11institutetext: University of Saskatchewan, Saskatoon SK S7N 5C9, Canada

# Integrating Dark Pattern Taxonomies

Frank B.W. Lewis 11 0000-0001-6929-4455<EMAIL_ADDRESS>Julita Vassileva 11
0000-0001-5050-3106<EMAIL_ADDRESS>
###### Abstract

The problem of “Dark Patterns” in user interface/user experience (UI/UX)
design has proven a difficult issue to tackle. Malicious and explotitative
design has expanded to multiple domains in the past 10 years and which has in
turn led to multiple taxonomies attempting to describe them. While these
taxonomies holds their own merit, and constitute unique contributions to the
literature, their usefulness as separate entities is limited. We believe that
in order to make meaningful progress in regulating malicious interface design,
we must first form a globally harmonized system (GHS) for the classification
and labeling of Dark Patterns. By leaning on network analysis tools and
methods, this paper synthesizes existing taxonomies and their elements through
as a directed graph. In doing so, the interconnectedness of Dark patterns can
be more clearly revealed via community (cluster) detection. Ultimately, we
hope that this work can serve as the inspiration for the creation of a glyph-
based GHS for the classification of Dark Patterns.

##  1 Introduction

After various catastrophes regarding the inadequate research and risk
communication regarding chemicals, it was decided at the 1992 Rio Earth summit
to begin the formation of a Globally Harmonized System (GHS) for the
classification and labeling of chemicals[19]. An international team of experts
was posed with the task of creating immediately intelligible warning labels
and data-sheets that could unify hazard communication globally. This was a
response to tragedies like DDT, Asbestos, and Thalidomide. These products did
exactly what they promised. DDT kills insects, asbestos is an excellent
insulator, thalidomide relieves symptoms of morning sickness. However, the
unintended damage caused by their use was immense. Similarly, the design of
shopping apps help in finding something to buy, the design of social media
applications facilitate connection, and video games can be a pleasurable
experience that builds communities and forms friendships. Unfortunately, often
cooperate greed is the driving force behind system design, and the so called
”Dark Patterns” [4] in the interface design transform seemingly harmless
benefit-providing systems into instruments of user exploitation. Predatory
Monetization[14], exploiting obsession[1], and disguised data collection[11]
are examples of dark patterns in the design of interactive technologies. The
massive and unconscious exposure to dark patterns can lead users to waste time
and money, to frustration, and even to mental health issues. Yet many users
are either unaware that they are victims of deliberate design ”traps” or
acquiesce to use the application because it offers some functionality they
need. If there were a unified system for labeling dark patterns in user
interface design, it would be possible to regulate their use similar to the
regulation of harmful chemicals. It would also be possible to educate
consumers and create appropriate warnings in the description of interactive
applications that use such patterns. Our vision is that a Globally Harmonized
System for Dark Patterns in software interface design is needed and our work
presented in this paper is a step in this direction.

##  2 Background and Related Work

This section provides an overview of the previous works on dark patterns that
we are aware of and defines the research questions we set out to answer.

###  2.1 Regarding “Dark” Patterns

The term ”Dark Pattern” (DP) was coined by Harry Brignull, a UK-based user
experience designer and consultant, in 2010. Brignull identified deceptive
User Interface (UI) techniques that trick users into actions they might not
have otherwise taken and created a website to raise awareness about them. This
term has since become widely recognized in discussing and critiquing unethical
design practices in digital interfaces. Recently, there has been some
controversy over the phrase, and motions have been made to replace the term
with “Deceptive”/“Manipulative” Design. We consciously made the choice to
stick with the original term because alternatives (i.e. “Deceptive”) describe
only a part of what such patterns can achieve. Manipulation, coercion, and
exploitation are equally common outcomes of interaction with these designs.
Thus relegating them to simple deception limits our perception of their depth.
This is not to downplay the legitimate concern surrounding the use of the term
“Dark” patterns, related to a possible connotation with race, but for a lack
of a commonly used and familiar term in UI and UX literature that encompasses
all the possible different aspects of these designs, we will use “Dark” in
this paper. Next, we present briefly the existing classifications of dark
patterns since 2010.

###  2.2 Related Works

The first taxonomy of dark patterns by Brignull (2010) [4] was derived through
personal observations and reporting, without a documented methodology of its
creation. Although Brignull’s work lacks scientific rigour, it captures the
essence of dark patterns and is considered a seminal work in the area. The
taxonomy of Conti & Sobiesk (2010) [8] focused on dark patterns across
domains. A year-long study involving 22 undergraduate students gathering dark
patterns was combined with input from roughly 75 participants of the “Hackers
of Planet Earth” Conference to create a multi-dimensional taxonomy of Dark
Patterns. Zagal et al. (2013) [21] focused on the domain of games. It was
constructed by considering system interaction as a contract from which ethical
boundaries could be derived between users and designers. Greenberg et al.
(2014) [11], using the “affinity diagramming” practice, clustered and
speculated upon examples of potential dark-pattern utilization within the
context of Proxemic Interactions . Rooted in the domain of user privacy, Bosch
et al. (2016) [5] constructed their taxonomy by considering established
privacy design patterns and deriving dark patterns from their antithesis.
These derived patterns were then evaluated against the known DPs at the time
(i.e. Brignull’s). This work was considered as a potential basis seeing as its
roots in design standards makke it domain independent, however its focus on
privacy makes it less generally applicable than Ahuja et. al’s[1]. [4]). Grey
et al. (2018)’s taxonomy [10] was constructed from examples across domains.
Examples of dark patterns were collected, catalogued, and sourced iterativly
over 2 months. The constant comparison method[17] was then applied along with
document analysis to describe the nature of the dark patterns found,
categorized according to Brignull’s[4] taxonomy before being re-categorized
via open coding. The resulting taxonomy is thus structured around dark
strategies and designer motivation rather than around context and content as
Brignull’s[4]. The Norwegian Consumer Council (NCC) (2018) analyzed the design
and wording of update prompts from Facebook, Google, and Microsoft from a data
protection standpoint after GDPR regulations were enacted[7]. Situated in the
domain of “Home Robots”, Lacey & Caudwell (2019) [15] did not explicitly
propose a taxonomy, but their work was flagged as such by Ahuja et al.[1] for
its proposal that “Cuteness” can be a dark pattern because a robot’s
“cuteness” encourages users to overlook or completely miss their devices’
data-collecting capabilities. By crawling and scraping image samples from
various e-commerce sites, Mathur et al. (2019) [12] abstracted a set of five
dark pattern attributes, which were then applied to 15 dark patterns within 7
super-categories, some of which have direct counterparts in Brignull’s
taxonomy [4]. The National Commission for Informatics and Liberty (CNIL)
(2020) [6] built their taxonomy with the goal of consumer protection, though
no formal methodology was documented in the document. Many of its items tie
directly to Brignull’s original set (i.e. “Trick Question”[4, 6]) while others
simply go by another name (i.e. Brignull’s “Bait and Switch”[4] and CNIL’s
“Bait and Change”[6]). Grey et. al (2020)’s work [9] focused on “Asshole
Design” as flagged by users of the Social Media platform Reddit. Posts on
Reddit were analyzed and open coded through several rounds of iterative
content analysis. This process rendered six dark patterns. Bongard-Blanchy et
al. (2021) administered an online survey to participants with the aim of
gauging user awareness of dark patterns. The patterns used to measure user
awareness constitute Bongard-Blancey’s contribution to the area of dark
pattern taxonomies[3]. Using techniques inspired by Value Sensitive Design and
scenario construction, Mhaidli & Schaub (2021) [13] critically examined some
potential advances in virtual/augmented/mixed reality (XR) technology
regarding their ethical implications. Scenarios and narratives were
constructed and used to generate a set of five dark patterns that could
operate in this space. Petrovskaya & Zendle (2021) [14] focus on the issue of
Predatory Monetization in the domain of games. By using the United Kingdom’s
unfair trading regulations, researchers released a survey requesting reports
of unfair/aggressive monetary encounters online. The results were transformed
into a two-tiered collection of 36 dark patterns in eight super categories.
Westin & Chiasson (2021) [18] likewise focused on a single dark pattern -
“Fear of Missing Out (FoMO) centric design” - in the context of user privacy.
By utilizing inductive grounded theory, researchers dimensionalized and
categorized design interactions to pose the idea that the core issue is not
with individual patterns but with their aggregated effects within “dark
digital infrastructure” . Wu et al. (2021) generated their taxonomy by
observing and coding live-stream shopping interactions on Taobao and TikTok.
This taxonomy is interesting, but focuses more on the habits of the streamers
than on interface design[20]. Many of their identified patterns have been
removed from our integration process for this reason. The work of Ahuja et al.
(2022) unifies existing taxonomies with respect to their relation to user
agency. This is, to our best knowledge, the most recent work in the area. It
was able to describe and categorize many existing taxonomies and provides a
good basis for further unification and integration.

###  2.3 Summary and Outlook: Synthesizing Existing Taxonomies

As previous taxonomies become the fuel for the next, existing literature seems
to have entered an endless cycle of splitting and joining dark pattern types.
It appears that research in Dark Pattern taxonomies has reached a saturation
point and researchers should begin the work of their integration to create a
global standard if we are to mitigate dark patterns to any meaningful capacity
- a process which this work strives to begin.

Our work represents an effort in this direction. We do not define any new dark
patterns but instead seek to reveal which of the existing ones are prevalent,
which ones are so similar that can be considered the same, and to uncover how
dark patterns relate to each other by representing all taxonomies within a
single graph (with a couple of exceptions that are too domain specific). Using
methods borrowed from network analysis we reveal naturally forming communities
of dark patterns. We must clarify that we use the term ”community” in the
sense it is used in the area of network analysis, as a group of nodes that are
similar in some specific features. The dark pattern communities provide a
level of abstraction that can simplify the task of identifying the pattern
employed by a suspect UI as it can be compared / contrasted with other
patterns in the relevant community. Our future work will define also
heuristics against which suspect UI designs can be evaluated with respect to
their ”darkness”.

The paper focuses on the following research questions:

###  2.4 Research Questions

  * •

RQ1: What general Dark Pattern communities emerge from existing literature?

  * •

RQ2: Can a process of heuristic evaluation be used to identify Dark Patterns
based on these emerging communities?

In the next section we present the methodology we used to construct the
integrated Dark Patterns taxonomy and the resulting communities.

##  3 Methodology

To construct this integrated taxonomy, we started with the most comprehensive
taxonomy to date (Ahuja et al. 2022[1]), and reviewed the papers relating to
its contained taxonomies. In fact, the early versions of our taxonomy were
simply verbatim graphical representations of Ahuja et al.’s work. What we add
to Ahuja et al.’s, as well as other taxonomies, is that we make explicit the
relationships between their contained dark patterns. This allows to describe
in detail exactly how they relate within different contexts.

When seeking to graphically represent an integrated taxonomy, many of the
previously mentioned taxonomies were considered as a base-taxonomy. We settled
on using Ahuja et. al’s work they have unified more previously defined
taxonomies similar works. What further distinguishes this taxonomy is its
roots in philosophical conceptualizations of autonomy. By basing the taxonomy
in ideals rather than specific domains, applications, or common industry
practice, its potential for generalization exceeds that of many taxonomies
while being able to completely describe them. Thus, it provides a solid
foundation for building systems that can track and identify recurring dark
patterns across domains. Moreover, while Ahuja et al.’s work does define some
of its own taxonomy items, the majority of them come from previous work. In
doing so, Ahuja et al. not only provides a common mapping, but does not
further dilute the Dark Pattern space, making the construction of our initial
graph trivial.

###  3.1 Process

Our first step was to represent he Ahuja et al.’s, taxonomy graphically. We
chose to use a directed graph with two node types and two edge types. Taxonomy
Nodes are nodes with represent taxonomies, and are named after their first
author. These nodes have only outward edges toward Pattern Nodes. Pattern
nodes have incoming edges from either patterns that implement/employ them, or
from the taxonomy they belong to. Likewise, pattern nodes only have outgoing
edges to patterns that they implemented, or employed (utilized). This allows
us to reveal which patterns are most commonly used/implemented across the
taxonomies by finding the pattern node with the highest number of incoming
links or in-degree.

In the first version of the graph, Ahuja et al.’s taxonomy was followed
exactly with no modifications (i.e. merging similar patterns). Minor versions
(i.e. 2.1, 3.2) were formed by analyzing the literature surrounding similar
patterns, and making an informed decision to merge them into a single node.
Each iteration of this process constituted a minor revision. A log of which
nodes were merged and why can be found in our project wiki(LINK REMOVED FOR
BLIND REVIEW).

We used an iterative process of community detection and node merging based on
pattern similarity to refine our graph. For this we used a software tool for
network analysis called Gephi.

Taxonomy Version 1: The first version of the taxonomy (1.0) is a verbatim
representation of Ahuja et al.’s[1] original taxonomy node/edge policy. Once
this taxonomy had been added, each of the taxonomies surveyed by Ahuja et
al.[1] were added in stages along with any patterns that did not make it into
Ahuja et al.’s original graph. This constituted version 1.1.

Taxonomy Version 2: The second version of the taxonomy sought to reduce
duplicates and condense the graph to a saturation point (no merge-able nodes
exist). Though time constraints prevented us from reaching saturation,
emergent communities were evident even after only a few iterations of the
process described in Figure1.

Taxonomy Version 3: Although we are still discovering the occasional merge
candidate, version 3 of the graph is nearly saturated. This iteration of the
taxonomy removed the Author-type nodes to reduce the graph complexity and
improve the ability of community detection to reveal prominent patterns and
clarify their interrelation. It also eliminated single-node communities either
by integration into larger communities, merging with identical nodes, or
removal due to irrelevance. This is the version of the graph that we have
based our analysis on.

####  3.1.1 Node-Merging Process

  1. 1.

Utilizing Gephi, we ran the Fast Unfolding algorithm[2] with a resolution of
1.0 on a randomized version of our graph to detect communities amongst the
nodes. We noticed that running detection would often produce a varying number
of communities so the detection was run five times with the number of
communities discovered most often being selected at the end. Should there be a
tie, the next tie breaking occurrence would be selected.

  2. 2.

After communities were detected, they were analyzed for patterns similar
enough to have their nodes merged, or related enough to form an edge that was
not previously identified in literature. When such nodes were found, they were
flagged as a merge candidate and the process continued.

  3. 3.

Once all of the change candidates were identified, the reasoning behind their
merge/new relation was explained, documented, and either approved or rejected.

  4. 4.

Approved merges and edges were enacted on the graph which would result in a
new minor version and signify that the process could iterate once again.

  5. 5.

Once saturation of nodes is reached the graph has been condensed enough, and
the iteration can cease.

See Fig1 for a graphical representation of this process.

Figure 1: The construction and reduction process applied to Ahuja et al.’s
2022 work.

###  3.2 Detected Communities and Prominent Nodes

The full integrated taxonomy is presented in Fig.2.In our research, we
detected 10 communities centered around 4 major patterns (Information Hiding,
Deceptive Information, Forced Action, and Misleading Information). In this
section we shall discuss these communities and their contained nodes in detail
from largest to smallest community in terms of members. Due to space
constraints the graphs representing in detail each community can be found in
Appendix available online.

Figure 2: Full Integrated Taxonomy 3.2

Forced Action \- Main Pattern: Forced Action This community captures dark
patterns which use their design to force or otherwise bend users into certain
interaction patterns. Many of the DPs it contains come from the games domain,
through gamification however, they exist in nearly any interactive system.
Whether in the form of prompts that must be forcefully dismissed by the user
(Nagging[10], Interruption[8]), monetary barriers to system use (Pay to
Win/Skip & Pay or Wait/Grind[14, 21]), or barriers demanding data in exchange
for the service(Impenetrable Wall[6]), the patterns in this community restrict
or coerce users into behaving a certain way.

Deceptive & Misleading Information \- Main Patterns: Deceptive

Information, Misleading Information This community deals with cases where the
information presented to the user is not necessarily false but is deceptive or
misleading in a way that meets the designers goals to influence the users.
This includes cases where user interactions with the UI lead to unexpected or
contradictory results (i.e. Wrong Signal[6], Manipulating Navigation[8]) and
when the UI has lead the user to believe things about products that are
untrue.

Regarding Consent \- Main Patterns: Lack of Consent, Implied Consent

This community contains patterns which relate to users ability/inability to
consent as well as scenarios where their consent was blatantly ignored.
Patterns like “Automating the User Away”[9] remove the ability for users to
consent while patterns like “Trick Question”[4] raise issue about whether
consent was informed. This community also deals with the common scenario of
default settings being skewed to meet the goals of the designers over the
users through patterns like “Bad Defaults”[5], “Default Sharing”[6]. This
community also seems to have captured cases where visual interference and bias
have played a role in influencing user interaction as it contains patterns
like Misdirection[8], Interface Interference[10], and Visual Bias[1].

Information Hiding \- Main Pattern: Information Hiding With an in-degree of
27, Information Hiding is the most utilized pattern in the taxonomy. None of
the other nodes in its community have near the same amount of utilizations
though they appear to converge around the theme of monetization, specifically
in-game currencies. Seeing as in game currencies serve to hide, obscure, or
otherwise disconnect user cognition of the actual value of items for sale[14],
this would make sense. Likewise, if we wanted to stop a user from comparing
two products (Price Comparison Prevention[4] or Comparison Obfuscation[6]),
hiding this information from the user will achieve this goal.

Regarding Emotions \- Main Pattern: Emotional Bias This community comprises
patterns which induce and/or exploit user emotions. Emotional Bias is the
engine behind patterns like “Limited Time Offers”[14] which can induce “fear”
of loss. “Confirmshaming” [4] is another long-standing pattern in the DP
space. It is difficult to determine when a line is crossed to make some of the
patterns of this community exploitative. When we use an interface that suits
our needs and helps us to achieve our goals, we feel good. Does this mean that
the interface is utilizing dark patterns as it “Induced Artificial
Emotions”[13]? Not necessarily, good UI/UX design should by its nature be
pleasant to interact with, or at least deliver an experience that both the
user and the designer are expecting. An interface pattern containing an appeal
for donation from the user if they enjoy the software would not be considered
a dark pattern, even if it happens to evoke a feeling of shame in the user
because the intention in the design is obvious and there is no hidden
manipulation. If emotions are induced such that they put the user in a state
to the benefit of the designer, they cannot truly be said to be behaving as
they would normally. Whether or not an offer is legitimately “Limited Time”,
communicating this to the user with the goal of purposefully inducing
fear/panic of missing an opportunity is emotionally manipulative and
exploitative.

Lack of Options \- Main Pattern: Lack of Options The “Lack of Options”[1]
community is quite similar to that of Forced Action. This is because when
presented only a limited and curated set of potential interactions, users are
essentially forced into choosing a path forward, none of which may be
agreeable to them. A common example of this is in any “Terms of service”
agreement. This is not to say that all such agreements are innately dark, only
that they can be used to achieve patterns like “Bundled Consent”[3] where
users must accept aspects of a system that they may not agree to in order to
achieve others. This community also features many game-specific patterns to
the effect of: “Pay or interact with an incomplete, under-powered, or useless
system”[14]. This essentially infringes on user agency by offering the
ultimatum: “Play by our rules, or do not play”. Users could, of course, take
their business elsewhere but this too runs into a “lack of options” problem.
Competitors may not deliver the desired quality and are likely offering their
own ultimatum to users anyway, so again users are essentially forced into
compliance for lack of desired options.

Regarding Privacy \- Main Pattern: Privacy Zukering This community captures
patterns involved in tricking users into sharing as much data as possible.
Privacy Zukering is a pattern that has stood the test of time. For example
“Obscure”[5] and “Information Framing”[1, 7] constitute patterns that can
achieve Privacy Zukering, whereas “Forced Enrollment” [12, 5] and “Safety
Blackmail”[6] are examples where it is applied. Though this community is
small, it reveals the mechanics of data collection and forms that it might
take.

Pressurizing \- Main Patterns: Scarcity, Time Pressure, Urgency This community
deals with patterns that pressurize the user. This is normally rooted in “Time
Pressure”[1] but is further specialized into instances of “Scarcity” or
“Urgency”[12], both of which have denote actions with consequences if not
acted upon soon. Patterns in this community usually create an emotion - fear
of missing an opportunity, so there are links between the patterns in these
communities.

Friction \- Main Pattern: Asymmetric Effort Previous version of the graph
struggled to separate “Asymmetric Effort”[1] from “Forced Action”[1, 10, 7,
12]. Asymmetric effort simply deals with scenarios where the effort to preform
an action are disproportionate to the effort required to undo them. Design
friction describes ways in which effort can be increased/reduced within a UI,
some of which are represented within this community (i.e. “Obfuscating
Settings”[6], Obstruction[10].

Bosch Outcasts \- Main Patterns: Maximize, Preserve Occasionally in the graph
construction process, certain communities remain around their defining author.
This was often the case when the items defined in their taxonomy were not
easily linked to rest of the graph. Such communities were labeled “outcasts”.
We speculate that this community has remained outcast because of its unique
construction. Reversing privacy-by-design principles to form their taxonomy
members put them at a higher level of abstraction. “Maximize”[5] for example,
is similar to the concept of “Privacy Zukering”[4] but at a system level, that
is, a system can maximize the amount of user data collected through Privacy
Zukering. Similarly “Preserve”[5] exists on a system level and describes
scenario’s where user data is stored in a non-aggregated form[5]. “We never
Forget“[11] and “Unintended Relationships”[11] are examples of patterns
(outside of Bosch et al.’s) that may preserve data this way, though because
the data lives on the server-side, this could not be discerned by a user. If
anything, the fact that this community has remained outcast for 3 series of
revisions suggests a gap in our reduction process.

##  4 Discussion

First we will revisit our research questions to asses if our work was able to
address them. Then we will look briefly at the implications of our work with
respect to the construction of a Globally Harmonized System (GHS) for dark
patterns formulated through heuristic evaluation before detailing our road-map
for the project in the future.

###  4.1 Research Questions Revisited

Now that we have a better idea of what the integrated taxonomy contains, we
will return to our research questions.

RQ1: What general Dark Pattern categories emerge from existing literature?

The present of the graph (3.2), continues to reveal distinct DP communities as
we outlined in section3.2

RQ2: Can a process of heuristic evaluation be used to identify Dark Patterns
based on emerging categories?

We attempted to form heuristics out of the resulting graph as early as version
2.1 and though it did render results, they are only meant as a proof of
concept 3. Current work on this front is applying Straussian Grounded
Theory[16] using the Dark patterns in version 3.2 and their definitions as
source material in an effort to contextualize the patterns and explicitly
define their relation to one another. We will revisit this in the following
section.

###  4.2 Future Work

As we progress to the next stage of our work, applying Straussian Grounded
Theory[16] (SGT), we have discovered only a handful of new merge candidates.
Because of this, we anticipate reaching a final set of Dark Patterns shortly
after we complete the axial coding. Future work focuses on using SGT to
contextualize and define edge types (relationships) between dark pattern nodes
(i.e. consequence of, cause of, property of, etc.). Preliminary efforts on
this front have already shown promising results. SGT has also helped in the
identification and categorization of dark patterns, their properties, and
dimensions. Higher-level categories rendered by this process, along with the
graph, will serve as a foundation to construct and justify design heuristics
capable of identifying malicious design. Finally, we will construct examples
of a glyph-based hazard communication system by mapping heuristic violations
to glyphs that can be included in the application/game description to inform
users, similar to the example shown in Fig.3. With these examples completed,
we will evaluate the system’s understandability, clarity, and applicability to
malicious interfaces across different domains (e-commerce, social media,
games) with law students, UI designers, and users. We hope that our work will
inspire regulators, industry standards developers, software professionals, and
UI designers to implement a GHS-similar standard notation to warn and protect
users from dark patterns in interactive applications.

Figure 3: Example glyph: Intermediate Currency

##  5 Conclusion

Everyday interaction with computers has become an essential prerequisite to
participating in our society. If the majority of users are exposed to, but
unaware of, dark patterns, the potential for harm and exploitation is
unacceptably high. A domain-independent, universally understood language
describing dark patterns is a critical prerequisite to creating regulation
that can outlaw the most harmful dark patterns and also effective user
education.

The integrated taxonomy presented here does not claim to be the ultimate
solution to the issue of hazard classification and communication in UI/UX
design. To define a language or classification system with that rigour would
require an international, interdisciplinary team of experts akin to that which
formed the GHS for hazardous materials. The contribution of our work is in
demonstrating a method for creating an integrated taxonomy based on all
available previous ones. By integrating the strongest examples of Dark Pattern
taxonomies in a graph structure, bolstered with heuristics to evaluate
against, our work could serve as a starting point for developing a GHS for
dark patterns.

##  6 Acknowledgements

This research was supported by NSERC through the Discovery Grant Program
RGPIN-2021-03521 to the second author.

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# Implementation of Allan Standard Deviation Technique in Stability Analysis
of 4C31.61 Quasar Position

Jessica Syafaq Muthmaina[1] Ibnu Nurul Huda[2] Dwi Satya Palupi[1]
[1]Department of Physics, Faculty of Mathematics and Natural Sciences,
Universitas Gadjah Mada, Sekip Utara, BLS 21, Yogyakarta 55281, Indonesia
[2]Research Center for Computation, National Research and Innovation Agency
(BRIN), Jalan Raya Jakarta-Bogor, 16915 Bogor, Indonesia
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

The International Celestial Reference Frame (ICRF) plays an important role in
astronomy and geodesy. The realization of ICRF is based on the position of
thousands of quasars observed using the Very-Long Baseline Interferometry
(VLBI) technique. Better quality of ICRF is achieved when the position of the
quasars is stable. In this study, we aim to analyze the stability of one of
the quasars in ICRF called 4C31.61 (2201+315). We performed VLBI data analysis
by using Vienna VLBI and Satellite Software (VieVS) to get the position of the
quasar. We also used the data of the quasar’s position from the Paris
Observatory Geodetic VLBI Center. We examined the stability of the quasar
position by using the Allan standard deviation technique. We found that the
quasar 4C31.61 (2201+315) has a stable position with the dominance of white
noise across the majority of time scales.

##  1 Introduction

Very Long Baseline Interferometry (VLBI) is an observational technique that
use some widely separated radio telescopes to observe astronomical radio
source simultaneously. VLBI has been measuring radio source positions since in
the mid-1960s [1]. VLBI has contributed to several domains. For instance, it
is the only technique that can monitor the Earth Orientation Parameters
completely. VLBI has contributed also to the realization of Celestial and
Terrestrial Reference Frame [2]. Indonesia has several ongoing radio telescope
construction projects, such as Bosscha Observatory, located in Bandung city,
and National Observatory, located in Timau Mountain. These telescopes are
targeted to join the global Very Long Baseline Interferometry (VLBI) network
[3].

A celestial reference frame has been used to observe the position of celestial
objects with high precision. Originally, the International Celestial Reference
Frame (ICRF-1) was proposed in 1998 to replace FK5 [4]. This ICRF is based on
Very Long Baseline Interferometry (VLBI) observation over 212 extragalactic
radio sources distributed over the entire sky. ICRF-1 was refined by ICRF-2
through incorporating more extragalactic radio sources [5]. ICRF-3 was
released in 2020 by offering increased precision and encompassing a greater
number of extragalactic radio sources compared to its predecessors [6].

One of the important issues in the realization of ICRF is the position
stability [6]. It has an implication for the quality of VLBI products.
Previous studies have dealt with this problem [7, 8, 9]. In this study, we
focused on the use of recent VLBI observation for studying the quasar position
stability. We analyzed the stability of one of the quasars named 4C31.61
(2201+315) by using the Allan standard deviation technique.

##  2 Data and Method

The position of the quasar is given in Right Ascension ($\alpha$) and
Declination ($\delta$). Here we considered the quasar position from two
sources. First, we adopted the data from the Paris Observatory VLBI Center
(https://syrte.obspm.fr/~lambert/ivsopar/). Second, we conducted a VLBI
analysis by using software Vienna VLBI Software or VieVS [10]. The VLBI
analysis was done by estimating the source positions as session-wise
parameters. The reduced least squares adjustment technique was used to
estimated the parameters. We used 6342 VLBI sessions in our calculation. We
used ICRF-3 [6] and ITRF-2020 [11] as our Celestial and Terrestrial Reference
Frame respectively. TPXO72 [12] was considered for the tidal oceanic loading
model and APL-VIENNA [13] for the atmospheric tidal and non-tidal loading
model. The Earth Orientation Parameters were estimated with respect to the EOP
C04 series [14]. Here we used 33 years of VLBI observation data ranging from
1990 to 2023.

We analyzed the stability of quasar 4C31.61 by using the Allan standard
deviation technique [15]. It is a technique that detect the type of the noise
in the time series as a function of the time scale. The overlapping Allan
standard deviation is given as follows [9]:

$\sigma^{2}(\tau)=\frac{1}{M-2m+1}\sum^{M-2m+1}_{j=1}\frac{1}{2}\left(\frac{1}{m}\sum^{j+m-1}_{i=j}(\bar{y}_{i+m}-\bar{y}_{i})\right)^{2}$
(1)

where $M$ is the number of possible windows in the time series,
$\tau=m\tau_{0}$ is the time scale, $\tau_{0}$ means the mean sampling, $m$ is
the integer, $\bar{y}$ mean of sample with considered time interval $\tau$.
The module Allantools (https://github.com/aewallin/allantools) was used to
calculate the overlapping Allan deviation.

The stability of quasar positions was analyzed by identifying the dominant
type of noise in Allan variance plots. Different types of noise were
categorized based on the slope of each plot (in logarithmic scale). There are
three noise types as follows: white noise or stable noise with a slope lower
than -0.25, flicker noise with a slope between -0.25 and 0.25, and random walk
or unstable noise with a slope greater than 0.25.

##  3 Results

Figure 1 shows the comparison of the 4C31.61 position derived from our VLBI
analysis and Paris Observatory Geodetic VLBI Center. The position was plotted
with respect to the reference value where $\alpha=330.8123990589822^{o}$ and
$\delta=31.7606305185240^{o}$. Generally, it shows that our results have a
good agreement with Paris. However, we noted that our VLBI analysis produced a
gap in some periods, e.g. 2007 - 2014, which caused by our technical problem
during data processing. Next, we processed the time series by removing the
outliers and applying the moving average. Figure 2 shows the results for the
data from our VLBI analysis. We also conducted a similar procedure for Paris
data.

The Allan deviation of 4C31.61 is shown in Figure 3. They show that white
noise dominated, suggesting that the position of quasar 4C31.61 (2201+315) was
stable for a short time scale. However, we noted that for a long time scale,
there exists random walk, which suggests instability.

Based on Figure 1, it is evident that there is variability in the quasar’s
position that can affect the Allan variance results. According to [16], this
variability is suspected to be explained by two types of changes in the quasar
nucleus. First, there may be ejections from the quasar nucleus that result in
jets. Second, there is a possibility of a Binary Black Hole (BBH) in the
quasar nucleus. Other factors can be considered as well, such as the
instrument, atmospheric condition, etc.

Figure 1: Comparison of 4C31.61 relative position given by our VLBI analysis
(VieVS) and Paris Observatory Geodetic VLBI Center (Paris). The position is
depicted relative to the reference value.

(a)

(b)

Figure 2:  Comparison of original data with the data after conducting moving
average technique. The position is depicted relative to the reference value.

(a)

(b)

(c)

(d)

Figure 3:  Allan Deviation of quasar 4C31.61. Up: data from Our VLBI analysis.
Bottom: data from Paris Observatory Geodetic VLBI Center

##  4 Conclusions

In this study, the position of the quasar 4C31.61 (2201+315) has been obtained
by processing VLBI observations, particularly for data spanning from 1990 to
2023. The quasar’s position results obtained using the VieVS software are
reasonably similar to those obtained from the Paris Observatory data set,
albeit with lower quality. We performed the analysis of the stability of the
quasar object 4C31.61 (2201+315) by using Allan variance technique. We found
that this quasar exhibits stable position with the dominance of white noise in
short time scale. However, in long time scale, the dominance is random walk,
which indicate instability.

## References

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