# Sociocultural Norm Similarities and Differences
via Situational Alignment and Explainable Textual Entailment

Sky CH-Wang1, Arkadiy Saakyan111footnotemark: 1, Oliver Li1, Zhou Yu1,
Smaranda Muresan1,2
1Department of Computer Science, Columbia University
2Data Science Institute, Columbia University
{skywang<EMAIL_ADDRESS>*Equal contribution.

###### Abstract

Designing systems that can reason across cultures requires that they are
grounded in the norms of the contexts in which they operate. However, current
research on developing computational models of social norms has primarily
focused on American society. Here, we propose a novel approach to discover and
compare descriptive social norms across Chinese and American cultures. We
demonstrate our approach by leveraging discussions on a Chinese Q&A
platform—知乎 (Zhihu)—and the existing SocialChemistry dataset as proxies for
contrasting cultural axes, align social situations cross-culturally, and
extract social norms from texts using in-context learning. Embedding Chain-of-
Thought prompting in a human-AI collaborative framework, we build a high-
quality dataset of 3,069 social norms aligned with social situations across
Chinese and American cultures alongside corresponding free-text explanations.
To test the ability of models to reason about social norms across cultures, we
introduce the task of explainable social norm entailment, showing that
existing models under 3B parameters have significant room for improvement in
both automatic and human evaluation. Further analysis of cross-cultural norm
differences based on our dataset shows empirical alignment with the social
orientations framework, revealing several situational and descriptive nuances
in norms across these cultures.

Figure 1: An example of descriptive norms conditioned on an aligned cross-
cultural situation, together with their inference relation and corresponding
textual explanation.

##  1 Introduction

Social norms are normative beliefs that guide behavior in groups and societies
Sherif (1936). Deviance from these expectations of behavior can cause
perceptions of impoliteness Culpeper (2011), feelings of offense Rubington and
Weinberg (2015), and pragmatic failure Thomas (1983). Social norms vary across
cultures Triandis et al. (1994); Finnemore (1996), and different cultural
norms can lead to conflict within intercultural interactions due to
perceptions of deviance Durkheim (1951). Creating computational systems that
can robustly reason and translate across cultures in pragmatic communication
requires that they be grounded in these norms and their differences across
contexts.

As an initial step in addressing this question, we propose a novel approach to
discover and compare social norms conditioned on social situations across
Chinese and American cultures. Leveraging 知乎 (Zhihu), a Chinese Q&A platform,
alongside the existing SocialChemistry Forbes et al. (2020) dataset on social
norms as respective proxies of Chinese and American cultural axes, our paper
offers the following three contributions:

  * •

A novel human-AI collaboration framework for cross-cultural descriptive norm
discovery consisting of (1) automatic situation alignment using cross-lingual
similarity between SocialChemstry situations and questions from Zhihu, (2)
Chinese social norm extraction from Zhihu answers using few-shot prompting
with GPT-3 Brown et al. (2020), (3) cross-cultural norm similarity and
difference identification as textual entailment with explanations using GPT-3
with Chain of Thought (CoT) Prompting Wei et al. (2022); and (4) human
feedback in verification and editing. An example of outputs is shown in Figure
1.

  * •

A new dataset for cross-cultural norms understanding with explainable textual
entailment. Our human-AI collaboration enables us to create a novel dataset of
3069 situation-aligned entailment pairs of Chinese and American norms together
with textual explanations. We introduce a new task of explainable social norm
entailment and show that it is challenging for models fine-tuned on related
tasks, and fine-tuning on our task directly still leaves significant space for
improvement.

  * •

An analysis of cross-cultural differences in social norms enabled by our
dataset. In Section 6, we show that the analysis enabled by our dataset
empirically aligns with prior work on differences in Chinese and American
cultures. Our empirical results align with the social orientations framework
Yang (1993) in understanding Chinese-American norm differences and reveal
several situational and descriptive nuances in norms across these cultures.

##  2 Related Work

Our work is situated in the broader literature on the study of social norms
Sherif (1936) and how they vary across cultures Thomas (1983). Here, our work
is rooted specifically in the study of descriptive norms Rawls (1951, 2004);
Cialdini et al. (1990)—what people actually do, rather than prescriptive
norms, or what they think people ought to do—and focuses on the differences
between Chinese and American cultures.

We build on recent computational work in creating systems capable of situated
reasoning in social situations, most closely adapting the rule-of-thumb
formalism for descriptive norms introduced in Forbes et al. (2020). This line
of work not only spans that of commonsense reasoning Sap et al. (2019);
Rashkin et al. (2018), but also in judgments of appropriate and ethical
behavior Emelin et al. (2021); Jiang et al. (2022), and in grounding behavior
in areas like dialogue Ziems et al. (2022) and situated question answering Gu
et al. (2022a) more specifically on underlying knowledge of social norms. In
recognizing that social norms are often culturally Haidt et al. (1993) and
even demographically Plepi et al. (2022); Wan et al. (2023) specific, prior
work in this area has primarily revolved around the normative judgments of
majority English-speaking cultures represented within North America. In
contrast, here, aligning with the broader goal of creating systems that can
effectively reason across cultures and languages Liu et al. (2021), we focus
on computationally studying norms across Chinese and American cultures,
expanding on the utility of large language models in ways that have the
potential to transform modern computational social science Ziems et al.
(2023).

Contemporary studies of Chinese cultural societies Yang (1993) emphasize
several broad differences relative to American culture. Under the framework of
social orientations, emphasis in Chinese society is placed especially on
family, relationship, authority, and personal reputation social orientations.
In particular, past work has shown a large significance compared to American
culture in familistic collectivism and harmony Ch’eng-K’Un (1944); Yang
(1988); Campos et al. (2014), relational determinism Chen and Chen (2004);
Chua et al. (2009), and authority worship Yang (1970); Thornton and Fricke
(1987); Hu (2016), among other factors, in influencing social behavior.
Critical reviews of past cross-cultural work have criticized weaknesses in
study design and their overly broad generalizations Voronov and Singer (2002),
in favor of a more fine-grained analysis. Here, under the framework of
descriptive norms and sourcing data from social media at scale, we conduct a
more nuanced analysis of how norms vary across cultures under situational
controls.

##  3 Data Sources

Our analysis of social norm variation across Chinese and American contexts
draws from the largest Q&A discussion platform in China—知乎 (Zhihu)—and
existing data gathered by SocialChemistry Forbes et al. (2020), treating these
data sources as different cultural axes.

### Social Chemistry 101 Forbes et al. (2020)

is a natural language corpus of ethical judgments and social norms on everyday
situations. Crowd-sourced social norms on situations scraped from Reddit
(i.e., r/AmITheAsshole) and other sources are expressed in free-text rule-of-
thumb form, where each rule-of-thumb consists of a judgment on an action,
i.e., “It’s rude to run the blender at 5 AM”. Annotators of this dataset are
55% women, and 94% of annotators had spent 10 or more years in the United
States; as such, we treat the normative judgments represented within this
dataset as originating from a predominantly English-speaking, American
context111Despite the many demographic similarities between our two cultural
axes, a few notable differences remain. Most notably of which is class
composition, where only 47% of annotators of Social Chemistry 101 considered
themselves to be middle-class compared to over 80% of users on Zhihu. See our
Limitations section for a discussion on potential impacts..

### 知乎 Zhihu

has over 101 million monthly active users Zhihu (2022) and is one of China’s
largest online knowledge communities. Similar to its international
counterparts like Quora, Zhihu is primarily a Q&A site where users can post
questions, answer existing questions, and up-vote answers to questions by
other users, among other platform interactions. Users are 59% women Yang
(2022a) and are primarily educated and middle-class, with research showing
that over 80% of its users possess at least a bachelor’s degree Zhang (2020).
This population is significant because the middle class is the primary
upholder of social stability Goodman (2014) and the primary driver of cultural
trends and public opinion Denemark and Chubb (2016) in China. An example of a
Zhihu question-answer pair is shown in Table 1.

Question: 当有人说家里有丧事时应如何回应更礼貌? (How to respond politely when someone says there
is a funeral in the family?)
---
Answer: 节哀。可以礼貌性的拍拍肩膀或者嘱咐对方虽然最近会比较操劳但也要注意身体。(Condolences. You can politely pat
on their shoulders or tell them to pay attention to their health even though
it will be hard for them recently.)
RoT 1: it is appropriate to say "节哀" to someone who has lost a family member
or friend
RoT 2: it is appropriate to pat someone on the back to show your sympathy to
them
RoT 3: it is appropriate to tell them to take care of themselves though they
are sad
Table 1: Example of a Zhihu question-answer pair (top) with English
translations and relevant social norms in rules-of-thumb form (bottom).

Questions on Zhihu are often posed as to inquire about the appropriate action
to partake in a given situation, i.e., “what do I do if my friend is cheating
on their exam?”, with other users indicating their views on appropriate
courses of action in the answers below. Reasoning that these questions align
most closely in form to situations in SocialChemistry, we translate and query
for all situations present in the SocialChemistry dataset through Zhihu’s
search function and save the top 100 question posts returned for every
translated SocialChemistry situation. Following the rationale that social
norms are the most common and broadly accepted judgments of actions in given
situations, we take the most up-voted answer222See Limitations for a
discussion on method caveats. to each question as the basis from which we
extract social norms, described in the following section. In total, we
obtained answers to 508,681 unique questions posed on Zhihu. The study and
data collection were approved by an Institutional Review Board prior to data
collection; a detailed breakdown of this corpus is detailed in Appendix
Section A. We reiterate both datasets can only be used as a proxy for social
norms in each culture and further discuss the limitations of our approach and
these assumptions in Section Limitations.

##  4 Human-AI Collaboration to Create a Cross-Cultural Social Norm Dataset

Entailment Relation
---
Situation: I think I’m jealous of my best friend.
US Norm: You should be proud of people and not jealous of them.
Chinese Norm: It is not appropriate to be jealous of your best friend.
Textual Explanation: Both norms express disapproval of being jealous of
someone, especially a best friend.
Contradiction Relation
Situation: telling my teacher a classmate cheated on a test.
US Norm: It’s wrong to be a tattle-tale.
Chinese Norm: It is not wrong to report a cheating student to the teacher
$<\cdots>$
Textual Explanation: The US norm expresses disapproval of telling on a
classmate, while the Chinese norm expresses neutrality towards the action.
Table 2: Examples of similarities (entailments, top) and differences
(contradictions, bottom) in situated norms between Chinese and American
cultures from our dataset, alongside relation explanations. Figure 2:  Our
human-AI collaboration framework for creating a cross-cultural Chinese-
American social norm NLI dataset through (1) situation alignment, aligning
cross-lingual situations between Zhihu and Social Chemistry, (2) social norm
extraction, from free-form answers to rules-of-thumb with in-context learning,
and (3) norm relation inference with textual explanation with CoT prompting,
coupled with (4) expert verification and editing.

We enable our computational analysis of social norm variation across Chinese
and American cultures through a framework of (1) automatic situation
alignment, (2) social norm extraction, (3) cross-cultural
similarity/difference identification as textual entailment with explanations
and (4) human feedback. An illustration of our human-AI collaboration
framework is presented in Figure 2.

### Aligning Situations Across Cultures.

Descriptive judgments of appropriate behavior are often situationally-
dependent Leung and Morris (2015); an accurate comparison of norms across
cultures must first ensure a similarity of contexts. For instance, Yamagishi
et al. (2008) showed that Japanese preferences for conformity disappeared in
private compared to when they were being observed. To obtain the closest
matching situations between US and Chinese contexts, we align situations found
in the SocialChemistry dataset with similar questions on Zhihu. While the
Zhihu search API allows for direct query searches of platform content,
semantic alignment of returned results with queries remains low due to an
observed bias in prioritizing entity matches. To improve this alignment of
situations between US and Chinese contexts, we use XLM-R Conneau et al. (2020)
to obtain cross-lingual representations of situations and further perform one-
to-one matching through cosine similarity. Setting the similarity threshold to
0.895 allowed us to align 3069 situations, of which around 80% were correctly
aligned, based on a manual review of a random sample of 100 situations. Here,
incorrectly aligned instances remain valuable for our data as negative samples
in our later entailment task as they can be assigned a No Relation label.

### Social Norm Extraction.

We follow the formalism introduced by Forbes et al. (2020) in structuring
descriptive norms as rules-of-thumb, or judgments of an action (i.e., “It’s
rude to run the blender at 5AM”). Taking 2 random top-aligned situations in
our dataset, we manually annotate their corresponding Zhihu answer for social
norms in rule-of-thumb form (RoT); an example of such an annotation is shown
in Table 1.

We then design a 2-shot prompt using these annotations (see Table 3) and use
GPT-3 Brown et al. (2020) to extract novel rules-of-thumb from unseen answers.
Running this model across all our aligned situations, we obtain a total of
6566 unique rules-of-thumb for our Chinese axis, relative to 1173 unique
rules-of-thumb for our American axis sourced from SocialChemistry (note, here,
that a rule-of-thumb may be associated with multiple situations).

Table 3: Prompt used for the extraction of social norms in rule-of-thumb form
from Zhihu questions and answers. The instruction precedes the in-context
example; the original question (in red, equivalent to the situation) is
followed directly by the answer, and sample annotated rules-of-thumb are
listed in blue.

### Identifying Cross-Cultural Norm Similarities & Differences as Textual
Entailment with Explanations.

Under our formalism, a difference in cultural norms equates to a disagreement
in judgments for an action relative to a given situation. Here, we structure
the identification of social norm differences across cultures as an
explainable textual entailment task (a.k.a natural language inference (NLI))
similar to e-SNLI Camburu et al. (2018); a difference in cultural norms
equates to a contradiction between norms of different cultures for a given
situation, and vice versa for entailment. Given the recent success of human-AI
collaboration frameworks Wiegreffe et al. (2022); Bartolo et al. (2022);
Chakrabarty et al. (2022a), the complex nature of our task, and the need for
interoperability in reasoning, we use Chain-of-Thought prompting Wei et al.
(2022) (see our prompt in Table 4) together with GPT-3 (text-davinci-003) to
generate most of the data automatically before manual verification. In order
to construct our data in the e-SNLI format and save on computation costs, for
every given American norm associated with a given situation, we (1) select the
most relevant Chinese norm for that situation as extracted in the previous
step, (2) identify the inference relationship (entailment, contradiction, or
no relation) between them, and (3) generate a free-text explanation for the
identified relationship. When no Chinese norms are selected as relevant, a
random norm is sampled from the aligned candidates, and an explanation is
generated given the No Relation label. Using this framework, we generate
social norm relationships and their justifications for all cross-culturally
aligned situations in our dataset.

Table 4: Chain-of-thought prompt used to identify (1) the most relevant (if
any) Chinese norm given an American norm from an aligned situation, (2)
determine the relationship between these norms, and (3) provide a free-text
explanation justifying the inferred relation.

### Human Verification and Editing.

To ensure the quality and accuracy of our dataset of situated social norm
relationships and their justifications across cultures, three students with a
background in both Chinese and American cultures further acted as annotators
by verifying and editing, if needed, the outputs of our framework jointly
(Figure 2). Specifically, authors ensured that (1) situations are correctly
aligned (i.e., entailment or contradiction labels are assigned correctly to
aligned norms, while no relation labels are assigned to misaligned norms), (2)
norms generated by GPT-3 are not hallucinated, and (3) the explanations are
correct. Annotators were able to discuss any questions and resolve any final
disagreements with each other. In total, we find that 51% of norms had a no
relation label, either due to misaligned situations or due to the absence of
extracted, relevant Chinese norms for corresponding US norms. Only a few
instances (around 5%) had hallucinated norms; all were further corrected
during annotation.

Generated explanations needed no further editing in 58.9% of the cases. In
38.1% of the cases, the inferred cross-cultural norm relation (and
corresponding explanations) were deemed incorrect and required the revision of
both the label and the explanation, while in the remaining instances (3.0%),
generated explanations still required major revisions even though the relation
label was deemed correct. Our final dataset contains 3,069 NLI instances of
social norm relations across cultures with explanations. Out of these, 432 are
contradictions (14%), 1059 are entailments (35%), and 1578 have a no relation
label (51%). In total, aligned norms comprise 1173 unique rules-of-thumb from
SocialChemistry (American axis) and 2273 as obtained from Zhihu using our
framework (Chinese axis). Examples from our dataset are shown in Table 2.

##  5 Experiments and Evaluation

Task. To test the ability of models to reason about social norms across
cultures, we introduce the task of explainable social norm entailment. Our
task is closely related to the explainable natural language inference task,
e-SNLI Camburu et al. (2018). For every pair of US and Chinese norms of a
cross-culturally aligned situation, we ask a model to predict the relationship
between them (Entailment, Contradiction, or No Relation) and output an
explanation for the relation. We hypothesize that models fine-tuned on
existing closely related and much larger textual entailment datasets (e.g.,
e-SNLI) and instruction-tuned models like FLAN-T5 perform poorly on the task
of explainable social norm entailment, showing that current models under 3B
parameters are not equipped to reason about cross-cultural norms. On the other
hand, we test if a simple fine-tuned baseline is sufficient to perform well on
the task. Finally, through explanation quality evaluation, we investigate
whether fine-tuning on our dataset may enhance a model’s ability to reason
about social norm entailment.

### Models.

We test the performance of a model fine-tuned on SocialChemistry rule
elaborations (DREAM) and an instruction-tuned model (FLAN-T5) in few-shot
settings. We further fine-tune joint self-rationalizing models on eSNLI and
our dataset.

Prior work in interpretability distinguishes between Pipeline (input
$\rightarrow$ output, output $\rightarrow$ explanation) and Joint Self-
Rationalizing models (input $\rightarrow$ output + explanation). Wiegreffe et
al. (2021) has shown that joint model rationales are more indicative of
labels; following this and Chakrabarty et al. (2022b), we fine-tune a joint
self-rationalizing T5 model in multiple settings. Extending on Chakrabarty et
al. (2022a) and leveraging the text-to-text framework of T5 Raffel et al.
(2020) as well as the benefits of instruction-based models Sanh et al. (2021);
Wei et al. (2021), we use the following instruction for a given American
social norm (P) and Chinese social norm (H):

> Does the sentence "P" entail, contradict or have no relation to the sentence
> "H"? Please answer between "Entailment" or "Contradiction" or "No Relation"
> and explain your decision.

We input the above instruction into the encoder of T5 and train to predict the
output label followed by an explanation. To summarize, we test the following
models:

  * •

DREAM Gu et al. (2022a): an elaboration model that uses T5 to generate details
about the input that improves the model’s prediction. Here, we test the DREAM-
FLUTE (social-norm) variant Gu et al. (2022b), which uses SocialChemistry
rules-of-thumb as elaborations to provide an answer containing a label and an
explanation; we hypothesize that providing social norms as input can lead to
better results with this model. We use this system off-the-shelf by slightly
modifying the instruction and providing 10 examples to evaluate in a few-shot
setting.

  * •

FLAN-T5-XL Chung et al. (2022): an enhanced version of the T5 Raffel et al.
(2020) 3B model fine-tuned on more than 1000 tasks, including e-SNLI Camburu
et al. (2018). We provide 10 examples from our dataset to evaluate the model
in a few-shot setting.

  * •

T5-eSNLI: a T5 3B model fine-tuned on the e-SNLI Camburu et al. (2018)
dataset. We fine-tune for two epochs with a batch size of 4096 (with 268 total
steps) and an AdamW optimizer with a learning rate of $5e-05$. We take the
longest explanation per example in e-SNLI, as our data contains only one
reference explanation. This leaves us with 549,367 training and 9,842
validation examples.

  * •

T5-SocNorm: a T5 3B model fine-tuned on our Social Norm Explainable NLI
dataset. We fine-tune for 20 epochs with a batch size of 256 (with 140 total
steps) and an AdamW optimizer with a learning rate of $5e-05$. Note that our
training set of 2,000 examples (see Table 5) is 274 times smaller than e-SNLI.

### Dataset Statistics.

We randomly split our data into 65% train, 10% validation, and 25% test set
splits (Table 5).

| Train | Valid | Test
---|---|---|---
Contradiction | 279 (14%) | 39 (13%) | 114 (15%)
No Relation | 700 (35%) | 110 (37%) | 249 (32%)
Entailment | 1022 (51%) | 151 (50%) | 405 (53%)
Table 5: Statistics of our cross-cultural Chinese-American social norm NLI
dataset, stratified by entailment relation across train, validation, and test
sets.

### Automatic Metrics.

Following Chakrabarty et al. (2022a), we evaluate the quality of model-
generated explanations using the explanation score metric: an average of
BLEURT Sellam et al. (2020); Pu et al. (2021) and BERTScore Zhang et al.
(2019). We report the macro average F1 score at three thresholds of the
explanation score: 0, 50, and 60. F1@0 is equivalent to simply computing the
F1 score, while F1@50 counts only the correctly predicted labels that achieve
an explanation score greater than 50 as correct.

As shown in Table 6, current off-the-shelf models lack heavily in performance
on our dataset, at most achieving an F1 score of 33.48, despite being fine-
tuned on closely related tasks such as e-SNLI. This verifies the need for a
domain-specific dataset, since the general NLI data is not sufficient to
perform well on our task. Even a model fine-tuned on our data only achieves
54.52 F1 score, showing that there is still ample room for improvement. This
result demonstrates the difficulty of reasoning about entailment of cross-
cultural social norms.

When considering quality of explanations, we see a very steep drop in
performance for models fine-tuned on related tasks (25.85 to 7.11 for FLAN-T5
and 33.48 to 1.14 for T5-eSNLI), indicating that current datasets do not
enable sufficient explanation quality for reasoning about social norm
entailment. For the model fine-tuned on our data, the performance drop when
accounting for explanation quality is not as sharp (21% for T5-SocNorm vs 72%
for FLAN-T5), indicating that our dataset may enhance the ability of reasoning
about social norm entailment.

Model | F1@0 | F1@50 | F1@60
---|---|---|---
DREAM (10-shot) | 17.68 | 4.31 | 0.0
FLAN-T5 (10-shot) | 25.85 | 8.92 | 7.11
T5-eSNLI | 33.48 | 8.27 | 1.14
T5-SocNorm | 54.52 | 51.68 | 43.07
Table 6: Automatic evaluation results of a series of competitive baseline
models measured by F1 scores at three thresholds of the explanation score (0,
50, and 60, indicated as F1@0, F1@50, and F1@60, respectively), and a model
fine-tuned on our data.

Interestingly, FLAN-T5 achieves a lower F1@0 score than a model fine-tuned on
eSNLI, possibly because of interference from non-eSNLI-related tasks it was
fine-tuned on. Further investigating the performance differences between
T5-eSNLI and FLAN-T5 (see Table 7), we observe that FLAN-T5 struggles, in
particular, to predict all relation classes equally well, instead predicting
most classes as No Relation (the majority class). This explains also a better
performance of FLAN-T5 when accounting for explanation score, as the neutral
explanations are easier to generate (they are typically more templatic).
T5-SocNorm and T5-eSNLI are seen as more robust in this regard.

Model | Entail. | Contra. | NoRel.
---|---|---|---
FLAN-T5 | 1.36 | 13.56 | 62.62
T5-eSNLI | 21.28 | 35.63 | 43.54
T5-SocNorm | 56.6 | 47.0 | 59.97
Table 7: F1 score breakdown by relation label. FLAN-T5 mostly correctly
predicts NoRelation class which allows it to achieve a higher F1@50 and F1@60
scores as these explanations are easier to generate. T5-SocNorm is more robust
across relation classes.

### Explanation Quality.

Wiegreffe et al. (2021) introduced an automatic metric for textual explanation
quality (termed as rationale quality) that compares the accuracy of the model
with and without provided explanations: acc(Input+Explanation $\rightarrow$
Output) $-$ acc(Input$\rightarrow$Output). We fine-tune models on
I+E$\rightarrow$O and I$\rightarrow$O versions of our dataset and compute the
test set accuracy difference with and without providing explanations. When
providing “gold” explanations, accuracy rises from 53.4% to 96.1% and achieves
a high explanation quality score of 42.7, emphasizing the quality of textual
explanations provided by our dataset.

### Human Evaluation of Generated Explanation Plausibility.

Three students with knowledge of Chinese and American cultures assessed the
quality of a subset of 50 randomly chosen model-generated explanations for
correctly predicted labels, evaluating performance between the two best-
performing models: T5-eSNLI and T5-SocNorm. Each annotator was asked to rate
which generated explanation they preferred more: T5-eSNLI, T5-SocNorm, or if
they thought the generated explanations were tied in quality. Annotators
showed inter-annotator agreement of 62.4 Fleiss’ kappa Fleiss (1971),
considered “substantial" in literature. T5-SocNorm explanations are preferred
in the vast majority of cases (73%); T5-eSNLI explanations were preferred in
11% of cases, while explanations tied in 16% of cases. An example of bad
generation from T5-eSNLI is shown in Table 8; whereas T5-SocNorm tries to
determine the attitude the norms express, T5-eSNLI attempts to generate a rule
of thumb (in red) instead. These results support the conclusion that our data
contains high-quality explanations—despite its small scale, our model is able
to produce better explanations for social norm entailment compared to a model
fine-tuned on the entirety of e-SNLI, which is 247 times larger in size.

T5-SocNorm |  | The US norm expresses approval
---
towards asking for money back,
while the Chinese norm suggests that
it is not polite to ask for it directly
T5-eSNLI |  | It is either OK to ask for your money
---
back or not polite to directly ask
Table 8: Example explanations generated by T5-SocNorm and T5-eSNLI for the
situation in Figure 1. The model fine-tuned on e-SNLI tries to generate a
social norm, whereas our model actually tries to explain the relationship
between two norms.

##  6 Cross-Cultural Norm Variation

Recalling that descriptive norms are situationally dependent, here, using our
dataset, we test for factors driving these cross-cultural differences in
social norms, testing specifically for (1) situational effects (i.e., when do
norms differ?) and (2) descriptive effects (i.e., what do norms differ about?)
across Chinese and American cultures.

### Situational Effects.

To capture thematic trends across situations, we train a 10-topic LDA model on
preprocessed situations and manually label each topic with its most prominent
theme; labeled situational topics alongside the top words that are associated
with each are shown in Appendix Section C. Testing for the effect of topic-
situational factors on differences in social norms, we measure the correlation
strength between the probability of a situation belonging to a given topic
against how likely norms will contradict for that given situation.

In this regression, we find that three situation topics positively predicted
how likely norms would contradict between Chinese and American cultures for a
given situation to a statistically significant degree. They are, as follows,
Lack of Intimacy/Separation ($\rho=0.07$, $p=0.01$), Family Discord/Divorce
($\rho=0.06$, $p=0.01$), and Loss of Family Connection/Changes in Life
($\rho=0.07$, $p=0.02$).

These findings are consistent with contemporary studies of Chinese cultural
societies under the framework of social orientations Yang (1993). In Chinese
culture, relational determinism strongly defines the social norms surrounding
social interactions in everyday situations Chen et al. (2013). One’s
relationship with another determines how one interacts with them; much
distinction is placed within Chinese culture between one’s own kith and kin
(自己人, zijiren)—which mostly includes family members and familiar persons such
as friends or classmates—and outsiders (外人, wairen), at a much stronger degree
than that which is present in American cultures Chen and Chen (2004); Chua et
al. (2009). Our results here show that in situations where this relationship
distinction is apparent, or in cases of change in relationship type, the norms
surrounding these situations are more likely to differ across Chinese and
American cultures.

### Descriptive Effects.

As we have done for situational effects, here, we train a 10-topic LDA model
on preprocessed norms in rules-of-thumb form, identify each norm topic’s most
prominent theme, and test for the effect of norm-topic factors on predicting
differences in these norms between Chinese and American cultures. As before,
labeled norm topics alongside their top words are shown in Appendix Section C.

Recalling that norms in rule-of-thumb form are judgments of actions, norm
topics associate with action topics; a contradiction between cross-culturally
aligned norms means that contrasting judgments are placed on those actions
across Chinese and American cultures. Here, we find that two norm topics
positively predicted how likely a contradiction would be present between the
norms of our two cultures. They are, specifically, Loss of Trust/Intimacy
($\rho=0.06$, $p=0.05$) and Support in Relationship ($\rho=0.04$, $p=0.04$).

Interpreting these descriptive results in the context of relational
determinism, our results above on situational effects, and through further
qualitative analysis, our findings show that strong differences exist between
Chinese and American cultures in judgments of actions that (1) would cause a
loss of trust or intimacy and (2) are taken to support an individual close to
you. These findings are consistent with longstanding work in Chinese familism
Ch’eng-K’Un (1944); Yang (1988); Campos et al. (2014), showing that
exceptional accommodations in circumventing typical social rules are made,
relative to American cultures, to pursue interpersonal and especially familial
harmony for those classed as one’s own kith and kin Dunfee and Warren (2001);
Chen et al. (2013).

##  7 Conclusion and Future Work

In this work, we sought to computationally model social norms across Chinese
and American cultures, via a human-AI collaboration framework to extract and
interpretably compare social norm differences in aligned situations across
contexts. Our analyses here reveal several nuances in how social norms vary
across these cultural contexts, incorporating principles of descriptive ethics
that prior studies have often lacked thus far. We see our present work
situated in the broader context of designing systems that are able to reason
across languages and cultures in an increasingly global world. Here, we
highlight a few directions we find exciting for future work; models, code, and
anonymized data will be made available for further
research.333https://github.com/asaakyan/SocNormNLI

Deviance from social norms can lead to miscommunication and pragmatic failure
Thomas (1983). Integrating cross-cultural norm knowledge into socially
situated communication systems Hovy and Yang (2021) could lead to fewer
miscommunications in everyday situations, bridge cultures, and increase the
accessibility of knowledge and of interpersonal technologies to a far greater
extent than traditional translation technologies.

While our work has focused on measuring differences in social norms across
cultures, culture, though important, is only one of many variables—like age
and gender, among others—that affect descriptive ethical judgments Kuntsche et
al. (2021). Neither are norms fixed in time Finnemore and Sikkink (1998);
Sethi and Somanathan (1996); future work could, with the aid of social
platforms like Zhihu and Reddit, quantitatively examine not only the evolution
of social norms across cultures and platforms but also compare changes between
cultures, further bridging theory and empirical study.

## Ethical Considerations

Data Release and User Privacy. The study and data collection was approved by
an Institutional Review Board prior to data collection. Nonetheless, while
online data in platforms such as social media has opened the door to
conducting computational social science research at scale, it is infeasible to
obtain explicit consent for large-scale datasets such as ours Buchanan (2017).
In order to preserve user privacy, we collected only publicly available data
and analyzed it in aggregate, not at the individual level. Furthermore, we
mirror Twitter academic data release guidelines in that we release only the
set of question and answer ids used in our analyses, which researchers are
able to use together with the Zhihu API to obtain original discussion content.

## Limitations

Cross-Cultural Demographic Differences. In studying cultural variations in
social norms, we do not argue that culture as a variable alone explains the
entirety of the observed variations. Most notably, intra-cultural variation in
social norms also exists depending on the scale examined; for example, among
multiple demographic groups or sub-communities Plepi et al. (2022); Wan et al.
(2023). Further, as the presence of variation in user and participant
demographics undoubtedly remains between the data from our opposite cultural
axes, it is crucial to interpret our results in the context of these
differences and to take note that findings in our data are biased toward
representing the viewpoints of individuals of these demographic groups.

Data Coverage. It is unrealistic to expect that either our data or that of
Social Chemistry can cover all possible social situations. As such, our
findings only represent a subset of the true underlying cultural differences
present between the norms of Chinese and American cultures. Furthermore, it
seems intuitive that questions about non-controversial social situations
“everyone” is familiar with will, if not be completely absent from online
discourse, otherwise get lower representation and engagement. Furthermore, as
we only extract from the most up-voted answer from each Zhihu discussion and
treat it as the most broadly adopted norm as a simplifying assumption, an open
question remains as to quantifying the “problem” of intra-cultural norm
disagreements and to investigate genuine human variations in judgments of
social norms Plank (2022). By releasing our data, we hope that future work can
take into account less up-voted answers. In moving towards more representative
studies, we encourage further work to examine these variations in intra-
cultural norms and tease out the details of human behavior.

Censorship and Moderation. Chinese social media platforms like Weibo, and
Wechat are mandated by law Xu and Albert (2014) to implement censorship
policies on the content created by their users. Zhihu is no different; the
presence of inherent content bias introduced by this form of active moderation
of user content has an effect on influencing the landscape of public discourse
Yang (2022b) and the data that we rely on to derive Chinese social norms. In
particular, past work has shown the existence of censorship programs aimed at
prohibiting "collective action by silencing comments that represent,
reinforce, or spur social mobilization" across primary Chinese social media
services King et al. (2013). Comments that contain politically sensitive
terms, such as mentions of the names of political leaders, are subject to a
higher rate of deletions Bamman et al. (2012). The extent to which these
actions lead to a biased public representation of the norms and beliefs
commonly shared in Chinese society remains unclear.

Language Model Biases. Advances in large language models like GPT-3 have
allowed for greater possibilities in human-AI collaboration, as we have done
here. Nonetheless, it is important to recognize that language models
ultimately mimic patterns in their training data Lucy and Bamman (2021) and
regurgitate structural and social biases Bender et al. (2021). While we have
incorporated these models under a human-AI collaboration framework where we
externally verify, validate, and edit their output in certain cases to
mitigate this risk, it would be remiss to say that we are capable of doing so
entirely in lieu of effects such as priming influencing our decisions.

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## Overview of Appendix

We provide as supplementary material, additional information about our
collected dataset from Zhihu, chosen hyperparameters for our models, and topic
model details from our analysis of cross-cultural norm variation.

##  Appendix A Zhihu Statistics

Questions in Zhihu are tagged by users with topic categories, which serve as
entities that individual users may browse, follow, and subscribe to. Figure 3
shows a breakdown of the top 20 user-tagged categories in our Zhihu questions
dataset (508,681 unique questions) alongside their English translations, as
well as a distribution of top-answer length. Following that of Social
Chemistry, most topics here are related in content to relationships.

Figure 3: A top 20 user-labeled topics breakdown of Zhihu questions in our
dataset (top) and the distribution of top-answer length measured in characters
(bottom).

##  Appendix B Hyperparameters

Norm Extraction. We use text-davinci-002 with the following hyperparameters:

temperature=0.7, max tokens=256, top p=1, frequency penalty=0, presence
penalty=0.

Inference Relation and Explanation Generation. We use text-davinci-003 with
the following hyperparameters:

temperature=0.7, max tokens=140, top p=1, frequency penalty=0, presence
penalty=0.

DREAM-FLUTE Instruction Modification. We structure the input of social norm
data into the DREAM-FLUTE instruction in the following manner:

Premise: [Premise - social norm] US NORM. Hypothesis: [Hypothesis - social
norm] CHINESE NORM. Is there a contradiction, entailment, or no relation
between the premise and hypothesis?".

We prefix the prompt with 10 examples from the validation set in the same
format.

##  Appendix C Topic Models

We train 10-topic LDA models using
MALLET444https://mimno.github.io/Mallet/topics.html to analyze cross-cultural
social norm variations on both situational and descriptive effects, manually
labeling each topic with its most prominent theme. Labeled topics and their
top words are shown in Tables 9 (topics on situations) and 10 (topics on
descriptive norms in rule-of-thumb form), with the topics that were
statistically significant in the prediction of cross-cultural norm
contradictions highlighted in bold.

Topic Theme |  Top Tokens
---|---
0\. Self-care/ Emotional Turmoil |  dog boyfriend living sad fears died wife doesn’t speak everytime someone’s petting hands washing morning teeth brush upset/irritated truth bed angrying stuff confess lie leads brother’s attracted suffers agitated i’m
1\. School Bullying/ Toxic Relationship |  school she’s forced bullied pressuring friendship valentines absolutely engagement year disgusted people expecting fact bitchy remarry day tears burst criticism threw mother ditching mad
2\. Lack of Intimacy/ Separation |  crying boyfriend won’t play stop can’t reason don’t consequences issues ill gravely starts panics lot unprofessional texting i’ve years that’s reconciliation daughter’s i’ve thing pathetic intimacy lacking public vulnerable separated
3\. Family Discord/ Divorce |  hate mother sister hating mom parents dad people wrong brother family father making wife cry starting divorce pissed what’s resent girl kinda aunt brothers asked parent dislike grandmother marry genuinely
4\. Conflicts in Romantic Relationship |  girlfriend boyfriend friend wanting mad friends telling birthday girl upset breaking break friend’s hating family jealous relationship teacher boyfriend’s hates angry boyfriends cheated gift dating depression wedding hang christmas likes
5 Struggles in Marriage |  birthday friends wanting fat dream husband night college part dont ashamed working cheat someone’s frustrates affection reciprocate inability wife’s complaining job open accepting remembered it’s lies dropout couple boyfriend’s pregnant
6\. Loss of Family Connection/ Changes in Life |  woman recently meet-up cancelled disappointed passing mother’s blaming job dress original wear selling sick care taking form exist disappear fall dad wonders anymore wedding ex-bestfriend unfollow instagram despise
7\. Emotional Struggles/ Loneliness |  fear son man trust thinking woman young married time covering welfare mom’s unhappy constant lives longs toe camel bathtub facebook friending forgetting social co-worker…i’m knowing close lazy extremely dogs depressed
8\. Fear/ Uncertainty |  love i’m don’t boyfriend friend i’m married feel scared don’t jealous anymore kids afraid mother life family yelling man younger cancer roommate dad advice can’t doesn’t telling terrified falling fiancée
9\. Unhealthy Relationship/ Mistreatment |  mom ballet ago girls bad years girlfriend’s ex-girlfriend scaring sounding insensitive ratting classmate hug holding she’s doctor bring stressed teen friendship effort puts man’s annoyed ex-wife learn lessons lie interested
Table 9: Manually labeled situation topics and their top tokens, as captured from a 10-topic LDA model trained on cross-culturally aligned English Social Chemistry 101 situations. Topic Theme |  Top Tokens
---|---
0\. Loss of Trust/ Intimacy |  abortion depressed hold sense loyal pet hatred talk kind doesn’t hang past you’re that’s disgusted access hurtful brushing fiance’s hide thoughts pushy depression pictures change breaking interact hard spite intimate
1\. Communication Issues/ Gifting |  communication refuse girlfriend decision reach true public christmas dress lie grateful relationship lives steal assume enrolled stressful happily jeopardy admit you’ll accepting interest interaction hangout debt loaned escalate friendly presents
2\. Support in Relationship |  it’s expected people wrong family shouldn’t friends good partner parents love hate rude bad significant understandable relationship normal feel don’t expect things friend you’re children feelings upset important talk friend’s
3\. Social Media/ Social Bonds |  families find you’ll service wedding choose involved songs broken gifts media emotion cohesion foster behave society job online teaching ties sexuality interfere develop hurts schools professionalism poor health struggling kid’s
4\. Responsibility/ Respect |  put mother relationship long person’s teacher understanding mental deserve lazy situation music partner aunt responsible wash face fix illegal material finances judge anger purposely concerns dog harass exchange college respond
5\. Care-taking/ Nurturing in Relationships |  give relationship health frowned polite attention desires working inconsiderate single encouraged hang rest immoral random ignoring routine consistent lot provide assist won’t strike arguments afraid information amends sister frequent concerns
6\. Personal Autonomy/ Control Over Life |  relative fear calm death time members remember inappropriate methods elderly fights intimidate consent frustrate starting step betray relate reasons shy future beds stalk father business mind sense behavior control divorce
7\. Diversity/ Inclusivity |  enjoy issues order college couples find aggressive place exclude petty fair gratitude trivial commitment grudges conversations you’ll information attention based argue alive selfish lifestyle free live transgender nowadays socially dropout
8\. Trust/ Commitment |  allowed spend common invite friend made plan supposed crush cheat interested activities hanging values chance contact tooth roommates toe lied betray deal extracurricular reasons member’s finish students concerts effort honor
9\. Hardships/ Refusal |  uncomfortable married accept frustrated interests bitter mom cheater hurtful who’s therapy yous nasty taste stand lifetime bothering fears no-contact arguments phone purpose self-sufficient adults reaction hostile receiving health full shun
Table 10: Manually labeled descriptive norm topics and their top tokens, as
captured from a 10-topic LDA model trained on relevant rules-of-thumb from
aligned cross-cultural situations.


1Indian Institute of Astrophysics, Block II, Koramangala, Bangalore 560 034,
India
2Space Astronomy Group, ISITE Campus, U. R. Rao Satellite Centre, Bangalore
560 037, India.

# X-ray polarization observations of IC 4329A with IXPE: Constraining the
geometry of the X-ray corona

Indrani Pal1,* C. S. Stalin1 Rwitika Chatterjee2 Vivek K. Agrawal2

###### Abstract

X-ray polarimetry is a powerful tool to probe the geometry of the hot X-ray
corona in active galactic nuclei (AGN). Here, we present our results on the
characterisation of the X-ray polarization of the radio-quiet Seyfert-type AGN
IC 4329A at a redshift of $z$ = 0.016. This is based on observations carried
out by the Imaging X-ray Polarimeter (IXPE). IXPE observed IC 4329A on January
5, 2023, for a total observing time of 458 ks. From the model-independent
analysis, we found a polarization degree ($\Pi_{X}$) of 3.7$\pm$1.5$\%$ and a
polarization position angle ($\Psi_{X}$) of 61∘$\pm$12∘ in the 2$-$8 keV
energy range (at 1$\sigma$ confidence level). This is also in agreement with
the values of $\Pi_{X}$ and $\Psi_{X}$ of 4.7$\pm$2.2$\%$ and 71∘ $\pm$14∘
respectively obtained from spectro-polarimetric analysis of the I, Q and U
Stokes spectra in the 2$-$8 keV energy band (at the 90$\%$ confidence). The
value of $\Pi_{X}$ in the 2-8 keV band obtained from the model-independent
analysis is lower than the minimum detectable polarization (MDP) value of
4.5$\%$. However, $\Pi_{X}$ obtained from spectro-polarimetric analysis in the
2-8 keV band is larger than the MDP value. In the 3-5 keV band, we found
$\Pi_{X}$ of 6.5 $\pm$ 1.8, which is larger than the MDP value of 5.5$\%$. The
observed moderate value of $\Pi_{X}$ obtained from the analysis of the IXPE
data in the 3$-$5 keV band argues against a spherical lamp$-$post geometry for
the X-ray corona in IC 4329A; however, considering simulations, the observed
polarization measurements tend to favour a conical shape geometry for the
corona. This is the first time measurement of X-ray polarization in IC 4329A.
Measurements of the X-ray polarization in many such radio-quiet AGN will help
in constraining the geometry of the X-ray corona in AGN.

###### keywords:

Galaxies:active—Galaxies:Seyfert—Individual:IC 4329A.

<EMAIL_ADDRESS>
1 January 20151 January 2015

12.3456/s78910-011-012-3 #### 000 0000 1– 1

##  1 Introduction

Active galactic nuclei (AGN), one among the luminous objects in the Universe,
are believed to be powered by the accretion of matter onto super-massive black
holes (SMBHs;$\sim$ 106 $-$ 1010 $M_{\odot}$) situated at the centres of
galaxies (Lynden-Bell, 1969; Shakura & Sunyaev, 1973; Antonucci, 1993; Rees,
1984; Urry & Padovani, 1995). They emit over the entire accessible
electromagnetic spectrum, such as the high energy gamma-rays (Hartman
$et~{}al$., 1999), X-rays (Fabian, 2012), UV (Murray $et~{}al$., 1995),
optical (Boroson & Green, 1992), infrared (Sanders & Mirabel, 1996) and radio
(Condon $et~{}al$., 1991). The AGN come under two broad categories, a majority
of them emit less or no radio emission and are called radio-quiet AGN, while a
minority of about 10 per cent emit copiously in the radio band and are called
radio-loud AGN (Kellermann $et~{}al$., 1989). Though X-rays are emitted by the
different classes of AGN, the detailed physics of the cause of X-ray emission
is less understood and is highly debated. Also, the relative contribution of
the physical processes to the X-ray emission may be different between the
different classes of AGN.

Figure 1: The XMM-Newton EPIC PN, NuSTAR FPMA and FPMB spectra fitted jointly
in 3$-$78 keV energy band using the model
const$\times$TBabs$\times$zTBabs$\times$(xillverCP). The observations were
taken simultaneously on August 12, 2021.

In the radio-quiet category of AGN, the observed X-ray emission is believed to
be due to inverse Compton scattering of optical-UV radiation from the
accretion disk by hot electrons ($\sim 10^{8-9}$ K) in the corona, a
constituent of AGN (Haardt & Maraschi, 1991, 1993; Haardt $et~{}al$., 1994).
The X-ray corona is believed to be located close to the accretion disk, with
microlensing studies pointing it to be compact with the size of a few
gravitational radii ($r_{g}=GM/c^{2}$;Chartas $et~{}al$. 2016). X-ray
reverberation mapping studies also indicate the corona to be compact, of the
order of 3$-$10 $r_{g}$ in radius (Fabian $et~{}al$., 2009).

Recent studies, most notably using observations from the Nuclear Spectroscopic
Telescope Array (NuSTAR, Harrison $et~{}al$. 2013) were able to characterize
the nature of the corona in AGN, such as its temperature ($\rm{kT_{e}}$) and
variation in its temperature (Zoghbi $et~{}al$., 2017; Ursini $et~{}al$.,
2016, 2015; Keek & Ballantyne, 2016; Kang $et~{}al$., 2021; Pal $et~{}al$.,
2022a, b; Pal & Stalin, 2023). This is achieved via modelling of their
broadband X-ray spectra, as the shape of the primary X-ray continuum in AGN is
sensitive to the temperature of the coronal plasma, its optical depth, the
geometry of the corona and the nature of the seed photons (Haardt & Maraschi,
1993; Haardt $et~{}al$., 1994).

The corona could be either a spherical structure above the black hole
(spherical lamp-post; Fabian $et~{}al$. 2017) or a slab-like structure
sandwiching the accretion disk (Haardt & Maraschi, 1993) or a conical
structure (Ursini $et~{}al$., 2021). From the physical model fits to the
observed high energy spectra of AGN, the $\rm{kT_{e}}$ reported in the
literature assumes the corona to have either a spherical or a slab geometry
(Rani & Stalin, 2018). Also, from the multi-epoch spectral analysis available
in the literature, several models of the corona, including changes in the
structure of the corona, are proposed to explain the observed changes in
$\rm{kT_{e}}$. (Pal $et~{}al$., 2022a; Pal & Stalin, 2023). However, from
spectral analysis of AGN, it is difficult to distinguish between different
coronal geometries (Tortosa $et~{}al$., 2018; Middei $et~{}al$., 2019).
Irrespective of several studies in the literature attempting to characterise
the corona in AGN, we still lack knowledge on (i) the origin of the corona,
(ii) the cause of its high temperature and (iii) its geometry.

X-ray polarimetric observations on AGN can yield the needed measurement to
constrain the geometry of the X-ray-emitting corona in AGN (Matt $et~{}al$.,
1989, 1993). This is because polarization depends on the geometry of the
emitting region and of the external photon field (Tamborra $et~{}al$., 2018;
Zhang $et~{}al$., 2019). The launch of the Imaging X-ray Polarimetry Explorer
(IXPE; Weisskopf $et~{}al$. 2022) on December 9, 2021, sensitive in the 2$-$8
keV band has enabled the studies of X-ray polarization from AGN. As of now,
IXPE has observed four radio-quiet AGN, namely MCG-05-23-16, the Circinus
galaxy, NGC 4151 and IC 4329A. Of these, for MCG-05-23-16, Marinucci
$et~{}al$. (2022), reported a polarization degree $\Pi_{X}$ $<$ 4.7$\%$. In
the case of the Circinus Galaxy, Ursini $et~{}al$. (2023), reported a high
value of $\Pi_{X}$ = 28$\%$, which is thought to be due to reflection from the
torus. For NGC 4151, Gianolli $et~{}al$. (2023), found values of $\Pi_{X}$ and
$\Psi_{X}$ of 4.9 $\pm$1.1$\%$ and 86∘$\pm$7∘ respectively, arguing for a slab
geometry of the corona. Here, we report the results of polarization on the
fourth radio-quiet AGN, IC 4329A.

IC 4329A with a black hole mass of 6.8${}^{+1.2}_{-1.1}$ $\times$ 107 M⊙
(Bentz $et~{}al$., 2023) is one of the brightest Seyfert 1.2 galaxies (Véron-
Cetty & Véron, 2010) in X-rays at a redshift z = 0.016 (Willmer $et~{}al$.,
1991) with an X-ray spectrum having many absorbing systems (Steenbrugge
$et~{}al$., 2005). It is an ideal object to study the intrinsic continuum and
reflection from any material surrounding the source. It has been studied
extensively for its X-ray spectral and timing properties (Dewangan $et~{}al$.,
2021). Observations of IC 4329A in the millimetre were explained as due to
synchrotron emission in the hot corona (Inoue & Doi, 2018). From
Comptonization model fits to the NuSTAR observations on IC 4329A, Lubiński
$et~{}al$. (2016), report a $\rm{kT_{e}}$ of $40^{+7}_{-5}$ keV using the
COMPPS model, assuming a spherical geometry of the corona. Alternatively,
Petrucci $et~{}al$. (2001), using the Comptonization model and a slab geometry
of the corona, found a value of $\rm{kT_{e}}$ = $170^{+10}_{-5}$ keV. Tortosa
$et~{}al$. (2018) reported $\rm{kT_{e}}$ = 37$\pm$7 keV from fitting compTT to
the source spectrum for slab geometry. Kang & Wang (2022) estimated
$\rm{kT_{e}}$ = 71${}^{+37}_{-15}$ keV using relxillCP model. Kamraj
$et~{}al$. (2022) also found $\rm{kT_{e}}$ = 82${}^{+16}_{-7}$ keV from
xillverCP fit to the source spectrum. We analyzed the NuSTAR spectrum taken in
2012. Fitting the spectrum using xillverCP, we obtained best-fit values of
$\Gamma$ and $\rm{kT_{e}}$ of 1.83${}^{+0.003}_{-0.003}$ and
64${}^{+15}_{-12}$ keV respectively (Pal et al. 2023, under preparation). From
a joint fit of XMM-Newton EPIC PN and NuSTAR spectra observed simultaneously
on August 12, 2021, we found $\Gamma$ = 1.88${}^{+0.01}_{-0.01}$ and
$\rm{kT_{e}}$ $>$ 135 keV. The best-fit model with data and the residues are
given in Fig. 1. All the spectral fits produced good fit statistics with
$\chi^{2}/dof$ $\sim$ 1.0, irrespective of the coronal geometry assumed in the
used models. Thus, from analysis of the AGN X-ray continuum, it is not
possible to constrain the geometry of the corona, while X-ray polarimetric
observations could provide the needed constraint on the coronal geometry.
Here, we present our results on the analysis of the first X-ray polarimetric
observations carried out on this source by IXPE. The observations and data
reduction are described in Section 2, the analysis is described in Section 3,
and the results are discussed in Section 4, followed by the summary in the
final section.

Figure 2: Normalized U/I and Q/I Stokes parameter in the total 2$-$8 keV band
of IXPE. The plotted errors are at the 1$\sigma$ uncertainties, and the
concentric circles correspond to different values of polarization degree.

##  2 Observations and data reduction

IXPE (Weisskopf $et~{}al$., 2022) observed IC 4329A on January 5, 2023, with
its three detector units (DUs) for a net exposure of about 458 ks. The log of
the IXPE observation is given in Table 1. The calibrated data were produced by
the standard IXPE pipeline provided by the Science Operation Center
(SOC)111https://heasarc.gsfc.nasa.gov/docs/ixpe/analysis/IXPE-SOC-
DOC-009-UserGuide-Software.pdf. We used the cleaned and calibrated level 2
data for the scientific analysis.

Figure 3: The 68$\%$, 90$\%$ and 99$\%$ confidence contours between $\Pi_{X}$
and $\Psi_{X}$ in the 2$-$8 keV (left panel) band and in three different
energy bands (right panel).

The publicly available level 2 data were analysed using IXPEOBSSIM software
v30.0.0 (Baldini $et~{}al$., 2022). A count map in sky coordinates was
generated using the CMAP algorithm within the xpbin task. We adopted a
circular region with a radius of $70^{\prime\prime}$ for the source extraction
from the three DUs, and a source-free region with a radius of
$100^{\prime\prime}$ was chosen for the background extraction for each DU. We
then used the xpselect task to generate the filtered source and background
regions. For the spectro-polarimetric analysis, the I, Q and U source and
background spectra were generated using the PHA1, PHA1Q and PHA1U algorithm
using xpbin task within IXPEOBSSIM for the three DUs. We used a minimum of 30
counts/bin to bin the I spectra, where a constant energy binning of 0.2 keV
was used for Q and U spectra.

Table 1: Log of IXPE observation. OBSID | Date | Exposure Time
---|---|---
|  | (secs)
01003601 | 2023-01-05 | 457715

##  3 Analysis

###  3.1 Polarimetry

The polarimetric signal from IC 4329A was analysed using the PCUBE algorithm
in the xpbin task. The three polarization cubes for the three DUs were
generated to extract information like the Stokes parameters (I, Q, U); the
minimum detectable polarization (MDP); the polarization degree ($\Pi_{X}$);
the polarization angle ($\Psi_{X}$) and their associated errors. We first
generated the three polarization cubes corresponding to three DUs in the
entire 2$-$8 keV energy band. The combined polarization parameters from the
three DUs in the 2$-$8 keV band are given in Table 2. We found $\Pi_{X}$ =
3.7$\pm$1.5$\%$, MDP = 4.5$\%$ and $\Psi_{X}$ = 61∘$\pm$12∘. The normalized
U/I and Q/I Stokes parameters obtained from the three polarization cubes
corresponding to the three DUs and from the combined cube are shown in Fig. 2.

To check for the energy dependence of the polarization parameters, we also
derived the polarization parameters in three energy bins of 2$-$3 keV, 3$-$5
keV and 5$-$8 keV using the PCUBE algorithm. The derived parameters are given
in Table 2. The polarization contours for the total energy range of 2$-$8 kev
as well as for the different energy ranges, are given in Fig. 3. From Table 2
and Fig. 3, it is evident that $\Pi_{X}$ and $\Psi_{X}$ are consistent within
errors in the energy range of 2$-$3, 3$-5$ and the 2$-$8 keV, while there is a
tendency for a decrease in $\Psi_{X}$ in the 5$-$8 keV band. However, the
error is so large to arrive at any firm conclusion on the change in $\Psi_{X}$
at the higher energy band.

Though the values of $\Pi_{X}$ in the 2$-$3, 5$-$8 and 2$-$8 keV bands are
close to or lower than the MDP values, at 3$-$5 keV, we found a $\Pi_{X}$ of
6.5$\pm$1.8$\%$ which is larger than the MDP value of 5.5$\%$. We thus
conclude to have detected significant X-ray polarization in IC 4329A, and this
is the first report of the detection of the X-ray polarization signal in IC
4329A.

###  3.2 Spectro-polarimetry

We carried out the spectro-polarimetric analysis of the IXPE I, Q, U spectra
in the 2$-$8 keV energy band. For the spectral fitting, we used an absorbed
powerlaw, modified by a multiplicative constant polarization model polconstant
in XSPEC V12.13.0c (Arnaud, 1996). This model assumes a constant polarization
degree and a constant polarization angle over the specific energy band. In
XPSEC the model takes the following form,

$constant\times TBabs\times zTBabs\times(polconst\times po)$ (1)

Here, the const represents the inter-calibration constant for each detector,
which varies between 0.95 to 1.00. TBabs was used to model the Milky Way
Galactic hydrogen column density, which was taken from Willingale $et~{}al$.
(2013). To model the host galaxy column density, we used zTBabs and let the
column density ($N_{H}$) vary during the fit. This model fits the I, Q, and U
spectra (from the three detectors) well with a reduced chi-square
($\Delta\chi^{2}$) = 1083/1064. The best fit I, Q and U spectra with the
residues are given in Fig. 4. The spectro-polarimetric fit produced a
$\Pi_{X}$ of 4.7$\pm$2.2$\%$ (larger than the MDP value of 4.5$\%$) and
$\Psi_{X}$ of 71∘$\pm$14∘ associated with the primary emission when modelled
with a power law of photon index ($\Gamma$) of 1.95$\pm$0.05. In Fig. 3, the
contours between $\Pi_{X}$ and $\Psi_{X}$ in 68$\%$, 90$\%$ and 99$\%$ are
plotted along with the contours obtained from the polarimetric analysis. All
the model parameters for each of the detectors were tied during the fit. The
errors were calculated at the 90$\%$ confidence ($\chi^{2}$ = 2.71 criterion).
The best-fit parameters are given in the Table 3. We also performed an MCMC
analysis to calculate the errors in 90$\%$ confidence associated with the
best-fit parameters. The errors from the MCMC analysis are also reported in
Table 3.

Table 2: Polarization parameters in different energy bands. Energy band | $\Pi_{X}\pm 1\sigma$ | MDP | $\Psi_{X}\pm 1\sigma$
---|---|---|---
keV | $\%$ | $\%$ | degree
2$-$ 8 | 3.7$\pm$1.5 | 4.5 | 61$\pm$12
2$-$ 3 | 3.6$\pm$1.8 | 5.5 | 66$\pm$14
3$-$ 5 | 6.5$\pm$1.8 | 5.5 | 74$\pm$8
5$-$ 8 | 5.4$\pm$3.5 | 10.73 | 21$\pm$19

##  4 Discussion

The measured polarised X-ray emission in the radio-quiet category of AGN is
believed to be due to the inverse Compton scattering of UV/optical accretion
disk photons by hot electrons in the corona. Therefore, the measured degree of
X-ray polarization depends on the geometry of the corona. We examined the
polarimetric properties of the Seyfert 1 galaxy IC 4329A using the IXPE data
through a model-independent as well as spectro-polarimetric analysis. Using
the model-independent approach in the 2$-$8 keV, we found a polarization angle
of 61∘$\pm$12∘ and a polarization degree of 3.7$\pm$1.5$\%$ which is slightly
lower than the MDP value of 4.5$\%$ (at the 1$\sigma$ confidence level). From
spectro-polarimetric analysis, we found values of $\Pi_{X}$ and $\Psi_{X}$ of
4.7$\pm$2.2% (larger than the MDP value of 4.5$\%$) and 71∘$\pm$14∘
respectively. Recently, Ursini $et~{}al$. (2021) simulated polarization
signals expected from AGN corona for three different geometries, namely, slab
(inner radius $\sim$ 10$R_{g}$), spherical lamp$-$post (radius $\sim$
10$R_{g}$ and height $\sim$30$R_{g}$ above the accretion disk) and the
truncated cone geometry for an outflowing corona (a failed jet with an
outflowing velocity of 0.3c and initial radius of 20$-$30$R_{g}$). The authors
claimed that for a slab coronal geometry, the polarization degree goes up to
12 per cent. For the symmetrical nature of a spherical lamp$-$post corona, it
is expected that the polarization signal received from such sources would be
lower than the slab one. For such geometrics, a very low polarization degree
($\sim$ 1$-$3 $\%$) is expected (Poutanen & Svensson, 1996; Tamborra
$et~{}al$., 2018). For the conical corona, the expected polarization could be
between the slab and the spherical ones. From their simulation using the MONK
(Zhang $et~{}al$., 2019) code, Ursini $et~{}al$. (2021) also reported that the
polarization angle is close to 180∘ for slab geometry, while for the spherical
and conical geometries, it is scattered around 90∘. Our measured value of
$\Pi_{X}$ = 6.5$\pm$1.8$\%$ in the 3-5 keV, larger than the MDP value of
5.5$\%$ rules out the spherical lamp$-$post geometry for the corona. However,
compared with the simulations of Ursini $et~{}al$. (2021), our measured values
argue for a conical geometry for the corona in IC 4329A.

Figure 4: Left panel: IXPE I Stokes best-fit spectra with residuals. Right
panel: Q and U stokes best-fit spectra with residuals.

##  5 Conclusions

We carried out the analysis of the first X-ray polarimetric observations
carried out by IXPE. The observation on IC 4329A for a total duration of 458
ksec was taken on 05 January 2023. The findings of the polarimetric study are
as follows,

  1. 1.

From a model-independent analysis, we found a value of $\Pi_{X}$ =
3.7$\pm$1.5% and $\Psi_{X}$ = 61∘$\pm$12∘ in the 2$-$8 keV band. This value of
$\Pi_{X}$ is slightly lower than the MDP value of 4.5$\%$.

  2. 2.

From the spectro-polarimetric analysis of model fits to the spectra, we found
values of $\Pi_{X}$ and $\Psi_{X}$ of 4.7$\pm$2.2% and 71∘$\pm$14∘
respectively in the 2$-$8 keV band. Thus, the polarimetric measurements
obtained from both model-independent and spectro-polarimetric analyses agree
with each other. Also, the value of $\Pi_{X}$ obtained from the model fit to
the spectrum is larger than the MDP value of 4.5$\%$.

  3. 3.

To check for energy-dependent polarization, we derived the polarization
parameters in different energy bands. While $\Pi_{X}$ is found to be similar
within error bars in all the energy bands, the derived values of $\Psi_{X}$
are found to agree within errors in the 2$-$3, 3$-$5 and 2$-$8 keV bands.
There is a tendency for lower values of $\Psi_{X}$ in the higher energy range
of 5$-$8 keV. However, the error bar is too large in this energy range. Our
observations do not find evidence of changes in polarization between energy
bands.

  4. 4.

In the 3$-$5 keV band, from model-independent analysis, we found a $\Pi_{X}$
of 6.5$\pm$1.8$\%$ which is larger than the MDP value of 5.5$\%$. Also, from
spectro-polarimetric analysis in the 2$-$8 keV band, we found a $\Pi_{X}$ of
4.7$\pm$2.2$\%$, which is larger than the MDP at that energy band. We,
therefore, conclude to have detected X-ray polarization in IC 4329A.

  5. 5.

Our observations, when compared with Monte-Carlo simulations in the literature
(Ursini $et~{}al$., 2021), rule out a spherical lamp$-$post geometry for the
corona in IC 4329A, instead tend to favour a corona with a conical geometry in
IC 4329A.

With the results reported in this work, the number of Seyfert type AGN with
measured X-ray polarization measurements from IXPE observations have increased
to four. X-ray polarimetric observations of more Seyfert-type AGN are needed
to put better constrain the geometry of the X-ray corona in AGN. Also,
repeated observations of the same source by IXPE would enable one to constrain
for variations in the geometry of the corona, as has been hinted at from
spectral modelling of the X-ray spectra of AGN.

Table 3: Results of spectro-polarimetric analysis. Parameters | XSPEC analysis | MCMC analysis
---|---|---
$N_{H}$ | 0.70${}^{+0.12}_{-0.12}$ | 0.70${}^{+0.12}_{-0.11}$
$\Pi_{X}$ ($\%$) | 4.7${}^{+2.2}_{-2.2}$ | 4.7${}^{+2.0}_{-2.4}$
$\Psi_{X}$ (∘) | 71${}^{+14}_{-14}$ | 71${}^{+14}_{-15}$
$\Gamma$ | 1.95${}^{+0.05}_{-0.05}$ | 1.95${}^{+0.05}_{-0.05}$
$N$ | 0.023${}^{+0.002}_{-0.002}$ | 0.023${}^{+0.002}_{-0.002}$

## Acknowledgements

The Imaging X-ray Polarimetry Explorer (IXPE) is a joint US and Italian
mission. The US contribution is supported by the National Aeronautics and
Space Administration (NASA) and led and managed by its Marshall Space Flight
Center (MSFC), with industry partner Ball Aerospace (contract NNM15AA18C). The
Italian contribution is supported by the Italian Space Agency (Agenzia
Spaziale Italiana, ASI) through contract ASI-OHBI-2017-12-I.0, agreements ASI-
INAF-2017-12-H0 and ASI-INFN-2017.13-H0, and its Space Science Data Center
(SSDC) with agreements ASI- INAF-2022-14- HH.0 and ASI-INFN 2021-43-HH.0, and
by the Istituto Nazionale di Astrofisica (INAF) and the Istituto Nazionale di
Fisica Nucleare (INFN) in Italy. This research used data products provided by
the IXPE Team (MSFC, SSDC, INAF, and INFN) and distributed with additional
software tools by the High-Energy Astrophysics Science Archive Research Center
(HEASARC), at NASA Goddard Space Flight Center (GSFC). Part of the French
contribution is supported by the Scientific Research National Center (CNRS)
and the French Space Agency (CNES). We thank the NuSTAR Operations, Software
and Calibration teams for support with the execution and analysis of these
observations. This research has made use of archival data of XMM-Newton and
NuSTAR observatories through the High Energy Astrophysics Science Archive
Research Center Online Service, provided by the NASA Goddard Space Flight
Center.

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