11institutetext: Zentrum für Astronomie der Universität Heidelberg,
Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany
11email<EMAIL_ADDRESS>22institutetext: Max Planck Institute for Astronomy,
Königstuhl 17, 69117, Heidelberg, Germany 33institutetext: Leibniz-Institut
für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
44institutetext: South-Western Institute for Astronomy Research, Yunnan
University, Kunming, Yunnan 650091, People’s Republic of China
55institutetext: Dipartimento di Fisica, Sezione di Astronomia, Università di
Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy 66institutetext: INAF –
Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34143 Trieste, Italy
77institutetext: INFN – Sezione di Trieste, Via A. Valerio 2, 34127 Trieste,
Italy 88institutetext: Institute of Space Sciences (ICE, CSIC), 08193,
Cerdanyola del Valles, Spain 99institutetext: Institut d’Estudis Espacials de
Catalunya (IEEC), 08034, Barcelona, Spain

# Observational constraints on the origin of the elements.
VIII. Constraining the Barium, Strontium and Yttrium chemical evolution in
metal-poor stars

G. Guiglion 11 2 2 3 3 M. Bergemann 22 N. Storm 22 J. Lian 44 2 2 G. Cescutti
55 6 6 7 7 A. Serenelli 88 9 9

(Received XXX; accepted XXX)

###### Abstract

Context. The chemical evolution history of slow neutron-capture elements in
the Milky Way is still a matter of debate, especially in the metal-poor regime
([Fe/H]¡-1).

Aims. Recently Lian et al. (2023), thanks to _Gaia_ -ESO spectroscopic data,
studied the chemical evolution of neutron-capture elements in the regime
[Fe/H]¿-1. We aim here to complement this study down to [Fe/H]=-3, and focus
on Ba, Y, Sr, and abundance ratios of [Ba/Y] and [Sr/Y], which give
comprehensive views on s-process nucleosynthesis channels.

Methods. We measured LTE and NLTE abundances of Ba, Y, and Sr in 323 Galactic
metal-poor stars using high-resolution optical spectra with high signal-to-
noise. We used the spectral fitting code TSFitPy, together with 1D model
atmospheres using previously determined LTE and NLTE atmospheric parameters.

Results. We find that the NLTE effects are on the order of $\sim-0.1$ to $\sim
0.2$ dex depending on the element. We find that stars enhanced(deficient) in
[Ba/Fe] and [Y/Fe] are also enhanced(deficient) in [Sr/Fe], suggesting a
common evolution channel for these three elements. We find that the ratio
between heavy and light s-process elements [Ba/Y] varies weakly with [Fe/H]
even in the metal-poor regime, consistent with the behaviour in the metal-rich
regime. The [Ba/Y] scatter at a given metallicity is larger than the abundance
measurement uncertainties. Homogeneous chemical evolution models with
different yields prescriptions are unable to accurately reproduce the [Ba/Y]
scatter in the low-[Fe/H] regime. Adopting the stochastic chemical evolution
model by Cescutti & Chiappini (2014) allows to reproduce the observed scatter
in the abundance pattern of [Ba/Y] and [Ba/Sr]. With our observations, we rule
out the need for an arbitrary scaling of the r-process contribution as
previously suggested by the model authors.

Conclusions. We have showed how important it is to properly include NLTE
effects when measuring chemical abundances, especially in the metal-poor
regime. This work shows that the choice of the Galactic chemical evolution
model (stochastic vs. 1-zone) is key when comparing models to observations.
The upcoming large scale spectroscopic surveys such as 4MOST and WEAVE will
deliver high quality data of many thousands of metal-poor stars, and this work
gives a typical case study of what could be achieved with such surveys.

###### Key Words.:

Galaxy: abundances – Galaxy: evolution – Galaxy: stellar content – stars:
abundances – ISM: abundances

##  1 Introduction

Neutron-capture elements have been extensively studied in the astronomy
community for more than three decades, but the chemical evolution of such type
of elements in the Milky Way is still a matter of debate (e.g. Sneden et al.
2008; Cowan et al. 2021). Neutron-capture elements are, for instance,
essential for tracing the accretion history of the Milky Way (e.g. Helmi 2020;
Matsuno et al. 2021), and its satellite Galaxies (e.g. Venn et al. 2012).

Figure 1: Left: Kiel diagram of the 323 stars of the sample (NLTE
$\textit{T}_{\text{eff}}$ vs. $\text{log}(\textit{g})$), colour-coded with
NLTE $[\text{Fe}/\text{H}]$. Middle: NLTE $[\text{Fe}/\text{H}]$ vs.
$\textit{T}_{\text{eff}}$ colour-coded with NLTE $\text{log}(\textit{g})$.
Right: NLTE $[\text{Fe}/\text{H}]$ vs. $\text{log}(\textit{g})$ colour-coded
with NLTE $\textit{T}_{\text{eff}}$.

In particular, the slow-neutron capture (s-process) dominated elements are
mainly organised in two peaks (Burbidge et al. 1957). The first peak is
located around the magic number 50, and is responsible for the synthesis of
the light-s elements Sr, Y, and Zr. The second peak produces Ba, La, Ce, Pr,
and Nd around the magic number 80. There exists a third peak as well, that
produces Pb. It is common to divide the s-process into a “main” process, a
“weak” process and a “strong” process. The main s-process occurs in asymptotic
giant branch (AGB) stars (Busso et al. 1999; Bisterzo et al. 2011) while the
weak s-process is known to occur in massive stars and it produces nuclei with
magic number below 88 (Pignatari et al. 2010). Finally, the strong s-process
is responsible for about 50% of solar 208Pb production by low-metallicity AGB
stars (Kaeppeler et al. 1982).

Figure 2: Examples of Ba II (left) and Y II (right) lines in the spectra of
two red giants with [Fe/H]${}_{\mathrm{NLTE}}=-1.65$ (top) and
[Fe/H]${}_{\mathrm{NLTE}}=-0.77$ (bottom). The red shaded area represents the
spectral range over which the line is fitted. The orange curve corresponds to
the best line-fit. The black vertical corresponds to the central wavelength of
the line.

The chemical evolution of neutron-capture elements has been rather well
constrained in the Milky Way disc (e.g. Battistini & Bensby 2016; Mishenina et
al. 2019). However, not many studies focused on the halo or halo/disc
interface. Even with the advent of large-scale spectroscopic surveys (e.g.
GALAH; Buder et al. 2019), neutron-capture abundance measurements are
available for only a few tens of very metal-poor stars (e.g. Mashonkina et al.
2007; Matsuno et al. 2021), as it requires high-quality and high signal-to-
noise ratio spectra in the metal-poor regime ($[\text{Fe}/\text{H}]<-1$). Past
GCE works also relied on compilations of abundances from various studies, but
these may suffer from systematic biases, owing to the fundamental assumption
of local thermodynamical equilibrium (LTE) (e.g. Cescutti & Chiappini 2014).
High-resolution spectroscopy is indeed a unique technique for determining
precise estimates of neutron-capture elemental abundances (e.g. Delgado Mena
et al. 2017; Guiglion et al. 2018; Roederer et al. 2022).

Recently Lian et al. (2023) studied the Galactic chemical evolution of Ba and
Y using the data from the _Gaia_ -ESO large spectroscopic survey. Most stars
in the sample of Lian et al. (2023) cover the metallicity range
$-1<[\text{Fe}/\text{H}]<0.5\,$dex, for which _Gaia_ -ESO measured and
released high-quality chemical abundances of neutron-capture elements. In this
letter, we aim to constrain the chemical evolution of Ba, Y, and Sr in the
metal-poor regime ($-3<[\text{Fe}/\text{H}]<-0.5\,$dex), in order to further
complement the study of Lian et al. (2023). We also make one step forward
towards a higher accuracy by computing our abundances in the framework of non-
local thermodynamic equilibrium (NLTE).

In Section 2, we present the spectroscopic data and spectral analysis. In
Section 3, we present LTE and NLTE chemical abundance trends of Sr, Y, and Ba,
while we confront our observations to Galactic chemical evolution models in
Section 4. Finally, we present our conclusions in Section 5.

Figure 3: Top row: chemical abundances of [Sr/Fe] (left), [Y/Fe] (center), and
[Ba/Fe] (right) in LTE as a function of LTE [Fe/H]. We both show individual
stars and contour-plot. Black error bars correspond to mean uncertainties
$\langle\sigma\rangle$. Bottom row: same as top row, but in NLTE.

##  2 Data and methodology

We took advantage of high-resolution spectra of Galactic disc and halo stars
from Ruchti et al. (2011). These targets were originally observed at
intermediate resolution by the RAVE survey (Steinmetz et al. 2006; Matijevič
et al. 2017). The sample consists of 323 metal-poor stars covering the ranges
$4050<\textit{T}_{\text{eff}}<6500\,$K, $0.5<\text{log}(\textit{g})<4.5$, and
$-2.8<[\text{Fe}/\text{H}]<-0.4$ (in NLTE; see Figure 1). The data have
already been used in our previous studies, e.g, in the analysis of NLTE
stellar parameters and metallicities (Ruchti et al. 2013), ages (Serenelli et
al. 2013), and NLTE Mg abundances (Bergemann et al. 2017a, b). We adopted the
1D-LTE and 1D-NLTE atmospheric parameters from Ruchti et al. (2013).

In order to derive chemical abundances of Ba II, Y II, and Sr I, we used the
spectral fitting code TSFitPy111https://github.com/TSFitPy-developers/TSFitPy,
which is based on the LTE version of TurboSpectrum (Plez 2012) as well as its
NLTE extension222https://github.com/bertrandplez/Turbospectrum_NLTE (Gerber et
al. 2023). TSFitPy allows to simultaneously fit the abundance, the micro- and
macro-turbulence, as well as to apply radial velocity corrections to the data,
which are typically needed owing to the lack or realistic convection and
turbulent flows in 1D hydrostatic models (see e.g. Dravins 2008; Nordlund et
al. 2009; Meunier et al. 2017).

The model atom of Sr used in this work is based on the model described in
Bergemann et al. (2012), however, it has been updated with new quantum-
mechanical data for inelastic transitions in Sr$+$H collisions (Gerber et al.
2023). The Ba model is that from Gallagher et al. (2020), and Y model from
Storm & Bergemann (2023). The atomic transition probabilities come from
Davidson et al. (1992) for Ba II lines, García & Campos (1988) for Sr I lines
and Biémont et al. (2011) for Y (see (Heiter et al. 2021) for more details).
Ba II lines suffer significantly from hyperfine splitting (HFS) and isotopic
shifts, and these effects have been included in the calculations as described
in (Gallagher et al. 2020). HFS is negligible for Y II (¡0.5 mÅ) and is not
included in the linelist. For Ba II, we adopted the lines at $5853.67$,
$6141.71$, $6496.90\,$Å that show rather strong features even down to
$[\text{Fe}/\text{H}]=-3$. For Sr, we used the strong and unblended spectral
line of Sr I at $4607.33\,$Å, while two Y II lines were adopted for the
Yttrium measurements ($4883.68$ and $5087.42\,$Å). It has already been
demonstrated in Bergemann et al. (2012) that NLTE provides a robust ionization
balance for Sr I and Sr II-based abundances for dwarfs and red giants over the
metallicity range relevant to the present work. For Y, the standard validation
tests of the NLTE model atom, including validation on metal-poor red giant
atmospheres, were presented in Storm & Bergemann (2023). For the atomic and
molecular blends, we took advantage of the comprehensive _Gaia_ -ESO survey
linelist (Heiter et al. 2021). We adopted the extensively used 1D MARCS model
atmospheres from Gustafsson et al. (2008). The solar abundances are taken from
Magg et al. (2022).

We carefully checked by eye the quality of the fitted spectral lines to ensure
the robustness of the abundance measurements. Examples of Ba II and Y II best-
fit profiles are showed in Figure 2 for two red giants with different
metallicities. For a given element, the error budget $\sigma$ was computed by
quadratically summing the line-to-line scatter ($\sigma_{sc}$) to the
propagated errors from the three atmospheric parameters
($\textit{T}_{\text{eff}}$, $\text{log}(\textit{g})$, $[\text{Fe}/\text{H}]$)
($\sigma_{atm}$).

##  3 Chemical abundance trends of [Sr/Fe], [Y/Fe], and [Ba/Fe]

In Figure 3, we show LTE (blue) and NLTE (red) abundances of Sr, Y, and Ba as
a function of LTE (top) and NLTE (bottom) metallicity [Fe/H], respectively.

LTE [Sr/Fe] shows a slightly increasing behaviour with [Fe/H], and the
abundance ratios tend to be strongly sub-solar over the entire metallicity
range. NLTE [Sr/Fe] is only slightly sub-solar for [Fe/H]¿-1, and solar for
[Fe/H]¡-1. We note a major difference between both LTE and NLTE of about $0.2$
dex in [Sr/Fe]. This is expected, because NLTE effects on the formation of the
Sr I line at 4 706 Å are positive, as in NLTE the line opacity decreases,
leading to weaker lines compared to LTE (Bergemann et al. 2012; Hansen et al.
2013). Overall, the stars-by-star scatter is around 0.17 dex for LTE [Sr/Fe],
while the scatter drops to 0.13 for NLTE [Sr/Fe], as a result of NLTE effects
shrinking the distribution. This is also the case for the individual abundance
uncertainties, as illustrated by the black error bars in the bottom of each
panel (computed as mean uncertainties in a 0.5 dex [Fe/H range]). We notice
that the overall distribution of NLTE [Sr/Fe] vs. [Fe/H] also shrinks on the
x-axis due to higher NLTE [Fe/H] ratios compared to LTE [Fe/H]. As presented
in Figure 4, it is evident that the metallicity distribution function below
[Fe/H]$=-1.5$ drastically differs between LTE and NLTE: the NLTE [Fe/H]
distribution shrinks, and we only probe the halo down to [Fe/H]$=-2.7$, due to
increasing NLTE correction with decreasing [Fe/H].

In the middle-top panels of Figure 3, we see that the LTE [Y/Fe] ratio shows a
concave shape with [Fe/H], and on average sub-solar
($\langle\mathrm{[Y/Fe]}\rangle=-0.09$), which is consistent with past LTE
studies (e.g. Delgado Mena et al. 2017). In contrast, NLTE [Y/Fe] ratios
slightly decrease with increasing [Fe/H], from roughly $0.1$ at [Fe/H]
$\lesssim-1.2$ to $\sim-0.1$ for [Fe/H] $\gtrsim-1.2$. We notice that the
overall star-to-star [Y/Fe] scatter is equal to 0.17 dex in both LTE and NLTE;
this scatter slightly increases with [Fe/H] and ranges from 0.14 to 0.18 in
LTE and 0.12 to 0.17 in NLTE. Such increase is likely due to the presence of
[Y/Fe]-rich/poor stars (see below). On average, NLTE [Y/Fe] ratios are higher
than LTE [Y/Fe] by $\sim 0.15\,$dex at [Fe/H] $\approx-2$, while the
difference between NLTE and LTE decreases to 0.04 for [Fe/H] $\gtrsim-1$,
which is similar but less pronounced than [Sr/Fe]. The overall behaviour of
NLTE effects in Y with metallicity is consistent with the results of Storm &
Bergemann (2023).

In the top-right panel of Figure 3, we show that LTE and NLTE [Ba/Fe]
abundances follow a similar, although not the same, trend. As metallicities
above $\sim-1$, NLTE [Ba/Fe] is slightly lower than LTE [Ba/Fe] by about 0.07
dex, consistent with past studies, e.g. our previous work in Gallagher et al.
(2020), as we expect Ba lines equivalent widths to increase due to NLTE
effects. NLTE [Ba/Fe] is rather flat for [Fe/H] $\gtrsim-1.25$, in agreement
with previous studies (e.g. Delgado Mena et al. 2017 in LTE and Korotin et al.
2011 in NLTE). The star-by-star standard deviation of NLTE [Ba/Fe] abundances
is 0.16 dex, while it reaches 0.21 dex for LTE [Ba/Fe]. This shows that NLTE
abundances have less intrinsic scatter, which has implications for the
chemical enrichment of the elements in the Galaxy, as we will show in Sect. 4
below.

We notice the presence of stars deficient in [Y/Fe], compared to the main
distribution at a given metallicity, as well as some stars with large [Ba/Fe]
and [Y/Fe] values. To search for possible correlations between these low- and
high-abundance stars, we present in Figure 5 the NLTE abundances of [Y/Fe] as
a function of [Ba/Fe], colour-coded with [Sr/Fe]. Firstly, we see that stars
deficient in [Y/Fe] show also both sub-solar [Ba/Fe] and [Sr/Fe]. Secondly,
stars with large [Y/Fe] ratios are also characterized by large [Ba/Fe] and
[Sr/Fe]. These enhanced(deficient) stars do not seem to be preferentially part
of any given Milky Way component, when following the thin/thick disc and halo
classification of Ruchti et al. (2011). We also checked that for dwarfs and
turn-off stars, there was no correlation with stellar ages from Serenelli et
al. (2013).

Figure 4: LTE and NLTE metallicity distribution of our stellar sample probing
the metal-weak Galactic disc and the halo (see Ruchti et al. 2013). The
distribution is not uniform and not statistically complete, because of the
observational selection function (Ruchti et al. 2011). Figure 5: NLTE chemical
abundances of [Y/Fe] as a function of [Ba/Fe], color-coded with [Sr/Fe].
Figure 6: Left panel: chemical abundance ratios [Ba/Y] in both LTE (blue
contours) and NLTE (red contours) as a function of [Fe/H] (LTE and NLTE,
respectively), for 187 stars. Error bars correspond to mean uncertainties in
LTE and NLTE. Right panel, we only show NLTE [Ba/Y] (red contours) together
with _Gaia_ -ESO sample used by Lian et al. (2023), as well as 1-zone chemical
evolution models with different yields prescriptions.

##  4 Confronting chemical evolution model with heavy-to-light s-process
element ratios

We investigate here the [Ba/Y] ratio, which is a proxy of the heavy to light
s-process elements (e.g. Lian et al. 2023). We compare our observations to
simple one-zone and inhomogeneous (stochastic) Galactic chemical evolution
models, the former primarily relevant to understanding the chemical enrichment
of the disc and latter qualitatively consistent with the present understanding
of the formation of the Galactic halo (see for instance Matteucci 2021 and
references there-in).

In the left panel of Figure 6, we present LTE (blue contours) and NLTE (red
contours) distributions of [Ba/Y] ratios for the 187 stars of our sample with
available Ba and Y abundances (in both LTE and NLTE). Both LTE and NLTE [Ba/Y]
abundances slightly increase with [Fe/H], and present both a similar scatter
of 0.17 dex, rather constant with [Fe/H]. Overall, We see that [Ba/Y] presents
a weak dependence on [Fe/H] over the entire range of [Fe/H]. The main
difference is a rigid shift of $-0.12$ dex between NLTE and LTE [Ba/Y]. The
intrinsic scatter of abundance ratios is larger than the individual
observational uncertainties of the measurement (ranging from 0.16 to 0.08 in
NLTE, see Sect. 2) suggesting that the observational scatter is a signature of
chemical enrichment processes. In the right panel of Figure 6, we show NLTE
[Ba/Y] ratio as a function of NLTE [Fe/H]. We also overplotted the _Gaia_ -ESO
NLTE [Ba/Y] abundances used in Lian et al. (2023). Even though the abundances
between this work and the Gaia-ESO were computed with different spectral
analysis pipelines, the data is rather complementary333For the present study
and the Gaia-ESO survey used the same linelist and model atmosphere grids..

###  4.1 One-zone GCE models

As in Lian et al. (2023), we made of the OMEGA+ Galactic chemical evolution
(GCE) model (Côté et al. 2017, 2018), which includes gas inflow and outflows.
The basic model includes core collapse supernova (CCSN) yields from (Limongi &
Chieffi 2018), as well as Type Ia supernovae with yields from different
Chandrasekhar- and sub-Chandrasekhar mass explosions as described in Eitner et
al. (2023). The GCE model also includes AGB yields from Cristallo et al.
(2015). This basic GCE model is displayed in orange in Figure 6. For
comparison, we also display a GCE model that includes recent AGB yields by
Karakas (2010), which account for n-capture elements nucleosynthesis for
metallicites down to $-2$ (see Cinquegrana & Karakas 2022 and references
there-in for more details). We also show one GCE model with no AGB
contribution (in purple), and one with metallicity-independent AGB yields (in
green). Finally, we added a GCE model that only includes non-rotating massive
stars.

Lian et al. (2023) concluded that the shape of [Ba/Y] in the metal-rich regime
([Fe/H] $\gtrsim-0.6$) is driven by the metallicity dependence in the neutron
capture efficiency in AGB stars. The mismatch between the GCE models and
observations in this [Fe/H] regime is likely due to an overestimation of the
s-process efficiency of low mass AGB stars (Magrini et al. 2021).

In the metallicity range -2 $\lesssim$ [Fe/H] $\lesssim-0.8$, the model
without massive star yields shows a strong underproduction of [Ba/Y] and it is
not consistent with the data. The large scatter in [Ba/Y] at a given
metallicity could be a sign of chemical enrichment from AGBs with masses
between 2 to 6 solar masses (Lian et al. 2023, their Fig. 5). We also find
that the GCE track computed with non-rotating CCSN yields underpredicts our
observations, which supports evidence from the literature that CCSN resulting
from the evolution of rapidly rotating massive stars are important sources of
s-process elements (e.g Limongi & Chieffi 2018). In conclusion, such chemical
evolution models with different nucleosynthesis prescriptions are not able to
reproduce the data, mainly due to the large scatter in [Ba/Y] at a given
[Fe/H].

###  4.2 Stochastic GCE models

Substantial efforts have been made in the GCE model community in trying to
reproduce the abundance patterns measured in the Galactic halo stars. Cescutti
& Chiappini (2014) and Rizzuti et al. (2021) developed stochastic GCE models.
Such models are meant to reproduce the chemical evolution of the Galactic
halo, implying a series of nucleosynthesis events, overall on a time scale of
1 Gyr. Their model MRD+s B2 includes r-process contribution from magneto-
rotational (MRD) supernovae and s-process nucleosynthesis from two channels:
low-mass AGB stars and rotating massive stars (see Cescutti & Chiappini 2014
for more details). We adopted the model MRD+s B2. We explore here whether such
models can reproduce the scatter we measure in our observations of [Ba/Y]. We
notice that contrary to the model of Lian et al. (2023), the models from
Cescutti & Chiappini (2014) do not include neutron star mergers.

In the top panel of Figure 7, we present LTE and NLTE [Ba/Y] abundance ratios
as a function of NLTE [Fe/H] (blue and red contours, respectively).
Additionally, we present stochastic GCE (colour-coded with number of stars in
the model, i.e. SFR tracer). For [Fe/H]$\lesssim-2.5$, the GCE model shows a
large scatter in the [Ba/Y] ratios, ranging from $\sim-1$ to $+0.3$. Such
behaviour is directly attributed to the stochastic sampling of the IMF during
the phase of halo formation (Cescutti & Chiappini 2014). The predicted [Ba/Y]
trend flattens out for metallicities [Fe/H]$\gtrsim-2.5$ and slightly rises up
to [Ba/Y] $\approx 0.25$ for [Fe/H]$\gtrsim-1$. This GCE model matches rather
well our LTE [Ba/Y] ratios, however, it overpredicts [Ba/Y] when compared to
NLTE [Ba/Y]. This mis-match is simply the consequence of the fact that in this
GCE model the yttrium yields were modified to match the LTE observations.
Specifically the r-yields were scaled the LTE pattern of r-process rich stars.
This pattern differs by a factor of 3 for Y, whereas it is consistent with the
r-process solar residual for the remaining elements (see Cescutti & Chiappini
2014 for more details). Hence the GCE matches rather well our LTE [Ba/Y]
pattern. Such results show that taking into account NLTE effects is key if one
wants to accurately compare GCEs and observations.

In the bottom panel of Figure 7, we show similar plots but for the [Ba/Sr]
ratios. The GCE model shows a similar trend with [Ba/Y]. Contrary to [Ba/Y],
the GCE model matches better the NLTE [Ba/Sr] ratios, while the LTE [Ba/Sr]
ratios are clearly over-abundant compared to the GCE model. This could be due
to the large NLTE effect when measuring the Sr line at 4607Å. Again, taking
properly into account NLTE effects is key when comparing chemical evolution
models to observations, especially in the metal-poor regime.

Considering that we provide new NLTE abundances of neutron-capture elements
for our stellar sample, it is necessary to confront our data to a stochastic
chemical evolution model that is not scaled to reproduce the LTE abundance
patterns. It corresponds to the model MRD+s B from Cescutti & Chiappini (2014)
which is similar to the model MRD+s B2, but the r-process contribution to Y
production scaled to the solar residual, as the other elements and therefore
not divided by a factor of 3. We show such a model in Figure 8, together with
the LTE and NLTE abundances of our metal-poor stars. Naturally, the predicted
ratio of [Ba/Y] is lower by 0.3 dex compared to the model MRD+s B2.
Interestingly, the GCE model based on r-process solar residual is indeed
closer to the NLTE observational distributions of [Ba/Y] and [Ba/Sr] in our
stellar sample. It is important to remind the reader that our abundances are
computed using 1D model atmospheres, and we expect the [Ba/Y] ratio to be
lower when adopting an updated model atom (Storm et al. in prep) with updated
Y+H collisional processes based on Wang et al. (2023). Also, adopting 3D model
atmospheres (Storm et al. in prep) can induce larger and more positive 3D NLTE
effects for Y II lines. As a result, we do not see evidence for re-scaling the
MRD yields for Y to the pattern of the r-process rich stars as used in the
model MRD+s B2 of Cescutti & Chiappini (2014); moreover, the r-process solar
residuals appear to be more reliable, as expected: they are not affected by
the NLTE corrections.

Figure 7: [Ba/Y] (top) and [Ba/Sr] ratios as a function of [Fe/H]. Blue and
red contours show LTE and NLTE abundances, respectively. We also show
stochastic chemical evolution models (MRD+s B2) from Cescutti & Chiappini
(2014). Figure 8: Same figure as Figure 7, but we show the model MRD+s B from
Cescutti & Chiappini (2014).

##  5 Conclusions

In this letter, we focused on constraining the chemical enrichment of [Ba/Fe],
[Sr/Fe], [Y/Fe] and [Ba/Y] ratios of Milky Way stars in the domain
$-2.5\lesssim[\text{Fe}/\text{H}]\lesssim-0.5$ There is lack of abundance
measurements in this [Fe/H] range that deems direct constraints of Galactic
chemical evolution challenging.

  1. 1.

We used high-resolution (R$\in[35\,000-45\,000]$) and high signal-to-noise
observations of RAVE metal-poor stars with previously determined
$\textit{T}_{\text{eff}}$, $\text{log}(\textit{g})$, and
$[\text{Fe}/\text{H}]$ in both LTE and NLTE (Ruchti et al. 2013).

  2. 2.

We measured 1D LTE and NLTE abundances of [Ba/Fe], [Sr/Fe], and [Y/Fe] with
associated uncertainties using the spectral synthesis code TSFitPy, a wrapper
for NLTE version of TurboSpectrum. Careful visual checks of the spectral fits
were performed in order to ensure the robustness of the determined chemical
abundances.

  3. 3.

We showed that the bulk of NLTE [Ba/Fe] ratios decreases with increasing
[Fe/H], while NLTE [Sr/Fe] is rather constant with [Fe/H], and NLTE [Y/Fe]
decreases with [Fe/H]. The combined NLTE effects are of the order of $-0.07$
dex for [Ba/Fe], $+0.18$ dex for [Sr/Fe], and $+0.10$ dex for [Y/Fe] that also
includes the NLTE effect on [Fe/H].

  4. 4.

Focusing on NLTE abundances, we find that stars enhanced(deficient) in [Ba/Fe]
and [Y/Fe] are enhanced(deficient) in [Sr/Fe].

  5. 5.

We showed that the NLTE ratios of [Ba/Y] are centred around solar values, and
the behaviour of the trend is rather flat with NLTE metallicity [Fe/H],
implying that [Ba/Y] is not sensitive to [Fe/H]. The star-to-star scatter is
substantial and is of the order of 0.2 dex. LTE [Ba/Y] ratios show a similar
dispersion as NLTE [Ba/Y], but are shitted by $+0.12$ dex relative to the
solar values even at metallicities close to solar.

  6. 6.

Single-zone chemical evolution models are unable to reproduce the [Ba/Y]
scatter observed at a given metallicity. Such a scatter can, however, be more
captured by stochastic GCE models.

  7. 7.

Most importantly, we find a better agreement of the NLTE abundance ratios of
light (Sr,Y) and heavy (Ba) element ratios compared to the GCE tracks from
stochastic chemical evolution models with r-yields scaled r-process solar
residual. There is not anymore need of modifications of the r-process yields
of yttrium following the pattern of r-process rich stars as was done e.g. in
Cescutti & Chiappini (2014). Therefore, we conclude that properly taking into
account NLTE effects when measuring abundances directly impacts comparisons
between galactic chemical evolution models and observations, hence on yield
prescriptions and nucleosynthesis channels.

The current studied sample is still rather limited in the number of stars and
in the metallicity coverage. Indeed, going to low-metallicity, typically down
to [Fe/H] $\sim-4$ or $-5$ will allow us to probe in more details the early
neutron-capture enrichment of the Milky Way. In the near future, 4MOST will
deliver hundreds of thousands of high-resolution (R$\sim$20000) optical
spectra of the Milky Way disc, halo and bulge stars(de Jong et al. 2019;
Bensby et al. 2019; Christlieb et al. 2019), and will open a new era for NLTE
abundances exploration down to very low metallicities. Strong effort will have
to be put in order to provide the community with precise and accurate neutron-
capture abundances from such a facility.

###### Acknowledgements.

G.G. acknowledges support by Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) – project-IDs: eBer-22-59652 (GU 2240/1-1 ”Galactic
Archaeology with Convolutional Neural-Networks: Realising the potential of
Gaia and 4MOST”). We acknowledge support by the Collaborative Research Centre
SFB 881 (projects A5, A10), Heidelberg University, of the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) and by the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement 949173). M.B. is supported through the
Lise Meitner grant from the Max Planck Society. This research was supported by
the Munich Institute for Astro-, Particle and BioPhysics (MIAPbP) which is
funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany´s Excellence Strategy – EXC-2094 – 390783311. A.S.
acknowledges grants PID2019-108709GB-I00 from Ministry of Science and
Innovation (MICINN, Spain), Spanish program Unidad de Excelencia María de
Maeztu CEX2020-001058-M, 2021-SGR-1526 (Generalitat de Catalunya). A.S. and
G.C. acknowledge support from ChETEC-INFRA (EU project no. 101008324). GC
acknowledges the grant PRIN project n.2022X4TM3H ”Cosmic POT” from Ministero
dell’Universitá e la Ricerca (MUR).

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