# Plumeria at SemEval-2022 Task 6: Robust Approaches for Sarcasm Detection for
English and Arabic Using Transformers and Data Augmentation

Shubham Kumar Nigam∗
Indian Institute of Technology Kanpur
<EMAIL_ADDRESS>
&Mosab Shaheen∗
Indian Institute of Technology Kanpur
<EMAIL_ADDRESS>

###### Abstract

This paper describes our submission to SemEval-2022 Task 6 on sarcasm
detection and its five subtasks for English and Arabic. Sarcasm conveys a
meaning which contradicts the literal meaning, and it is mainly found on
social networks. It has a significant role in understanding the intention of
the user. For detecting sarcasm, we used deep learning techniques based on
transformers due to its success in the field of Natural Language Processing
(NLP) without the need for feature engineering. The datasets were taken from
tweets. We created new datasets by augmenting with external data or by using
word embeddings and repetition of instances. Experiments were done on the
datasets with different types of preprocessing because it is crucial in this
task. The rank of our team was consistent across four subtasks (fourth rank in
three subtasks and sixth rank in one subtask); whereas other teams might be in
the top ranks for some subtasks but rank drastically less in other subtasks.
This implies the robustness and stability of the models and the techniques we
used.

Plumeria at SemEval-2022 Task 6: Robust Approaches for Sarcasm Detection for
English and Arabic Using Transformers and Data Augmentation

Shubham Kumar Nigam∗ Indian Institute of Technology Kanpur<EMAIL_ADDRESS>Mosab Shaheen∗ Indian Institute of Technology Kanpur<EMAIL_ADDRESS>

**footnotetext: These authors contributed equally to this work

##  1 Introduction

Sarcasm is a figurative language where speakers or writers usually mean the
contrary of what they say. Recognizing whether a speaker or writer is
sarcastic is essential to downstream applications to understand the
sentiments, opinions, and beliefs correctly Ghosh et al. (2020). Sarcasm is
ubiquitous on the social media text and, due to its nature, can be highly
divisive of computational systems that perform tasks on that kind of data such
as sentiment analysis, opinion mining, and harassment detection Van Hee et al.
(2018); Bing (2012); Rosenthal et al. (2014); Maynard and Greenwood (2014).

Our team Plumeria participated in SemEval 2022 task 6 Abu Farha et al. (2022)
in all its subtasks on English and Arabic. Previous shared tasks on sarcasm
detection Hee et al. (2018); Ghanem et al. (2019); Ghosh et al. (2020); Abu
Farha et al. (2021) have only two subtasks; one is sarcasm detection and
another is predicting the type of sarcasm. However, in SemEval 2022 task 6 Abu
Farha et al. (2022) organizers formulate three subtasks for both languages
following the methods described in Oprea and Magdy (2020).

Using the two datasets for English and Arabic, organizers formulate three
subtasks as follows:

  * •

Subtask A (English and Arabic): It is a binary classification subtask where
submitted systems have to predict whether a tweet is sarcastic or not.

  * •

Subtask B (for English only): It is a multi-label classification subtask where
submitted systems have to predict one or more labels out of six ironic-speech
labels: sarcasm, irony, satire, understatement, overstatement, and rhetorical
question.

  * •

Subtask C (English and Arabic): It is a binary classification subtask. Given
two texts, a sarcastic tweet and its non-sarcastic rephrase which conveys the
same meaning, submitted systems have to predict which text is the sarcastic
one.

In this shared task, the systems we submitted for all three subtasks primarily
focused on the transformer based approaches because of their success in the
field of NLP. Moreover, we used a hierarchical network by stacking a BiLSTM
layer on top of a transformer either with or without attention mechanism.
However, the most significant constraint of a neural network is that they need
lots of data for training to give satisfactory results. In addition, if the
dataset is imbalanced with fewer instances of some class, this can result in
poor results for detecting this class. That motivates us to create biased
datasets, towards the concerned class/label, from existing datasets by
increasing the number of instances of such a class/label. A detailed
explanation of dataset creation is in section 3. We also illustrate the
composition of created datasets in each subtask and the performance of the
models on them.

The rank of our team was consistent across most subtasks (fourth rank in three
subtasks, sixth rank in one subtask, and tenth rank in one subtask); unlike
many teams which scored high in one or two subtasks but scored considerably
less in other subtasks. This shows that the robustness and the consistency of
our methods. The bias in created datasets was crucial for subtask A and
subtask B, while augmenting a dataset plays a key role in subtask C. We
released the codes and datasets for all subtasks via
GitHub111https://github.com/ShubhamKumarNigam/iSarcasm-SemEval-2022-Task-6.

##  2 Abbreviations

The following abbreviations were used frequently, and are shown in Table 1.

Full Form | Abbreviation
---|---
Language | Lang
Sarcastic | S
Non-Sarcastic | NS
English | En
Arabic | Ar
External | Ext
Table 1: Abbreviations used in the paper

##  3 Dataset

The organizers provided datasets for English and Arabic. Regardless of the
dataset, these are the fields in each row of a dataset:

  * •

Tweet: A text specifying a tweet. This field is for all subtasks.

  * •

Sarcastic: A binary field specifying whether a tweet is sarcastic or not. This
field is for subtask A.

  * •

Rephrase: A text specifying a non-sarcastic rephrase of a sarcastic tweet.
This field is for subtask C.

  * •

Sarcasm, Irony, Satire, Understatement, Overstatement, and Rhetorical question
(English only): These binary fields are the labels of a sarcastic tweet. These
fields are for subtask B.

  * •

Dialect (Arabic only): A text specifying the dialect of a tweet from one of
five dialects: Modern Standard Arabic (MSA), Egyptian, Levantine, Maghrebi,
and Gulf. This field is for subtask A and C.

In the following sections we will describe the datasets given by the
organizers, other available datasets, and augmented datasets.

###  3.1 Datasets given by organisers (Original)

The organizers released two training datasets for Arabic and English to train
the systems on them for all subtasks. Later on, they released one testing
dataset for each subtask. We called these datasets "original" datasets as they
are the official datasets for the subtasks. Information about the distribution
of sarcastic and non-sarcastic tweets is presented in Table 2 and in the
appendix A.7 \- Figure 7. Furthermore, information about sarcastic labels for
subtask B is presented in Table 3 and in the appendix A.7 \- Figure 8.

###  3.2 Other Available Datasets (External)

The datasets in this section are not the official datasets and thus we called
them "external" datasets. However, we used these datasets for subtask A and
subtask B as they are created for similar subtasks.

Datasets Downloaded using Twitter API: Initially the organizers provided the
participants with a training and testing datasets which covered subtask A and
subtask B for English. However, they provided the tweet ID instead of the
tweet text and they asked the participants to download the tweet text using
the tweet ID via Twitter API222developer.twitter.com/en/docs/api-reference-
index. Therefore, we downloaded some of the tweet texts for these two datasets
and other tweet texts we could not find. We were able to download 2841 tweets
for training and 713 tweets for testing as shown in Table 2. The distribution
of the tweets over the sarcastic labels is presented in Table 3.

Datasets of SemEval-2018 Task 3: These datasets are on same subtasks of
subtask A and subtask B but for SemEval 2018 (Hee et al., 2018). We used the
dataset for subtask A which has emojis and sarcasm hashtags. The datasets are
available for download in this link333SemEval2018-Task3 Dataset. More
information about the distribution of sarcastic and non-sarcastic tweets is
presented in Table 2.

ArSarcasm-v2 Dataset: It contains a training and testing datasets for sarcasm
detection in Arabic (Abu Farha et al., 2021). Each row contains a tweet,
sarcastic class, sentiment, and dialect. The datasets are available for
download in this link444ArSarcasm-v2. More information about the distribution
of sarcastic and non-sarcastic tweets is presented in Table 2.

Dataset | Split | Lang | Total | S% | NS%
---|---|---|---|---|---
Original | Train | En | 3468 | 25 | 75
Original | Train | Ar | 3102 | 24 | 76
Original | Test | En | 1400 | 14.3 | 85.7
Original | Test | Ar | 1400 | 14.3 | 85.7
Twitter API | Train | En | 2841 | 16.8 | 83.2
Twitter API | Test | En | 713 | 16.8 | 83.2
SemEval 2018 | Train | En | 3834 | 49.8 | 50.2
ArSarcasm-v2 | Train | Ar | 12548 | 17.3 | 82.7
ArSarcasm-v2 | Test | Ar | 3000 | 27.4 | 72.6

Table 2: Total number of tweets and percentage of sarcastic and non-sarcastic
tweets in each dataset for subtask A.

|  |  | Sarcasm% | Irony% | Satire%
---|---|---|---|---|---
Dataset | Split | Total |  Under- statement% |  Over- statement% |  Rhetorical question%
|  |  | 68.3 | 14.8 | 2.4
| Train | 3468 | 1 | 3.8 | 9.7
|  |  | 66.4 | 7.4 | 18.1
Original | Test | 1400 | 0.4 | 3.7 | 4
|  |  | 41.5 | 30.6 | 10.9
| Train | 2841 | 1 | 8.2 | 7.8
|  |  | 41.7 | 33.3 | 11.7
Twitter API | Test | 713 | 3.3 | 6.7 | 3.3

Table 3: Total number of tweets and percentage of sarcastic labels in each
dataset for subtask B.

###  3.3 Augmented Datasets

In addition to the original and external datasets, we created more datasets
with more number of instances using the following methods:

  1. 1.

Augmenting an original dataset with external datasets: We added instances to
an original dataset from the matching external datasets either to balance it
or just to augment it, and we filtered out the NAN entries .

  2. 2.

Augmenting a dataset using word embeddings: For word embeddings we used Gensim
library555Gensim Library together with GloVe word vectors666GloVe Word Vectors
trained on two billion tweets with 100 dimension word vectors (glove-
twitter-100). To create new instances in a dataset, we took a copy of one
instance in the dataset and replaced up to four keywords in a tweet (or its
rephrase) with one of the top three similar words according to the similarity
between the word vectors, then we added the copied modified instance to the
dataset and we repeated the process for other instances.

  3. 3.

Augmenting a dataset by repeating instances: Instances from a dataset are
mostly repeated to balance the classes/labels in a dataset.

The final datasets used for each subtask is explained in the dedicated section
for the subtask.

##  4 Preprocessing

  * •

Type I: No preprocessing

  * •

Type II: Emotion icons were converted to their string text using the "emoji"
Python library. Then, URLs were converted to "HTTPURL" token, also every
mention in a tweet was converted to "@USER" token using regular expressions.
These conversions was done because the BERTweet model was pre-trained on
tweets after these conversions.

  * •

Type III: Same as in Type-III besides converting the smiley face codes e.g.
":-)" and ":)" to one of three values (smiley, sad, and playful). More than
two successive occurrences of any punctuation like in "why?!!!!" were removed,
then we removed more than two successive occurrences of same character like in
"Superrrr" which can be found frequently in tweets. Moreover, a contraction
(e.g. "isn’t and "’cause") was replaced with its full form (e.g. "is not" and
"because").

  * •

Type IV: Same as in Type-III besides stemming and stop-word removal. For
English we used WordNet lemmatizer and for Arabic we used ISRI stemmer, all
from the NLTK Python library777NLTK Python Library.

##  5 Methodology, Results and Analysis

###  5.1 Conventions

In the following tables, if a table cell is highlighted with a light brown
color, it means that the score is among the best results on the validation
dataset in the corresponding section of the table; whereas the one with brown
color is the highest score. Furthermore, if a cell is highlighted with a green
color, it means that the score is our final submission score (released by the
organizers) in the subtask on the test dataset; whereas the one with blue
color is a score of a submitted model but not the final one (a team can have
multiple submissions).

###  5.2 Subtask A (English)

####  5.2.1 Datasets

  * •

Original: The training split of the original dataset for English in Table 2 is
splitted into training and validation datasets as shown in Table 4.

  * •

External: As the measure for this task is F1-score for the sarcastic class,
thus we created datasets which are biased towards the sarcastic class as shown
in Table 5.

Dataset | Total | S% | NS%
---|---|---|---
Original Train | 2080 | 25 | 75
Original Val | 1388 | 25 | 75

Table 4: Original datasets for subtask A (English) with the total number of
tweets and the percentage of sarcastic (S%) and non-sarcastic (NS%) tweets.

Dataset |  Contributing Datasets |  Additional Non Sarcastic Tweets from SemEval 2018-Training | Total | S% | NS%
---|---|---|---|---|---
B0 |  | 0 | 4578 | 66 | 34
B1 |  | 145 | 4723 | 64 | 36
B2 |  | 290 | 4868 | 62 | 38
B3 |  | 435 | 5013 | 60 | 40
B4 |  | 580 | 5158 | 59 | 41
B5 |  | 725 | 5303 | 57 | 43
B6 |  | 870 | 5448 | 55 | 45
B7 |  | 1015 | 5593 | 54 | 46
B8 |  | 1160 | 5738 | 53 | 47
B9 |  Original Train + Twitter API Train (only sarcastic) + Twitter API Test (only sarcastic) + SemEval 2018 Train (1911 sarcastic) | 1305 | 5883 | 51 | 49

Table 5: External datasets for subtask A (English).

####  5.2.2 Approaches

We primarily focused on the transformer based models. Since the task is a
binary classification on tweets, the excellent choice to start with is
BERTweet-base888HuggingFace Bertweet-Base and BERTweet-large999HuggingFace
Bertweet-Large Nguyen et al. (2020), a pre-trained language model on 845M
English Tweets. Likewise, we tried the ELECTRA101010HuggingFace Electra Large
Discriminator Clark et al. (2020) replaced token detection model (a pre-
training task in which the model learns to distinguish real input tokens). In
ELECTRA model, some tokens in the input are replaced with sample tokens
instead of masking the tokens as in BERT. Moreover, we used a hierarchical
network by passing the input tokens to the BERT model, then each token
embedding is passed to a Bi-LSTM layer either with or without attention. The
architecture of the BERT model, ELECTRA model, and hierarchical network is
shown in appendix A.3, A.4, and A.1 respectively. The final layer of each
model was a linear layer with softmax activation function and we used the
cross entropy loss function.

Note: We ran several experiments on all the approaches of this subtask with
different datasets and preprocessing types. We also experimented with
different learning rates, epochs, and loss functions to verify which one is
performing best.

####  5.2.3 Results and Analysis

Metric: The main metric is F1-score for the sarcastic class.

BERT: We used BERTweet-large, as it gave better performance than BERTweet-
base, on the original training dataset shown in Table 4. We experimented with
different learning rates and preprocessing types, and ran for 5 epochs. The
results are shown in Table 6.

Learning Rate | Type | Val | Test
---|---|---|---
| I | 0.0057 | 0.0293
| II | 0.5017 | 0.457
| III | 0 | 0
2 e - 6 | IV | 0 | 0
| I | 0.3786 | 0.5068
| II | 0.5552 | 0.4874
| III | 0.5405 | 0.4972
3 e - 6 | IV | 0 | 0
| I | 0.5585 | 0.4981
| II | 0.4926 | 0.4717
| III | 0.5407 | 0.4772
4 e - 6 | IV | 0 | 0
| I | 0.5275 | 0.4724
| II | 0.5655 | 0.4841
| III | 0 | 0
5 e - 6 | IV | 0 | 0
Table 6: Results of the BERT model for subtask A (English) on original
datasets

From these experiments we found that Type-II preprocessing is performing
better than other types and same applies for the learning rate 4e-6. We
conducted similar experiments on the external datasets in Table 5 and we found
similar results. We tried using the cross entropy loss function with and
without weights on the external datasets using the same learning rate,
preprocessing type, and number of epochs. We got our best result on the B4
dataset with weighted loss function which was our official submission score
for this subtask. The results are shown in Table 7.

|  Loss1: Without Weights |  Loss2: W1=1/#NS, W2=1/#S
---|---|---
Biased | Val | Test | Val | Test
B0 | 0.5784 | 0.4487 | 0.5944 | 0.4519
B1 | 0.5714 | 0.4548 | 0.5738 | 0.479
B2 | 0.5767 | 0.465 | 0.5951 | 0.4917
B3 | 0.601 | 0.4626 | 0.5931 | 0.4817
B4 | 0.5954 | 0.4727 | 0.6025 | 0.4769
B5 | 0.5874 | 0.5142 | 0.5803 | 0.5008
B6 | 0.5858 | 0.4791 | 0.5624 | 0.4884
B7 | 0.5957 | 0.5016 | 0.5637 | 0.5034
B8 | 0.584 | 0.492 | 0.5814 | 0.5
B9 | 0.5723 | 0.487 | 0.5554 | 0.49

Table 7: Results of the BERT model for subtask A (English) on external
datasets.

We used 5 epochs and 4e-6 learning rate because they gave the best results as
shown in appendix A.5.

The official scores and leader-board ranks of the teams for subtask A
(English) are shown in Table 8.

Rank | User | F-1 sarcastic
---|---|---
1 | stce | 0.6052
2 | emma | 0.5691
3 | saroyehun | 0.5295
4 |  | ShubhamKumarNigam
---
0.4769

Table 8: Scores and leader-board ranks for subtask A (English)

ELECTRA: We used the ELECTRA model on the external datasets with Type-II
preprocessing, 6e-6 learning rate, and 5 epochs as they were performing the
best as shown in Table 9.

Biased | Val | Test
---|---|---
B0 | 0.5525 | 0.4684
B1 | 0.4002 | 0.25
B2 | 0.5738 | 0.4762
B3 | 0.4002 | 0.25
B4 | 0.5756 | 0.4879
B5 | 0.4002 | 0.25
B6 | 0.5468 | 0.4642
B7 | 0.5702 | 0.4789
B8 | 0.479 | 0.5073
B9 | 0.4002 | 0.25
Table 9: Results of the ELECTRA model for subtask A (English) on external
datasets.

BERT+BiLSTM with and without attention: The results we got using this
architecture was not much stable (i.e. they may change when re-running the
experiment) and thus we did not use this model for the official submission.
More details about the results of the model can be found in the appendix A.6.

###  5.3 Subtask A (Arabic)

####  5.3.1 Datasets

Original: The training split of the original dataset for Arabic in Table 2 is
splitted into training and validation datasets as shown in Table 10.

Dataset | Total | S% | NS%
---|---|---|---
Original Train | 1861 | 24 | 76
Original Val | 1241 | 24 | 76

Table 10: Original datasets for subtask A (Arabic).

External: Same as in subtask A (English), we created datasets which are biased
towards the sarcastic class as shown in Table 11.

Dataset |  Contributing Datasets |  Additional Non Sarcastic Tweets from SemEval 2018-Training | Total | S% | NS%
---|---|---|---|---|---
B0 |  | 0 | 4850 | 71 | 29
B1 |  | 202 | 5052 | 68 | 32
B2 |  | 404 | 5254 | 65 | 35
B3 |  | 606 | 5456 | 63 | 37
B4 |  | 808 | 5658 | 61 | 39
B5 |  | 1010 | 5860 | 59 | 41
B6 |  | 1212 | 6062 | 57 | 43
B7 |  | 1414 | 6264 | 55 | 45
B8 |  | 1616 | 6466 | 53 | 47
B9 |  Original Train+ ArSarcasm-v2 Train (only sarcastic)+ ArSarcasm-v2 Test (821 sarcastic) | 1818 | 6668 | 52 | 48

Table 11: External datasets for subtask A (Arabic)

####  5.3.2 Approaches

The approached used here are similar to subtask A (English) except for the
used transformers. Since the data is in the Arabic language, we tried some
models from The Computational Approaches to Modeling Language (CAMeL) research
lab 111111HuggingFace CAMeL-Lab. They majorly focused on Arabic and Arabic
dialect processing, machine translation, text analysis, and dialogue systems.

The models are available on the Hugging Face library. CAMeLBERT is a
collection of BERT models pre-trained on Arabic texts with different sizes and
variants Inoue et al. (2021). They released pre-trained language models for
Modern Standard Arabic (MSA), dialectal Arabic (DA), and classical Arabic
(CA). We tried CAMeLBERT-DA and CAMeLBERT-Mix for sarcasm detection. Likewise,
we tried the AraBERT v2 which is a pre-trained BERT based on Google’s BERT
architecture for Arabic Language Understanding121212HuggingFace Bert-Base-
Arabert-v02 Antoun et al. .

####  5.3.3 Results and Analysis

Metric: The main metric is F1-score for the sarcastic class.

BERT: We used CAMeLBERT-Mix as it performed the best among other BERT models.
We applied it on the external datasets with non-weighted cross entropy loss
function, 5 epochs, and 2e-5 learning rate because they gave the best results
which are shown in Table 12.

Biased | Val | Test
---|---|---
B0 | 0.7168 | 0.3438
B1 | 0.7025 | 0.4163
B2 | 0.7131 | 0.4071
B3 | 0.6804 | 0.4335
B4 | 0.7015 | 0.4186
B5 | 0.6927 | 0.4332
B6 | 0.7012 | 0.4048
B7 | 0.7124 | 0.4365
B8 | 0.6731 | 0.4589
B9 | 0.7094 | 0.4589
Table 12: Results of the BERT model for subtask A (Arabic) on external
datasets.

BERT+BiLSTM+Attention: Same in subtask A (English), We used attention with
BiLSTM on top of BERT model. The results also were not much stable. However,
the best results for this architecture occurred when using 5 epochs and 9e-6
learning rate on B3 and B9 datasets as shown in Table 13.

Biased |  Hidden State Size | Val | Test
---|---|---|---
B3 | 50 | 0.6849 | 0.4234
B9 | 1000 | 0.7123 | 0.4693
Table 13: Results of the BERT+BiLSTM+Attention model for subtask A (Arabic)

The official scores and leader-board ranks of the teams for subtask A (Arabic)
are shown in Table 14.

Rank | User | F-1 sarcastic
---|---|---
1 | Abdelkader | 0.5632
2 | Aya | 0.5076
3 | rematchka | 0.4767
10 |  | ShubhamKumarNigam
---
0.4072

Table 14: Scores and leader-board ranks for subtask A (Arabic)

###  5.4 Subtask B

####  5.4.1 Datasets

Original: The training split of the original dataset for English in Table 3 is
splitted into training and validation datasets as shown in Table 15.

|  | Sarcasm | Irony | Satire
---|---|---|---|---
Dataset | Total |  Under- statement |  Over- statement |  Rhetorical question
|  | 67.60% | 15.10% | 2.60%
Original Train | 606 | 1% | 3.50% | 10.20%
|  | 70% | 14.20% | 1.90%
Original Val | 261 | 1% | 4.50% | 8.40%

Table 15: Original datasets for subtask B (English)

External: The original and external datasets presented in Table 3 (without the
validation dataset) were added together to form a new dataset (Ext-NB). Then
the resulting dataset was balanced either by using word embeddings (Ext-UW) or
by repeating instances (Ext-UR). We created a dataset (Ext-EB) to give more
importance to the labels of low number of instances by repeating the instances
of these labels up to the limits specified by these heuristic formulas:
#irony=#sarcasm*(1+1/sqrt(#irony)) (1) #satire=#sarcasm*(1+2/sqrt(#satire))
(2)
#understatement=#sarcasm*(1+3/sqrt(understatement)) (3)
#overstatement=#sarcasm*(1+1.5/sqrt(overstatement)) (4)
#rhetorical=#sarcasm*(1+1.2/sqrt(#rhetorical)) (5)
The datasets are shown in Table 16.

|  |  |  | Sarcasm |  Under- statement
---|---|---|---|---|---
|  |  |  |  Irony |  Over- statement
Dataset | Balanced |  Contributing Datasets | Total | Satire |  Rhetorical question
|  |  |  | 55.90% | 1.20%
|  |  |  | 22.30% | 5.50%
Ext-NB | Not Balanced |  | 1203 | 6.40% | 8.70%
|  |  |  | 16.50% | 16.60%
|  |  |  | 16.50% | 16.80%
Ext-UW |  Using Word Embedding |  | 4336 | 16.60% | 17%
|  |  |  | 16.50% | 16.60%
|  |  |  | 16.50% | 16.80%
Ext-UR |  Using Repetition |  | 4336 | 16.60% | 16.90%
|  |  |  | 15% | 18.80%
|  |  |  | 15.80% | 17%
Ext-EB | Not Balanced |  Original Train + Twitter API Train + Twitter API Test | 5314 | 16.70% | 16.80%

Table 16: External datasets for subtask B (English).

####  5.4.2 Approaches

This subtask primarily focused on BERTweet-large. As it is a multi labeling
subtask, we used sigmoid as the activation function in the last layer and
binary cross entropy as the loss function.

####  5.4.3 Results and Analysis

Metric: The main metric is Macro-F1 score.

BERT: We used BERTweet-large on the external datasets using 5 epochs, 6e-6
learning rate, and Type-II preprocessing. The results are shown in Table 17.

Dataset | Val | Test
---|---|---
Ext-NB | 0.1513 | 0.038
Ext-UW | 0.318 | 0.0716
Ext-UR | 0.3412 | 0.076
Ext-EB | 0.4152 | 0.0778
Table 17: Results of the BERT model for subtask B (English) on external
datasets.

The official scores and leader-board ranks of the teams for subtask B
(English) are shown in Table 18.

Rank | User | macro F-score
---|---|---
1 | Duxy | 0.163
2 | Abdelkader | 0.0875
3 | robvanderg | 0.0851
6 |  | ShubhamKumarNigam
---
0.0778

Table 18: Scores and leader-board ranks for subtask B (English)

###  5.5 Subtask C (English)

####  5.5.1 Datasets

Original: The training split of the original dataset for English in Table 2 is
splitted into training and validation datasets. As we do not have external
datasets here, so we augmented the training split once with word embeddings
(Original-Embedding) and once with repetition (Original-Repetition). We
swapped between the tweet and its rephrase for half of the instances together
with flipping the value of the sarcastic field, so that the model will be able
to learn. Otherwise, it may always predict the first text as the tweet and the
second one as the rephrase. The datasets are shown in Table 19.

Dataset | Total
---|---
Original-Train | 606
Original-Validation | 261
Original-Embedding | 1606
Original-Repetition | 1606
Table 19: Original datasets for subtask C (English)

####  5.5.2 Approaches

Organizers provide a sarcastic text, and its non-sarcastic rephrase, i.e., two
texts convey the same meaning. Since the input format changed in this subtask,
we input both texts together to the BERT model as one text separating them by
the separating token. We focused on transformers which are trained on
question-answering tasks. We tried BERT models trained on the Stanford
Question Answering Dataset (SQuAD) dataset Rajpurkar et al. (2018). SQuAD is a
reading comprehension dataset consisting of questions posed by crowdworkers on
a set of Wikipedia articles.

We took models from the Hugging Face library; one is BERT large model
(cased)131313HuggingFace Bert-Large-Cased-Whole-Word-Masking-Finetuned-Squad,
trained on whole word masking, and fine-tuned on the SQuAD dataset. Another is
BERT base model (uncased)141414HuggingFace Bert-Base-Uncased-Squad2, trained
on Masked language modeling (MLM), and fine-tuned on the SQuAD dataset.

####  5.5.3 Results and Analysis

Metric: The main metric is the accuracy.

BERT: We used BERT large model (cased) on the original datasets, because it
gave better results among the other models, using 15 epochs, 8e-6 learning
rate, and the cross entropy as the loss function. The results are shown in
Table 20. We did our submission using Type-I preprocessing even though Type-II
was performing better on the validation dataset.

Dataset | Type | Val | Test
---|---|---|---
| I | 0.951 | 0.79
| II | 0.9395 | 0.8
| III | 0.9193 | 0.83
Original- Train | IV | 0.9135 | 0.79
| I | 0.9654 | 0.83
| II | 0.9654 | 0.8
| III | 0.9366 | 0.82
Original- Embedding | IV | 0.8588 | 0.72
| I | 0.9395 | 0.8
| II | 0.9222 | 0.815
| III | 0.9078 | 0.8
Original- Repetition | IV | 0.9078 | 0.68
Table 20: Results of the BERT model for subtask C (English) on original
datasets.

The official scores and leader-board ranks of the teams for subtask C
(English) are shown in Table 21.

Rank | User | Accuracy
---|---|---
1 | emma | 0.87
2 | lizefeng | 0.855
3 | leon14138 | 0.805
4 |  | ShubhamKumarNigam
---
0.79

Table 21: Scores and leader-board ranks for subtask C (English)

###  5.6 Subtask C (Arabic)

####  5.6.1 Datasets

Original: The datasets were generated in the same way as in subtask C
(Engligh) and are shown in Table 22

Dataset | Total
---|---
Original-Train | 521
Original-Validation | 224
Original-Embedding | 1521
Original-Repetition | 1521
Table 22: Original datasets for subtask C (Arabic)

####  5.6.2 Approaches

The approached used here are similar to subtask C (English) except for the
used transformers. Since the data is in the Arabic language, we took a couple
of models from the Hugging Face library like the multilingual model mBERT base
(cased), trained on the QA dataset in seven languages and fine-tuned on the
combination of XQuAD Artetxe et al. (2020) and MLQA Lewis et al. (2020)
datasets. We compared their performance to the CAMeLBERT-Mix model.

####  5.6.3 Results and Analysis

Metric: The main metric is the accuracy.

BERT: We used CAMeLBERT-Mix model on the original datasets using 5 epochs,
3e-5 learning rate, and the cross entropy as the loss function. The results
are shown in Table 23. We did our submission using Type-II preprocessing as it
is the best performing.

Dataset | Type | Val | Test
---|---|---|---
| I | 0.6242 | 0.5
| II | 0.6242 | 0.5
| III | 0.6711 | 0.72
Original- Train | IV | 0.3758 | 0.5
| I | 0.8792 | 0.825
| II | 0.8792 | 0.845
| III | 0.8691 | 0.845
Original- Embedding | IV | 0.7517 | 0.71
| I | 0.8993 | 0.855
| II | 0.9262 | 0.87
| III | 0.8658 | 0.86
Original- Repetition | IV | 0.6409 | 0.705
Table 23: Results of BERT model for subtask C (Arabic) on original datasets

The official scores and leader-board ranks of the teams for subtask C (Arabic)
is shown in Table 24.

Rank | User | Accuracy
---|---|---
1 | lizefeng | 0.93
2 | AlamiHamza | 0.885
3 | maryam.najafi | 0.875
4 |  | ShubhamKumarNigam
---
0.87

Table 24: Scores and leader-board ranks for subtask C (Arabic)

##  6 Conclusion and Future Direction

We built our systems using stand-alone transformer based models and
hierarchical ones by adding a BiLSTM layer with or without attention
mechanism. In addition to this, we created new datasets depending on the
subtask using a combination of original and external datasets besides
augmenting using word embedding or repetition. Our results shows that the
augmented datasets enhanced the results for all subtasks. Moreover, we found
that the fine-tuned stand-alone transformer based models in each subtask gave
the best results especially with Type-II preprocessing. We also showed the
enhancement when using a weighted loss function and the effect of using
different learning-rates, epochs, and preprocessing types. Moreover, the rank
of our team was consistent across most of the subtasks (the fourth rank) which
shows the robustness of the techniques we used.

## References

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##  Appendix A Appendix

###  A.1 Hierarchical Architecture

Figure 1 shows a hierarchical network based on a transformer. The input tokens
are passed to the transformer (BERTweet), then the output token embeddings are
passed to a Bi-LSTM layer which can be with or without attention mechanism.

Figure 1: Hierarchical architecture

###  A.2 Sarcasm Types Description

  1. 1.

Sarcasm: tweets that contradict the state of affairs and are critical towards
an addressee.

  2. 2.

Irony: tweets that contradict the state of affairs but are not obviously
critical towards an addressee.

  3. 3.

Satire: tweets that appear to support an addressee, but contain underlying
disagreement and mocking.

  4. 4.

Understatement: tweets that undermine the importance of the state of affairs
they refer to.

  5. 5.

Overstatement: tweets that describe the state of affairs in obviously
exaggerated terms.

  6. 6.

Rhetorical question: tweets that include a question whose invited inference
(implicature) is obviously contradicting the state of affairs.

###  A.3 BERT Classification Architecture

Figure 2 shows the BERT-base classification architecture151515BERT Fine-Tuning
Tutorial with PyTorch by Chris McCormick and Nick Ryan. From the output of the
final (12th) transformer, only the first embedding (corresponding to the [CLS]
token) is used by a classifier.

Figure 2: BERT classification architecture

###  A.4 ELECTRA:- Replaced Token Detection

ELECTRA (Efficiently Learning an Encoder that Classifies Token Replacement
Accurately) Clark et al. (2020) replaces the MLM of BERT with Replaced Token
Detection (RTD), which looks to be more efficient and produces better results.
In BERT, the input is replaced by some tokens with [MASK] and then a model is
trained to reconstruct the original tokens.

In ELECTRA, instead of masking the input, the approach corrupts it by
replacing some input tokens with plausible alternatives sampled from a small
generator network. Then, instead of training a model that predicts the
original tokens, a discriminative model is trained that predicts whether each
token in the corrupted input was replaced by a generator sample or not.

This approach trains two neural networks, a generator and a discriminator.
Each one primarily consists of an encoder (e.g., a transformer network) that
maps a sequence of input tokens into a sequence of contextualized vector
representations. The discriminator then predicts whether it’s fake by
analyzing its data distribution. An overview of replaced token detection is
shown in Figure 3.

Figure 3: An overview of replaced token detection

###  A.5 Effect of Learning Rates and Epochs in Subtask A (English)

In Subtask A (English), we experimented the BERT model on the B4 dataset with
different learning rates and epochs as shown in Table 25 and Table 26
respectively. As shown in the tables the best learning rate was 4e-6 and the
best number of epochs was 5.

Val | Test | Learning Rate
---|---|---
0.4002 | 0.25 | 1 e - 5
0.5871 | 0.4558 | 9 e - 6
0.5913 | 0.4639 | 8 e - 6
0.4002 | 0.25 | 7 e - 6
0.4002 | 0.25 | 6 e - 6
0.5952 | 0.4883 | 5 e - 6
0.6025 | 0.4769 | 4 e - 6
0.5798 | 0.475 | 3 e - 6
0.5644 | 0.4724 | 2 e - 6
0.6012 | 0.5017 | 1 e - 6
0.4002 | 0.25 | 9 e - 7
0.4002 | 0.25 | 8 e - 7
Table 25: The effect of learning rates on performance of the BERT model on the B4 dataset with weighted loss function Val | Test | Epochs
---|---|---
0.5282 | 0.5304 | 1
0.5877 | 0.5092 | 3
0.6025 | 0.4769 | 5
0.6019 | 0.4647 | 7
0.5856 | 0.457 | 10
0.6017 | 0.5099 | 13
0.594 | 0.475 | 15
0.575 | 0.4943 | 17
0.5882 | 0.4675 | 20
0.5938 | 0.4633 | 23
0.575 | 0.4926 | 25
Table 26: The effect of epochs on performance of the BERT model on the B4
dataset with weighted loss function

###  A.6 Performance of BERT+BiLSTM with and without Attention in Subtask A
(English)

BERT+BiLSTM: The best results we got using this architecture were on the B4
dataset with 4e-6 learning rate, 10 epochs, and 50 LSTM hidden state size.
Table 27 shows the results using same hyperparameters but with different
hidden state sizes.

Hidden State Size | Val | Test
---|---|---
50 | 0.6027 | 0.4741
100 | 0.5882 | 0.4765
300 | 0.5813 | 0.4627
600 | 0.561 | 0.4702
900 | 0.5831 | 0.4516
Table 27: Results of the BERT+BiLSTM model for SubTask A (English) on the B4
dataset

BERT+BiLSTM+Attention: The best results we got using this architecture were on
the B3 dataset with 4e-6 learning rate, 5 epochs, and 600 LSTM hidden state
size. Table 28 shows the results using same hyperparameters but with different
hidden state sizes.

Hidden State Size | Val | Test
---|---|---
50 | 0.5726 | 0.4685
100 | 0.5978 | 0.468
300 | 0.5935 | 0.4627
600 | 0.6087 | 0.4625
900 | 0.5777 | 0.4618
Table 28: Results of the BERT+BiLSTM+Attention model for SubTask A (English)
on B3 dataset

###  A.7 More Information about the Datasets:

Density of the number of words in tweets and their rephrases in the original
datasets is shown in Figure 4 for English and in Figure 5 for Arabic.

Figure 4: Density of the number of words in the original English training
(top) and testing (bottom) datasets. Figure 5: Density of the number of words
in the original Arabic training (top) and testing (bottom) datasets.

In addition to this, information about dialects for Arabic subtasks is
presented in Figure 6 and Table 29.

Figure 6: Percentage of dialects of tweets in the original Arabic training (top) and testing (bottom) datasets. |  |  | Eygptian | MSA
---|---|---|---|---
|  |  | Levantine | Gulf
Dataset | Split | Total | Maghrebi |
|  |  | 41.7 | 49
|  |  | 3.7 | 2.7
| Train | 3102 | 2.9 |
|  |  | 37.1 | 34.4
|  |  | 12 | 12.6
Original | Test | 1400 | 3.9 |
|  |  | 21.2 | 68.2
|  |  | 5 | 5.1
| Train | 12548 | 0.3 |
|  |  | 10.2 | 77.4
|  |  | 1.6 | 10.7
ArSarcasm -v2 | Test | 3000 | 0.1 |
Table 29: Distribution of tweets over dialects in Arabic Datasets

Information about the distribution of sarcastic and non-sarcastic tweets in
the original datasets is presented in Figure 7.

Figure 7: Percentage of sarcastic and non-sarcastic tweets in the original
English and Arabic training (top) and testing (bottom) datasets.

Information about sarcastic labels, for subTask B, in the original datasets is
shown in Figure 8.

Figure 8: Percentage of tweets under each sarcastic label in the original
English training (top) and testing (bottom) datasets.


# Evolution of double oxygen-neon white dwarf merger remnant

Chengyuan Wu1,2,3, Heran Xiong4, Zhanwen Han1,2,3, Bo Wang1,2,3
1Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, China
2Key Laboratory for the Structure and Evolution of Celestial Objects, Yunnan
Observatories, CAS, Kunming 650216, China
3International Centre of Supernovae, Yunnan Key Laboratory, Kunming, 650216,
China
4Research School of Astronomy and Astrophysics, The Australian National
University, Canberra, ACT 2611, Australia
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Double white dwarf (WD) merger process and their post-merger evolution are
important in many fields of astronomy, such as supernovae, gamma-ray bursts,
gravitational waves, etc. The evolutionary outcomes of double ultra-massive WD
merger remnants are still a subject of debate, though the general consensus is
that the merger remnant will collapse to form a neutron star. In this work, we
investigate the evolution of a $2.20{M}_{\odot}$ merger remnant stemmed from
the coalescence of double $1.10{M}_{\odot}$ ONe WDs. We find that the remnant
ignites off-centre neon burning at the position near the surface of primary WD
soon after the merger, resulting in the stable inwardly propagating
oxygen/neon (O/Ne) flame. The final outcomes of the merger remnant are
sensitive to the effect of convective boundary mixing. If the mixing cannot
stall the O/Ne flame, the flame will reach the centre within $20$ years,
leading to the formation of super Chandrasekhar mass silicon core, and its
final fate probably be neutron star (NS) through iron-core-collapse supernova.
In contrast, if the convective mixing is effective enough to prevent the O/Ne
flame from reaching the centre, the merger remnant will undergo electron
capture supernova to form an ONeFe WD. Meanwhile, we find that the wind mass
loss process may hardly alter the final fate of the remnant due to its fast
evolution. Our results imply that the coalescence of double ONe WDs can form
short lived giant like object, but the final outcomes (NS or ONeFe WD) are
influenced by the uncertain convective mixing in O/Ne flame.

###### keywords:

stars: evolution – binaries: close – stars: white dwarfs

††pubyear: 2023††pagerange: Evolution of double oxygen-neon white dwarf merger
remnant–Evolution of double oxygen-neon white dwarf merger remnant

##  1 Introduction

White dwarfs (WDs) are the most numerous members of the stellar graveyard. It
is accepted that more than $95\%$ of all stars in the Universe will evolve
into WDs (e.g. Córsico et al. 2019). Double white dwarfs (WDs) in binary
systems with sufficiently short orbital periods may merge within the Hubble
time due to the angular momentum loss from the gravitational wave radiation.
The coalescences of double white dwarfs are thought to be one of the most
common evolutionary endpoints of binary systems, and may relevant to some
important objects or astrophysical phenomena. For example, (1) type Ia
supernovae may be stemmed from the mergers of double carbon-oxygen (CO) WDs or
the mergers of CO WD and helium (He) WD (e.g. Iben & Tutukov 1984; Webbink
1984; Han 1998; Fink et al. 2010; Wang 2018; Shen et al. 2018); (2) massive
double WD mergers, containing at least one oxygen-neon (ONe) WDs are thought
to be related to some accretion-induced-collapse (AIC) events or high-energy
phenomena such as gamma-ray bursts or high-energy neutrino emissions (e.g.
Lyutikov & Toonen 2017; Ruiter et al. 2019); (3) double WD systems are
verified gravitational wave (GW) sources (e.g. Kilic et al. 2014), which can
be observed by the future space-based GW detectors like LISA or TianQin (e.g.
Ruiter et al. 2010; Kremer et al. 2017; Wang & Liu 2020; Huang et al. 2020).

Double CO or ONe WD mergers may produce massive remnants with mass greater
than Chandrasekhar mass limit (${M}_{\rm{ch}}\approx 1.38{M}_{\odot}$). The
evolutionary fates of these massive remnants is still a subject of debate. For
example, the coalescence of double CO WD is thought to be the progenitor of SN
Ia, however, it was quickly pointed out that the rapid mass transfer in such
merger process would lead to the off-centre carbon ignition, triggering the
inwardly propagating carbon flame which may transform the remnant to an ONe
composition (e.g. Nomoto & Iben 1985; Saio & Nomoto 1985; Kawai et al. 1987;
Chen et al. 2014). For the more massive double ONe WDs, although the general
consensus is that the merger remnant will collapse to form a neutron star (NS)
(e.g. Miyaji et al. 1980; Schwab et al. 2015; Wu & Wang 2018), recent studies
claimed that the uncertainties of the outcomes of Chandrasekhar mass ONe WD
may arise from the competition between the thermal nuclear runaway of O/Ne and
electron capture reactions of magnesium (Mg) and Ne. If an ONe WD can undergo
thermal explosion, its light curve may similar to that of 1991T-like events
(e.g. Marquardt et al. 2015). On the contrary, if the central density of ONe
WD is able to achieve the order of $\sim{10}^{10}\,{\rm g}\,{\rm{cm}^{-3}}$,
electron-capture reactions on ${}^{\rm 20}{\rm Ne}$ and ${}^{\rm 24}{\rm Mg}$
likely cause the WD to collapse into NS (e.g. Jones et al. 2016, 2019).

A theoretical method in understanding the final fates of double WD merger
remnants is to construct the model of remnant that mimics the results of the
SPH simulations using 1D stellar evolutionary code and then follow its secular
evolution. Although the evolution of double CO WD and CO+He WD merger remnants
have been widely studied so far (e.g. Yoon et al. 2007; Zhang et al. 2014;
Schwab et al. 2016; Brooks et al. 2017; Wu et al. 2019; Wu & Wang 2019; Lauer
et al. 2019; Schwab 2021; Wu et al. 2022), there are only few works pay
attention to the evolution of ultra-massive double WD mergers in which the
remnants are composed of degenerate ONe core. Brooks et al. (2017)
investigated the evolution of ONe WD+He WD, and argued that the merger remnant
will evolve to He-giant and finally experience supernova explosion to form a
fast and luminous transient. Kashyap et al. (2018) carried out the first fully
3D simulation of the merger of a $1.20{M}_{\odot}$ ONe WD with a
$1.10{M}_{\odot}$ CO WD, and found that material from the CO WD secondary may
readily to detonation during the merger, resulting in the faint and rapidly
fading transient. More recently, Wu et al. (2023) investigated the evolution
of a series of ONe WD+CO WD merger remnants. They found that if the remnants
are more massive than a critical mass which is between $1.90{M}_{\odot}$ to
$1.95{M}_{\odot}$, off-central Ne ignition will occur soon after the merger,
resulting in the formation of ONeFe WDs through electron-capture supernova
(ECSN) explosions. While, if the remnants are less massive than the critical
mass, the final outcome of the remnants would be either NSs through ECSNe or
ONe WDs, which is depended on the wind mass-loss process during the evolution.

The evolution of double ONe WD merger remnants have not been well studied so
far. Many questions such as whether Ne detonation would occur during merger
process, how fast is the inwardly propagating Ne flame, and what is their
evolutionary outcome are still remain uncertain. In this work, we construct
the 1D structure of double $1.10{M}_{\odot}$ ONe WD merger remnant based on
the information from Dan et al. (2014), and to follow its post-merger
evolution. The article is organized as follows. In Sect. 2, we introduce our
initial models of merger remnant. The input physics and the results of
simulations are shown in Sect. 3. We discuss the model uncertainties in Sect.
4, and summarize our results in Sect. 5.

##  2 Initial models

In a double WD system, the orbital shrink due to the gravitational wave
radiation could cause the secondary (less massive WD) fill in its Roche Lobe
(RL) and transfer material to the primary WD. Previous works indicated that
the mass ratio of two WDs, $q={m}_{2}/{m}_{1}$ (${m}_{1}$ and ${m}_{2}$ are
the masses of primary and secondary WDs, respectively), is a pivotal parameter
in affecting the mass transfer process. If $q$ is larger than the critical
mass ratio,

${q}_{\rm{crit}}=\frac{5}{6}+\frac{1}{2}\frac{{\rm{dln}R}}{{\rm{dln}}M},$ (1)

where $R$ and $M$ are radius and mass of the secondary, the increase of the
radius of the secondary due to the reduction of its mass will exceed the
increase of its RL radius caused by the transfer of orbital angular momentum,
resulting in the dynamically unstable transfer and then leads to the
coalescence of two WDs (e.g. Pringle & Webbink 1975; Tutukov & Yungelson
1979). The criterion of stable or unstable mass transfer of two WDs is
influenced by the synchronization time-scale of spin-orbit coupling,
${\tau}_{\rm s}$. Under strong coupling (${\tau}_{\rm s}\rightarrow{0}$),
${q}_{\rm{crit}}\approx\frac{2}{3}$. By contrast, if ${\tau}_{\rm
s}\rightarrow{\infty}$, i.e. no angular momentum is transferred from the
primary to the secondary, ${q}_{\rm{crit}}$ could decrease to about $0.2$
(e.g. Marsh et al. 2004).

Smoothed particle hydrodynamics (SPH) simulations show that the unstable mass
transfer process could lead to the merger of double WDs. The primary WD will
be survived during the merger, whereas the secondary will be tidally disrupted
in which a significant amount of material will form a rotationally supported
disc surround the primary WD (e.g. Guerrero et al. 2004). In order to
understand the conditions of hydrodynamical burning minutes after double WD
merger, Dan et al. (2014) performed a large grid of double WD merger systems,
covering a wide range of WD masses and chemical compositions. They found that
the merger remnants are divided into four components in their simulations:
cool degenerate core, hot envelope, Keplerian disc and tidal tail. They
provided 1D approximate formulas for the masses of these regions. The fitting
formulas for the mass coordinate of highest temperature in the envelope,
$M$(${T}_{\rm{max}}$), and the masses of each components are as follows:

${M}({T}_{\rm{max}})={M}_{\rm{tot}}(0.863-0.3335q),$ (2)
${M}_{\rm{core}}={M}_{\rm{tot}}(0.7786-0.5114q),$ (3)
${M}_{\rm{env}}={M}_{\rm{tot}}(0.2779-0.464q+0.716{q}^{2}),$ (4)
${M}_{\rm{disc}}={M}_{\rm{tot}}(-0.1185+0.9763q-0.6559{q}^{2}),$ (5)

where, ${M}_{\rm{core}}$, ${M}_{\rm{env}}$, ${M}_{\rm{disc}}$,
${M}_{\rm{tot}}$ and $q$ are the mass of cool degenerate core, hot envelope,
Keplerian disc, total mass of the merger remnant and the mass ratio of double
WDs before merger, respectively. We use their provided fitting formulae to
construct the merger structure of double ONe WDs and investigate its further
evolution. Since the tidal tail accounts for only a few percent of the total
mass, same as previous works, we do not consider the mass of tidal tail and
that unbound from the system in our simulation (e.g. Schwab 2021; Wu et al.
2023). In this case, the initial remnant mass remains the same as the total
mass of the merging WDs.

We construct the merger structure by employing stellar evolution code
$\tt{MESA}$ (version: 12778) (e.g. Paxton et al. 2011; 2013; 2015; 2018;
2019). In our calculation, we consider an $2.20{M}_{\odot}$ remnant which is
stemmed from the merger of double $1.10{M}_{\odot}$ ONe WDs. We first create a
$2.20{M}_{\odot}$ helium-pre-main-sequence-star (equals to the total mass of
double ONe WDs) and evolve it until central density (${\rho}_{\rm c}$)
achieves ${10}^{5}\,{\rm g}\,{\rm{cm}^{-3}}$. During the evolution, we ignored
all the nuclear reactions and mixing processes to maintain the abundance
unchanged. At the end of the first step, the central temperature of the
remnant reaches ${\rm{log}}({T}/{\rm K})=8.77$, and the corresponding
${\rho}-{T}$ structure can be represented by the blue dotted line in Fig. 1.

Secondly, we use the built-in ${\tt{MESA}}$ capability to adjust the elemental
abundance distribution of the merger remnant to the desired mass fraction.
According to Dan et al. (2014), the initial abundance of ONe WD is: ${}^{\rm
16}{\rm O}=60\%$, ${}^{\rm 20}{\rm{Ne}}=35\%$ and ${}^{\rm 24}{\rm{Mg}}=5\%$.
In our simulation, we adjust the abundance of our model to the uniform
distribution same as Dan et al. (2014).

Finally, we injected energy into different mass shell of the remnant to
construct the thermal structure of the merger remnant. The prescription of
energy injection is similar to that described in Schwab (2021). For
$0\leq{M}_{\rm r}\leq{M}_{\rm{core}}$,

$T({M}_{\rm r})={T}_{\rm{core}}.$ (6)

For ${M}_{\rm{core}}\leq{M}_{\rm r}\leq{M}_{\rm{core}}+{M}_{\rm{env}}$,

$s({M}_{\rm
r})={s}_{\rm{core}}+[{s}_{\rm{env}}-s({M}_{\rm{core}})]\frac{{M}_{\rm{r}}-{M}_{\rm{core}}}{{M}_{\rm{peak}}}.$
(7)

And for ${M}_{\rm{core}}+{M}_{\rm{env}}\leq{M}_{\rm r}\leq{M}_{\rm{tot}}$,

$s({M}_{\rm r})={s}_{\rm{env}}.$ (8)

In these equations, ${M}_{\rm{core}}$, ${M}_{\rm{env}}$ and ${M}_{\rm{peak}}$
are core masses, envelope masses and the mass coordinates of the maximum
temperature of the merger remnants, respectively. ${T}_{\rm{core}}$ is the
temperature of isothermal core, which are set to be ${10}^{8}{\rm K}$.
${s}_{\rm{core}}$ and ${s}_{\rm{env}}$ are, the specific entropies of the core
and the envelope, respectively. We set ${s}_{\rm{core}}$ equals to the
specific entropy of the core when ${T}_{\rm{core}}={10}^{8}\,{\rm K}$, and
${s}_{\rm{env}}$ equals to the following equation:

${\rm
log}({s}_{\rm{env}}/{\rm{erg}}\,{\rm{g}^{-1}}\,{\rm{K}^{-1}})=8.7+0.3({M}_{\rm{tot}}/{M}_{\odot}-1.5).$
(9)

After the energy injection process, we obtained the initial 1D structure of
the merger remnant. The ${\rho}-{T}$ profile is shown as the red solid line in
Fig. 1. The merger remnant has an $0.576{M}_{\odot}$ isothermal core, and the
mass coordinate of ${T}_{\rm{max}}$ is at $1.091{M}_{\odot}$. By comparison,
the density and temperature at the ${T}_{\rm{max}}$ position in our model is
consisted with that in SPH simulations provided by Dan et al. (2014).

Figure 1: Density-temperature (${\rho}-{T}$) structure diagram of the double
$1.10{M}_{\odot}$ ONe WD merger remnant before (blue dashed line) and after
(red solid line) energy injection. Black solid lines indicate the
(${\rho}-{T}$) limits for electron degeneracy, radiation pressure equals to
pressure of gas, He, C and O burning. Black filled circle and blue circle
represent the position of the boundary of degenerate core and the
${T}_{\rm{max}}$ of our model, respectively. Masses of the corresponding
positions are marked nearby. The magenta triangle represents the position of
${T}_{\rm{max}}$ given in Dan et al. (2014).

##  3 Evolution of the remnant

###  3.1 Input physics

The composition of the merger remnant is oxygen enhancement. We use the OPAL
radiative opacities for C/O-rich mixtures (e.g. Iglesias & Rogers 1993, 1996),
which are referred to as OPAL “Type 2” tables in ${\tt{MESA}}$. As the
remnants evolve to giant phase, the surface temperature may decrease to lower
than ${\rm log}(T/{\rm K})=3.70$. Since the lower boundary of the OPAL
tabulations is ${\rm log}(T/{\rm K})=3.75$, and ${\tt{MESA}}$ does not provide
low-temperature opacities that include separate C/O enhancements. Hence,
similar to the prescription described in Schwab et al. (2016), we adopt Kasen
opacities (${\rm{log}}({T}/{\rm K})\sim 3.4-4.1$ to deal with the low
temperature conditions, and blend the OPAL and Kasen opacities between ${\rm
log}({T}/{\rm K})=4.1$ and $4.2$. This supplement is suitable for H- and He-
deficient cool giant-like stars.

The nuclear reaction network adopted in the present work is
“${\tt{approx21.net}}$” from ${\tt{MESA}}$ default, which is a 21-isotope
$\alpha$-chain nuclear network. As the remnant expands toward giant phase, the
superadiabatic gradient arising in radiation-dominated envelopes can extremely
reduce computational efficiency. To circumvent this issue, we apply the
treatment of convective energy transport “MLT++” (e.g. Paxton et al. 2013) to
reduce the superadiabaticity in the radiation-dominated convective regions. We
constrain the time resolution in our calculations by adopting
“${\tt{varcontral\\_target=1d-4}}$”. In order to have a better treatment on
the propagation of off-center flame, we control the spatial resolution by
changing “${\tt{mesh\\_dlog\\_burn\\_o\\_dlogP\\_extra=0.1}}$”,
“${\tt{mesh\\_dlog\\_burn\\_ne\\_dlogP\\_extra=0.1}}$” and
“${\tt{mesh\\_dlog\\_oo\\_dlogP\\_extra=0.1}}$” to increase the mesh grid
nearby the flame.

###  3.2 Neon ignition and flame

After obtained the profile of merger remnant, we restored the nuclear
reactions to evolve the remnant forward in time. The remnant initially undergo
the Kelvin–Helmholtz contract to increase the temperature of O/Ne shell. The
contract process lasts for about $8.85$ hours when the temperature at the base
of O/Ne shell achieves ${\rm{log}}({T}/{\rm K})\approx 9.182$. Various
properties and elemental abundance distribution of the merger remnant at the
onset of Ne ignition are shown in Fig. 2. Ne ignition occurs at the position
very close to the surface of primary ONe WD where ${M}_{\rm r}\approx
1.08{M}_{\odot}$ and ${R}\approx 3000{\rm{km}}$. Due to the initially compact
configuration of the merger remnant, the neon ignition begins in a nuclear
burning flash. Afterwards, the envelope quickly inflate to giant structure
where the energy produced by the nuclear reactions balance with the thermal
energy transported from convection and neutrino loss. The evolution of the
remnant on Hertzsprung-Russell (HR) diagram is shown in Fig. 3.

Figure 2: Properties (panel a) and elements abundance distributions (panel b)
of the $2.20{M}_{\odot}$ double ONe WD merger remnant at the onset of neon
ignition. Blue, green, magenta and golden solid lines in panel (a) represent
nuclear reaction rate of neon burning, energy loss rate due to neutrinos,
density and temperature profiles, respectively. Mass fractions of four major
elements (${}^{\rm 16}{\rm O}$, ${}^{\rm 20}{\rm Ne}$, ${}^{\rm 24}{\rm Mg}$
and ${}^{\rm 28}{\rm Si}$) are shown in panel (b).

At the onset of neon ignition, the temperature at the base of the shell is not
high enough to lead to the substantial inwardly motion of the burning front by
conduction. As the layer directly beneath the burning layer is heated up
primarily via electron conduction from the burning layer above, the
temperature of O/Ne shell increases until it is hot enough to sustain its own
O/Ne burning. In this case, the steady O/Ne burning starts and quickly forms a
O/Ne burning front which begins to propagate inwards towards the centre of the
remnant. During this stage, a portion of energy of O/Ne burning used to heat
the core and the others expands the envelope. The flame propagates inwards
continuously, living behind burning ashes mainly consists of silicon-group
(Si-group) elements. As can be seen from Fig. 4, the location of the outer
boundary of the convection zone varies significantly from timestep-to-timestep
because of the high temperatures and energy generation rates associated with
O/Ne fusion. The density of the material beneath the flame increases as the
flame moves inward, making the timestep of calculation become extremely short.
We stop our calculation when the flame almost reaches the centre (${M}_{\rm
r}=2.38\times{10}^{-6}\,{M}_{\odot}$). At this moment, the remnant has evolved
for about $20$ years, which costs approximately three wall-clock months and
more than $9$ million timesteps of calculation. It takes about $20$ years for
the flame to propagates $3000{\rm{km}}$, which means that the average velocity
of the flame is about $0.475{\rm{cm}}/{\rm s}$. For more rigorous estimate,
Timmes et al. (1994) deduced that the velocity of off-centre burning flame is
about

${v}_{\rm flame}\approx(\frac{{\rm c}{\epsilon}_{\rm
nuc}}{{\kappa}{\rho}{E}})^{\frac{1}{2}},$ (10)

and the flame width is about (e.g. Woosley & Heger 2015)

${\delta}_{\rm flame}\approx(\frac{{\rm c}{E}}{{\kappa}{\rho}{\epsilon}_{\rm
nuc}})^{\frac{1}{2}},$ (11)

where, $c$, ${\epsilon}_{\rm nuc}$, $\kappa$, $\rho$, and $E$(equals to
${C}_{\rm P}{T}$) are speed of light, nuclear burning rate, opacity, density
and internal thermal energy per gram, respectively. We use the corresponding
equation to estimate the theoretical velocity, which is shown as blue solid
line in Fig. 5. Initially, the flame moves relatively fast. As the flame moves
inward, the density beneath the front of the flame increases, which slows down
the propagation of the flame. The velocity decreases to about
$0.2-0.5{\rm{cm}}/{\rm s}$ $570$ days after O/Ne ignition when the flame
reached the mass coordinate of about $0.58{M}_{\odot}$. On the other hand, we
can also estimate the velocity of neon flame from the numerical data. The
Eulerian velocity of the flame can be determined by ${\rm
d}{R}({T}_{\rm{max}})$/${\rm d}{t}$, where, ${R}({T}_{\rm{max}})$ is the
radius at the maximum temperature (the position of the flame). However, the
inner core undergoes thermal pulsation during the O/Ne burning, making the
${R}({T}_{\rm{max}})$ is difficult to refer to the position of the flame. We
thus use the Lagrangian velocity to indicates the numerical flame velocity,
i.e.

${v}_{\rm flame}\approx{\dot{M}}/(4{\pi}{{r}^{2}}{\rho}),$ (12)

Where, ${\dot{M}}$ is the mass of the shell that the flame crosses during per
unit time. The Lagrangian velocity of the O/Ne flame is shown as red solid
line in Fig. 5. The shapes of the two curves match, which means that the
numerical results are consistent with the theoretical results.

Figure 3: The HR diagram of the merger remnant. The remnant undergoes
Kelvin–Helmholtz contract and inflates to giant structure. Grey solid diagonal
lines represent all of the locations where stars are found that have the same
radius. Different evolutionary durations are shown in the diagram. Figure 4:
The propagation of neon flame with no convective boundary mixing. x-axis shows
the time since neon ignition whereas y-axis represents the Lagrangian mass
coordinate. Shaded region represents the convective zone associated with
flame, whereas the red solid line at the bottom of the region represents the
position of the flame. Figure 5: The velocity of the inwardly propagating neon
flame changing with time since neon ignition. Blue and red solid lines
represent the theoretical ﬂame velocity and Lagrangian (numerical) velocity,
respectively. Figure 6: Properties of the merger remnant when the neon flame
moves close to the centre (${M}_{\rm r}=2.38\times{10}^{-6}\,{M}_{\odot}$).
Panel (a): T-Rho profile, where black solid lines represent Pgas= Prad,
degenerate line, burning line for helium, carbon, oxygen, respectively. Cyan
line represents the convective zone, while blue, green and red thick lines
represent burning region with different nuclear reaction rates, respectively.
Triangle, cycle and square represent the positions of the boundary of core,
central convective zone, and the ${T}_{\rm{max}}$, respectively. Panel (b):
elements abundance distributions for different elements.

###  3.3 Final fates

As the O/Ne flame migrates to the centre, it leaves behind hot Si-group ashes
(${}^{\rm 28}{\rm Si}$ and ${}^{\rm 32}{\rm S}$). As mentioned above, the
timescale of calculation becomes extremely short when the neon flame moves
close to the centre, and we do not follow the further evolution of merger
remnant since it is very time consuming. We stop the simulation when the flame
reached ${M}_{\rm r}=2.38\times{10}^{-6}\,{M}_{\odot}$. Fig. 6 shows the
${\rho}-{T}$ and elemental abundance profiles of the merger remnant at the
time when we stop the simulation. At this moment, the remnant is consisted of
an $1.5{M}_{\odot}$ core with Si-group elements and an $0.7{M}_{\odot}$ ONeMg
envelope. We predict that the flame will eventually reach the centre, and then
undergo Kelvin-Helmholtz contract. Still, some Si flashes occur, leading to
the off-centre Si burning. Schwab et al. (2016) found that the off-centre Si
ignition occurs when the remnant mass is greater than $1.41{M}_{\odot}$. The
mass coordinate of ${T}_{\rm{max}}$ in Si ashes of our model is at about
$1.0{M}_{\odot}$, which means that the off-centre Si ignition may occur at
this position. Subsequently, the Si flame will move towards the centre, and if
the inwardly propagating Si flame could finally reach the centre, the super
Chandrasekhar remnant will consist of an iron core, resulting in the formation
of single NS through iron-core-collapse supernova.

If we assume that the outer ONeMg envelope could be ejected through the
supernova explosion, the remnant will form an $1.5{M}_{\odot}$ NS with
$0.7{M}_{\odot}$ ejecta. Owing to the low ejecta mass and the outer
composition of the remnant, the supernova explosion may appear as a fast
evolved subluminous transient, similar to some particular type Ic supernovae
(e.g. Tauris et al. 2013, 2015 Moriya et al. 2017; Pellegrino et al. 2022).
Note that for another possibility, if the collapsing core of the merger
remnant could remain sufficient angular momentum to support an accretion disk
or belt around the newly born NS, the jet launched from the disk collides with
the circumstellar medium that was ejected during the merger of double WD. The
interaction process could transform portion of kinetic energy of the jet into
radiation, which may cause the formation of energetic supernova (e.g. Soker
2016, 2019, 2022; Gilkis & Soker 2015; Gilkis et al. 2016; Kaplan & Soker
2020).

##  4 Discussion

###  4.1 Convective boundary mixing

At the onset of evolution, the merger remnant undergoes the Kelvin–Helmholtz
contract to ignite off-centre O/Ne burning which result in the formation of
convective region outside the flame. At the boundary of shell-flash
convection, shear motion induced by convective flows and internal gravity
waves lead to the mixing beyond the Schwarzschild convective boundaries,
making the shell burning ashes intrude into the unburned material beneath the
burning flame, which is known as convective boundary mixing. Previous works
found that the convective boundary mixing could stall the inwardly propagating
carbon flame in super-AGB stars and accreting CO WDs, resulting in the
formation of CONe WDs or COSi WDs (e.g. Denissenkov et al. 2013; Farmer et al.
2015; Wu et al. 2020).

If a similar phenomenon occurs in the double ONe WD merger remnant, the death
of the O/Ne flame would lead to qualitatively different results. In order to
investigate the corresponding effect, we recalculate the ONe+ONe remnant by
considering convective boundary mixing. In the ${\tt{MESA}}$ standard options,
some parameterization of convective boundary mixing is generally employed
alongside the mixing-length theory (MLT) to allow convective motions to extend
outside of the MLT convection zone, and it allows us to take this mixing into
account as a diffusion process. The corresponding diffusion coefficient in
radiative layers adjacent to a convective boundary is (e.g. Freytag et al.
1996; Herwig 2000; Denissenkov et al. 2013)

${D}_{\rm{CBM}}={D}_{\rm{MLT}}({r}_{\rm
0}){\rm{exp}}\left(-\frac{2|{r}-{r}_{\rm 0}|}{f{H}_{\rm p}}\right),$ (13)

where ${H}_{\rm P}$ is the pressure scale height and ${D}_{\rm{MLT}}({r}_{\rm
0})$ is a convective diffusion coefficient calculated based on MLT. The
${\tt{MESA}}$ “mlt” module assumes that
${D}_{\rm{MLT}}={\lambda}{v}_{\rm{conv}}/3$, where ${\lambda}={\alpha}{H}_{\rm
P}$ is the mixing length (we use the default value of ${\alpha}=2$) and
${v}_{\rm{conv}}$ is the convective velocity. The radius ${r}_{\rm 0}$ is
located at the distance of ${f}{H}_{\rm P}$ from the Schwarzschild boundary
inside the convective zone. The free parameter ${f}$ should be calibrated
through observations, or through hydrodynamic simulations. Similar to Farmer
et al. (2015), we set ${f}$ equals to $0.016$ in this simulation. Meanwhile,
in order to investigate the effects of electron capture and Urca cooling
process, we reconstruct the $2.20{M}_{\odot}$ merger remnant with 5% of
${}^{\rm 23}{\rm Na}$ and 1% of ${}^{\rm 25}{\rm Mg}$ in the initial ONe WD
(e.g. Schwab et al. 2017), and change our nuclear reaction network to
“${\tt{wd\\_aic.net}}$” in “${\tt{MESA\,\,default}}$” with artificially added
isotopes (such as ${}^{\rm 20}{\rm O}$, ${}^{\rm 20}{\rm F}$, ${}^{\rm 24}{\rm
Ne}$ and ${}^{\rm 20}{\rm Na}$) and the corresponding weak reactions. The weak
interaction rates are from Schwab et al. (2015). We apply the
“${\tt{MESA\,\,default}}$” screening factors to correct nuclear reaction rates
for plasma interactions (e.g. Chugunov et al. 2007). The cooling rates from
thermal neutrinos are derived from the fitting formulae of Itoh et al. (1996).

Fig. 7 presents the structure of the merger remnant at the end of simulation
under condition of convective boundary mixing. During the evolution, the
convective flows penetrate the Schwarzschild convective boundaries, leading to
the extra mixing between material at both sides of the flame, which decrease
the O/Ne abundance ahead of the burning front. Since the nuclear reaction rate
(${\epsilon}_{\rm nuc}$) is relevant to the abundance of fuel
(${\epsilon}_{\rm nuc}$ can be approximated as
${\epsilon}_{\rm{nuc}}\propto{\rho}{\chi}^{\rm 2}{T}^{\rm n}$; i.e. nuclear
reaction rate is more sensitive to the temperature, for example, for carbon
burning at ${\rm{log}{T/{\rm K}}}=8.8-8.9$, ${n}\approx{\rm{40}}$), the O/Ne
flame will quench gradually as the flame moves inward. Afterwards, the Kelvin-
Helmholtz contract will increase the central density until it is high enough
to trigger the electron capture reactions. We stop our calculation when the
central temperature ${\rm{log}}{T/{\rm K}}>9.3$, where explosive O/Ne burning
occurs. For the $2.20{M}_{\odot}$ merger remnant with overshooting parameter
of ${f}=0.016$, the central O/Ne deflagration occurs when the inwardly
propagating O/Ne flame reaches the mass coordinate of about $0.62{M}_{\odot}$.
Eventually, the remnant will experience electron capture supernova to form an
ONeFe WD 111The mass of ONeFe WD is influenced by the resolution of
simulations, the central density of ONe core and whether the Coulomb
corrections are included in the equation of state during calculation. Hence,
the mass of ONeFe WD would either be about $0.44-0.65{M}_{\odot}$ or
$1.2-1.3{M}_{\odot}$ (see table 1 of Jones et al. 2016 for detail). due to its
low central density (e.g. Jones et al. 2016, 2019).

Figure 7: Properties of the merger remnant when considering convective
boundary mixing. Panel (a): the evolutionary track for central temperature-
density. Black dotted lines represent carbon and oxygen burning lines, whereas
brown and magenta dotted lines represent electron capture lines for ${}^{\rm
24}{\rm{Mg}}$ and ${}^{\rm 20}{\rm{Ne}}$. Panel(b): T-Rho profile for the
merger remnant at the final stage when explosive O/Ne burning occurs. Black
solid lines represent Pgas=Prad, dengerate line, helium, carbon and oxygen
burning lines. Cyan line presents convective zone, while blue, green and red
thick lines represent burning region with different nuclear reaction rates.
Panel (c): the elemental abundance distributions of the merger remnant at its
final evolutionary stage.

###  4.2 Wind mass-loss

As the envelope responds to the energy deposited during the merger, the
remnant begins to radiate away this energy which causes the remnant to inflate
towards the giant structure. The stellar wind during the giant phase may be
high enough to decrease the mass of the remnant and may further impact its
final fate.

Since the envelope of the merger remnant is O/Ne dominated composition, it
seems likely that these objects will drive dusty winds. The mass-loss rate of
such objects is not observationally well constrained, and theoretically, there
has no reliable way to estimate the corresponding mass-loss rate. Previous
works usually assumed a wind mass-loss prescription to mimic the mass-loss
rate of such merger remnant. For example, by assuming that the object will
shed a fraction of its mass (${\beta}$) on a timescale $\frac{{\rm G}{M}^{\rm
2}}{{R}{L}}$ evaluating at the surface, Schwab (2021) suggested that the mass-
loss rate of such remnant is

${\dot{M}}={10}^{-5}{M}_{\odot}{\rm{yr}}^{-1}\left(\frac{\beta}{{10}^{-4}}\right)\left(\frac{R}{{100}{R}_{\odot}}\right)\left(\frac{L}{{3}\times{10}^{4}{L}_{\odot}}\right){\left(\frac{M}{{M}_{\odot}}\right)}^{-1}.$
(14)

In this case, they found that if ${\beta}={10}^{-5}$, the mass-loss rate for
an $1.50{M}_{\odot}$ double CO WD merger remnant is equivalent to the one if
we adopt Reimers’ wind mass-loss prescription (e.g. Reimers 1975) with typical
value for normal red giant of ${\eta}_{\rm{R}}=0.5$. Wu et al. (2023) assumed
a Blöcker wind mass-loss prescription (e.g. Blöcker 1995) to investigated the
effect of wind mass-loss process on ONe+CO WD merger remnants. They found that
the wind mass-loss process could alter the final outcome for the merger
remnants with masses lower than $1.95{M}_{\odot}$. Furthermore, they suggested
that the $1.60{M}_{\odot}$ merger remnant under the Blöcker’s wind mass-loss
rate with typical value for AGB stars (${\eta}_{\rm{B}}=0.05$) can explain the
origin of CO-rich object - IRAS $00500+6713$.

In order to investigate the effect of the wind mass-loss process on double ONe
WD merger remnant, we recalculate the $2.20{M}_{\odot}$ model by considering
the Blöcker’s wind mass-loss prescription with ${\eta}_{\rm B}=0.05$. We
evolve the remnant for $13.2$ years. At the time when we stop our simulation,
the off-centre O/Ne flame reaches the position of ${M}_{\rm
r}=0.018{M}_{\odot}$, and the remnant only shed ${\Delta}{M}\approx
5\times{10}^{-5}{M}_{\odot}$. On the HR diagram, the evolutionary tracks of
the merger remnant with and without wind mass-loss match, which means that the
stellar wind process may not significantly impacting the final fate of double
ONe WD merger remnants.

###  4.3 Rotation

The merger remnant could remain a portion of orbital angular momentum during
the merger process. The condition of the O/Ne flame would be changed if the
rotational velocity of the core is high enough, which may lead to a different
evolutionary fate of the remnant. Previous works found that, for the double WD
merger remnant, the angular momentum can be transported from the core to the
envelope rapidly, and the core will have the angular velocity similar to the
envelope several hours after merger. Afterwards, the angular velocity of the
envelope will decrease obviously as the remnant inflate to the giant (e.g.
Schwab 2021; Wu et al. 2023). In the present work, we have not simulated the
evolution of rotational model. Nevertheless, according to the results of
previous works, we infer that the rotation can hardly alter the evolution and
final fate of double ONe WD merger remnant.

##  5 Summary

In this work, we simulated the evolution of double ONe+ONe WD merger remnant.
The remnant underwent Kelvin–Helmholtz contract and ignited off-centre O/Ne
burning soon after the merger. We found that it takes only about $20$ years
for the fast moving O/Ne flame to reach the centre, making a short lifetime of
the remnant. The final fate of the remnant is impacted by the process of
convective boundary mixing. If the mixing process can prohibit the O/Ne flame
from reaching the centre, the final outcome of the merger remnant would be an
ONeFe WD through electron-capture supernova. Otherwise, the remnant may
experience iron-core-collapse supernova to form an NS. Besides, due to the
short lifetime of the remnant, we suggest that the wind mass-loss process may
not affect the evolution and final fate of the remnant too much, unless an
extremely strong wind mass-loss prescription is assumed. Finally, based on the
results from previous works, we suggest that the rotation may not affect their
evolution and final fate.

## Acknowledgements

We thank the referee Noam Soker for helpful comments. This study is supported
by the National Natural Science Foundation of China (NSFC grants 12288102,
12003013, 12225304), the National Key R&D Program of China (No.
2021YFA1600404), the Western Light Project of CAS (No. XBZG-ZDSYS-202117), the
science research grant from the China Manned Space Project (No. CMS-
CSST-2021-A12), the Yunnan Fundamental Research Projects (Nos 202301AU070039,
202001AS070029 and 202201BC070003), the Frontier Scientific Research Program
of Deep Space Exploration Laboratory (No. 2022-QYKYJH-ZYTS-016), and the
International Centre of Supernovae, Yunnan Key Laboratory (No.
202302AN360001).

## Data Availability

Evolutionary models were computed with the version 12778 of MESA. The required
inlists in this study can be available via request to the corresponding
author.

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