# PoliWAM: An Exploration of a Large Scale Corpus of Political Discussions on
WhatsApp Messenger

Vivek Srivastava
TCS Research
Pune, Maharashtra, India
<EMAIL_ADDRESS>
Mayank Singh
IIT Gandhinagar
Gandhinagar, Gujarat, India
<EMAIL_ADDRESS>

###### Abstract

WhatsApp Messenger is one of the most popular channels for spreading
information with a current reach of more than 180 countries and 2 billion
people. Its widespread usage has made it one of the most popular media for
information propagation among the masses during any socially engaging event.
In the recent past, several countries have witnessed its effectiveness and
influence in political and social campaigns. We observe a high surge in
information and propaganda flow during election campaigning. In this paper, we
explore a high-quality large-scale user-generated dataset curated from
WhatsApp comprising of 281 groups, 31,078 unique users, and 223,404 messages
shared before, during, and after the Indian General Elections 2019,
encompassing all major Indian political parties and leaders. In addition to
the raw noisy user-generated data, we present a fine-grained annotated dataset
of 3,848 messages that will be useful to understand the various dimensions of
WhatsApp political campaigning. We present several complementary insights into
the investigative and sensational news stories from the same period.
Exploratory data analysis and experiments showcase several exciting results
and future research opportunities. To facilitate reproducible research, we
make the anonymized datasets available in the public domain.

##  1 Introduction

In the last decade, the majority of the political parties around the world are
heavily spending on social media engagement platforms like Facebook, Twitter,
Quora, WhatsApp, and Sharechat for fast and secure information spread.
WhatsApp Messenger (hereafter ‘WAM’) is highly prevalent in 180 countries with
installation over 90% of devices Bobrov (2018). WAM allows users to send
instant messages, photos, videos, and voice messages in addition to voice and
video calls over a secure end-to-end encryption channel. However, data
curation from WAM remains a challenging task owing to privacy concerns,
stringent encryption strategies, and system requirements.

WAM as Political Propaganda Tool: Several investigative journalism stories
Tech (2018); Conversation (2018); Indian (2019) suggest ever-increasing global
penetration of WAM-based political propaganda and the resultant mass
polarization effects. India, the second-most-populous country with 1.3 billion
population, has witnessed similar trends News (2018); Uttam (2018) during the
past two General Elections Ruble (2014). WAM has emerged as a primary leader
for delivery for political messaging with 95% of Android devices in India
having WAM installation and maintaining a 75% daily active users percentage
Bobrov (2018). For the first time, complementing the existing investigative
journalism stories, we present a scientific study to understand the WAM
messaging patterns and spread in the political scenario.

WAM Data Curation: To adhere to the WAM’s privacy policy Garimella and Tyson
(2018), we consider only WAM public groups where users willingly share
messages with known and unknown people. The biggest challenge with restricting
to public groups is a large number of fake and dubious groups and the
unavailability of a standard in-app filter functionality to identify such
groups. To the best of our information, none of the previous works on WAM data
curation have discussed any methodologies for filtering irrelevant groups. One
of the earliest works on WAM dataset curation Garimella and Tyson (2018)
considers a list of all WAM public groups available online. We claim that due
to multilingualism coupled with code-mixing and multi-modal metadata, the
genuine group identification problem is non-trivial. We present a novel manual
group filtering strategy to filter fake and dubious groups by leveraging group
metadata, i.e., group name, display picture, and the description. Owing to the
user’s privacy in the WAM groups, we release the anonymized
dataset111https://zenodo.org/record/4115660#.YUSln54zZQI. In addition, we are
also releasing a fine-grained annotated dataset of 3,848 messages (see Section
3.2) for future research opportunities. The annotated dataset contains
interesting fine-grained labels in four categories i.e., malicious activity,
political orientation, political inclination, and message language.

Our Contributions: The main contributions are:

  * •

We present a novel WAM group filtering strategy leveraging the group’s
metadata to filter the fake and dubious groups.

  * •

We analyze a total of 281 public groups distributed among 26 political
parties, including all the seven national political parties.

  * •

In addition to the original anonymized dataset with 223,403 messages and
31,078 unique WAM users, we also release a publicly available fine-grained
annotated dataset of 3,848 WAM messages with language, malicious activity,
political orientation, and political inclination as labels.

  * •

We present several interesting insights from the analysis of users and the
message content. We establish several correlations with the claims and reports
of news media and survey articles from the same period.

  * •

We draw several interesting insights on co-occurrences of the political
entities (leaders and parties) and social factors (agendas, religions, castes,
and languages/ethnicity) from the linguistic perspective.

##  2 Related Work

People engage in various social media platforms such as Twitter, Facebook,
etc., to discuss socially relevant topics such as politics. We witness a large
volume of research focused on Twitter-based political discussions due to the
easier availability of data and the large-scale involvement of the masses. For
example, Bovet and Makse (2019) conducted a large-scale analysis of fake news
propagation on Twitter during the 2016 U.S. presidential elections. Tumasjan
et al. (2010) studied the usage of Twitter as a tool for political
deliberation and election forecasting. They also used Twitter as a means to
understand the political sentiment of the politicians and parties in the
election campaigning. Conover et al. (2011) presented a study of the
interaction between the network of users of different ideologies. They used
Twitter as a medium to understand the political communication network.
Colleoni et al. (2014) studied the structure of political homophily between
different political groups on Twitter to understand the public sphere and echo
chamber effect.

In contrast to Twitter-based studies, Vitak et al. (2011) studied student’s
involvement in the political discussions on Facebook for the 2008 U.S.
presidential election. Several studies looked at different offline modes of
political discussions as well. For example, Ansolabehere et al. (2006)
explored the effect of newspaper endorsement on the shift of vote margin. The
largest circulation newspaper during the period of 1940–2002 is part of this
experiment for the various U.S. elections. Barrett and Barrington (2005)
conducted a study to understand the visual perception of the voter by the
candidate’s photograph in the newspaper. Wang et al. (2015) proposed an
innovative methodology on non-representative polls to forecast elections in
contrast to the survey methods. They experiment with the data from the Xbox
gaming platform for the 2012 U.S. presidential election. Ferreira et al.
(2018) discuss the involvement of the ideological communities over 15 years.
They used data on the public voting of Brazil and the U.S and study the
polarization in the communities. Caetano et al. (2018) presented an analysis
and characterization of WAM messages at three different layers.

Recently, we observe a growing interest in understanding the information flow
on WAM with political discussions in focus Resende et al. (2019b, a); Pang and
Woo (2020); Vermeer et al. (2021); Velasquez et al. (2021); Garimella and
Eckles (2020); Saha et al. (2021); Javed et al. (2020); Yadav et al. (2020).
In contrast to the existing works, we present a novel manual filtering
strategy (see Section 3) to identify the potential WAM groups. Our group
identification strategy results in a high-quality dataset with less dubious
groups. Also, to understand the various user and message characteristics, we
present a fine-grained annotated dataset of 3,848 messages.

##  3 Dataset

In contrast to other social media platforms, data curation from WAM public
groups is a non-trivial task. Even, group identification itself is a
challenging task as WAM does not support advanced content search feature.
Majority of the online forums/blogs222https://www.opentechinfo.com/WhatsApp-
groups/333https://chatwhatsappgrouplink.blogspot.com/p/join-whatsapp-group-
links.html?m=1 comprises dubious public group links containing pornographic
content, lucrative job, and lottery offers (see Figure 1).

|
---|---
(a) | (b)
Figure 1: Example metadata snapshot of (a) a dubious and (b) a genuine WAM
group. The personal information is anonymized.

As the initial step of data curation, we identify and join the relevant
groups. We construct a seed set of Indian political WAM groups (based on the
names of political parties and their top leaders) from several forums/blogs
and social media platforms like Google, Facebook, and Twitter. The seed set
consists of 50 groups. The seed set is obtained after manual pre-processing of
$\sim$600 groups. Further, we enrich the seed set by following groups that
were shared within the followed groups. Overall, we obtained 2600 group links
collected between January 19, 2019 – May 19, 2019. Out of 2600, we only
identify 281 ($\sim$11%) relevant groups that are actively participating in
Indian political discussions. Groups in which all the three metadata
categories (i.e., name, display picture, and description) are indicative of
the same political affiliation are considered genuine and relevant.

For decryption of the WAM database stored locally on the mobile device, we use
a cipher key and a database extractor tool444 https://forum.xda-
developers.com/showthread.php?t=2770982. We divide the complete data
collection into three phases:

  * •

Before elections: January 19, 2019 – March 5, 2019

  * •

Active campaigning phase: March 6, 2019 – May 19, 2019

  * •

After elections: May 20, 2019 – June 15, 2019

Figure 2 presents user and content statistics at three different phases. We
observe a sharp decline in the message count after elections. Similarly,
before elections, we find a low user count. Thus, in the rest of the paper, we
focus on the active campaigning phase, where the maximum number of users has
shared the highest number of messages.

|
---|---
(a) | (b)
Figure 2: Status of different phases of data collection: (a) Number of total
and unique users present and (b) Total messages shared in each phase.

###  3.1 Metadata Analysis

Name | Count | Name | Count | Name | Count | Name | Count | Name | Count
---|---|---|---|---|---|---|---|---|---
BJP | 144 | AAP | 20 | AIMIM | 4 | RJD | 3 | Shivsena | 1
INC | 45 | BSP | 9 | AIADMK | 3 | AITC | 3 | Others | 19
SP | 21 | YSRCP | 5 | NCP | 3 | CPI(M) | 1 |  |

Table 1: Number of WAM groups affiliated to different political parties.

Table 1 shows the representation of different political parties out of the
total 281 groups. Each group is manually affiliated to a single political
party based on the group name, display picture, and description. BJP shows
highest representation followed by INC and SP. All state-level parties, except
AAP, show poor representation. Several media reports TOI (2019); BBC (2019)
supports the insurgence of BJP WAM groups to communicate with the various
stakeholders.

We found a total of 37,984 participants in 281 groups. Out of which, 31,078
(81.8%) comprise unique users. Figure 3 shows the user presence in multiple
groups. Even though the majority of users (88.5%) are members of a single
group, we find instances where few users are members of more than 20 political
groups. For instance, one user is a member of 25 groups, whereas seven users
are part of 20 or more groups. In addition, we find that during active
campaigning phase, only a few (12.45%) of these groups have group strength
${\leq}$ 50 users. 63.34% of groups have 100 or more members.

####  3.1.1 Message formats

In phase II, a total of 1,47,220 messages are shared, out of which 58,008
messages contain media files. Table 2 shows the distribution of media files.
67.59% of the total media files are the image files in the JPEG format. This
is consistent with the claims of several news articles that memes Hindu
(2019a); Samosa (2019) are a powerful tool to attack or praise individuals and
parties during campaigning. Images (in JPEG format) and videos (in MP4 format)
constitute 95.06% of all the media files shared. Researchers conclude that
image-based message sharing has extensively led to propaganda propagation
Madhumita Murgia (2019). For example, political parties/candidates use
doctored images Times (2019b); News (2019) of articles from reputable news
media sources to demean opponent political parties/candidates.

Figure 3: User presence in multiple groups. One user is present in 25 groups.
Seven users are part of 20 or more groups.

Type | Count | Type | Count | Type | Count | Type | Count
---|---|---|---|---|---|---|---
JPEG | 39,210 | OGG | 371 | 3GPP | 37 | MP3 | 1
MP4 | 15,934 | MPEG | 288 | AAC | 39 | Octet-stream | 1
WEBP | 1,221 | MP4 | 75 | AMR | 35 | Spreadsheets | 1
PDF | 719 | APK | 66 | TXT | 10 |  |

Table 2: (Best viewed in color) Distribution of shared media items. Blue, Red,
Violet, Green and Black color represent video, audio, images, document and
compressed files, respectively.

####  3.1.2 Group metadata

Group metadata comprises a display picture, name, and description. Most of the
group display pictures are the official party symbols, pictures of the top
leaders/influencers, and religious symbols/idols. The textual content in group
names and descriptions shows phrases used in social election campaigning.
Figures 4(a) and 4(b) show word clouds of the group names and group
descriptions, respectively. We observe the most frequently used words to be in
consistent with the claims newslaundry (2019); Scroll (2019a); SBS (2019) of
various news and investigative studies. Several research and survey articles
Hindu (2019b); Livemint (2019) shows conflicting user opinion on the impact of
slogans and influencers in the campaigning. Group names mainly consist of
party names as English tokens. Group descriptions mostly contain Hindi
language tokens. Thus, any group identification process, either manual or
automatic, require a deep understanding of multiple languages.

####  3.1.3 External link sharing

Several website links are shared among group members. We find a total of
16,582 links comprising news, video, and social media websites. YouTube videos
with 5,456 links are the most shared external links. This high number is in
line with the claims of several studies Scroll (2019b); Times (2019d)
indicating the high influence of YouTube videos in the campaigning. Facebook,
Twitter, Dailyhunt (Indian News mobile application), Jansatta (Hindi daily for
North India), NDTV (an Indian television media company), etc., are the other
popular websites with high number of links. The majority of the video links
shared contain the news articles, speeches of the political leaders, and
promotional content.

####  3.1.4 Contribution of top active users

All users do not actively participate in the conversations. The majority of
the group members are passive consumers, while few users drive the topics of
the conversation. In about 250 groups, the top 50% active users share 80-100%
messages. Table 3 shows the contribution of top 1%, 10%, and 50% active users
in the groups of different political parties. AAP has the most contribution
from the top 1% users, whereas SP has the least contribution from top 1%, 10%,
and 50% users. BJP and INC, the top two political parties (based on the number
of groups), show similar participation from the top 50% active users. But, BJP
leads INC in the participation of the top 1% active users. This
disproportionate distribution of user activity can be attributed to:

  * •

Influencers: Presence of a few active participants/influencers in the groups
who are possibly responsible for official campaigning of the party/candidates.

  * •

Neutral stance: Less participation from other members might indicate their
neutral stance towards the ongoing campaigning, debates, and discussions Times
(2019c).

  * •

Group invasion: Members from different political inclination join groups to
share misinformation and fake news. Also, group invasion is possible to
monitor (with least participation in discussions) the election campaigning of
the opposition parties on WAM. Several claims Wire (2019); Diplomat (2019b)
have been made that indicates the high usage of WAM for such activities.

|
---|---
(a) | (b)
Figure 4: Word clouds of common phrases from group (a) names and (b)
descriptions.

| BJP | INC | AAP | SP | BSP | Others
---|---|---|---|---|---|---
Top 1% | 30.84 | 27.33 | 33.88 | 18.04 | 24.44 | 28.44
Top 10% | 67.20 | 64.63 | 69.82 | 52.17 | 56.20 | 65.23
Top 50% | 93.53 | 93.97 | 94.37 | 88.67 | 90.25 | 93.05

Table 3: Percentage of messages shared by top 1%, 10%, and 50% active users
across different political parties.

####  3.1.5 Geographical analysis

Next, we conduct the geographical analysis of group members based on their
registered mobile number.555https://www.searchyellowdirectory.com/reverse-
phone/ Surprisingly, we find users from 46 different countries discussing
Indian politics. However, the majority of users belong to India. Figure 5(a)
and 5(b) collectively show user locations outside and inside India. We also
find that group administrators belong to five different countries (India,
Pakistan, UAE, Latvia, and the USA). The above empirical findings confirm
several claims about non-resident Indians participating in social media
campaigns Chaturvedi (2020); Times (2019a); Diplomat (2019a). Figure 5(c)
shows the locations of Indian group administrators. The majority of users and
group administrators belong to northern and central India, strengthening the
popular belief that WAM-based political campaigns are centrally managed by a
team of IT experts headquartered in the Delhi-NCR region Ayush Tiwari (2020).

Figure 5: (Best viewed in color) (a) User locations in the World. (b) User
locations in India. (c) Group administrator locations in India.

####  3.1.6 Group creation time

Table 4 shows the group creation time of all the 281 groups. As we can see, a
significant number (51.60%) of groups are created in the first five months of
the year 2019, which is consistent with claims made by several news articles
Madhumita Murgia (2019); News (2018); Uttam (2018); Iyengar (2019).

Interval | Groups | Interval | Groups | Interval | Groups
---|---|---|---|---|---
May’14-Dec’14 | 4 | May’16-Dec’16 | 11 | May’18-Dec’18 | 66
Jan’15-Aug’15 | 2 | Jan’17-Aug’17 | 18 | Jan’19-May’19 | 145
Sep’15-Apr’16 | 4 | Sep’17-Apr’18 | 31 |  |

Table 4: Frequency of WAM group creation in different intervals.

####  3.1.7 Languages

Table 5 presents language
identification666https://pypi.org/project/langdetect/ statistics. A total of
31, 22, and 45 unique languages are used in writing group names, group
descriptions, and messages, respectively. English and Hindi are the two most
frequently used languages. The findings reiterate the challenges in conducting
WAM-based user analysis, due to multilingualism, in highly diversified
countries like India.

| Top-5 languages in decreasing order of frequency
---|---
Names |  Hindi, English, Nepali, Marathi, Indonesian
Descriptions |  Hindi, English, Nepali, Marathi, Tagalog
Messages |  Hindi, English, Indonesian, Marathi, Somali

Table 5: Top-5 languages found in group name and description and messages.
Figure 6: Example annotation of the messages.

###  3.2 Annotation

We construct a fine-grained manually annotated dataset of 3,848 messages.
Eight annotators have performed annotation of the messages. All of the eight
annotators are native Hindi speaker and proficient in speaking and writing
English. Figure 6 shows the example annotation of the messages. Before
annotation, we pre-process the original dataset to filter out irrelevant/noisy
messages by removing non-textual data like hyperlinks, emoticons, images, and
videos, duplicate messages, and messages with length less than five characters
or more than 150 characters and keeping messages written in either of two
scripts Roman or Devanagari. Pre-processing results in 48,474 messages. We
randomly sample 3,848 messages from pre-processed data for annotation. Each
annotator annotates 481 samples. Each message has a fine-grained annotation
with the labels in the following categories:

| Malicious activity | Political orientation | Language
---|---|---|---
| Spam | Offensive | Advertisement | Others | Political | Non-political | Hindi | English | Others
Count | 759 | 219 | 142 | 971 | 1797 | 2051 | 2965 | 549 | 334

Table 6: Distribution of malicious activity, political orientation, and
language in the annotated dataset.

  * •

Malicious activity: This category helps in identifying unusual and irrelevant
activity within a group. A message is assigned one of the four labels in this
category, i.e., spam, advertisement, offensive content, and others. Spam
contains the textual messages that are irrelevant to the group and not part of
any promotion of product/website/video/etc. Advertisement is specific to the
promotional content. Others category contains the messages that are non-
political and do not involve any other categories of malicious activities such
as a non-political joke, historical content, personal conversation, etc.
Others could be a set of messages with non-political and non-malicious
content. Table 6 shows the malicious activity distribution. Spam is more
prominent as compared to advertisement and offensive content.

  * •

Political orientation: Each message is assigned a binary label for the
political orientation — political or non-political. Table 6 shows the count of
messages having political or non-political orientation. Even though the group
identification process is completely manual with strict selection guidelines,
we witness non-political messages surpassing political messages. We claim that
without a strict selection criterion (as presented in earlier works Resende et
al. (2019b, a)), the insights will be highly noisy.

  * •

Political inclination: This category helps in identifying the political
inclination (favor and against) of the messages based on their political
affiliation. Similar to the categorization described in the previous section,
we assign one of the seven labels (BJP, INC, SP, BSP, AAP, AITC, and Others)
to each message. Table 7 shows the inclination of the messages for different
political parties. BJP is the most favored party based on the number of
messages shared in favor. Whereas INC is the most targeted party.

  * •

Language: Each message is assigned one of the three labels Hindi, English, and
Others. Table 6 shows the distribution of languages used in different
messages. Hindi is the most preferred language.

| BJP | INC | AAP | SP | BSP | AITC | Others
---|---|---|---|---|---|---|---
Favour | 651 | 96 | 18 | 8 | 9 | 8 | 116
Against | 298 | 600 | 44 | 42 | 44 | 52 | 114

Table 7: Messages shared in favour and against of different political parties
in the annotated dataset.

##  4 A Study on Political and Social Co-occurrences

The majority of the political parties often declare the agendas for their
election campaigns. These agendas are mostly driven by various factors that
touch upon the needs, beliefs, and necessities of the stakeholders. During the
election campaign, the information propagation on various social media
platforms gets heavily influenced by these social factors.

In this section, we present a discussion on the co-occurrence of two political
entities (i.e., leaders and parties) and four social factors (i.e., agenda,
religion, caste, and languages/ethnicity) in the dataset. Table 8 shows the
fine-grained categorization of the political entities and the social factors.
In our analysis, we select the six political parties (i.e. BJP, INC, AAP, SP,
BSP, and AITC) and the most popular leader from each of these political
parties (Narendra Modi–BJP, Rahul Gandhi–INC, Arvind Kejriwal–AAP, Akhilesh
Yadav–SP, Mayawati–BSP, and Mamata Banarjee–AITC). The choice of social
factors is motivated by the various influential topics being continuously
reported to impact the political discourse in India.

To this end, we learn the word representation using FastText Bojanowski et al.
(2017) on the textual data in the messages. We pre-filter the noisy content in
the dataset i.e. emoticons, special characters, and hyperlinks. To learn the
representation, we use
Gensim777https://radimrehurek.com/gensim/models/fasttext.html with Python
interfaces and default parameters. English and Hindi are the two most popular
languages in the dataset. The word representations from FastText has different
representation for the same word in two languages. To address this challenge,
we translate the political entities and the social factors in the English
languages (Roman script) to the Hindi language (Devanagari script) using
Google Translate888https://translate.google.com/. To understand the co-
occurrence of the political entities and social factors in the dataset, we
compute the cosine similarity between them. For similarity computation, we use
the words in both languages (i.e. English and Hindi). The similarity between
political entity $w_{1}$ and social factor $w_{2}$ is given as:

sim($w_{1}$, $w_{2}$) = max{sim($hw_{1}$, $hw_{2}$), sim($hw_{1}$, $ew_{2}$),
sim($ew_{1}$, $hw_{2}$), sim($ew_{1}$, $ew_{2}$)}, where $hw_{i}$ and $ew_{i}$
represents the word representation of word $w_{i}$ in the Hindi and the
English language respectively.

For the entity/social factor with more than one word, we take the average of
the word representation of the constituent words. Table 9 and 10 presents the
top-k (k=5 for ‘Agendas’, ‘Religions’, ‘Languages/Ethnicity’ and k=4 for
‘Castes’) most similar social factors for the political leaders and political
parties respectively. We draw following major insights from the co-occurrence
analysis:

Political | Parties | BJP, INC, AAP, SP, BSP, AITC
---|---|---
Leaders | Narendra Modi, Rahul Gandhi, Arvind Kejriwal, Akhilesh Yadav, Mayawati, Mamata Banerjee
Social | Agendas |  | Education, Development, Healthcare, Infrastructure, Manufacturing, Defense, Economy,
---
Transportation, Unemployment, Poverty, Terrorism, Literacy, Corruption,
Inflation,
Taxation, Pollution, Digitization, Privatisation, Agriculture
Religion | Hinduism, Islam, Sikhism, Christianity, Buddhism, Jainism
Castes | Forward Castes, Other Backward Class (OBC), Scheduled Castes (SC), Scheduled Tribes (ST)
| Languages/
---
Ethnicity
| Hindi, Bengali, Marathi, Telugu, Tamil, Gujarati, Urdu, Kannada, Odia,
Malayalam, Punjabi,
---
Assamese, Maithili, Sanskrit

Table 8: Fine-grained categorization of the political entities and the social
factors.

| Agendas | Religions | Castes | Languages/Ethnicity
---|---|---|---|---
Narendra Modi |  | Corruption, Literacy, Development,
---
Privatisation, Terrorism
| Sikhism, Buddhism, Jainism,
---
Hinduism, Islamism
| FW, SC,
---
OBC, ST
| Odia, Assamese, Gujarati,
---
Sanskrit, Marathi
Rahul Gandhi |  | Corruption, Unemployment, Literacy,
---
Development, Healthcare
| Sikhism, Buddhism, Islamism,
---
Jainism, Hinduism
| FW, OBC,
---
SC, ST
| Odia, Assamese, Maithili,
---
Tamil, Marathi
Arvind Kejriwal |  | Corruption, Literacy, Taxation,
---
Terrorism, Healthcare
| Sikhism, Buddhism, Islamism,
---
Jainism, Hinduism
| OBC, FW,
---
SC, ST
| Odia, Assamese, Bengali,
---
Tamil, Maithili
Akhilesh Yadav |  | Corruption, Development, Taxation,
---
Unemployment, Education
| Sikhism, Hinduism, Jainism,
---
Islamism, Buddhism
| FW, OBC,
---
ST, SC
| Maithili, Assamese, Odia,
---
Malayalam, Kannada
Mayawati |  | Corruption, Literacy, Terrorism,
---
Taxation, Unemployment
| Sikhism, Islamism, Hinduism,
---
Christianity, Buddhism
| FW, OBC,
---
ST, SC
| Odia, Assamese, Malayalam,
---
Maithili, Bengali
Mamata Banerjee |  | Literacy, Corruption, Poverty,
---
Development, Terrorism
| Jainism, Sikhism, Buddhism,
---
Christianity, Hinduism
| OBC, SC,
---
FW, ST
| Malayalam, Maithili, Marathi,
---
Sanskrit, Gujarati

Table 9: Top-k most similar social factors with each of the six political
leaders. k=5 for the social factors ‘Agendas’, ‘Religions’, and
‘Languages/Ethnicity’. k=4 for the social factor ‘Castes’. Here, FW: Forward
Castes , OBC: Other Backward Class, SC: Scheduled Castes, and ST: Scheduled
Tribes.

| Agendas | Religions | Castes | Languages/Ethnicity
---|---|---|---|---
BJP |  | Corruption, Terrorism, Literacy,
---
Development, Unemployment
| Hinduism, Islamism, Sikhism,
---
Jainism, Buddhism
| OBC, FW,
---
SC, ST
| Assamese, Odia, Bengali,
---
Sanskrit, Hindi
INC |  | Corruption, Terrorism, Unemployment,
---
Literacy, Development
| Islamism, Hinduism, Sikhism,
---
Jainism, Buddhism
| OBC, FW,
---
SC, ST
| Odia, Assamese, Bengali,
---
Hindi, Sanskrit
AAP |  | Literacy, Taxation, Development,
---
Corruption, Unemployment
| Hinduism, Sikhism, Islamism,
---
Christianity, Jainism
| OBC, FW,
---
SC, ST
| Hindi, Bengali, Sanskrit,
---
Maithili, Punjabi
SP |  | Unemployment, Corruption, Development,
---
Agriculture, Literacy
| Hinduism, Islamism, Christianity,
---
Jainism, Sikhism
| OBC, ST,
---
FW, SC
| Maithili, Odia, Assamese,
---
Gujarati, Punjabi
BSP |  | Unemployment, Corruption, Taxation,
---
Development, Education
| Hinduism, Islamism, Jainism,
---
Sikhism, Christianity
| OBC, SC,
---
ST, FW
| Assamese, Odia, Bengali,
---
Gujarati, Maithili
AITC |  | Digitization, Literacy, Corruption,
---
Development, Poverty
| Christianity, Sikhism, Jainism,
---
Islamism, Hinduism
| ST, SC,
---
OBC, FW
| Odia, Assamese, Hindi,
---
Maithili, Punjabi

Table 10: Top-k most similar social factors with each of the six political
parties. k=5 for the social factors ‘Agendas’, ‘Religions’, and
‘Languages/Ethnicity’. k=4 for the social factor ‘Castes’. Here, FW: Forward
Castes , OBC: Other Backward Class, SC: Scheduled Castes, and ST: Scheduled
Tribes.

  * •

‘Corruption’, ‘Literacy’, and ‘Development’ are three most sought after
agendas for political leaders and the parties including the ruling (i.e. BJP)
and the opposition parties.

  * •

‘Privatisation’ is among the top-5 social factors for ‘Narendra Modi’. No
other leader or party has ‘Privatisation’ as the top-5 agendas.

  * •

Though ‘Poverty’ is a major concern for India, only ‘Mamata Banarjee’ from
‘AITC’ has ‘Poverty’ as the top-5 agendas.

  * •

Apart from ‘Corruption’, ‘Literacy’, and ‘Development’, the opposition leaders
and parties shows high similarity with some fundamental issues such as
‘Healthcare’, ‘Unemployment’, ‘Education’, and ‘Taxation’.

  * •

Most of the political leaders shows low similarity with the two most debated
religions in India (i.e. ‘Hinduism’ and ‘Islamism’). The political parties
shows the opposite behaviour with ‘Hinduism’ and ‘Islamism’ as the most
associated religions.

  * •

The order of similarity with ‘Hinduism’ and ‘Islamism’ for ‘BJP’ and ‘INC’ is
opposite. ‘BJP’ is more similar with ‘Hinduism’ than ‘Islamism’ and vice-
versa.

  * •

Most of the political leaders shows high similarity with the ‘Forward Castes’
whereas the political parties are more similar with the ‘Other Backward Class
(OBC)’.

  * •

Apart from ‘Akhilesh Yadav’ and ‘Mayawati’, the ‘Scheduled Tribes (ST)’
remains the least similar with the political leaders.

  * •

The opposition leaders (i.e. leaders except ‘Narendra Modi’) shows high
similarity with the Dravidian languages/ethnicity (i.e. ‘Tamil’, ‘Malayalam’,
and ‘Kannada’).

  * •

‘Odia’ and ‘Assamese’ consistently shows high similarity with the political
leaders and parties. The high similarity of ‘Odia’ can be attributed to the
fact that state assembly elections of the state Odisha took place along with
the Indian general elections 2019.

##  5 Conclusion and Future Work

In this paper, we present an exploration of the noisy user-generated data on
WAM with a focus on Indian general elections 2019. In contrast to the existing
works, we discuss a novel manual group filtering strategy to reduce the
presence of noisy and dubious groups in the dataset. In addition, we present a
fine-grained annotated dataset with multi-dimensional labels to understand
various linguistic characteristics. Lastly, the co-occurrence analysis put
forward several interesting insights from the Indian general elections 2019.
In the future, the presented dataset would be useful in understanding various
aspects (e.g., named-entities, POS tagging, language identification, etc.) of
the noisy user generated textual data.

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# The physical origin of the periodic activity for FRB 20180916B

Hao-Tian Lan  School of Astronomy and Space Science, Nanjing University
Nanjing 210023, People’s Republic of China  Zhen-Yin Zhao School of Astronomy
and Space Science, Nanjing University Nanjing 210023, People’s Republic of
China  Yu-Jia Wei  Key Laboratory of Dark Matter and Space Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
School of Astronomy and Space Science, University of Science and Technology of
China, Hefei 230026, China  Fa-Yin Wang School of Astronomy and Space Science,
Nanjing University Nanjing 210023, People’s Republic of China  Key Laboratory
of Modern Astronomy and Astrophysics (Nanjing University) Ministry of
Education, People’s Republic of China  Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, China

###### Abstract

Fast radio bursts (FRBs) are transient radio signals with millisecond-
duration, large dispersion measure (DM) and extremely high brightness
temperature. Among them, FRB 20180916B has been found to have a 16-day
periodic activity. However, the physical origin of the periodicity is still a
mystery. Here, we utilize the comprehensive observational data to diagnose the
periodic models. We find that the ultra-long rotation model is the most
probable one for the periodic activity. However, this model cannot reproduce
the observed rotation measure (RM) variations. We propose a self-consistent
model, i.e., a massive binary containing a slowly rotational neutron star and
a massive star with large mass loss, which can naturally accommodate the
wealth of observational features for FRB 20180916B. In this model, the RM
variation is periodic, which can be tested by future observations.

##  1 Introduction

Fast radio bursts (FRBs) are transient radio signals which have a
milliseconds-duration, large DM and extremely high brightness temperature
(Cordes & Chatterjee, 2019; Xiao et al., 2021; Zhang, 2023). They were first
discovered in 2007 and then were verified in 2013 (Lorimer et al., 2007;
Thornton et al., 2013). Since then, hundreds of FRB sources had been detected
and they are classified as repeating FRBs and non-repeating FRBs. Among the
repeating FRBs, FRB 20180916B (Chime/Frb Collaboration et al., 2020) and FRB
20121102 (Rajwade et al., 2020; Cruces et al., 2021) are found to have a
period of 16.35d and 157 d, which offers a great opportunity to study the
physical origin of FRBs. FRB 20180916B is a repeating FRB source first
detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME)
(CHIME/FRB Collaboration et al., 2019) and it was localized to a star-forming
region in a nearby massive spiral galaxy with a redshift of $0.0337$ (Marcote
et al., 2020). Different from many other FRB sources, FRB 20180916B exhibits a
period of 16.35 days and an active window of five days (Chime/Frb
Collaboration et al., 2020). With the help of the follow-up observational data
from the Low-Frequency Array (LOFAR) (Pastor-Marazuela et al., 2021; Pleunis
et al., 2021a) and Apertif (Pastor-Marazuela et al., 2021), the active window
shows a strong dependency on frequency, with higher frequency having a
narrower active window and the phase center of higher frequency occurring
earlier than the lower frequency (Pastor-Marazuela et al., 2021). For other
observational properties, the DM of FRB 20180916B is approximately $349$ pc
cm-3 and its variation between different bursts is very small ($\Delta$DM $<1$
pc cm-3) (CHIME/FRB Collaboration et al., 2019; Mckinven et al., 2023; Pastor-
Marazuela et al., 2021). The RM of FRB 20180916B keeps stable (Mckinven et
al., 2023) in the first three years after its discovery in 2018. Then the RM
increases monotonically over a 9 month duration to $-54.4$ rad m-2. But the RM
variations is unrelated to the 16.3-day period (Mckinven et al., 2023). For a
single burst, the variation of linear polarization angle is less than
$10^{\circ}\sim 20^{\circ}$ and for different bursts, the variation of linear
polarization angle is less than $50^{\circ}$ (Nimmo et al., 2021; Pleunis et
al., 2021a).

To explain this special periodic activity, numerous models have been proposed.
Encouraged by the observation of FRB 20200428 which is associated with SGR
J1935+2154 in the Milky Way (CHIME/FRB Collaboration et al., 2020; Bochenek et
al., 2020), some theoretical models propose strongly magnetized neutron stars
as the emitting source of FRBs. For these models, the periodic activity can be
explained by the orbital motion of a binary system with a neutron star and a
massive star with mass loss (Lyutikov et al., 2020; Ioka & Zhang, 2020; Wada
et al., 2021; Li et al., 2021), the free or forced precession of a neutron
star (Levin et al., 2020; Zanazzi & Lai, 2020; Yang & Zou, 2020; Tong et al.,
2020) or a ultra-long rotation of a neutron star (Beniamini et al., 2020). A
binary system undergoing super-Eddington accretion can also be considered as
the source of this FRB and the periodicity can be explained by the precession
of the compact star (Katz, 2020; Sridhar et al., 2021). These theoretical
models not only make different predictions on the temporal evolution of the
observed period (Katz, 2021; Wei et al., 2022), but also on the distribution
of various observational parameters, such as DM, polarization angle and RM.
There are also some other models, such as a magnetized pulsar traveling
through an asteroid belts in a binary system (Dai & Zhong, 2020), a binary
system with a neutron star and a white dwarf undergoing mass transfer (Gu et
al., 2020), a planet partially disrupted by a neutron star at periastron
(Kurban et al., 2022) and a massive binary consisting of a magnetar and an
early-type star (Barkov & Popov, 2022). Since they are lack of explicit
predictions, we will not discuss them in this work.

The paper is organized as follows. We calculate the period and period
derivation of FRB 20180916B in Section 2. Then, we use the observational data
to constrain the periodic model in Section 3. Finally, conclusions are given
in Section 4.

##  2 Period and period derivation

Based on the discovery of periodic activity (Chime/Frb Collaboration et al.,
2020), the observational data of FRB 20180916B have significantly expanded
which offers an opportunity to get a more precise period and its temporal
evolution. Firstly, we calculate the period of FRB 20180916B with the epoch-
folding method, which had been used to discover its period by CHIME team
(Chime/Frb Collaboration et al., 2020). In this method, we first fold the
arrival time of each burst into a normalization phase using the following
equation

$\phi=\frac{t-t_{0}}{P}.$ (1)

where $t_{0}$ is set as MJD $=58369.40$, $\phi$ is the normalization phase and
P is the observational period. Then, the Pearson $\chi^{2}$ test is performed
on the phase of the bursts against rectangular distribution for a given
period. The higher $\chi^{2}$ of the period, the more reliability of the
period.

We list the results in Table 1. In the first line of Table 1, we use the 111
bursts detected by CHIME till the middle of 2023 to calculate the period
(https://www.chime-frb.ca/). The result is $16.33\pm 0.05$ days, which is
similar to the one found by CHIME/FRB (Chime/Frb Collaboration et al., 2020).
We also utilize 29 bursts provided by LOFAR (Pastor-Marazuela et al., 2021;
Pleunis et al., 2021a; Gopinath et al., 2023) and get a period of $16.32\pm
0.06$ days, which is consistent with the result derived from the data of
CHIME, as shown in the second line of Table 1. To investigate the possible
temporal evolution of the period, we divide the bursts observed by CHIME into
different time bins to calculate the period. In the last five lines of Table
1, we first divide the bursts of CHIME into two time bins. We get $16.33\pm
0.11$ days and $16.32\pm 0.09$ days which are almost the same. Then we divide
the bursts of CHIME into three time bins. The results are $16.34\pm 0.17$
days, $16.38\pm 0.17$ days and $16.32\pm 0.11$ days, respectively. These
results support that the period of FRB 20180916B possesses a minimal
variation, which falls well within the range of the error bar.

Table 1: The period of FRB 20180916B derived from the epoch-folding method. Telescope | Burst number | Time range | Period (d) | Error (d) | References
---|---|---|---|---|---
CHIME | 111 | 2018.09.16-2023.06.30 | 16.33 | 0.05 | https://www.chime-frb.ca/
LOFAR | 29 | 2019.08.13-2022.09.28 | 16.32 | 0.06 | (Pleunis et al., 2021a; Gopinath et al., 2023)
CHIME | 56 | 2018.09.16-2020.11.23 | 16.33 | 0.11 | (Chime/Frb Collaboration et al., 2020)
CHIME | 55 | 2021-01-11-2023.06.30 | 16.32 | 0.09 | (Mckinven et al., 2023)
CHIME | 37 | 2018.09.16-2020.02.04 | 16.34 | 0.17 | (Chime/Frb Collaboration et al., 2020)
CHIME | 37 | 2020.02.04-2021.06.26 | 16.38 | 0.17 | (Mckinven et al., 2023)
CHIME | 37 | 2021.07.11-2023.06.30 | 16.32 | 0.11 | https://www.chime-frb.ca/

In order to get a more accurate constraint on the period derivative
($\dot{P}$), we consider the effect of the $\dot{P}$ when calculating the
phase in the epoch-folding method, i.e.,

$\phi=\frac{2\pi(t-t_{0})}{P}-\pi\frac{\dot{P}}{P^{2}}(t-t_{0})^{2},$ (2)

Two methods are used to estimate $P$ and $\dot{P}$. For the First method, we
utilize the epoch-folding method as shown in Equation (2). The two-dimensional
Gaussian functions are used to fit the result. The 1$\sigma$ range is taken as
the error bar (Sand et al., 2023). We find $P=16.31\pm 0.32$ days and
$\dot{P}=-2.4\times 10^{-5}\pm 1.1\times 10^{-4}$ day day-1, which is
consistent with the derivative $\dot{P}=0$. A similar result
$\dot{P}=-2.0\times 10^{-5}\pm 1.5\times 10^{-4}$ is also found by CHIME team
(Sand et al., 2023). However, it may be not appropriate to assume that the
$\chi^{2}$ distributions of $P$ and $\dot{P}$ obeys two-dimensional Gaussian
function. So we use the second method to give a $\dot{P}$ ranges for different
periods.

Figure 1: The reduced $\chi^{2}$ of different $P$ and $\dot{P}$. Top panel
shows the result of epoch-folding method for different $P$ and $\dot{P}$ with
the use of Equation (2). A higher $\chi^{2}$ means that the period and its
$\dot{P}$ are more reliable respectively. Bottom panel is the two dimensional
Gaussian fitting results of the top panel.

For the second method, we use the earlier 56 bursts from CHIME to establish an
active window, and then verify if the subsequent 55 bursts fall within the
active window. This method is similar to the one used to get the error bar of
the period of FRB 20180916B (Chime/Frb Collaboration et al., 2020). We derive
the $\dot{P}$ range for each period value, as shown in Figure 2. The blue part
is acceptable and the yellow area is unacceptable. Using this method, we get
the $\dot{P}$ range for the best fitting results of the period in Table 1. The
result is $-8.5\times 10^{-5}<\dot{P}<3\times 10^{-5}$ day day-1 as listed in
Table 2.

Table 2: The range of $\dot{P}$ for different periods. Period |  $\dot{P}$ range (day day-1)
---|---
16.32 | $-5\times 10^{-6}\sim 3\times 10^{-5}$
16.33 | $-2\times 10^{-5}\sim 2\times 10^{-5}$
16.34 | $-3.5\times 10^{-5}\sim 1\times 10^{-5}$
16.35 | $-4.5\times 10^{-5}\sim 5\times 10^{-6}$
16.38 | $-8.5\times 10^{-5}\sim-2\times 10^{-6}$
Figure 2: Constraints on the period derivative $\dot{P}$ and period $P$. The
range of period $P$ is adopted from Table 1. The blue area is acceptable,
which means that all of the subsequent 55 bursts can fall into the active
window predicted by the earlier 56 bursts. The yellow area is not acceptable,
which means that there are some bursts can not fall into the active window
predicted by the earlier 56 bursts.

This method is based on the assumption that the active window remains the same
over time. This assumption can be satisfied for three reasons. First,
according to Table 1 the $\dot{P}$ is relatively small, resulting in
negligible changes in the period over a given period of time. Second, for
models of FRB 20180916B such as binary model or precession model, the active
window will not change over time. Third, we believe that the active window
provided by 56 bursts is sufficiently accurate. In order to mitigate the
potential for slight inaccuracies, we extend the active window by 1.3 times
its original width for verification. We give two examples in Figure 3 to help
understand this method. The top panel of Figure 3 is an acceptable example and
we can see that the bursts fall in a stable active window which is consistent
with the prediction of the periodic model for FRB 20180916B. The bottom panel
of Figure 3 is an unacceptable example and we can see the phase of the active
window evolves over time which means the $\dot{P}$ is not suitable.

Figure 3: The relationship between MJD and phase for the bursts observed by
CHIME after folding with two different $\dot{P}$. The bursts observed by CHIME
are folded with Equation (2). The blue points represents the prior 56 bursts
and the orange points represents the subsequent 55 bursts. The top panel shows
an acceptable example with a period of 16.33 days and a $\dot{P}$ of
$1.0\times 10^{-5}$ day day-1. The bottom panel shows an unacceptable example
with a period of 16.33 days and a $\dot{P}$ of $8.6\times 10^{-5}$ day day-1.
We can see in the bottom panel that the active window has a phase shift over
time.

##  3 Constraint on the periodic models

###  3.1 The Binary models

With current observational data, we can test the periodic models for FRB
20180916B. First, the binary model is considered. The binary model explains
the 16-day periodicity by the orbital period, while the 5-day active window
can be attributed to the free-free absorption of the companion star wind
(Lyutikov et al., 2020; Ioka & Zhang, 2020; Wada et al., 2021). We compile the
bursts from recent observations detected by CHIME (CHIME/FRB Collaboration et
al., 2019; Chime/Frb Collaboration et al., 2020; Mckinven et al., 2023), LOFAR
(Gopinath et al., 2023) and Effelsberg radio telescope (Bethapudi et al.,
2023). The bursts detected by Effelsberg radio telescope can expand the
frequency to 8 GHz. In Figure 4, we show the relationship between phase and
active windows for bursts detected by different telescopes. The period used
for folding is 16.33 days, which is the best result with the epoch-folding
method. We can see that the active window is narrower and earlier at higher
frequencies. Because the higher frequency FRBs are less likely obscured by the
companion star wind, this model predicts a narrower active window in lower
frequency, which contradicts the chromatic activity discussed above (Pastor-
Marazuela et al., 2021; Pleunis et al., 2021b). However, a revised binary
model was proposed, which explains the chromatic activity of FRB 20180916B
with the intrinsic emission mechanism (Wada et al., 2021). The binary model
predicts that the DM of bursts varies within the active windows (Wada et al.,
2021; Lyutikov et al., 2020; Ioka & Zhang, 2020). So, we perform the analysis
of DM variance in different phases to test this prediction. We use all the
bursts provided by CHIME and divide them into three bins with the same phase
width. The value of $F$ distribution $F(2,108)=0.045$ and the $p$ value
$p=0.95$ are derived, where 2 and 108 in $F(2,108)$ represent the degrees of
freedom for $F$ distribution and $p$ represents the possibility to accept the
null hypothesis. In this case, the null hypothesis of this analysis is that
the mean value of DM for the three phase bins is the same. The $p=0.95$
indicates that the phase is unrelated to the DM of bursts, which contradicts
the prediction of this model.

Figure 4: Chromatic periodic activity for different telescopes: Effelsberg
(Bethapudi et al., 2023) (blue), Apertif (Pastor-Marazuela et al., 2021)
(orange), CHIME (CHIME/FRB Collaboration et al., 2019; Chime/Frb Collaboration
et al., 2020; Mckinven et al., 2023) (green) and LOFAR (Pastor-Marazuela et
al., 2021; Pleunis et al., 2021a) (red). The period used for the folding is
16.33 days, which is the best-fitting result with epoch-folding method. The
colored lines are kernel density estimations. The active window is narrower
and earlier at higher frequencies up to 8 GHz.

###  3.2 The free precession model

Another explanation of the 16.3-day period is the free precession of a neutron
star (Levin et al., 2020; Zanazzi & Lai, 2020). The five-day active window
requires a fixed emission region, which can be explained by a dipole displaced
from the neutron star center. The chromatic activity is attributed to the
curvature radiation whose characteristic frequency is dependent on the
altitude (Li & Zanazzi, 2021). This model predicts an increase of the period
of FRB 20180916B over time due to the loss of mechanical energy (Katz, 2021;
Wei et al., 2022). Although there is no obvious increasing trend for the
period of FRB 20180916B, the lifetime of free precession derived from the
error bar of $\dot{P}$ is still in an acceptable range. However, there is
another constraint on the internal magnetic field of the neutron star.

Considering a neutron star exhibiting free precession, its free precession
period is related to its rotational period as (Zanazzi & Lai, 2020)

$P_{\mathrm{pre}}=\frac{P_{\mathrm{rot}}}{\epsilon\cos\theta}.$ (3)

Here, $\theta$ is the angle between the rotation axis and the maximum moment
of inertia and $P_{\mathrm{pre}}$ is the period of precession.
$P_{\mathrm{rot}}$ represents the spin period of the neutron star. $\epsilon$
is the ellipticity. In the scenario of the free precession model, the neutron
star is deformed by the internal magnetic field $B_{\mathrm{int}}$ (Zanazzi &
Lai, 2020)

$\epsilon=\beta\frac{R^{4}_{\mathrm{ns}}B^{2}_{\mathrm{int}}}{GM^{2}_{\mathrm{ns}}}.$
(4)

Here, $\beta$ is a constant depending on the topology of the magnetic field
and typically we have $|\beta|\ll 1$ (Zanazzi & Lai, 2020). $M_{\mathrm{ns}}$
is the mass of the neutron star which is set as $1.4$ $M_{\odot}$,
$R_{\mathrm{ns}}$ is the radius of the neutron star which is set as $10$ km
and $G$ is the gravitational constant.

With time going by, the precession period will increase due to the dissipation
of mechanical energy. The period derivation can be given by (Katz, 2021)

$\dot{P}_{\mathrm{pre}}=\frac{P_{\mathrm{pre}}}{t_{\mathrm{sd}}},$ (5)

where $t_{\mathrm{sd}}$ is the spin-down age which serves as an upper limit
for the actual age of precession as discussed before (Katz, 2021). The spin-
down age $t_{\mathrm{sd}}$ can be determined by the dipole field
$B_{\mathrm{dip}}$ (Zanazzi & Lai, 2020)

$t_{\mathrm{sd}}=\frac{12c^{3}M_{\mathrm{ns}}}{5B^{2}_{\mathrm{dip}}R^{4}_{\mathrm{ns}}\Omega^{2}_{\mathrm{rot}}},$
(6)

where $\Omega_{\mathrm{rot}}$ is the angular frequency of the rotation and $c$
is the speed of light. By combining the Equation (3), Equation (5) and
Equation (6), we can get (Wei et al., 2022)

$B_{\mathrm{dip}}=\epsilon\cos\theta\sqrt{\frac{3c^{3}M_{\mathrm{ns}}P^{3}_{\mathrm{pre}}|\dot{\Omega}_{\mathrm{pre}}|}{5\pi^{3}R_{\mathrm{ns}}^{4}}}.$
(7)

By combining Eqs. (4) and (7) and considering the relationship
$B_{\mathrm{dip}}\sim 0.1B_{\mathrm{int}}$ which is commonly employed (Katz,
2021; Wei et al., 2022), we can get $B_{\mathrm{int}}$ with
$\dot{P}_{\mathrm{pre}}$ (Wei et al., 2022)

$B_{\mathrm{int}}=\frac{G}{10\beta
R^{2}_{\mathrm{ns}}\cos\theta}\sqrt{\frac{5\pi^{2}M^{3}_{\mathrm{ns}}}{6c^{3}P_{\mathrm{pre}}\dot{P}_{\mathrm{pre}}}}.$
(8)

With this equation, we show the relationship between $B_{\mathrm{int}}$ and
$\dot{P}_{\mathrm{pre}}$ in Figure 5. With the upper limit of
$\dot{P}_{\mathrm{pre}}$ derived above, the lower limit of $B_{\mathrm{int}}$
can be given. Astro-Rivelatore Gamma a Immagini Leggero (AGILE) and Swift
observed the source of FRB 20180916B in X-ray and $\gamma$-ray bands (Tavani
et al., 2020). They detected no extended X-ray and $\gamma$-ray emission, and
gave an upper limit of the internal magnetic field (Tavani et al., 2020; Wei
et al., 2022), estimated to be in the range of $10^{13.5}-10^{14.5}$G. Here,
with the conservative value $\cos\theta<1$, $\beta<0.1$ and
$\dot{P}_{\mathrm{pre}}<3.0\times 10^{-5}$ day day-1, we have
$B_{\mathrm{int}}>8.32\times 10^{14}$ G, shown in the green part of Figure 5.
It well exceeds the upper limit of $B_{\mathrm{int}}=10^{14.5}$G given by the
X-ray and $\gamma$-ray observation (Tavani et al., 2020) as shown in the red
part of Figure 5. So the free precession model cannot explain the active
period.

Figure 5: Constraint on the internal magnetic field $B_{\mathrm{int}}$ and
period derivative $\dot{P}_{\mathrm{pre}}$ for the free precession model. The
Bule line shows the relationship between $B_{\mathrm{int}}$ and
$\dot{P}_{\mathrm{pre}}$ from Equation (8). The orange line represents the
$\dot{P}_{\mathrm{pre}}=8.6\times 10^{-5}$ day day-1 and the orange area shows
the acceptable value for $\dot{P}_{\mathrm{pre}}$. The green line represents
the $\dot{P}_{\mathrm{pre}}=3.0\times 10^{-5}$ day day-1 and the green area
shows the acceptable value for $\dot{P}_{\mathrm{pre}}$. The red line shows
the $B_{\mathrm{int}}=10^{14.5}$ G and the red area represents the allowable
region for the upper limit given by X-ray and $\gamma$-ray observation (Tavani
et al., 2020).

###  3.3 The forced precession model

Forced precession of a neutron star is another model proposed to explain the
period of FRB 20180916B. One of the forced precession models is the orbit-
induced spin precession model (Yang & Zou, 2020), in which the FRB source
possesses a precession due to the influence of a companion around it. The
precession frequency angular $\Omega_{\mathrm{pre}}$ can be derived as (Yang &
Zou, 2020)

$\Omega_{\mathrm{pre}}=\frac{(4+3q)GL}{2a^{3}c^{2}(\sqrt{1-e^{2}})^{3}},$ (9)

where $q=\frac{M_{1}}{M_{2}}$ and $M_{2}$ is the mass of the neutron star and
$M_{1}$ is the mass of the companion. $L$ is the orbital angular momentum:

$L=\frac{M_{1}M_{2}}{M_{1}+M_{2}}a^{2}\sqrt{\frac{G(M_{1}+M_{2})}{a^{3}}}\sqrt{1-e^{2}},$
(10)

where $a$ is the semimajor axis of the binary and $e$ is the eccentricity of
the binary. We set $e=0$ which was used before (Yang & Zou, 2020; Wei et al.,
2022). In this scenario, the precession period is decreasing due to the
radiation of gravitational waves,

$\displaystyle-\frac{dE}{dt}$
$\displaystyle=\frac{32GM_{1}^{2}M_{2}^{2}(M_{1}+M_{2})}{5c^{5}R^{5}},$ (11)
$\displaystyle E$ $\displaystyle=-\frac{GM_{1}M_{2}}{2a}.$ (12)

Here, we assume the initial period as 16.33 days which is the best fitting
result as discussed above and calculate the period after evolution of four
years for different mass ratios $q$. Then by comparing with the
$\dot{P}_{\mathrm{pre}}$ we get above, we have $q>0.3$ as shown in Figure 6.

Figure 6: The relationship between mass ratio $q$ and the period after the
evolution of four years for orbit-induced spin model. The initial period is
set as 16.33 days which is the best fitting results. The blue line shows the
period after the evolution of four years as a function of mass ratio $q$. The
green line shows the period of 16.206 days which is the temporal results of
$\dot{P}_{\mathrm{pre}}=-8.5\times 10^{-5}$ day day-1. The green area are the
acceptable range for mass ratio $q$.

For the fall-back disk model, the neutron star will precess when the rotation
axis becomes misaligned with the normal axis of the fall-back disk (Tong et
al., 2020):

$\displaystyle\Omega_{\mathrm{pre}}$
$\displaystyle=\frac{9\epsilon}{4}\frac{M_{\theta}}{M_{\mathrm{ns}}\kappa^{3}}\Omega_{\mathrm{rot}},$
(13) $\displaystyle M_{\theta}$ $\displaystyle=M_{0}\cos\theta_{\mathrm{fb}},$
(14)

where $M_{0}$ is the total mass of the fall-back disk and
$\theta_{\mathrm{fb}}$ is the angle between the rotational axis and the normal
direction of a fall-back disk. $\kappa$ is a dimensionless parameter can be
set as 1 (Tong et al., 2020; Wei et al., 2022). The evolution of $M_{0}$ can
be neglected, so (Wei et al., 2022)

$\displaystyle\dot{\Omega}_{\mathrm{pre}}$
$\displaystyle=\frac{9\epsilon}{4}\frac{M_{\theta}}{M_{\mathrm{ns}}\kappa^{3}}\dot{\Omega}_{\mathrm{rot}},$
(15) $\displaystyle\dot{\Omega}_{\mathrm{rot}}$
$\displaystyle=\frac{\sin^{2}\theta}{t_{\mathrm{sd}}}\Omega_{\mathrm{rot}}.$
(16)

where $\theta$ is the angle between the rotational axis and the precession
axis. With the two equations and with $|\dot{P}_{\mathrm{pre}}|\leq 8.5\times
10^{-5}$ day day-1, we can get

$B_{\mathrm{int}}\geq 8.41\times
10^{14}\mathrm{G}|\sin\theta|\frac{0.1M_{\odot}}{M_{0}\cos\theta_{\mathrm{fb}}},$
(17)

Since there are many uncertain parameters, the fall-back disk model can not be
constrained by the internal magnetic field.

However, the phenomenon that the centers of the active windows for different
frequency bands are in different phases is challenging in the context of the
forced precession models (Li & Zanazzi, 2021). As shown in Figure 7, the
active windows of the forced precession models for different frequency bands
show no phase shift, which contradicts previous observations (Li & Zanazzi,
2021).

Figure 7:  The predicted burst numbers of forced precession model for
different frequency bands: 110-188MHz (red), 400-800MHz (green), 1.36-2GHz
(orange) and 4-8GHz (blue) under the assumption that the FRBs are emitted due
to the curvature radiation. The frequency bands given in this figure are
consistent with the frequency bands of LOFAR (Pastor-Marazuela et al., 2021;
Pleunis et al., 2021a), CHIME (CHIME/FRB Collaboration et al., 2019; Chime/Frb
Collaboration et al., 2020; Mckinven et al., 2023), Apertif (Pastor-Marazuela
et al., 2021) and Effelsberg (Bethapudi et al., 2023).

###  3.4 The ultra-luminous X-ray binary model

Except the neutron star, FRBs can be also generated from an ultra-luminous
X-ray binary, in which there are a compact object and a companion star
undergoing sustained super-Eddington accretion (Katz, 2020; Sridhar et al.,
2021). In this case, the 16-day period can be attributed to the precession of
the compact object. The chromatic activity may result from the curvature of
the quiescent jet cavity due to the motion of the disk winds driven by
precession motion. However, in order to explain the extremely high luminosity
of FRBs, the system must undergo unstable mass transfer whose lifetime is
about (5-100)$P_{\mathrm{orb}}$ (Sridhar & Metzger, 2022). For a 16-day
precession period, the $P_{\mathrm{orb}}$ is less than one day, which means
the lifetime of the system is less than 100 days and this is much less than
the active duration of FRB 20180916B. Another difficulty is the evolution of
RM. This model predicts that the $|$RM$|$ of bursts decreases when the DM also
decreases (Sridhar & Metzger, 2022). However, the observed data shows a
decreasing trend in the $|$RM$|$ of the bursts, while the DM of bursts remains
constant.

###  3.5 The ultra-long rotation model

For the ultra-long rotation model, the period of FRB 20180916B is considered
as the rotational period of a neutron star. The spin down of the rotation is
enhanced due to the particle winds or a fallback accretion. So the neutron
star can still possess strong magnetic field to power FRBs (Beniamini et al.,
2020). The phase shift and different width of active window for different
frequency bands can be explained by the the curvature radiation of a displaced
dipole consistent with the explanation of free precession above (Li & Zanazzi,
2021). The period of rotation will freeze (Beniamini et al., 2020) which is
consistent with the $\dot{P}$ derived from observation. Although it has been
not found a neutron star with such a long rotational period, recently two
observations reported their discovery of ultra-long period magnetars
(Beniamini et al., 2023) and radio transient (Hurley-Walker et al., 2023),
which extended the population of radio transients with ultra-long period. PSR
J0901-4046 was found to have a period of of 76 s (Caleb et al., 2022) and
GLEAM-X J162759.5 was argued to be a magnetar with a period of 1091 s (Hurley-
Walker et al., 2022). Recently, a 21-min period radio transient GPMJ1839-10
was reported (Hurley-Walker et al., 2023). Therefore, the discovery of neutron
stars with ultra-long rotational periods is promising in the future.

With the help of the Hubble Space Telescope and 10.4 m Gran Telescope
Canarias, an optical and infrared imaging as well as integral field
spectroscopy observations were presented on FRB 20180916B (Tendulkar et al.,
2021). These observations suggest that the source of FRB 20180916B is 250 pc
away from the nearest young stellar clump where there are lack of stars to
create a magnetar (Tendulkar et al., 2021). If the neutron star is born in the
star-forming region and travels to the place of FRB 20180916B, it will need
800 kyr to 7 Myr which exceeds the active age of neutron stars of 10 kyr.
However, there still exits the possibility to create a neutron star in the
place of FRB 20180916B. Firstly, a compact-binary mergers or accretion-induced
collapse can substitute for the core collapse of a massive star to create a
neutron star (Margalit et al., 2019; Wang et al., 2020). In addition, a B star
ejected from the dense stellar cluster can possess high velocities ($>30$ km
s-1) through binary interactions. With this velocity, the B star is able to
move to the region of FRB 20180916B and produce the neutron star with a
supernova explosion. Because of that, utilizing a neutron star as the source
of FRB 20180916B is still possible.

###  3.6 A self-consistent model for FRB 20180916B

Another crucial feature of FRB 20180916B is the increase of the RM with the
stability of DM in the meanwhile. This phenomenon is difficult to explain in
the context of the ultra-long rotation model. For isolated neutron stars, the
value of RM is stable. Below, we propose a self-consistent model for FRB
20180916B as shown in Figure 8, which can accommodate the wealth of
observational features for FRB 20180916, especially the periodic activity and
RM variation. We consider a massive binary containing a slowly rotational
neutron star and a massive star with large mass loss. Radio bursts are
possibly generated in the magnetosphere through curvature radiation (Yang &
Zhang, 2018; Lu et al., 2020). The period can be caused by the ultra-long
rotation, and the variation of RM is attributed to the mass loss of the
massive star. Within this model, RM variations are caused by the interaction
between the radio signal and the magnetized decretion disk or stellar wind
during periastron passage of the neutron star. An interacting binary system
featuring a magnetar and high-mass stellar star had been proposed to explain
the RM variations of FRB 20201124A (Wang et al., 2022) and FRB 20190520B (Wang
et al., 2022; Anna-Thomas et al., 2023). In this scenario, the variation of RM
is unrelated to the period (Zhao et al., 2023). For a large space of model
parameters, this model can explain the increase of RM and the stability of DM
for FRB 20180916B (Zhao et al., 2023). In this model, the variation of RM is
also periodic, which can be tested by future observations, especially the
CHIME telescope.

Figure 8: The Schematic diagram of the self-consistent model for FRB
20180916B. The green cricle corresponds to the neutron star with a ultra-long
rotation period. The orange circle represents the massive star with stellar
wind shown as yellow part. The 16-day period is due to the ultra-long rotation
of the neutron star and the variation of the RM is attributed to the orbital
motion of this binary system.

##  4 Conclusions

In this work, we calculate the period and $\dot{P}$ with the bursts detected
by CHIME and LOFAR in Sec 2 and find the period keep stable over time. Then,
we use the observational data to constrain the periodic model for FRB
20180916B. We find the ultra-long rotation model appears to be the best-fit
periodic model for FRB 20180916B. However, the previous ultra-long rotation
model considers an isolated neutron star which contradicts the recent
observation of RM. So we propose a self-consistent model, which is a massive
binary containing a slowly rotational neutron star and a massive star with
large mass loss. This modified model can naturally accommodate the wealth of
observational features for FRB 20180916B. Moreover, the RM variation of this
model is periodic, which can be tested by future observations.

## Acknowledgements

This work was supported by the National Natural Science Foundation of China
(grant No. 12273009), and the National SKA Program of China (grant No.
2022SKA0130100). This work made use of data from FAST, a Chinese national
mega-science facility built and operated by the National Astronomical
Observatories, Chinese Academy of Sciences. We acknowledge use of the
CHIME/FRB Public Database, provided at https://www.chime-frb.ca/ by the
CHIME/FRB Collaboration.

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