky Way-like galaxy.

For completeness, in App. C we show the elemental abundances and resulting
elemental abundance trends for the five remaining schemes listed in Table 2.
These abundance trends display overall the same features as those displayed in
Fig. 8.

##  5 Literature comparison with recent elemental abundance studies

Several dedicated studies have measured the abundances of heavy elements in
the Gaia-Sausage-Enceladus stellar population, including Monty et al. (2020),
Aguado et al. (2021), Matsuno et al. (2021, 2022), and Naidu et al. (2022).
Fishlock et al. (2017) derived Eu for the low- and high-$\alpha$ halo stars
from Nissen & Schuster (2010) sample.

Aguado et al. (2021) and Naidu et al. (2022) derived [Eu/Ba] for 4 and 11
stars, respectively. Both studies find an elevated [Eu/Ba] in Gaia-Sausage-
Enceladus, $\sim 0.7$ at [Fe/H] $\sim-1.5$ and $0.5$ at $-1.2<$ [Fe/H]
$<-0.8$, respectively, $\sim 0.2$ – $0.4$ dex higher than Milky Way disk stars
at the same [Fe/H] (Skúladóttir & Salvadori, 2020). This is roughly consistent
with our sample. These two studies each cover narrow but complementary [Fe/H]
ranges ($-2.0<$ [Fe/H] $<-1.4$ and $-1.2<$ [Fe/H] $<-0.8$, respectively). Our
SAGA data covers a much larger [Fe/H] range than either individual study
($-2.2<$ [Fe/H] $<-0.7$). We note that the Aguado et al. (2021) and Matsuno et
al. (2021) samples are included in our SAGA dataset.

Naidu et al. (2022) measured [Eu/Mg] for their stars, finding an enhancement
of $\sim 0.5$, consistent with our final sample. Fishlock et al. (2017)
measured [Eu/Fe] to be enhanced in the Nissen & Schuster (2010) low-$\alpha$
stars ($\rm[Eu/Fe]=0.3$ at $\rm[Fe/H]=-1.0$).

Finally, Monty et al. (2020) analysed 11 stars, selected via the kinematic
scheme of Myeong et al. (2019). The stars span $-2.5<\rm[Fe/H]<-1.0$, with one
star at $-3.5$ dex. They measured [Ba/Fe], finding that Gaia-Sausage-Enceladus
is enhanced by $\sim 0.4$ dex relative to the Milky Way thick disk population.
In their sample, there are no $r$-process-enhanced stars. This is inconsistent
with the results from Aguado et al. (2021) and our SAGA dataset.

##  6 Disentangling the star formation history of Gaia-Sausage-Enceladus

Figure 9:  Median abundance trends of stars in the Gaia-Sausage-Enceladus
(Fig. 7), and the dSph galaxies Fornax and Sculptor from Skúladóttir &
Salvadori (2020). Abundance ratios are shown as a function of [Fe/H] for: a)
[Fe/Mg]; b) [Ba/Mg]; c) [Eu/Mg]; and d) [Eu/Ba].

Our main goal is to characterise the star formation history of the Gaia-
Sausage-Enceladus progenitor galaxy using constraints derived from the
elemental abundance trends of its stellar debris. We assume that the debris
originates from a single, ancient, low-mass galaxy. We therefore interpret the
elemental abundance trends as representing an individual galaxy with its own
star formation history and, consequently, its own chemical enrichment.
Skúladóttir & Salvadori (2020) use the known star formation histories of
several local dwarf galaxies to place constraints on the enrichment timescale
of individual nucleosynthetic channels given the observed elemental abundance
trends in each galaxy’s stellar population. We reverse the methodology of
Skúladóttir & Salvadori (2020) and use observed elemental abundance ratios
combined with the enrichment timescales of Mg, Fe, Ba, and Eu to constrain the
star formation history.

To place the star formation history of the Gaia-Sausage-Enceladus progenitor
in context, we compare the elemental abundance trends of [Fe/Mg], [Ba/Mg],
[Eu/Mg], and [Eu/Ba] with the same trends measured in the nearby dSph galaxies
Sculptor and Fornax (Fig. 9), whose star formation histories are known. These
two galaxies have very different star formation histories. The Sculptor dSph
galaxy had a short star formation history with a strong initial starburst
(Bettinelli et al., 2019; de Boer et al., 2012b) while the Fornax dSph galaxy
had a more extended star formation history (de Boer et al., 2012b). These two
extremes of star formation make them ideal objects of comparison when
interpreting how the features we see in the elemental abundance trends of
Gaia-Sausage-Enceladus correlate to its star formation history.

Characterising the star formation of Gaia-Sausage-Enceladus via elemental
abundance trends requires an understanding of the enrichment timescales for
the individual elements. We use Mg, Fe, Ba, and Eu because these elements
represent four different nucleosynthetic channels and were found by
Skúladóttir & Salvadori (2020) to reflect different aspects of the star
formation history of a low-mass galaxy.

###  6.1 Nucleosynthesis of Mg, Fe, Ba, and Eu

Core-collapse Supernovae (ccSN) are the primary end-stage of high mass stellar
evolution (11 – 40 $\textup{M}_{\odot}$, Woosley & Weaver 1995). Due to the
short lifetimes of massive stars, the enrichment of elements formed primarily
through ccSN can serve as a tracer of star formation (e.g. McWilliam et al.,
2013). The element Mg is synthesised almost exclusively in ccSN (Woosley &
Weaver, 1995; Woosley & Heger, 2007). We use the Mg enrichment in each of the
dwarf galaxy stellar populations as a direct reflection of the ongoing star
formation. Fe is also synthesised in ccSN, however, this is not the only major
nucleosynthetic source of Fe.

Unlike ccSN, enrichment of elements produced in Type Ia Supernovae (SN Ia) can
have a wide time delay, between $\sim$ 0.1 – 2 Gyr (Maoz et al., 2014) with a
typical time delay of 1 Gyr (Dubay et al., 2024; Palicio et al., 2024), from
the epoch of star formation because the SN Ia mechanism requires an evolved
binary system with a white dwarf. Fe is synthesised through SN Ia (Woosley &
Weaver, 1995; Nomoto & Leung, 2018). The enrichment of Fe is therefore
complex, depending on both immediate ccSN and delayed SNIa, however, the
contribution of Fe from SNIa will be delayed compared to the contribution from
ccSN.

The slow neutron capture process ($s$-process) primarily occurs in
intermediate-mass Asymptotic Giant Branch (AGB) stars (0.9 – 10
$\textup{M}_{\odot}$, Karakas & Lattanzio, 2014). Due to the range of masses,
and therefore lifetimes, of these stars, the $s$-process is considered to have
both a delayed and extended contribution. The element Ba is produced almost
exclusively via the $s$-process (e.g. Bisterzo et al., 2014). We therefore
assume that the enrichment of Ba from a single starburst will be delayed
compared to the enrichment of Mg. This is because of the difference in initial
mass of AGB stars and ccSN, which causes a delay of between 0.1 – 10 Gyr
(Raiteri et al., 1996), depending on the AGB star mass.

The rapid neutron capture process ($r$-process) is less understood than the
$s$-process. This process requires a large neutron flux and possible sources
have existed only in theory until recently (Burbidge et al., 1957; Winteler et
al., 2012; Skúladóttir et al., 2019; Wanajo et al., 2009; Côté et al., 2019;
Holmbeck & Andrews, 2024). Recent observations have confirmed neutron star
mergers as a viable site for the $r$-process (Abbott et al., 2017; Rosswog et
al., 2018; Watson et al., 2019). The contribution of neutron star mergers to
chemical enrichment is expected to be delayed, again due to the requirement of
an evolved binary system, although the exact timescale is not currently well
constrained (Matteucci et al., 2014; Hirai et al., 2015; Rosswog et al.,
2018). However, studies of stellar elemental abundance patterns suggest there
is another $r$-source without significant time delay relative to ccSN (e.g.
Skúladóttir et al., 2019; Watson et al., 2019; Côté et al., 2019).

The element Eu is produced primarily via the $r$-process and can therefore be
used to constrain its timescale. Skúladóttir & Salvadori (2020) demonstrated
that both a quick and a delayed source of Eu is needed to explain the measured
[Eu/Mg] in the Milky Way and three dSph galaxies: Sagittarius, Fornax, and
Sculptor. The quick source is found to contribute Eu on timescales similar to
Mg, timescales similar to ccSN, which directly traces star formation. The
delayed source is found to operate on timescales longer than SN Ia.
Skúladóttir & Salvadori (2020) suggest that the timescales of the delayed
source can be constrained by the star formation history of the Sculptor dSph
galaxy. There is no evidence of an enhanced enrichment of Eu relative to Mg in
Sculptor. Therefore, the delayed enrichment source of Eu did not contribute
significantly during the time Sculptor was forming stars. Skúladóttir &
Salvadori (2020) therefore constrain the delayed source of Eu to at least
$\gtrsim 4$ Gyr by using the star formation history of Sculptor from (de Boer
et al., 2012a). However, an improved star formation history of Sculptor from
Bettinelli et al. (2019) finds that Sculptor only formed stars for $\sim$2
Gyr. We therefore assume that the typical timescale of the delayed $r$-process
is $\gtrsim$ 2 Gyr.

###  6.2 Evidence of truncated star formation in [Fe/Mg]

The elemental abundance ratio [Fe/Mg] shows the balance of the quick
enrichment from ccSN (Mg and Fe) versus the delayed enrichment from SNIa (Fe).
The low [Fe/H] stars in all three galaxies, $\rm[Fe/H]\lesssim-1.8$, have low
[Fe/Mg] as the only source of enrichment is ccSN, see Fig. 9a. As the SNIa
begin to contribute Fe, the ratio of [Fe/Mg] increases. In this space, the
stronger the contribution of SNIa relative to ccSN, the steeper the slope of
[Fe/Mg]. As the amount of star formation decreases in a galaxy, the delayed
SNIa will continue contributing Fe at a rate proportional to the star
formation $\sim$1 Gyr ago, while the ccSN contribution remains proportional to
the ongoing star formation. This results in a positive [Fe/Mg] at high [Fe/H]
in galaxies that experience a gradual decline in star formation, as seen in
Fornax and Sculptor, Fig. 9a. We find that the Gaia-Sausage-Enceladus trend
does not extend to positive [Fe/Mg] values, suggesting that star formation was
quenched and not allowed to exhaust its gas supply naturally.

###  6.3 Extended star formation inferred from [Ba/Mg]

The [Ba/Mg] ratio indicates the balance between the quick contribution of ccSN
(Mg) and delayed, extended contribution of AGB stars (Ba). At low [Fe/H], this
ratio reflects the strength of the initial star formation in a galaxy. This is
well demonstrated in Sculptor, Fig. 9b, which experienced a robust initial
burst of star formation. Consequently, the [Ba/Mg] ratio is extremely low at
low $\rm[Fe/H]\lesssim-1.8$. Sculptor experienced significant enrichment from
ccSN before AGB stars had time to contribute. In contrast, Fornax did not have
a strong initial burst of star formation, but began forming stars more
gradually. This is reflected in the higher [Ba/Mg] at low [Fe/H]. The [Ba/Mg]
in Gaia-Sausage-Enceladus at low [Fe/H] is very similar to Fornax, suggesting
that Gaia-Sausage-Enceladus also began forming stars more gradually and did
not have a strong initial burst of star formation.

With increasing [Fe/H], the [Ba/Mg] trend reflects whether or not star
formation continued for an extended period. Sculptor had a short star
formation history and consequently its stellar populations shows a steep and
monotonic increase in [Ba/Mg] with [Fe/H]. This reflects the increasing
influence of lower mass AGB stars with time, while the ccSN contribution
diminishes with the decreasing star formation. In Fornax, the [Ba/Mg] ratio
remains relatively stable until $\rm[Fe/H]\approx-1.2$, at which point it
increases with a slope similar to Sculptor. The stable balance of [Ba/Mg] over
a range of [Fe/H] thus reflects the extended star formation experienced by
Fornax.

In Gaia-Sausage-Enceladus stars, the [Ba/Mg] ratio increases smoothly across
the entire [Fe/H] range, see Fig. 9b. This suggests that Gaia-Sausage-
Enceladus experienced an extended star formation, similar to Fornax, where AGB
stars of a wider range of masses progressively contribute without a sudden
decrease in the contribution from ccSN. However, unlike Fornax, Gaia-Sausage-
Enceladus does not have a high [Fe/H] tail of increasing [Ba/Mg]. This
suggests that there was no period of gradually decreasing star formation, but
that Gaia-Sausage-Enceladus stopped forming stars suddenly.

Similar to the [Fe/Mg] trends, Sculptor and Fornax extend into positive values
of [Ba/Mg] due to a natural decline in star formation caused by gas loss, see
Fig. 9a,b. Gaia-Sausage-Enceladus does not reach positive values of neither
[Fe/Mg] nor [Ba/Mg], suggesting an abrupt cessation of star formation in Gaia-
Sausage-Enceladus.

###  6.4 Star formation lasted over $2$ Gyr according to [Eu/Mg]

The [Eu/Mg] ratio reflects the balance of the quick ccSN contribution (Mg) and
the multiple sources of Eu, one quick, tracking star formation and another
source delayed by at least $\sim$2 Gyr (Sect. 6.1). Thus, we assume that a
flat trend of [Eu/Mg] will persist for at least the first $\sim$2 Gyr in the
star formation history of a galaxy, as in seen in Sculptor, Fig. 9c.

Fornax shows a flat [Eu/Mg] ratio until $\rm[Fe/H]\approx-1.2$, at which point
there is a increase in [Eu/Mg]. This suggests Fornax enriched its gas to
$\rm[Fe/H]\approx-1.2$ after at least 2 Gyr. The subsequent increase in
[Eu/Mg] is due to the onset of the delayed Eu source. We note that Eu
measurements are unavailable in Fornax at [Fe/H] $\leq$ -1.7 dex, but
$\rm[Eu/Mg]$ is measured to be $\sim 0$ at the lowest [Fe/H] available. This
trend of near solar ratio of the median [Eu/Mg] is expected at lower
metallicities as well. In addition, the Fornax data is sparse between
$-1.3\leq$ [Fe/H] $\leq-1.0$ (Reichert et al., 2020). It is clear that at
$\rm[Fe/H]<-1.0$ the [Eu/Mg] ratio in Fornax is flat and increases at higher
[Fe/H], however, the transition region is unfortunately under-sampled. The
sharp increase in [Eu/Mg] could actually be more gradual.

In Gaia-Sausage-Enceladus, the [Eu/Mg] ratio starts to increase at very low
[Fe/H], which suggests it was inefficient at forming stars within the first
$\sim$2 Gyr, in agreement with the higher [Ba/Mg] at low [Fe/H]. However, the
Gaia-Sausage-Enceladus progenitor stellar mass is estimated to be $10^{8.85}$
to $10^{9.85}$ M⊙ by Feuillet et al. (2020) and $4\times 10^{8}$ M⊙ by
Carrillo et al. (2024) using the mass-metallicity relations of Kirby et al.
(2013) and Ma et al. (2016). Because of the high mass of Gaia-Sausage-
Enceladus relative to Fornax and Sculptor ($\sim 10^{7}$ and $\sim 10^{6}$ M⊙,
respectively, McConnachie, 2012), we would expect star formation in Gaia-
Sausage-Enceladus to be more efficient than suggested by the low [Fe/H] at
which the [Eu/Mg] increases. A possible mechanism for keeping the [Fe/H] low
over the first $\sim$2 Gyr of star formation could be prolonged accretion of
pristine gas early in its star formation phase. Above $\rm[Fe/H]\approx-2.0$,
the [Eu/Mg] of Gaia-Sausage-Enceladus smoothly increases with [Fe/H],
suggesting that as the delayed source of Eu begins to contribute, there is
still enrichment of Mg from ccSN. This implies that there was no dramatic
change in the star formation over the [Fe/H] range represented in Fig. 9.

###  6.5 Quenching seen in [Eu/Ba]

The [Eu/Ba] ratio represents the balance of the delayed and extended
enrichment from AGB stars of a range of masses (Ba), and the two sources of
$r$-process enrichment (Eu), one quick and one delayed. In Sculptor, at low
[Fe/H], the [Eu/Ba] ratio is very high and then steeply decreases across the
entire [Fe/H] range. This trend is simply the inverse of the [Ba/Mg] trend
because Sculptor’s short star formation history does not allow for the delayed
source of Eu to significantly affect the stellar elemental abundance trends.
As a result, the Eu enrichment tracks closely the Mg enrichment. Therefore in
Sculptor, [Eu/Ba] traces the balance between the delayed and extended
enrichment of Ba from AGB stars and (only) the quick source of Eu, and
reflects the strong star formation early in the history of Sculptor, which
then gradually died out.

As noted above, Eu measurements are not available for Fornax at low
$\rm[Fe/H]<-1.7$, however, we expect the [Eu/Ba] in Fornax at low [Fe/H] to be
lower than in Sculptor and similar to that of Gaia-Sausage-Enceladus. At these
[Fe/H], the timescale of Eu enrichment is the same as the timescale of Mg
enrichment, therefore, the [Eu/Ba] trend is expected to be the inverse of the
[Ba/Mg] trend.

As [Fe/H] increases, [Eu/Ba] in Fornax remains relatively flat with a slight
decrease. The extended star formation history of Fornax allows the delayed
source of Eu to begin contributing as AGB enrichment of Ba increases. This
results in a much higher [Eu/Ba] than in Sculptor. The [Eu/Ba] ratio decreased
due to the decline in star formation, resulting in an increased number of AGB
contributions relative to ccSNe. The low star formation at late times in
Fornax (de Boer et al., 2012b) results in a minimal contribution of Eu from
the quick source.

In Gaia-Sausage-Enceladus, at low [Fe/H], the [Eu/Ba] ratio is lower than in
Sculptor, similar to [Eu/Ba] in Fornax and reflecting low initial star
formation, as was noted in [Ba/Mg]. However, with increasing [Fe/H], the
[Eu/Ba] ratio in Gaia-Sausage-Enceladus gradually rises. This suggests that
star formation remained relatively stable throughout its star-forming period,
necessitating continual contribution from the quick source of Eu to generate
high amounts of Eu, while Ba production increased with time from lower mass
AGB stars. Unlike in Fornax, which experienced a gradual decline in star
formation, the combination of the quick and delayed sources of the $r$-process
is efficient enough to increase the [Eu/Ba] ratio in Gaia-Sausage-Enceladus,
suggesting it did not experience a gradual decline in star formation.

##  7 Overview of the Gaia-Sausage-Enceladus
star formation history

###  7.1 Low initial star formation with inflows

We find that the star formation in Gaia-Sausage-Enceladus was initially
relatively low, and did not start with a strong burst as indicated by the high
[Ba/Mg] and low [Eu/Ba] ratios at low [Fe/H], especially when compared to
Sculptor, which did experience a strong initial burst of star formation before
quickly dying out.

The increase in [Eu/Mg] of Gaia-Sausage-Enceladus occurs at a relatively low
$\rm[Fe/H]\approx-2$, suggesting that in its first 2 Gyr the progenitor galaxy
enriched the gas less than expected for such a massive galaxy. Most literature
studies estimate the Gaia-Sausage-Enceladus progenitor mass to be relatively
massive compared to Fornax and Sculptor (see e.g. Feuillet et al., 2020;
Carrillo et al., 2024; McConnachie, 2012). The most likely scenario that could
explain why Gaia-Sausage-Enceladus was relatively inefficient in enriching its
gas, is that it was still accreting significant amounts of (near) pristine gas
in the first Gyrs of star formation.

###  7.2 Star formation extended and beyond 2 Gyr

Our analysis shows that the star formation of Gaia-Sausage-Enceladus lasted
for more than 2 Gyr as required by the very clear increase in [Eu/Mg] with
[Fe/H]. Based on constraints from Skúladóttir & Salvadori (2020) and an
updated star formation history of Sculptor from Bettinelli et al. (2019), we
assume the typical timescale of the delayed $r$-process to be $\gtrsim 2$ Gyr
(Sect. 6.4). Therefore, the increase in [Eu/Mg] with [Fe/H] indicates that
star formation lasted longer than in Sculptor, which shows no change in
[Eu/Mg].

The star formation likely remained relatively high for an extended period,
supported by the high or even increasing [Eu/Ba] ratio (Sect. 6.5). Further
evidence of the continued star formation is given by the shallower slope of
[Fe/Mg] in Gaia-Sausage-Enceladus relative to that seen in the Sculptor and
Fornax dSph galaxies.

###  7.3 Quenched star formation

Quenching of the star formation likely occurred as Gaia-Sausage-Enceladus fell
into the Milky Way (Gallart et al., 2019). We see evidence of quenching in our
dataset from the [Fe/Mg], [Ba/Mg], and [Eu/Ba] at high [Fe/H]. The star
formation in both Sculptor and Fornax died out naturally as the galaxies
gradually lost their gas. Because of low star formation at later times, the
effects of SNIa and AGB stars becomes more enhanced, resulting in supersolar
values of [Fe/Mg] and [Ba/Mg] in both Sculptor and Fornax (Fig. 9a,b). The
lower values of [Fe/Mg] and [Ba/Mg] at high [Fe/H] in Gaia-Sausage-Enceladus
thus suggest that its star formation was quenched, and did not die out
naturally through gradual loss of gas.

Additional evidence for quenching in Gaia-Sausage-Enceladus comes from the
[Eu/Ba] ratio. In both Fornax and Sculptor, [Eu/Ba] decreases towards the end
of star formation (at high [Fe/H]), but this is not seen in Gaia-Sausage-
Enceladus, suggesting a lack of a tail in its star formation history.

###  7.4 Literature Comparison

Previous literature works have explored the star formation history of the
Gaia-Sausage-Enceladus using different methodologies. Here we compare the main
results of our analysis with those available in the literature.

Hasselquist et al. (2021) uses Si and Mg elemental abundances from APOGEE DR17
to fit two different galactic chemical evolution models, flexCE (Andrews et
al., 2017) and a model described by Lian et al. (2018, 2020). Both models
present similar characteristics: low initial star formation, increasing to a
peak in star formation, leading to quenching of star formation when Gaia-
Sausage-Enceladus reached $\rm[Fe/H]\approx-0.6$. The flexCE model shows that
the Gaia-Sausage-Enceladus star formation peaks at $\sim$4 Gyr and quenched at
$\sim$4-5 Gyr. Further evidence that quenching occurred after 2-4 Gyr is based
on the deficiency in [Ce/Mg] and [(C+N)/Mg]. The model based on Lian et al.
(2018, 2020) peaks earlier and is quenched relatively quickly. Therefore, we
find that the model using flexCE is more consistent with our view of Gaia-
Sausage-Enceladus star formation history, having a broader and more extended
peak in star formation and quenching at a time of high star formation after
2-4 Gyr.

Johnson et al. (2023) use the galactic chemical evolution model VICE (Johnson
& Weinberg, 2020) to fit the [Mg/Fe] distribution of H3 observations (Conroy
et al., 2019). They show that Gaia-Sausage-Enceladus had an initially low star
formation that peaked within $\sim$2 Gyr and subsequently decreased until it
quenched around 8 Gyr ago, suggesting that it formed stars for 5 to 6 Gyr.
This model is consistent with our view of the Gaia-Sausage-Enceladus star
formation history, and is also quite similar to the Hasselquist et al. (2021)
flexCE model, but with a slightly longer duration of star formation.

Feuillet et al. (2021) derive an age distribution for Gaia-Sausage-Enceladus
stars, finding an age spread of $\sim$ 3 Gyr with a peak at $\sim$ 11 Gyr.
This is consistent with our view of how long Gaia-Sausage-Enceladus formed
stars, but perhaps on the short side of our estimate.

In our analysis, we limited our selection from the SAGA database to stars with
$\rm-2.2<[Fe/H]<-0.5$. From the literature, the metallicity distribution of
the kinematically-selected Gaia-Sausage-Enceladus contains small numbers of
stars at $\rm[Fe/H]\gtrsim-0.5$, and most of these are found to be Milky Way
members using individual elemental abundances (e.g. Feuillet et al., 2021). In
our SAGA sample we do not find any kinematically selected Gaia-Sausage-
Enceladus stars with $\rm[Fe/H]>-0.7$. Mori et al. (2024) show that the
highest metallicity stars from an infalling satellite would preferentially be
seen today moving with the disk of a Milky Way-like galaxy, with prograde
orbits. However, a relatively low number of stars are expected to be found
moving with the disk. If the Gaia-Sausage-Enceladus debris has a strong
metallicity gradient in the kinematics, this could result in high [Fe/H]
members missing from our sample. Any missing data at the high [Fe/H] would
most significantly affect our conclusion that Gaia-Sausage-Enceladus was
quenched. However, any potential internal metallicity gradient in Gaia-
Sausage-Enceladus is expected to be small (Khoperskov et al., 2023).

##  8 Conclusions

Our study examines the abundance trends of the $r$\- and $s$-process elements,
Eu and Ba, alongside Mg and Fe, across the metallicity range of Gaia-Sausage-
Enceladus, $\rm-2.2<[Fe/H]<-0.5$. Utilizing a meticulously curated literature
compilation from the SAGA database, we constrain the star formation of the
progenitor galaxy of Gaia-Sausage-Enceladus. Employing a unique analytical
approach, we interpret elemental abundance trends, particularly focusing on
the ratios [Fe/Mg], [Ba/Mg], [Eu/Mg], and [Eu/Ba] relative to [Fe/H].
Furthermore, we consider the temporal discrepancies in the nucleosynthetic
processes governing these elements. By comparing our findings with known dwarf
galaxies such as Fornax and Sculptor, we highlight the similarities and
differences.

From these elemental abundance ratios and in comparison with the known star
formation histories of Fornax and Sculptor, we place three main constraints on
the star formation history of Gaia-Sausage-Enceladus.

1) At low [Fe/H], the high [Ba/Mg] and low [Eu/Ba] require that the star
formation in Gaia-Sausage-Enceladus was relatively low, as compared with
Sculptor where the strong initial burst of star formation drove high
enrichment of Mg from ccSN before significant enrichment of Ba from AGB stars
occurred, resulting in a very low [Ba/Mg].

2) The increase in [Eu/Mg] in Gaia-Sausage-Enceladus requires that star
formation was extended for longer than $\sim 2$ Gyr, continuing at least until
the delayed enrichment source of Eu began contributing. In contrast, star
formation in Sculptor did not last long enough for the [Eu/Mg] to increase,
where as star formation in Fornax was extended, resulting in high [Eu/Mg] at
high [Fe/H].

3) The continued high [Eu/Ba] at high [Fe/H] in Gaia-Sausage-Enceladus
requires that star formation was quenched around [Fe/H] $\sim-0.5$, preventing
a period when enrichment of Ba from AGB stars dominated over enrichment of Eu.
This would have resulted in a decrease in [Eu/Ba], as is seen Fornax and
expected in galaxies that naturally exhaust their gas supply. Additionally,
the maximum [Fe/Mg] and [Ba/Mg] of $\sim 0$ in Gaia-Sausage-Enceladus, as
compared to the super-solar values in Fornax and Sculptor, imply that Gaia-
Sausage-Enceladus did not naturally consume its gas supply.

Looking ahead, we anticipate that the forthcoming 4MOST data will provide
valuable insights into the Milky Way accreted populations understanding,
particularly for this major accretion event, Gaia-Sausage-Enceladus. Surveys
which include data from the halo, disk, and bulge (Surveys 1-4 Helmi et al.,
2019; Christlieb et al., 2019; Chiappini et al., 2019; Bensby et al., 2019),
as well as information from dwarf galaxies and their stellar streams in Survey
14 (Skúladóttir et al., 2023), will greatly improve our understanding of how
the Milky Way formed and evolved with greater accuracy than ever before.

## Software and database notes

In our work, we made use of the following software and databases:

  * •

SAGA database (Suda et al., 2008)

  * •

SIMBAD (Wenger et al., 2000)

  * •

astroquery.simbad (Ginsburg et al., 2019)

  * •

astropy (Astropy Collaboration et al., 2013, 2018, 2022)

  * •

galpy (Bovy, 2015)

  * •

Gaia DR3 (Gaia Collaboration et al., 2021)

## Acknowledgements

We thank Haining Li for sharing the Gaia DR3 IDs for their targets (Li et al.,
2022).

H.E., S.F. and D.F. were supported by a project grant from the Knut and Alice
Wallenberg Foundation (KAW 2020.0061 Galactic Time Machine, PI Feltzing). This
project was supported by funds from the Crafoord foundation (reference
20230890). Á.S. acknowledges funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No. 101117455).

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##  Appendix A Ba stars not considered in the analysis

To ensure the meaningfulness of the elemental abundance trends, we have chosen
to exclude so called Ba stars. These stars do not provide insights into a
galaxy’s chemical enrichment but are the results of the evolution in binary
systems. Apart from being high in Ba, such stars can also have enhanced carbon
abundances. We therefore checked the C abundances in all stars and found that
all the stars listed in Table 3 exhibit both high Ba and high C abundances,
and are therefore removed from our sample.

Table 3: Ba stars selected as Gaia-Sausage-Enceladus members, following Feuillet et al. (2021) selection, that were not considered in the analysis. Gaia ID | [Fe/H] | [Ba/Fe]
---|---|---
Gaia DR3 2982933097213087616 | –1.39 | 1.85
Gaia DR3 3686190458143012352 | –2.04 | 2.40
Gaia DR3 2722263350106417152 | –1.20 | 1.17
Gaia DR3 2601354871056014336 | –2.09 | 1.55
Gaia DR3 2448568453248165504 | –2.11 | 2.20

##  Appendix B Effective temperatures and stellar ages

###  B.1 Effective temperatures – additional checks

When estimating the stellar ages (Sec. 3.4), we opted to use the photometric
$T_{\rm eff}$ instead of $T_{\rm eff}$ from Gaia RVS or the SAGA $T_{\rm
eff}$. The SAGA stellar parameters are not homogeneously derived since it is a
literature compilation, and some stars have $T_{\rm eff}$ reported from more
than one study. When we compared the photometric $T_{\rm eff}$ with the Gaia
RVS $T_{\rm eff}$ for our primary Gaia-Sausage-Enceladus sample, we see a
large scatter and an offset. When we compared the photometric $T_{\rm eff}$
with the median SAGA literature $T_{\rm eff}$, we have less scatter and a very
small offset. A homogeneous input dataset is crucial for ensuring our derived
stellar ages are directly comparable and on the same absolute scale.
Therefore, we conclude that the photometric $T_{\rm eff}$ is more precise than
Gaia RVS $T_{\rm eff}$ for our Gaia-Sausage-Enceladus sample. A comparison is
shown in Fig. 10.

Figure 10: a) the difference between photometric $T_{\rm eff}$ and Gaia RVS
$T_{\rm eff}$ as a function of photometric $T_{\rm eff}$. b) the difference
between photometric $T_{\rm eff}$ and median $T_{\rm eff}$ in the SAGA
database as a function of photometric $T_{\rm eff}$. In both panels the
colour-coding indicates the median SAGA [Fe/H].

###  B.2 Age estimates for 16 dwarf stars with poorly constrained probability
distribution functions

Figure 11: Age probability distribution functions for 16 dwarf stars selected
as members of Gaia-Sausage-Enceladus according to Feuillet et al. (2021)
scheme that do meet our quality criteria.

For completeness, we show in Fig. 11 the probability distribution functions
for the 16 dwarf stars, that do not meet our quality criteria, described in
Sec 3.4. No age estimates are listed for these stars in Table LABEL:tab:data.

##  Appendix C Elemental abundance trends for the Gaia-Sausage-Enceladus based
on different selection schemes

For completeness, we show the elemental abundances and their derived median
trends for the other five selection schemes listed in Table 2. The error-bars
represent the MAD for stars with multiple measurements of a particular
elemental abundance ratio. These error-bars are not taken into account when
deriving the the trends. We also include the $r$-II stars and high-light them.
They follow the general trends apart from that their Eu abundances are high.

Figure 12:  The Gaia-Sausage-Enceladus stars in the SAGA data sample selected
according to the “Sausage” scheme. Different types of stars are identified
according to the legend. The running median is also shown.  Figure 13:  The
Gaia-Sausage-Enceladus stars in the SAGA data sample selected according to the
scheme from Helmi et al. (2018). Different types of stars are identified
according to the legend. The running median is also shown.  Figure 14: The
Gaia-Sausage-Enceladus stars in the SAGA data sample selected according to the
scheme from Myeong et al. (2019). Different types of stars are identified
according to the legend. The running median is also shown.  Figure 15: The
Gaia-Sausage-Enceladus stars in the SAGA data sample selected according to the
scheme from Horta et al. (2023). Different types of stars are identified
according to the legend. The running median is also shown.  Figure 16: The
Gaia-Sausage-Enceladus stars in the SAGA data sample selected according to the
scheme from Naidu et al. (2020). Different types of stars are identified
according to the legend. The running median is also shown.