# DATScore: Evaluating Translation with Data Augmented Translations

Moussa Kamal Eddine  École Polytechnique, 2Linagora, 3AUEB  Guokan Shang
Michalis Vazirgiannis  École Polytechnique, 2Linagora, 3AUEB

###### Abstract

The rapid development of large pretrained language models has revolutionized
not only the field of Natural Language Generation (NLG) but also its
evaluation. Inspired by the recent work of BARTScore: a metric leveraging the
BART language model to evaluate the quality of generated text from various
aspects, we introduce DATScore. DATScore uses data augmentation techniques to
improve the evaluation of machine translation. Our main finding is that
introducing data augmented translations of the source and reference texts is
greatly helpful in evaluating the quality of the generated translation. We
also propose two novel score averaging and term weighting strategies to
improve the original score computing process of BARTScore. Experimental
results on WMT show that DATScore correlates better with human meta-
evaluations than the other recent state-of-the-art metrics, especially for
low-resource languages. Ablation studies demonstrate the value added by our
new scoring strategies. Moreover, we report in our extended experiments the
performance of DATScore on 3 NLG tasks other than translation. Code is
publicly available111https://github.com/moussaKam/dat_score.

##  1 Introduction

Massive pretrained language models have brought significant improvement to NLG
tasks (Lewis et al., 2020). Recent systems can even generate texts of higher
quality than human-annotated ones Peyrard (2019). At the same time, standard
metrics, such as BLEU (Papineni et al., 2002) and ROUGE (Lin, 2004), for
translation and summarization respectively, have not evolved for the past two
decades (Bhandari et al., 2020). These metrics rely on surface lexicographic
matches, making them particularly unsuitable for evaluating modern systems
operating with embeddings at the semantic level that often generate
paraphrases (Ng and Abrecht, 2015). To address this issue, many metrics have
been proposed (Sai et al., 2022), but none of them were widely adopted until
the release of BERTSore (Zhang et al., 2019) and MoverScore (Zhao et al.,
2019). These metrics take advantage of large pretrained language models like
BERT (Devlin et al., 2019), which are now being used in nearly all NLP tasks
(Qiu et al., 2020; Min et al., 2021).

In this work, we focus on the task of evaluating machine translation. We
propose an extension of BARTScore (Yuan et al., 2021), a recent metric
exploiting the BART seq2seq language model (Lewis et al., 2020) to evaluate
the quality of generated text from various aspects. BARTScore covers four
evaluation facets: Faithfulness, Precision, Recall, and F-score, derived from
different generation directions between the source text, the hypothesis (the
text generated by a system given the source), and the reference (the reference
text for the generation, often provided by human annotators). The scores are
obtained by pairing the three entities differently at the input or the output
side of a trained seq2seq model for fetching conditional generation
probabilities.

Based on BARTScore, and motivated by the general idea and positive effect of
data augmentation techniques, we found that adding augmented, translated
copies of the source and reference texts in BARTScore, can greatly help
evaluate the quality of the hypothesis translation. We also propose two novel
score averaging and term weighting strategies to improve the original score
computing process of BARTScore. Results and ablation studies show that our
metric DATScore (Data Augmented Translation Score) outperforms the other
recent state-of-the-art metrics, and our new scoring strategies are effective.
Moreover, the performance of DATScore is also reported on three other NLG
tasks than translation: data-to-text, summarization, and image captioning.

To the best of our knowledge, no prior work has been done on leveraging data
augmentation techniques for untrained NLG evaluation metrics. Our work will
help fill this gap. Our contributions include:
1) Inspired by BARTScore, we developed DATScore, incorporating augmented data
translated from the source and reference texts. DATScore is an untrained and
unsupervised translation evaluation metric that offers a larger performance
boost in evaluating low-resource language generation. In contrast to other
widely adopted metrics, DATScore can efficiently incorporate both the source
and reference texts in the evaluation.
2) We introduced a novel one-vs-rest method to average the scores for
different generation directions with different weights, which improves over
the simple arithmetic averaging method used in BARTScore.
3) We proposed a novel entropy-based scheme for weighting the target generated
terms so that higher informative tokens receive more importance in accounting
for the score, which outperforms the naive uniform weighting employed in
BARTScore.

##  2 Related work

###  2.1 Translation evaluation metrics

BLEU (Papineni et al., 2002) is the de facto metric for evaluating machine
translation. It simply calculates $n$-gram matching between the reference and
the hypothesis using precision scores with a brevity penalty. METEOR (Banerjee
and Lavie, 2005) was developed to address two drawbacks of BLEU. It is F-score
based (thus taking recall into account) and allows for a more relaxed
matching, based on three forms: extract unigram, stemmed word, and synonym
with WordNet (Miller, 1994). Apart from the above word-based metrics, some
approaches operate at the character level. For example, chrF (Popović, 2015)
computes the overall precision and recall over the character $n$-grams with
various values of $n$. More recently, static word embeddings (Mikolov et al.,
2013) have enabled capturing the semantic similarity between two texts
possible, of what the historical metrics are incapable. Several metrics have
been proposed to incorporate word vectors. For example, MEANT 2.0 (Lo, 2017)
evaluates translation adequacy by measuring the similarity of the semantic
frames and their role fillers between the human and machine translations.

Lately, pretrained language models have become popular, because they provide
context-dependent embeddings. This proved beneficial to all NLP tasks, but
also to evaluation metrics. For example, using a modified version of the Word
Mover’s Distance (Kusner et al., 2015), the Sentence Mover’s Similarity (Clark
et al., 2019) measures the minimum cost of transforming one text into the
other as the evaluation score, where sentences are represented as the average
of their ELMo word embeddings (Peters et al., 2018). BERTr (Mathur et al.,
2019) computes approximate recall based on the pairwise cosine similarity
between the BERT word embeddings (Devlin et al., 2019) of two translations.
UniTE (Wan et al., 2022) proposes a unified framework for modeling three
evaluation prototypes: estimating the quality of the translation hypothesis by
comparing it with reference-only, source-only, or source-reference-combined
data. UniTE is built upon XLM-R multilingual language model (Conneau et al.,
2020).

Among several alternatives, BERTSore (Zhang et al., 2019) and MoverScore (Zhao
et al., 2019) have received more attention, and have been adopted for
reporting results in recent NLG publications (Lin et al., 2022; Weston et al.,
2022). They both are unsupervised, general-purpose metrics and leverage BERT-
like language models, however, with one difference lying in the similarity
function for matching the two sequence representations. BERTScore greedily
matches each token from one sequence to the single most similar token in the
other sequence, in terms of the cosine similarity of their token embeddings.
While MoverScore conducts soft one-to-many matching using an $n$-gram
generalization of the Word Mover’s Distance (Kusner et al., 2015).

Finally, the work closely related to ours is BARTScore (Yuan et al., 2021).
Unlike all the above metrics trying to match tokens or their embeddings,
BARTScore proposes a novel conceptual view. It treats the evaluation of
generated text as a text generation problem, with the help of a pretrained
seq2seq model BART (Lewis et al., 2020). At the time of writing, this metric
represents the state-of-the-art in the NLG evaluation. We will provide more
details about it in Section 3.

###  2.2 Data augmentation

As deep learning models are often heavily reliant on large amounts of training
data, a common attempt to get around the data scarcity problem is by applying
data augmentation techniques (Shorten and Khoshgoftaar, 2019). These
techniques increase the size of the training set by making slightly modified
copies of already-existing instances or by creating new, synthetic ones. Such
augmented data have proven to be beneficial to the training of models in a
wide variety of contexts, from computer vision (Shorten and Khoshgoftaar,
2019) to speech recognition (Bird et al., 2020), to NLP (Feng et al., 2021),
as it acts as a regularizer and helps reduce overfitting (Krizhevsky et al.,
2012). For dealing with textual data, a suite of augmentation techniques
exists. To name only a few, backtranslation (Sennrich et al., 2016) translates
a text into an intermediate language and then back into the original language,
as a way of paraphrasing the initial text. Contextual augmentation (Kobayashi,
2018) generates augmented samples by randomly replacing words with others
drawn following the in-context word distribution of a recurrent language
model. SeqMix method (Guo et al., 2020) creates synthetic examples by softly
mixing parts of two sentences via a convex combination.

Data augmentation has also been applied to the field of NLG evaluation
metrics. BLEURT (Sellam et al., 2020) is a supervised metric, i.e., it
requires to be finetuned on human meta-evaluations. Before finetuning, BLEURT
creates an augmented synthetic dataset by perturbing Wikipedia sentences with
BERT mask-filling, backtranslation, and random word dropping techniques. The
data are then annotated with some automatic numerical and categorical signals
as pretraining labels. FrugalScore (Kamal Eddine et al., 2022) proposes the
first knowledge distillation approach for NLG evaluation metrics, to alleviate
the significant requirement of computational resources by the heavy metrics
based on large pretrained language models (e.g., BERTScore and MoverScore).
Unlike BLEURT, it is purely trained on a synthetic dataset consisting of pairs
of more or less related sentences, created via various data augmentation
techniques (e.g., paraphrasing with backtranslation, perturbation then
denoising, etc.). The sentence pairs for training the student model are
annotated with scores given by the metrics to be learned.

Differences. Note that BLEURT and FrugalScore use augmented data to train
their parameterized metric models, while our DATScore is an untrained and
unsupervised metric not requiring human judgments for training and using
augmented translation for the sole purpose of scoring.

##  3 DATScore

As mentioned in Subsection 2.1, BARTScore is not based on matching tokens nor
their embeddings as the other evaluation metrics. Instead, it uses a novel
approach by framing the evaluation of generated text as a text generation
problem. Assuming first a pretrained seq2seq model is “ideal” (e.g., BART),
BARTScore directly uses the model’s conditional probability of generating a
provided target text $Y$ given a provided input text $X$, as the evaluation
score of the generation direction $X\rightarrow Y$. For example, $Y$
corresponds to a translation hypothesis generated by any system, and $X$ is
the reference. If $Y$ is of high quality, then by providing the pair to the
pretrained BART model, the estimated conditional generation probability
(evaluation score) $P(Y|X)$ should be high.

Therefore, by placing differently the source (Src), the reference (Ref), and
the hypothesis (Hypo) in pair at the input or the output side of the trained
seq2seq model for fetching conditional generation probabilities, BARTScore
considers three different generation directions illustrated as dashed arrows
in Figure 1. The conditional probabilities associated with the directions are
denoted as: Precision (Ref$\rightarrow$Hypo), Recall (Hypo$\rightarrow$Ref)
and Faithfulness222BART being a monolingual model, faithfulness is only
relevant in the context of abstractive summarization, and its corresponding
direction cannot be applied to machine translation evaluation.
(Src$\rightarrow$Hypo). Additionally, an F-score, the arithmetic average of
Precision and Recall.

Figure 1: Dashed arrows denote the generation directions covered by BARTScore.
Solid black arrows indicate our newly introduced directions for calculating
DATScore of the example hypothesis in English (Hypoen). Trans1xx and Trans2yy
represent data augmented translations in any languages xx and yy, obtained by
applying a translation model (grey arrows) to the example source in French
(Srcfr) and example reference in English (Refen), respectively.

The score (conditional probability) for the generation direction from a source
sequence $X=\\{x_{t}\\}_{t=1}^{n}$ to a target sequence
$Y=\\{y_{t}\\}_{t=1}^{m}$ is calculated as the factorized, weighted log
probability over all generation steps:

$\mathrm{Score}_{X\rightarrow
Y}=\sum_{t=1}^{m}w_{t}\mathrm{log}P(y_{t}|X,\\{y_{t^{\prime}}\\}_{t^{\prime}=1}^{t-1};\theta)$
(1)

where $w_{t}$ denotes the term importance score to put different emphasis on
different target tokens $y_{t}$. BARTScore simply employs a uniform weighting
scheme (all equal to 1). $\theta$ denotes the parameterized seq2seq model.

Our contributions consist of three modifications tailored to machine
translation:

Data augmented translations. Unlike BARTScore, we employ M2M-100 (Fan et al.,
2021), a non-English-centric multilingual machine translation system as our
backbone seq2seq model, due to its superior performance. As our main
contribution, we translate the source (e.g., Srcfr in Figure 1) and the
reference (Refen) into any languages as our augmented data (Trans1xx and
Trans2yy) for evaluating the hypothesis (Hypoen). In addition to the three
directions covered by BARTScore, our metric takes into consideration all
generation directions centered on the hypothesis connecting the source, the
reference, and the two data augmented translations, i.e., in total 8
directions as the black (dashed and solid) arrows depicted in Figure 1.
DATScore is calculated as the weighted average of the scores associated with
all the directions:

$\mathrm{DATScore}=\sum_{X,Y}w_{X\rightarrow Y}\mathrm{Score}_{X\rightarrow
Y};X\neq Y$ (2)

where $w_{X\rightarrow Y}$ denotes the weight of the direction ${X\rightarrow
Y}$, as detailed below.

One-vs-rest score averaging method. We observed empirically that sometimes,
one direction score might strongly disagree with the others, likely being an
outlier (failed evaluation). This may significantly affect the final DATScore
correlations with the human meta-evaluations, if a simple arithmetic averaging
method is applied (like BARTScore in computing F-score). To reduce this
effect, we weigh each direction with the sum of the Pearson correlations of
its scores with the scores of all the other directions:

$w_{X\rightarrow
Y}=\sum_{X^{\prime},Y^{\prime}}Corr(\mathrm{Score}_{X\rightarrow
Y},\mathrm{Score}_{X^{\prime}\rightarrow Y^{\prime}})\\\
\mathrm{s.t.}\quad(X,Y)\neq(X^{\prime},Y^{\prime})$ (3)

This one-vs-rest method will assign a low weight to the direction score poorly
correlated with the rest scores, thus reducing its negative effect on the
averaging result.

Entropy-based term weighting scheme. BARTScore gives an equal weight $w_{t}$
to every token in Equation 1 (uniform weighting). Instead, we introduce a
novel scheme to give different importance to different target tokens $y_{t}$,
based on the entropy:

$w_{t}=-\sum_{i=1}^{v}\mathrm{P_{t}}(z_{i})\mathrm{logP_{t}}(z_{i})$ (4)

where $v$ denotes the size of the output generation vocabulary.
$\mathrm{P_{t}}(z_{i})$ represents the probability of the $i$-th token in the
vocabulary at time step $t$. We assume that when the model is very confident
in generating the target token (low entropy), then this token is non-
informative (e.g., stopword). On the other hand, when the model is less
confident (higher entropy), the target word is more informative, and then a
higher weight should be assigned.

The effectiveness of all our choices regarding the above contributions is
shown by our ablation studies (see Section 6).

Metric |  | Model |  $|r|$:cs  en / $\tau$:en  cs |  $|r|$:de  en / $\tau$:en  de |  $|r|$:fi  en / $\tau$:en  fi |  $|r|$:lv  en / $\tau$:en  lv |  $|r|$:ru  en / - |  $|r|$:tr  en / $\tau$:en  tr |  $|r|$:zh  en / - | Avg.
---|---|---|---|---|---|---|---|---|---|---
BLEU | 1a) | N/A | 34.4/22.0 | 36.6/23.6 | 44.4/42.1 | 32.1/21.5 | 41.3/- | 44.1/33.6 | 44.0/- | 37.8/27.3
BERTScore | 1b) | RL/mBERT | 71.0/43.8 |  74.5/40.4 | 83.3/58.8 | 75.6/46.6 | 74.6/- | 75.1/57.1 | 77.5/- | 75.9/49.3
MoverScore | 1c) | BB/mBERT | 66.6/38.3 | 70.6/35.9 | 82.2/54.2 | 71.7/37.8 | 73.7/- | 76.1/49.8 | 74.3/- | 73.6/43.2
BARTScore | 1d) | BL+para/mBART | 68.4/39.0 | 70.8/33.4 | 79.4/50.4 | 74.9/50.4 | 71.8/- | 73.9/53.8 | 76.0/- | 73.6/45.4
1e) | M2M-100_418M | 65.9/45.0 | 66.1/44.5 | 79.9/59.2 | 71.7/40.3 | 69.0/- | 71.8/70.9 | 71.6/- | 70.9/52.0
1f) | M2M-100_1.2B | 67.4/49.6 | 69.3/49.2 | 80.7/63.5 | 73.7/46.9 | 70.4/- | 71.6/72.5 | 73.0/- | 72.3/56.3
DATScore | 1g) | M2M-100_418M | 68.6/51.1 | 68.5/48.1 | 82.0/63.7 | 74.7/48.3 | 73.0/- | 77.6/70.9 | 76.5/- | 74.4/56.4
1h) | M2M-100_1.2B |  71.3/53.9 | 72.9/52.2 |  83.5/66.3 |  76.8/52.0 |  75.9/- |  78.1/70.9 |  77.7/- |  76.6/59.1
Table 1: Absolute Pearson correlation ($|r|$) for to-English and Kendall correlations ($\tau$) for from-English with segment-level human scores on WMT17. BB stands of Bert-Base, RL for RoBERTa-Large and BL for BART-Large. Metric |  | Model |  $\tau$:cs  en / $\tau$:en  cs |  $\tau$:de  en / $\tau$:en  de |  $\tau$:et  en / $\tau$:en  et |  $\tau$:fi  en / $\tau$:en  fi |  $\tau$:ru  en / $\tau$:en  ru |  $\tau$:tr  en / $\tau$:en  tr |  $\tau$:zh  en / $\tau$:en  zh | Avg.
---|---|---|---|---|---|---|---|---|---|---
BLEU | 2a) | N/A | 23.3/38.9 | 41.5/62.0 | 38.5/41.4 | 15.4/35.5 | 22.8/33.0 | 14.5/26.1 | 17.8/31.1 | 24.8/38.3
BERTScore | 2b) | RL/mBERT | 40.4/55.9 |  55.0/72.7 | 39.7/58.4 | 29.6/53.9 | 35.3/42.4 | 29.2/38.9 |  26.4/36.1 | 36.5/51.2
MoverScore | 2c) | BB/mBERT | 36.8/44.6 | 53.9/68.4 | 39.4/52.7 | 28.7/50.9 | 27.9/40.1 |  33.6/32.5 | 25.6/35.2 | 35.1/46.3
BARTScore | 2d) | BL+para/mBART | 39.6/50.2 | 54.7/65.0 | 39.4/53.3 | 28.9/57.2 | 34.6/37.0 | 27.4/37.7 | 24.9/32.4 | 35.6/47.5
2e) | M2M-100_418M | 36.3/55.4 | 53.5/72.2 | 37.6/58.4 | 26.3/60.2 | 33.4/44.4 | 26.8/45.1 | 23.4/31.3 | 33.9/52.4
2f) | M2M-100_1.2B | 38.4/63.5 | 54.6/76.2 | 39.2/63.2 | 27.9/64.5 | 35.7/45.6 | 28.5/50.2 | 24.3/34.7 | 35.5/56.8
DATScore | 2g) | M2M-100_418M | 38.6/53.5 | 53.5/71.3 | 39.3/64.0 | 28.4/62.2 | 34.9/44.4 | 28.5/47.9 | 25.3/34.0 | 35.5/53.9
2h) | M2M-100_1.2B |  40.7/61.9 | 54.9/76.2 |  40.5/68.2 |  30.4/67.9 |  36.4/46.2 | 31.0/52.7 | 26.3/36.6 |  37.2/58.5
Table 2: Kendall correlations ($\tau$) for to-English and from-English with
segment-level human scores on WMT18. BB stands of Bert-Base, RL for RoBERTa-
Large and BL for BART-Large.

##  4 Experiments

###  4.1 Experimental settings

We benchmark DATScore on two commonly used meta-evaluation datasets for
machine translation metrics: WMT17 Bojar et al. (2017) and WMT18 Ma et al.
(2018) consisting of multiple to_English and from_English language pairs. For
each pair, a few thousand examples are available, each being made of a source,
a reference, a hypothesis and a label produced by human annotators, assessing
the quality of the system generated hypothesis. Depending on the label type,
we use Kendall’s Tau $\tau$ correlations or absolute Pearson $|r|$
correlations. The former is used when relative ranking is provided, and the
latter in the case of direct assessment. We adopt the Kendall’s Tau-like
formulation proposed in (Bojar et al., 2017):

$\tau=\frac{|Concordant|-|Discordant|}{|Concordant|+|Discordant|}$ (5)

where $|Concordant|$ is the number of examples on which the metric agrees with
the human relative ranking, and $|Discordant|$ is the number of examples when
they disagree.

To compute DATScore, two M2M-100 models:
M2M-100_418M333https://huggingface.co/facebook/m2m100_418M and
M2M-100_1.2B444https://huggingface.co/facebook/m2m100_1.2B are adopted (418M
and 1.2B refer to the model sizes). They are finetuned to translate a source
text to a target text by providing the source language code (e.g. "fr") at the
beginning of the encoder input sequence, and a target language code at the
beginning of the decoder input sequence. In our experiments, when English is
the target language (to-English), we choose English for Trans1 and Spanish for
Trans2 (see Figure 1). Otherwise, whenever English is the source language
(from-English), we choose Spanish for Trans1 and English for Trans2. This
choice is motivated by the fact that English and Spanish are the top two
represented languages in the training set of M2M-100 Fan et al. (2021).

###  4.2 Main results

We compare the performance of our metric against BLEU and three other
reference-based unsupervised metrics:
BERTScore555https://github.com/Tiiiger/bert_score,
MoverScore666https://github.com/AIPHES/emnlp19-moverscore and
BARTScore777https://github.com/neulab/BARTScore (detailed in Subsection 2.1
and Section 3), using their official implementations. Experimental results are
reported in Table 1 and 2. Following their original settings, we use different
underlying language models for each baseline metric. For BERTScore and
MoverScore, RoBERTa-Large (RL; Liu et al., 2019) and Bert-Base (BB) are used
respectively when we evaluate to-English translations, and mBERT Devlin et al.
(2019) for from-English translations. In the case of BARTScore, we use a BART-
Large (BL) checkpoint (finetuned on CNNDM See et al. (2017) and ParaBank2 Hu
et al. (2019) datasets) for evaluating to-English translations, and an
mBART-50 model Escolano et al. (2021) for from-English translations.

Overall, results show that, on average, across all language pairs, DATScore
significantly outperforms all 4 baseline metrics under their original model
settings (rows 1a-1d and 2a-2d). Specifically, with respect to the best
performing baseline BERTScore (row 1b and 2b), our metric provides a
performance boost of 0.7 for to-English case and of 9.8 for from-English case
on WMT17 dataset in Table 1, and achieves a gain of 0.7 and of 7.3
respectively on WMT18 dataset in Table 2. These averaging results demonstrate
the superiority and applicability of DATScore in evaluating general machine
translations of many languages. Moreover, it is interesting to note that our
improvement is much more significant in from-English case, which makes
DATScore particularly well-suited to evaluate hypothesis translations in non-
English languages, often with low resource. We hypothesize that this is due to
the inconsistency of underlying language models. The baselines adopt a
monolingual model for evaluating English, but a multilingual one for non-
English languages. However, DATScore uses a single multilingual M2M-100 model
for both cases. It is known that, in general, monolingual models outperform
multilingual competitors. Thus, it is reasonable that when comparing
multilingual-based DATScore against monolingual baselines in the to-English
case, DATScore achieves a smaller improvement than in the other from-English
case, where the comparison is fairer (multilingual vs. multilingual).

By looking across specific language pairs and directions, we observe DATScore
constantly performs better than 4 baseline metrics with a few exceptions,
i.e., de  en (-1.6) in Table 1, and de  en (-0.1), tr  en (-2.6), and zh  en
(-0.1) in Table 2. Despite these small drops in the performance, DATScore
brings a larger margin of improvement in most cases, such as en  tr up to 13.8
both on WMT17 and WMT18 datasets.

In the end, for the sake of having a complete comparison, we additionally
evaluate BARTScore888The official implementation of BARTScore is slightly
modified to take into account the languages tokens when using a multilingual
model. with M2M-100_418M and M2M-100_1.2B models (row 1e, 1f, 2e, and 2f) that
are used as DATScore’s underlying models. Results show that, only in the from-
English case, while they bring an improvement compared to the vanilla
BARTScore (row 1d and 2d), they are not able to yield as big of a gain as our
metric, indicating that our achieved improvement is not solely due to the
underlying language model, but also to taking additional generation directions
into account, including those related to data augmented translations.

Metric | Model | WebNLG
---|---|---
SEMA | GRAM | FLU
BLEU | N/A | 45.5 | 36.0 | 34.9
BERTScore | RoBERTa-Large | 56.1 | 60.8 | 54.8
MoverScore | BERT-Base | -9.9 | -27.8 | -20.6
BARTScore | BART-Large+para | 71.9 | 61.3 | 57.4
M2M-100_418M | 64.9 | 62.8 | 56.0
M2M-100_1.2B | 66.1 | 63.9 | 57.2
DATScore | M2M-100_418M | 69.9 | 62.9 | 57.2
M2M-100_1.2B | 70.4 | 63.7 | 57.9
Table 3: Pearson correlation results on WebNLG dataset. Metric | Model | REALSumm | SummEval
---|---|---|---
COV | COH | CONS | FLU | REL
BLEU | N/A | 37.9 | 11.8 | 6.3 | 7.7 | 18.6
BERTScore | RoRERTa-Large | 41.2 | 33.9 | 10.5 | 15.0 | 35.9
MoverScore | BERT-Base | 44.1 | 14.4 | 14.7 | 13.8 | 29.1
BARTScore | BART-Large+para | 31.7 | 20.8 | -3.5 | 6.7 | 22.2
M2M-100_418M | 30.1 | 14.8 | -2.3 | 3.0 | 19.8
M2M-100_1.2B | 32.0 | 17.1 | 1.1 | 6.7 | 22.8
DATScore | M2M-100_418M | 44.7 | 17.1 | 4.4 | 4.6 | 26.3
M2M-100_1.2B | 45.5 | 19.5 | 6.8 | 8.2 | 30.2
Table 4: Pearson correlation results on two summarization datasets: REALSumm
and SummEval.

##  5 Other NLG tasks

In addition to machine translation, our main focus, we evaluate DATScore on
other NLG tasks, including data-to-text generation, abstractive summarization,
and image captioning. To work around the different modalities of source inputs
represented in these tasks (e.g., not able to create a data augmented
translation with an image), we adapt DATScore to only consider 4 generation
directions: Hypo$\leftrightarrow$Ref and Hypo$\leftrightarrow$Trans2.

Data-to-text. Table 3 shows the performance of DATScore compared to the other
baselines on the WebNLG data-to-text dataset Shimorina et al. (2018), which
contains 2000 descriptions of structured tables along with their corresponding
references. In addition, human assessments covering three dimensions are
provided (semantics, grammar, and fluency). The results show that DATScore
significantly outperforms all the other metrics in two settings (grammar and
fluency) out of three, while being very competitive in the third setting
(semantics). Surprisingly, BERTScore is largely behind DATScore, and
MoverScore failed to correlate positively with human judgments in all
dimensions.

Summarization. Table 4 shows the evaluation of the different metrics on two
summarization meta-evaluation datasets: REALSumm Bhandari et al. (2020) and
SummEval Fabbri et al. (2021). Both datasets contain a few thousand examples
of system-generated summaries and their references. The generated summaries
are annotated with lightweight pyramids Shapira et al. (2019) method in the
case of REALSumm, while the annotations in SummEval cover four dimensions:
coherence, consistency, fluency, and relevance. On REALSumm, DATScore has the
best performance compared to all the other baselines even when using its
smaller version (M2M-100_418M). However, despite its higher correlations
compared to BARTScore and MoverScore, DATScore fails to outperform BERTScore
on the different dimensions of SummEval.

Image captioning. We consider Flickr8K Hodosh et al. (2013) and PASCAL-50S
Vedantam et al. (2015), two image captioning datasets. The former is annotated
with scores from 1 to 4 assessing the relevance of the captions, and the
latter is annotated with relative ranking (i.e., given two descriptions which
one is better). Table 5 shows that in this task, DATScore is competitive to
BARTScore and BERTScore. Surprisingly, MoverScore significantly outperforms
all the other metrics despite its poor performance on the other datasets.

Finally, although not the top-performing metric across all tasks, DATScore
showed an overall stable and competitive performance. Conversely, each of the
other metrics fails in evaluating generations, at least in one of the tasks.
For example, BERTScore and MoverScore have poor performance on the WebNLG
dataset. On the other hand, although BARTScore is finetuned on an abstractive
summarization dataset, it fails to correlate well with human judgment on
REALSumm and SummEval. This finding suggests that DATScore can be safely used
to evaluate NLG systems in other tasks for different evaluation dimensions,
regardless of being initially designed for machine translation evaluation.

Metric | Model | Flickr8K | PASCAL-50S
---|---|---|---
RELE | RR
BLEU | N/A | 13.8 | 8.1
BERTScore | RoBERTa-Large | 46.1 | 33.8
MoverScore | BERT-Base | 52.5 | 33.2
BARTScore | BART-Large+para | 44.8 | 33.1
M2M-100_418M | 34.3 | 29.6
M2M-100_1.2B | 34.6 | 26.3
DATScore | M2M-100_418M | 42.6 | 29.6
M2M-100_1.2B | 45.3 | 31.4
Table 5: Pearson correlation Results on two Image Captioning datasets: Flickr8K and PASCAL-50S. Entropy-based weighting |  One-vs-rest weighting | to_English | from_English
---|---|---|---
✓ | ✓ | 37.2 | 58.5
✓ | ✗ | 37.1 | 58.1
✗ | ✓ | 36.4 | 55.9
✗ | ✗ | 36.4 | 56.0
Table 6: The average Kendall correlation (to/from)-English when the entropy-
based and one-vs-rest weighting are included or excluded. Experiments are
conducted on WMT18. Figure 2: (a): The horizontal bars represent the Kendall
correlations of each individual generation direction. (b): The horizontal bar
represents the Kendall correlation of a variant of DATScore with excluding the
single generation direction of the line. Both in (a) and (b), the dashed
vertical lines represent the Kendall correlation of the vanilla and complete
DATScore. Correlation results of to-English (in green) and from-English (in
red) cases are calculated w.r.t human judgments, and averaged over all
languages pairs. Experiments are conducted on WMT18.

##  6 Ablation study

To validate our different choices with regard to DATScore, we conducted
ablation studies on:
1) the contributions of all 8 direction scores, results are illustrated in
Figure 2.
2) the effectiveness of our one-vs-rest score averaging and entropy-based term
weighting strategies (See Section 3), results are reported in Table 6.

Contributions of all direction scores. From Figure 2(a), we observe that none
of the individual directions (horizontal bars) has a better correlation with
human judgments than DATScore (dashed vertical lines), which confirms the
importance of our ensemble approach. In Figure 2(b), we can see that all
variants excluding one direction will lead, in almost all cases, to a drop in
the performance, compared to the complete DATScore in which all directions are
included. Besides, in the case of to-English translations, we can see that the
drop in the performance is almost the same for all exclusions of direction.
While for from-English translations, the largest drop in performance is
observed when Hypo$\rightarrow$Trans2 and Trans2$\rightarrow$Hypo are
excluded. This finding highlights the important contribution of our augmented
data, especially in the low resource language settings (from-English). In the
end, we can see that excluding Src$\rightarrow$Hypo or Trans1$\rightarrow$Hypo
directions can lead to a slightly better final score. We leave the
investigation of the potential negative impact of the two directions to future
work.

One-vs-rest and entropy-based weighting strategies. Table 6 shows the
performance of DATScore variants with respect to different combinations of
applying or not our proposed weighting strategies. Note that when one-vs-rest
and entropy-based weightings are not applied, they are replaced with a simple
uniform averaging approach (as used in BARTScore). A performance drop is
observed when excluding one of the two weighting strategies, especially for
the entropy-based method, whose inclusion leads to an improvement of 2.5
compared to the uniform weighting. This experiment confirms the positive
impact of our proposed weighting methods and motivates future work further to
investigate a more elaborated approach in this direction.

##  7 Conclusion

In this work, we proposed one of the first applications of data augmentation
techniques to NLG evaluation. To obtain an evaluation score of the translation
hypothesis, our developed metric DATScore additionally leverages newly
translated copies augmented from the source and reference texts. We also
proposed two novel strategies for score averaging and term weighting to
improve the original, naive score computing process of BARTScore, on the basis
of which our work is built. Experimental results show that DATScore achieved a
higher correlation with human meta-evaluations, in comparison with the other
recent state-of-the-art metrics, especially for those less represented
languages other than English. Moreover, ablation studies show the
effectiveness of our newly proposed score computing approaches, and extended
experiments showed an overall stable and competitive performance of DATScore
on more NLG tasks.

## Limitations

In this section, we list some limitations that are worth further investigation
in future works:

1) DATScore requires generating additional data augmented translations to
perform the evaluation. This process might be time-consuming depending on the
adopted backbone seq2seq model, especially if the original text is long. Thus,
the performance scalability can be investigated in future complementary
experiments.

2) We chose to use English and Spanish to create data augmented translations
for the reason that they are the two most represented languages in the
training of the M2M-100 model (see Subsection 4.1). However, this leaves a
question about the performance of DATScore with augmentations varying in other
languages (e.g., Chinese). Moreover, for the sake of simplicity, we decided
only to include a single translated copy of the source text and the reference
text. However, this can be easily extended, and more augmented translations
can be created in more languages. We expect to see an improvement in
performance with diminishing returns.

3) BARTScore only considers the 8 generation directions centered on the
hypothesis connecting with the source, the reference, and the two data
augmented translations (see Section 3). However, other connections exist
between these entities, such as Src$\rightarrow$Ref and Trans1$\rightarrow$Src
(see Figure 1). Therefore, future research could be dedicated to discovering
the effect of these other directions and potentially leveraging them to
improve the performance of DATScore.

4) Since our focus was on evaluating machine translation, we naturally chose
translation for augmenting the data. However, other data augmentation
techniques could seamlessly integrate into DATScore, such as using a text
paraphrasing model (Bandel et al., 2022).

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11institutetext: INAF, Osservatorio Astronomico di Trieste, Via Tiepolo 11,
I-34143 Trieste, Italy 22institutetext: IFPU, Institute for the Fundamental
Physics of the Universe, Via Beirut, 2, I-34151 Grignano, Trieste, Italy
33institutetext: INFN, Sezione di Trieste, Via A. Valerio 2, I-34127 Trieste,
Italy 44institutetext: Leibniz-Institut für Astrophysik Potsdam (AIP), An der
Sternwarte 16, 14482, Potsdam, Germany 55institutetext: GEPI - Observatoire de
Paris, 64 avenue de l’Observatoire, 75014, Paris, France 66institutetext:
Université de Picardie Jules Verne, 33 rue St-Leu, 80080 Amiens, France
77institutetext: Zentrum für Astronomie der Universität Heidelberg,
Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany 88institutetext:
Departamento de Física, Facultad de Ciencias Básicas, Universidad
Metropolitana de la Educación, Av. José Pedro Alessandri 774, 7760197 Nuñoa,
Santiago, Chile 99institutetext: Millennium Institute of Astrophysics (MAS),
Santiago, Chile 1010institutetext: Centre for Astrophysics Research,
Department of Physics, Astronomy and Mathematics, University of Hertfordshire,
College Lane,Hatfield AL10 9AB, UK 1111institutetext: South African
Astronomical Observatory (SAAO), Observatory Road Observatory Cape Town, WC
7925, South Africa

# Barium lines in high-quality spectra of two metal-poor giants in the
Galactic halo††thanks: Based on observations made with the UVES at the ESO
Very Large Telescope, Paranal Observatory, Chile (ID 098.B-0094(A); P.I. G.
Cescutti).

G. Cescutti Email<EMAIL_ADDRESS>C. Morossi 11 M. Franchini
11 P. Di Marcantonio 11 C. Chiappini 44 M. Steffen 44 M. Valentini 44 P.
François 5566 N. Christlieb 77 C. Cortés 8899 C. Kobayashi &
E. Depagne 10101111

(Received xxxx / Accepted xxxx)

###### Abstract

Context. Theoretical results showed the possibility that neutron capture
elements were produced in the early Universe by two different sources: a
frequent $s-$process source hosted by rotating massive stars, and a rare
$r-$process source hosted most likely by neutron star mergers. The two sources
produce barium with different isotopic compositions.

Aims. We aim to investigate the lines of barium in two halo stars, HD 6268 and
HD 4306. The spectra present an exquisite quality, both in terms of resolution
($R>100,000)$ and signal-to-noise ($\sim 400$). Due to hyperfine splitting
(hfs) effects, barium lines are expected to show slightly different profiles
depending on the barium isotopic fraction.

Methods. We applied a standard local thermodynamic equilibrium synthesis of
the barium lines. We compared the synthetic results assuming an $s-$process
isotopic pattern or an $r-$process isotopic pattern for the two barium lines
for each star that exhibited hfs. We also applied a methodology, less
dependent on the accuracy of the theoretical Ba hfs structure, that transforms
the lines of HD 4306 into those we would observe if its atmospheric parameter
values (i.e. $T_{\rm eff}$, log $g$, micro- and macro-turbulence, V$\sin i$,
and Ba abundance) were the same as those of HD 6268.

Results. With both methods, our results show that the barium lines with hfs
effects of HD 4306 are in agreement with an $s-$process composition and the
lines in HD 6268 have a different profile, which is most likely linked to the
presence of an $r-$process isotopic pattern.

Conclusions. Two lines of barium of HD 6268 and HD 4306 seem to confirm the
theoretical expectation that both $r-$process events and also $s-$process
contribution by rotating massive stars have polluted the ancient halo of our
Galaxy.

###### Key Words.:

Galaxy: evolution – Galaxy: halo – stars: abundances – stars: massive – stars:
rotation – nuclear reactions, nucleosynthesis, abundances

##  1 Introduction

The past decade has seen an explosion of elemental abundance determinations
for the most metal-poor stars in the Galaxy. These new data have shown many
surprising results, including the fact that light neutron capture elements
(such as Sr, Y, and Zr) are more enriched in some extremely metal-poor (EMP)
stars compared to the expectations of a pure $r-$process pattern (Thielemann
et al., 2011), and they show an increasing scatter towards low metallicities,
down to [Fe/H] 111We assumed the common approximation in which iron is a proxy
for the entire metal content, and we adopted the notation [A/B]$\equiv$
log10(NA/NB)-log10(NA/NB)⊙ and $\epsilon$(A)$\equiv$ log 10(NA/NH) for
elements A and B. $\sim-$4 (Honda et al., 2004; Barklem et al., 2005; François
et al., 2007; Spite et al., 2018).

Astronomers then invoked the need for a new process (e.g. Travaglio et al.,
2004) able to provide the additional contribution to light neutron capture
elements. The astrophysical conditions that would create this additional
contribution are still unknown, and both an $s-$process-like or an r-process-
like mechanism was found to reproduce the abundance pattern between Sr and Ag
observed in many of the most extreme metal poor stars (Montes et al., 2007).
The s-process production in massive stars (weak s-process) was shown to be
inefficient at low metallicity (Raiteri et al., 1992), so most authors have
focused on the existence of a possible second $r-$process (also called the
weak $r-$process; see Arcones & Montes, 2011).

However, the recent nucleosynthesis computations by Frischknecht et al. (2016)
showing that rotating massive stars can support the $s-$process, and hence
pollute the early Universe with these elements on a timescale comparable to
that of the $r-$process, have brought a new twist to the interpretation of the
neutron capture element abundances of stars at very low metallicity.
Interestingly, the existence of rotating massive stars in the early Universe
has already been suggested as the only solution for at least four ’anomalies’
observed in other chemical elements in very metal-poor stars ([Fe/H] $<-$2.5);
namely, the rise of N/O and C/O towards lower metallicities (Chiappini et al.,
2006); the low 12C/13C (Chiappini et al., 2008) and the primary-like behaviour
of Be and B (Prantzos, 2012). Recently, we claimed to have found a fifth
signature of the impact of rotating massive stars, namely an early enrichment
of the Universe in $s-$process elements (Chiappini et al., 2011; Cescutti et
al., 2013). More recently, the impact of rotation in the nucleosynthesis of
neutron capture elements was also confirmed by the studies of Limongi &
Chieffi (2018) and Choplin et al. (2018). Moreover, chemical evolution models
have again confirmed that adopting these yields of rotating massive stars can
explain the increase in [Sr/Ba] towards low metallicity (Prantzos et al.,
2018; Rizzuti et al., 2019, 2021). A similar increase was obtained by
Kobayashi et al. (2020) thanks to the strontium production by electron capture
SNe, a potential source of weak r-process; in this case, the barium is formed
only by an r-process.

In this framework, the oldest halo stars can form from an ISM enriched by an
$r-$process source or an $s-$process source (or both). A clear prediction of
stochastic models with rotating massive stars is that EMP stars with high
[Sr/Ba] ratio should be almost entirely enriched by the $s-$process (see Fig.
2 in Cescutti & Chiappini, 2014). On the other hand, an $r-$process enrichment
is expected for stars that show a lower [Sr/Ba] ratio, closer to the
$r-$process solar residual222The residual abundances of chemical species of
the solar abundances; after that, theoretical s-process abundances have been
removed. ratio (Arlandini et al., 1999a). Following this interpretation, the
abundances of the isotopes of the elements produced are expected to present
different patterns among these two classes of stars. Usually, atomic lines of
heavy elements do not allow us to distinguish the isotopic composition of the
element. However, Ba is an attractive heavy element in this respect. In fact,
it presents a hyperfine splitting (hfs) of its 4554 Å line and its 4934 Å line
from the singly ionised stage, which is large enough to be detected (Rutten,
1978) and hence offers the possibility of measuring the fraction of odd
isotopes (hereafter, $f_{\rm odd}$333$f_{\rm odd}=[N(^{135}{\rm
Ba})+N(^{137}{\rm Ba})]/N({\rm Ba})$) via resolved asymmetric lines. According
to nucleosynthesis calculations (Arlandini et al., 1999a), one expects an
$f_{\rm odd}$ = 0.11 $\pm$ 0.01 in the case of a pure $s-$process, and an
$f_{\rm odd}$ = 0.46 $\pm$ 0.06 in the case of the $r-$process solar residual.
So, in the case of an s-process enrichment, even isotopes and no hfs effects
are almost exclusively expected; on the other hand, in the case of an
r-process the impact of the profile of the barium lines is relatively strong
and driven by the large fraction of odd isotopes prone to hfs effects.
Kobayashi et al. (2020) found a higher $f_{\rm odd}$ = 0.3 for their chemical
evolution model with rotating massive stars at [Fe/H]=$-$2.7; this is due to
the model, which is in fact a homogeneous one that mixes the contribution of
the r-process events and rotating massive stars. The same work, based on
recent theoretical computations of nucleosynthesis, found a slightly higher
fraction of odd isotopes ($f_{\rm odd}$ = 0.63) for the pure r-process.

The measurement of the Ba-isotopic ratio, although feasible, is very
challenging. Magain (1995) measured the isotopic ratio of a very bright halo
star, HD 140283, for the first time. He found an $s-$process signature with a
high [Sr/Ba]=0.9, which was in agreement with the theoretical expectations of
the chemical models of Cescutti & Chiappini (2014). However, this result on HD
140283 has been challenged and still needs to be confirmed (see Lambert &
Allende Prieto, 2002; Collet et al., 2009; Gallagher et al., 2010). Gallagher
et al. (2012) attempted to measure isotopic ratios in five $s-$process-
dominated metal-poor stars, obtaining isotopic fractions more compatible with
an s-process-dominated composition. Indeed, one of the biggest difficulties in
this case is properly accounting for 3D effects on the line formation.
Gallagher et al. (2015) adopted a 3D modelling to obtain an r-process isotopic
composition for HD 140283, contrary to their previous results in 1D and also
differently to the similar attempt in 3D carried out by Collet et al. (2009).
In the same year, Jablonka et al. (2015) also managed to determine this
isotopic fraction in stars belonging to the dwarf spheroidal Sculptor.

In this work, we investigated two spectra of extremely high quality (signal-
to-noise, $S/N>$400 and $R\sim$ 100,000) for two stars, HD 4306 and HD 6268.
The spectra were obtained homogeneously with the same instrument, which was
set up and during the same night. The final goal is to compare the barium
lines of these two stars. For this purpose, the stars were selected to have
parameters as similar as possible: [Fe/H]$\sim-$2.5 dex, log $g$ $\sim$ 1, and
$T_{\rm eff}\sim$ 4500 K, but with a different ratio of [Sr/Ba]; so, we expect
HD 4306 to show barium with an isotopic pattern typical of an $s-$process, and
HD 6268 to show that typical of an $r-$process enrichment. The parameters were
not as close as ideally desired, but the constraints of bright halo stars with
[Fe/H]$<-$2.5 resulted in the choice of these two candidates. The paper is
structured as follows: in Sect. 2, we describe the observations and the
reductions of the stellar spectra; in Sect. 3, we provide new atmospheric
parameters, with a comparison to the previous literature results; in Sect. 4,
we present the chemical abundances obtained from equivalent widths; in Sect.
5, we show the comparison of the synthetic spectra with $r-$ and $s-$process
isotopic compositions to the observational ones; in Sect. 6, a new empirical
method is described to directly compare the two observational spectra; in
Sect. 7, we draw our conclusions.

##  2 Observations and data reduction

The observations were performed using the UVES high-resolution spectrograph
(Dekker et al., 2000), mounted at the UT2 Kueyen Telescope at the ESO Paranal
Observatory (Chile), in slit mode. We adopted the standard R530 set-up (red
arm only, cross disperser 3, centred at 5200 covering the 4140–6210 Å
wavelength interval with a resolving power of $R\leavevmode\nobreak\
\sim$100,000.

The spectra were acquired on the night of 18th October 2016, with three
exposures of 2400 seconds (40 minutes) for HD 4306 and two exposures of 1600
seconds (26 minutes and 40 seconds) for HD 6268. Each of the resulting spectra
have approximately an average S/N of 250 for HD 4306 and 350 for HD 6268.
Details of the observations are summarised in Table 1.

Table 1: Observing log Object | R.A. | Dec. | B | G | Exp. | $<S/N>$ | Obs. Date | No of
---|---|---|---|---|---|---|---|---
| (J2000.0) | (J2000.0) | (mag) | (mag) | time (s) |  | (UT) | exp.s
HD 4306 | 00 45 27 | -09 32 44 | 9.71 | 8.76 | 2400s | 250 | 19th Oct. 2016 | 3
HD 6268 | 01 03 18 | -27 52 54 | 8.89 | 7.80 | 1600s | 350 | 19th Oct. 2016 | 2

The spectra were reduced using the standard UVES pipeline with the following
exceptions:

  * •

23 high-quality flat fields were purposely obtained and used to build the
MASTERFLAT;

  * •

wavelength calibration was achieved by using ThAr lamps obtained immediately
after the stellar observations;

  * •

flat-fielding is obtained in pixel-pixel space before extraction
(reduce.ffmethod=pixel) and not using the default option ’extract’;

  * •

all the extracted spectral orders were normalised individually before merging.

Then, the spectra of each star were Doppler$-$shifted to put them in the
laboratory reference frame, cleaned by cosmic ray, and, eventually averaged to
achieve the highest possible $S/N$. Using DER_SNR, a ’simple and general
spectroscopic signal-to-noise measurement algorithm’ (Stoehr et al., 2007), we
obtained S/N $\simeq$ 390/640 and S/N $\simeq 430/720$, for HD 4306 and HD
6268 respectively, in the blue and in the red parts of the spectra.

##  3 Atmospheric parameters

We re-determined the stellar parameters of HD 4306 and HD 6268 in order to
take advantage of the very high S/N of our mean spectra, even if these stars
have been studied several times in the literature; among the most recent
results with a detailed chemistry, we used the works by Honda et al. (2004),
Roederer et al. (2014), and Mashonkina et al. (2017) for a direct comparison.
The full list of sixteen original atmospheric parameter determinations for HD
6268 is presented in the appendix (Table 6), with the first determination from
40 years ago by Luck & Bond (1981), and the most recent one by Arentsen et al.
(2019).

We derived the stellar parameters of the two stars via the spectroscopic
approach; namely, the effective temperature $T_{\rm eff}$ was determined by
requiring the iron abundance from Fe I lines to be independent of their
excitation potential, and the surface gravity log g was derived from the
ionisation equilibrium of Fe I and Fe II . The microturbulence velocity $\xi$
was estimated by requiring the [Fe/H] derived from the Fe I lines to be
independent of their equivalent widths. The equivalent widths of a list of 81
Fe I and of 14 Fe II lines and of 99 Fe I and 16 Fe II lines were measured in
the spectra of HD 6268 and HD 4306, respectively. Then, an iterative procedure
was adopted to derive the stellar parameters using as initial guess for the
parameter values those taken from the latest literature. We used the ABUNDANCE
and the BLACKWEL codes444http://www.appstate.edu/
grayro/spectrum/spectrum.html to derive estimates of $T_{\rm eff}$, log $g$,
[Fe/H], and $\xi$. In Fig. 1, we show that at the adopted temperature $T_{\rm
eff}$=4500 K the iron abundance of HD 6268 obtained from Fe I lines is almost
independent of their excitation potential; on the other hand, a significant
slope is obtained at a temperature lower/higher of 100 K. The atmosphere
models of the two stars were calculated for the newly derived stellar
parameters by using ATLAS12 (Kurucz, 2005). As discussed in Kurucz (2005) and
Castelli (2005), ATLAS12 can generate an atmosphere model for any desired
chemical composition of individual elements and microturbulent velocity, since
its treatment of opacity is based on the opacity sampling technique instead of
the use of opacity distribution functions as, for example, in ATLAS9.

Figure 1:  Iron abundance from Fe I lines versus excitation potential of HD
6268 for the adopted $T_{\rm eff}$=4500 K (middle panel) and for a temperature
lower ($T_{\rm eff}$=4400 K, top panel) and higher ($T_{\rm eff}$=4600 K,
bottom panel). Table 2: Atmospheric parameters  HD 4306
---
$T_{\rm eff}$ | log $g$ | [M/H] | $\xi$ | Reference
K | dex | dex | km s-1 |
4700$\pm$ 50 | 1.80$\pm$ 0.10 | -2.90$\pm$ 0.10 | 1.50$\pm$ 0.13 | this paper
4810 | 1.80 | -2.89 | 1.60 | Honda et al. (2004)
4960 | 2.18 | -2.74 | 1.30 | Mashonkina et al. (2017)
HD 6268
$T_{\rm eff}$ | log $g$ | [M/H] | $\xi$ | Reference
K | dex | dex | km s-1 |
4500$\pm$ 50 | 0.80$\pm$ 0.10 | -2.50$\pm$ 0.10 | 2.25$\pm$ 0.13 | this paper
4600 | 1.00 | -2.63 | 2.1 | Honda et al. (2004)
4570 | 0.70 | -2.69 | 1.85 | Roederer et al. (2014)

Table 2 shows the obtained atmospheric parameters for HD 4306 and HD 6268
together with estimates from the literature. We found atmospheric parameters
that are reasonably close with those available in literature, even if we
estimate lower effective temperatures for both stars; in fact, both Honda et
al. (2004) and Mashonkina et al. (2017) estimated $T_{\rm eff}$ with a
different approach based on the photometric data. On the contrary, in Roederer
et al. (2014) $T_{\rm eff}$ is derived with our same approach, by requiring
that abundances derived from Fe I lines show no trend with the excitation
potential and indeed their estimated $T_{\rm eff}$ for HD 6268 is the closest
to our result.

##  4 Chemical abundances from equivalent widths

We used the measured equivalent widths of other weak lines present in our
spectra to derive abundances for the elements listed in Table 3. The errors in
our abundances reported in the table are based only on the standard deviation
to the mean from the abundances measured in the different lines. These errors
are considered as lower limits because we did not compute the impact of the
atmospheric parameters on the error budget for all the elements. Nevertheless,
in Table 4 we show the impact of the variation of the atmospheric parameters
on the abundance of barium for HD 6268. The variation is small, 0.03 dex, and
there is a total budget of 0.08 dex for the errors on the abundance of barium
of this star; a similar impact is expected for HD 4306. For Sr, we can measure
only one line, and for this reason we cannot compute this error. It is worth
noticing that after deriving the abundances of the different elements with the
code ABUNDANCE, we used them to recompute the corresponding atmosphere models
with ATLAS12 for the two stars, and we iterated in order to have a full
consistency between the abundances derived from the spectra and those used in
constructing the atmosphere structures.

Table 3: Chemical abundances of the two stars and comparison to similar
results in literature. For solar abundances - [X/H] - we considered Grevesse
et al. (2007). For the literature data, we also provide the information on how
the the abundances were computed assuming the LTE approximation or NLTE. HD
4306
---
this paper | Honda et al. (2004) | Mashonkina et al. (2017) | Roederer et al. (2014)
Elem | [X/H] - LTE | A(X) | N lines | A(X) - LTE | A(X) LTE | A(X) NLTE | A(X) -LTE
Mg I | -2.49$\pm$0.09 | 5.04 | 4 | 5.25 | 5.27 | 5.30 | -
Ca I | -2.49$\pm$0.02 | 3.82 | 14 | 3.97 | 3.98 | 4.11 | -
Sc II | -2.75$\pm$0.07 | 0.42 | 5 | 0.45 | - | - | -
Ti I | -2.77$\pm$0.02 | 2.13 | 11 | 2.55 | 2.41 | 2.63 | -
Ti II | -2.33$\pm$0.04 | 2.57 | 23 | 2.55 | 2.58 | 2.59 | -
Cr II | -2.74$\pm$0.04 | 2.90 | 2 | 2.97 | - | - | -
Mn I | -3.67$\pm$0.01 | 1.72 | 2 | 2.08 | - | - | -
Fe I | -3.00$\pm$0.01 | 4.45 | 99 | 4.62 | 4.60 | 4.71 | -
Fe II | -2.90$\pm$0.02 | 4.55 | 16 | 4.62 | 4.76 | 4.76 | -
Sr II | -3.27 | -0.35 | 1 | -0.08 | 0.17 | 0.13 | -
Ba II | -4.05$\pm$0.07 | -1.88 | 2 | -1.84 | -1.62 | -1.62 | -
HD 6268
this paper | Honda et al. (2004) | Mashonkina et al. (2017) | Roederer et al. (2014)
Elem | [X/H] - LTE | A(X) | N lines | A(X) - LTE | A(X) LTE | A(X) NLTE | [X/H] -LTE
Mg I | -2.13$\pm$0.17 | 5.40 | 4 | 5.44 | - | - | 5.35
Ca I | -2.27$\pm$0.02 | 4.04 | 13 | 4.09 | - | - | 3.98
Sc II | -2.65$\pm$0.08 | 0.52 | 4 | 0.51 | - | - | 0.39
Ti I | -2.55$\pm$0.02 | 2.35 | 10 | 2.62 | - | - | 2.25
Ti II | -2.23$\pm$0.04 | 2.67 | 14 | 2.62 | - | - | 2.54
Cr II | -2.37$\pm$0.11 | 3.27 | 2 | 3.20 | - | - | 3.11
Mn I | -3.10$\pm$0.01 | 2.29 | 2 | 2.49 | - | - | 2.54
Fe I | -2.51$\pm$0.01 | 4.94 | 81 | 4.88 | - | - | 4.68
Fe II | -2.51$\pm$0.03 | 4.94 | 14 | 4.88 | - | - | 4.81
Sr II | -2.59 | 0.33 | 1 | 0.36 | - | - | 0.33
Ba II | -2.62$\pm$0.07 | -0.45 | 2 | -0.45 | - | - | -0.46
Table 4: Variations of barium abundances obtained from the lines at 5853.668Åand 6141.730 Å as a function of the atmospheric parameters. We present the abundance derived from the single barium lines with three digits; in fact, they are considered to compute the mean and $\Delta$ [Ba/H] (the following as usual with two digits). | best model |  $\Delta$ $T_{\rm eff}$ =50K |  $\Delta$ $T_{\rm eff}$ =$-$50K |  $\Delta$ $\log(g)$ =+0.1 |  $\Delta$ $\log(g)$ =$-$0.1
---|---|---|---|---|---
[Ba/H] from 5853.668 Å | -2.611 | -2.581 | -2.639 | -2.585 | -2.637
[Ba/H] from 6141.730 Å | -2.635 | -2.599 | -2.669 | -2.608 | -2.662
mean [Ba/H] | -2.62 | -2.59 | -2.65 | -2.60 | -2.65
$\Delta$ [Ba/H] |  | 0.03 | -0.03 | 0.02 | 0.03

Even if a detailed study of the chemical composition of HD 4306 and HD 6268 is
not the purpose of this paper, in which we want to study the profiles of Ba II
lines, the results shown in Table 3 indicate that, starting from our measured
equivalent widths and adopting the derived atmosphere parameters, we obtain
abundances that are consistent with those reported in literature. We thus
provide further confirmation of the reliability of the results reported in
Table 2. Regarding the abundances, the enrichment in terms of neutron capture
elements in the two stars is quite different: HD 6268 is more abundant in
heavy elements compared to HD 4306 and has a ratio of [Sr/Ba]$\sim$0; with
abundances of [Sr/Fe]$<$0 and [Ba/Fe]$<-$1, HD 4306 presents a high
[Sr/Ba]$>0.75$. It is important to confirm this enrichment pattern, since it
is on this basis that we select these stars to have, respectively, an expected
barium with r- or s- process isotopic ratios, following the theoretical
outcomes of Cescutti & Chiappini (2014). It must be pointed out that the
different abundance values we derived for Fe I and Fe II and for Ti I and Ti
II are the result of deviations from local thermodynamic equilibrium (LTE), in
particular for Fe I and Ti I (see Mashonkina et al., 2017). It is also worth
underlining that the impacts of the non-local thermodynamic equilibrium (NLTE)
approach to the barium abundances are negligible for HD 4306 according to the
results in Mashonkina et al. (2017). On the other hand, the following
estimates were also obtained for the star HD 4306 ($T_{\rm eff}$ = 4700;
$\log(g)$ = 1.8; [Fe/H] = -2.8): for the barium abundance of -1.88, $\delta$
NLTE = +0.14 for the 6141 line and $\delta$NLTE = +0.21 for the 4554 line; for
the barium abundance of -1.62, $\delta$NLTE = +0.11 for the 6141 line and
$\delta$NLTE = +0.17 for the 4554 line; for the barium abundance of -1.32,
$\delta$NLTE = +0.09 for the 6141 line and $\delta$NLTE = +0.09 for the 4554
line (Korotin et al., 2015, and Sergey Korotin private communication ). With
these estimates of the NLTE impact, we assume an abundance for Ba too high by
0.06-0.07 dex by considering the abundance of line at 6141Å for the line at
4554Å. Indeed, the difference is not negligible, but still within the error.
Finally, we also expect NLTE to have a very small impact on Ba for HD 6268,
following the results for a similar star in terms of stellar atmosphere and
barium abundance again in the Mashonkina et al. (2017) dataset (UMi 36886).

Figure 2: Ca I line at 6102.7 Å. In the upper panel, we show the observed
spectra with a black line. The purple lines are the synthetic spectra
obtained; in the lower panel, the residuals between synthetic spectra and
observed spectra are reported. In the left panel, we present the results for
HD 6268, and on the right we show those for HD 4306. Figure 3: Same as Fig. 2,
but for Ca I line at 6122.2 Å. Figure 4: Same as Fig. 2, but for Fe II line at
4555.8 Å.

##  5 Spectral Synthesis

###  5.1 Synthesis of calcium and iron lines

Using the obtained atmosphere models and the stellar abundances, we computed
the LTE synthetic spectra of HD 4306 and of HD 6268 with SPECTRUM. In order to
compare them with those observed, we need to take into account the broadening
introduced by the instrument and by macroturbulence, $V_{\rm mac}$, and
rotation, $V\sin i$. The shape of the instrumental profile used in degrading
the synthetic spectra to the UVES resolution was derived by fitting the
profile of several emission lines in the ThAr lamp spectra taken during the
observing run. This kind of analysis provides an instrumental profile, which
is a linear combination of a Gaussian and a Lorentzian both with $R$=110,000
and with relative weights of 0.9 and 0.1, respectively. As far as
macroturbulence and rotation broadening are concerned, we compared the
observed and broadened synthetic profiles of three lines: CaI at 6102.7 Å, CaI
at 6122.2 Å, and FeII at 4555.8 Å. We used the combination of Gaussian
profiles computed with $V_{\rm mac}$ varying from 0 to 6 km s-1 at step 0.5 km
s-1 and rotational profiles 555See Eq. 18.14 in Gray (2008); that is, flux
convolution approximation including the limb-darkening coefficient $\epsilon$
(in this work $\epsilon$=0.6). with $V\sin i$=0,1,2,3, and 4 km s-1 as
broadening functions. In Figs. 2, 3, and 4, we show the best resulting
synthetic broadened profiles compared to the observed ones, achieved by using
$V_{\rm mac}$=2.5 and 5.5 km s-1 and $V\sin i$=3.0 and 3.0 km s-1 for HD 4306
and HD 6268, respectively.

###  5.2 Synthesis of barium lines

The same broadening was then adopted to obtain synthetic line profiles for
four Ba II lines, namely the lines at 4554.0, 4934.1, 5853.7, and 6141.7 Å.
The first two lines’ profiles are strongly dependent on the Ba isotope ratios,
while the other two are almost independent of them. In computing the
theoretical line profiles, we used the $s-$ and $r-$ process contributions to
the five isotopes from Arlandini et al. (1999b) to construct pure $s-$process
and pure $r-$process Ba II lines. The Ba hfs line list is the one we used for
the resonant lines at 4554 Åline and 4934 Åis from McWilliam (1998, Table 1),
and it is shown here in Table 5 together with the mass fractions considered
for each isotope in the $s-$process and $r-$process cases.

Table 5: Parameters of barium lines at 4554 Åand 4934 Å used in our calculations with hfs, including the wavelengths, excitation potentials of the lower level, numbers of isotopes, the mass fraction for each isotope, and oscillator strengths. Ba II | Elow=0.00 eV log gf=+0.17 | Elow=0.00 eV log gf=$-$0.15 |  $s-$process |  $r-$process
---|---|---|---|---
| Wavelength (Å) | Strength | Wavelength (Å) | Strength | fraction | fraction
${}^{134}Ba$ |  |  |  |  | 0.02 | 0.00
| 4554.032 | 1.000 | 4934.075 | 1.000 |  |
135Ba |  |  |  |  | 0.03 | 0.40
| 4554.001 | 0.1562 | 4934.034 | 0.3125 |  |
| 4554.002 | 0.1562 | 4934.045 | 0.0625 |  |
| 4554.003 | 0.0625 | 4934.093 | 0.3125 |  |
| 4554.049 | 0.4375 | 4934.104 | 0.3125 |  |
| 4554.052 | 0.1562 |  |  |  |
| 4554.053 | 0.0313 |  |  |  |
136Ba |  |  |  |  | 0.10 | 0.00
| 4554.032 | 1.000 | 4934.075 | 1.000 |  |
137Ba |  |  |  |  | 0.09 | 0.32
| 4553.997 | 0.1562 | 4934.029 | 0.3125 |  |
| 4553.999 | 0.1562 | 4934.041 | 0.0625 |  |
| 4554.000 | 0.0625 | 4934.096 | 0.3125 |  |
| 4554.052 | 0.4375 | 4934.107 | 0.3125 |  |
| 4554.054 | 0.1562 |  |  |  |
| 4554.055 | 0.0313 |  |  |  |
138Ba |  |  |  |  | 0.76 | 0.28
| 4554.032 | 1.0000 | 4934.075 | 1.0 |  |

Figures 5-6 show comparisons among the observed profiles (black) and the
broadened synthetic ones for the lines at 5853.7Å and at 6141.7 Å. As
mentioned above, these lines do not have strong hfs effects, and therefore
they do not show any significant difference in their synthetic profiles
between the $s-$ and the $r-$ cases, which appear as a single purple line. The
comparison between observed and synthetic lines for 5853.7Å and at 6141.7 Å is
good, although the line at 5853.7Å for HD 4306 is really weak; these two lines
were also used to derive the Ba II abundances given in Table 3. On the other
hand, the two lines at 4554.0, 4934.1Å are sensitive to hfs effects and
therefore can be used to infer the role of $s-$ and $r-$processes in the two
stars. In Figs. 7 and 8, we show the comparison of the observed profiles
(black) to the broadened synthetic ones computed for pure r$-$(blue) and
s$-$process (red). In the case of HD 4306 the observed profiles are very well
matched by the synthetic ones computed assuming a pure $s-$process (see also
the small residuals plotted at the bottom of the figures). The observed
profiles of the 4554.0 and 4934.1 Å lines in HD 6268 are not very well
reproduced by the synthetic ones, either assuming a pure $s-$ or pure
$r-$process. On the other hand, the discrepancies are smaller in the case of
the pure $r-$process (see also the residuals). In HD 6268, both these two
lines are much stronger than the corresponding ones in HD 4306, thus the
mismatch of the total equivalent width between observation and synthetic
profile can be ascribed to a problem with the adopted $\xi$ or with deviation
from LTE and can be explained only in part by differences in the isotopic
composition. An increase of the Ba abundance of 0.7 and 0.5 dex is needed to
match the observed equivalent width, assuming an s- and r-process isotopic
composition, respectively. The necessary correction is smaller for the
r-process case, and the resulting line profile fit is better than that of the
s-process assumption. This gives additional support for the conclusion that
the barium of HD 6268 most likely has an r-process origin. In conclusion, by
looking at Figs. 7 and 8 we can say that while the Ba II lines in HD 4306 are
fully consistent with a pure $s-$process origin, those in HD 6268 are better
reproduced assuming the predominance of the $r-$process.

Figure 5: Ba II line at 5853 Å. In the upper panel, we show the observed
spectra with a black line. The purple line is actually two nearly identical
profiles, computed for pure s- and pure r-process hfs, respectively; in the
lower panel, the residuals between synthetic spectra and observed spectra are
reported. In the left panel, we present the results for HD 6268, and on the
right we show those for HD 4306. Figure 6: Same as Fig. 5, but for Ba II line
at 6141 Å. Figure 7: Ba II line at 4554 Å. In the upper panel, we show the
observed spectra with a black line. The blue lines are the synthetic spectra
obtained with an $r-$process isotopic composition of barium. The red lines are
the synthetic spectra obtained with an $s-$process composition. In the lower
panel, the residual for both synthetic spectra are reported. In the left
panel, we present the results for HD 6268, and on the right we show those for
HD 4306. Figure 8: Same as Fig. 7, but for Ba II line at 4934 Å.

##  6 Comparison of observed spectra

Figure 9: Left panels: Comparison of synthetic pure-s profiles of a scaled
fake-HD 6268 star (dark green) with those of HD 6268 (red). Right panels:
Comparison of scaled ‘observed’ profiles of a fake-HD 6268 (light green) with
the observed ones of HD 6268 (black) (see text). Vertical blue lines show the
hfs lines of odd Ba isotopes, and vertical red lines show lines of the even Ba
isotopes.

The results presented thus far are indeed model dependent. In particular, they
depend heavily on the accuracy of the hfs data used to build our synthetic
spectra and on the reliability of the spectrum and atmosphere model codes in
reproducing the real spectra and atmosphere of the two stars. For this reason,
it would be worthwhile to perform a relative analysis exclusively using the
two observed spectra. Unfortunately, such an approach would require the two
stars to be perfectly equal, apart from the relative contributions of the $s-$
and $r-$process to the formation of Ba. Even if the 4554.0 and 4934.1 Å Ba
line profiles depend on the Ba isotope ratios, their profiles are mainly
determined by the values of the stellar atmospheric parameters, by the Ba
abundance, and by the $\xi$, $V_{\rm mac}$, and V$\sin i$ velocities. In the
following, we use the pure-s synthetic spectra of the two stars in a
differential way in order to transform the observed spectrum of HD 4306 into
the spectrum this star would have if its atmospheric parameters and velocities
were exactly the same as those of HD 6268. In such a way, our results are
still built with the help of the synthetic spectra, but they should be less
model dependent than those described in Sect. 5. The idea is to build a
spectrum of a pure-s Ba star with the same stellar atmosphere parameters and
abundances of HD 6268 (hereafter fake-HD 6268) starting from the spectrum of
HD 4306 and to compare it with the spectrum of the real HD 6268 in order to
search for a possible contribution of non-s-processed Ba in the latter star.
The lines in HD 4306 and in the fake-HD 6268 spectrum will differ in strength
(equivalent width) and broadening due to the different stellar atmosphere
characteristics and chemical compositions. If the line profiles are mainly
Doppler profiles, it is easy to scale those of HD 4306 (in a velocity scale
centred at the nominal wavelength of each line) to obtain the broadening of
the fake-HD6268 by taking into account the different effective temperatures
and macroturbulence velocities in the two stars. On the other hand, if other
broadening mechanisms are present (such as, for example, collision broadening,
van der Waals broadening, and Stark broadening) it is not easy to take them
into account within a simple equation; therefore we adopted a parametric
multiplication factor, b, to address their effects. Thus, we initially changed
from the wavelength scale to a velocity scale; that is,
$\Delta\,v=c\times\frac{(\lambda-\lambda_{0})}{\lambda_{0}}$. Then, to take
into account the differences in broadening, we scaled each pure-s synthetic HD
4306 line profile to build the corresponding line of the fake-HD 6268 using
the following equation:

$\Delta\,v^{\rm\scriptscriptstyle fake-
HD\,6268}=b\cdot\Delta\,v^{\rm\scriptscriptstyle HD\,4306}\sqrt{\frac{T_{\rm
eff}^{\rm\scriptscriptstyle HD6268}}{T_{\rm eff}^{\rm\scriptscriptstyle
HD4306}}}\frac{V_{\rm mac}^{\rm\scriptscriptstyle HD6268}}{V_{\rm
mac}^{\rm\scriptscriptstyle HD4306}}.$ (1)

All the resulting fake-HD 6268 lines were then scaled to have the same
equivalent width of the corresponding HD 6268 lines removing the effects of
the different abundances and microturbulences. The b value for each line was
empirically derived by applying the above procedure to the synthetic pure-s
spectra of the two stars by iterating and varying b until we achieved a good
match between the synthetic fake-HD 6268 and the pure-s synthetic HD 6268
lines. We did not use the observed spectra, since we wanted to avoid
incorporating any broadening in the empirically derived b values caused by hfs
effects produced by odd isotopes in the Ba lines. In the left panels of Fig.
9, we plot the obtained synthetic line profiles of the fake-HD 6268 (dark
green lines) superimposed on the original pure-s synthetic profiles of HD 6268
(red lines) after re-sampling all of them at steps of 0.1 km s-1 for all the
lines analysed in Sect. 5. This was done with the exception of the Fe II line
that is blended with the CrI line (4556.163Å) and the BaII 5853.7Å line that
is too week in HD 4306. The values of the b factor are around one (i.e. 0.97,
0.97, 1.15, 1.35, and 1.27 for CaI 6102.7, CaI 6122.2, BaII 6141.7, BaII
4554.0, and BaII 4934.1 Å, respectively), as expected since we already
corrected for the Doppler effects. As can be seen in the left column panels of
Fig. 9, the fake synthetic profiles match very well those of HD 6268 apart for
the blue wing of the BaII 4934.1 Å line that has a known blend with a weak FeI
line (see Fig 5 in Gallagher et al., 2010) since the two stars have different
iron abundances. Thus, our procedure works effectively to remove practically
all the differences between the two stars and to transform the synthetic
pure-s profiles of HD 4306 in those we should expect if HD 4306 were actually
identical to HD 6268.

Eventually, we apply the so derived individual b factors to scale the observed
HD 4306 lines to obtain the observed fake-HD 6268 lines by assuming a pure
s-process for HD 6268. In the right column panels of Fig. 9, we plot the
observed fake-HD 6268 profiles (light green lines) superimposed on the
corresponding observed profiles of HD 6268 (black lines) in order to check our
assumption. Our procedure removed practically all the differences between the
two stars and transform the observed profiles of HD 4306 in those we should
expect if HD 4306 was actually identical to HD 6268 when we look at the two
CaI lines and at the BaII 6141.7 line, which are unaffected by the hypothesis
that both stars are pure-s Ba objects. On the other hand, when we apply the
same technique to the 4554.0 and 4934.1 Å BaII lines, whose profiles are
sensitive to the relative contributions of $s-$ and $r-$processes in the two
stars, the observed fake-HD 6268 profiles do not reproduce the observed
profiles of HD 6268 as well as in the case of the corresponding synthetic ones
(left panels in the bottom two lines of Fig. 9). In particular, we notice main
differences in the cores where the even Ba isotopes shape the lines and in the
regions of the hfs lines of odd Ba isotopes, indicated by vertical red and
blue lines in Fig. 9, respectively. So, these results suggest that the
assumption of a pure $s-$process for HD 6268 should be rejected since it leads
to fake observed profiles of HD 6268 that are different from the real observed
ones, in particular in the region sensitive to s- and r-process contribution.

We cannot firmly conclude that the barium isotopes in HD 6268 have a pure
r-process pattern. On the other hand, the differences shown in the right
panels of the two bottom lines should be due to an effect that does not occur
in the other lines. In this respect, the most likely reason is the different
pattern of barium isotopes between the two stars; therefore, these differences
can be ascribed to the enrichment of an $r-$process with a large fraction of
odd isotopes in HD 6268, absent from the fake-HD 6268 spectrum. This outcome
arises from the differential analysis of synthetic and observed spectra, and
so it is almost independent of the theoretical hfs Ba data; the only
dependence is in the negligible hfs effects of the scarce odd isotopes within
the s-process pattern.

##  7 Conclusions

According to our results, the two stars analysed here present two different
isotopic compositions of barium. In fact, the results obtained in Sections 5
and 6 are both consistent with the hypothesis that the barium in HD 4306 was
produced exclusively by an s$-$process, while the one in HD 6268 also shows a
contribution by an $r-$process. The predictions of the previous chemical
evolution models in Cescutti & Chiappini (2014) pointed out exactly this
possibility, that in the Galactic halo both an $s-$process and an $r-$process
can pollute the ISM and therefore preserve this differential signature. The
high [Ba/Fe] stars that typically show a solar or slightly sub-solar [Sr/Ba]
ratio are most likely polluted by an $r-$process source, in this case HD 6268
with [Ba/Fe]=0.09 and [Sr/Ba]=0.03. On the other hand, an $s-$process source
should have polluted the stars with a low [Ba/Fe] and with a [Sr/Ba] that,
according to the theoretical yields for rotating massive stars, can go from
about solar (possibly even below solar) up to a [Sr/Ba]$\sim$1.5 (Frischknecht
et al., 2016; Limongi & Chieffi, 2018), in our case HD 4306 with
[Ba/Fe]=$-$1.05 and [Sr/Ba]=0.78. Therefore, it could be that the light
elements’ primary production, empirically introduced by Travaglio et al.
(2004), is an $s-$process that is activated almost as a primary process by
rotation. This possibility was not excluded by the study of Montes et al.
(2007), together with the more commonly invoked weak $r-$process. Clearly, the
fact that this happens for two stars does not provide firm conclusions, and
more stars must be measured to determine the real statistical impact of the
$s-$process in massive stars at low metallicity. Nevertheless, we think that
this work provides insight into the impact of detailed studies of isotopes and
the possibilities that high-quality spectra can provide.

###### Acknowledgements.

MV and NC acknowledge support by Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) – project-IDs: 428473034, and 138713538 (SFB 881 “The
Milky Way System”, subproject A04). CK acknowledges funding from the UK
Science and Technology Facility Council (STFC) through grant ST/M000958/1 &
ST/V000632/1. This work was partially supported by the European Union (ChETEC-
INFRA, project no. 101008324 and ChETEC, CA16117).

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##  Appendix A Additional Table

Table 6: List of the atmosphere parameters of HD 6268 from literature. Column ’r’ indicates the data type: ’H’ is high-resolution spectra, ’L’ is low-resolution spectra, and ’P’ is photometry. Column ’c’ indicates whether the data are original measurements (’O’) or a compilation of re-calibrated sources (’C’). Column ’m’ indicates the method: ’A’ stands for model atmosphere and ’T’ stands for empirical calibration. Teff | err | logg | err | [Fe/H] | err | r | c | m | Reference
---|---|---|---|---|---|---|---|---|---
4667 |  | 1.25 |  | -2.42 |  | H | O | A | Luck & Bond (1981)
4755 |  | 1.2 |  | -2.1 |  | H | O | A | Luck & Bond (1985)
4582 |  | 0.75 |  | -2.4 |  | H | O | A | Barbuy et al. (1985)
4800 | 100 | 0.84 | 0.03 | -2.56 | 0.05 | H | O | A | Gratton (1989)
4670 |  | 0.75 |  | -2.58 |  | H | O | A | McWilliam et al. (1995)
4800 | 100 | 0.84 | 0.03 | -2.52 | 0.05 | H | O | A | Francois (1996)
4700 |  | 1.6 |  | -2.36 |  | H | O | A | Pilachowski et al. (1996)
4705 |  | 1.5 |  | -2.35 |  | H | O | A | Meléndez & Barbuy (2002)
4600 |  | 1. |  | -2.62 | 0.11 | H | O | A | Honda et al. (2004)
4740 |  | 1.2 |  | -2.32 |  |  | C |  | Cenarro et al. (2007)
4735 | 113 | 1.42 | 0.26 | -2.36 | 0.11 | L | O | T | Prugniel et al. (2011)
4570 | 34 | 0.7 | 0.16 | -2.82 | 0.15 | H | O | A | Roederer et al. (2014)
4726 |  | 1.14 |  | -2.63 |  | H | O | A | Wu et al. (2015)
4571 | 161 | 1.13 | 0.39 | -2.63 | 0.18 | L | O | T | Sharma et al. (2016)
4837 | 125 | 1.59 |  |  |  | P | O | T | McDonald et al. (2017)
4662 | 47 | 1.37 | 0.14 | -2.47 | 0.07 | H | O | A | Arentsen et al. (2019)