# Hey Dona! Can you help me with student course registration?

Vishesh Kalvakurthi
Dept. of Computer Science
Montclair State University
Montclair, NJ, USA
<EMAIL_ADDRESS>&Aparna S. Varde
Dept. of Computer Science,
Faculty, Computational Linguistics
Montclair State University, NJ, USA
<EMAIL_ADDRESS>&John Jenq
Dept. of Computer Science
Montclair State University
Montclair, NJ, USA
<EMAIL_ADDRESS>
###### Abstract

In this paper. we present a demo of an intelligent personal agent _Hey Dona_
or just _Dona_ with virtual voice assistance in student course registration.
It is a deployed project in the theme of AI for education. In this digital age
with a myriad of smart devices, users often delegate tasks to agents. While
pointing and clicking supersedes the erstwhile command-typing, modern devices
allow users to speak commands for agents to execute tasks, enhancing speed and
convenience. In line with this progress, Dona is an intelligent agent catering
to student needs by automated, voice-operated course registration, spanning a
multitude of accents, entailing task planning optimization, with some language
translation as needed. Dona accepts voice input by microphone (Bluetooth,
wired microphone), converts human voice to computer understandable language,
performs query processing as per user commands, connects with the Web to
search for answers, models task dependencies, imbibes quality control, and
conveys output by speaking to users as well as displaying text, thus enabling
human-AI interaction by speech cum text. It is meant to work seamlessly on
desktops, smartphones etc. and in indoor / outdoor settings. To the best of
our knowledge, Dona is among the first of its kind as an intelligent personal
agent for voice assistance in student course registration. Due to its
ubiquitous access for educational needs, Dona directly impacts AI for
education. It makes a broader impact on smart city characteristics of smart
living and smart people due to its contributions to providing benefits for new
ways of living and assisting 21st century education, respectively.

## Introduction

An application called _Dona_ or _Hey Dona_ is motivated by the need to have a
greater proliferation of intelligent personal agents for student course
registration in the overall realm of AI for education. While there is a
multitude of apps developed for several purposes, we find the need to build
one for student course registration to provide virtual voice assistance, such
that it caters to a variety of needs. We thus address our motivation, problem
definition, related work and main contributions, with respect to our deployed
project on the Dona intelligent agent.

### Motivation and Problem Definition

In the modern era, we have smartphones at our fingertips, yet don’t always
need to use fingers. We speak of a task, and it is done, e.g. “Text Dad: I’ll
be late today” with the text sent by a virtual voice assistant (?). Voice is
used for rapid search, $\sim$4 times faster than written search (?) (humans
can write $\sim$40 words/min, speak $\sim$150). IoT devices, e.g. smart
thermostats & speakers give voice assistants high utility. Experts predict
almost every application being integrated with voice technology in 5 years
(?). Many virtual assistants exist but may have problems. They may fathom
English phrases, but fail to recognize various accents. Some are developed for
mobile devices, though users would also want them on desktops for good human-
AI interaction. It is desirable to get some language translation too. A
virtual assistant may not able to answer all queries well, as it lacks context
/ misinterprets questions. In order to cater to various users and work
seamlessly, it needs rigorous optimization via human interaction, machine
learning and natural language instruction (?). Quality control strategies can
help combat issues such as background noise, e.g. in outdoor settings. Complex
task dependencies should be modeled to recommend optimized plans for users.
All these issues are significant in student course registration; hence
motivating our work. We thus define our problem as the need to develop an
intelligent personal agent for virtual voice assistance in student course
registration, catering to issues such as different accents, indoor / outdoor
settings, language translation, and desktops usage.

Figure 1: Overview of Hey Dona: Intelligent Personal Agent

### Related Work

The $1^{st}$ speech recognition system, Audrey at Bell Labs in 1952 fathomed
10 digits spoken by specific people (?). IBM built the Shoebox Machine,
responding to 16 spoken words (digits $0\dots 9$, commands $+$, $-$) (?).
Hidden Markov Models improved speech recognition by statistical methods
measuring probability of unknown sounds as words (?). The $1^{st}$ mass-
accessible voice command system was launched by Apple as Siri in 2011
embodying NLP to answer questions and outsource requests to web services (?).
Hal was made by Zabaware as a virtual assistant to converse with users and
take notes (?). IBM created Watson to compete on the TV show Jeopardy!
defeating top human players (?). Technologies are patented in this area, e.g.
“intelligent virtual assistant” (?), “Natural-language voice-activated
personal assistant” (?). Though voice assistants abound, they are not too
prevalent in course registration, paving the way for Dona.

### Contributions

This paper presents the _Dona_ agent, an application deployed in AI for
education, to provide a solution to the problem of virtual voice assistance in
student course registration, catering to several modern-day needs. Dona or
”Hey Dona” entails the following aspects.

  * •

Comprehend English well in various accents

  * •

Work seamlessly on desktops and mobile devices

  * •

Imbibe quality control, e.g. combating noise

  * •

Model task dependencies and find optimal solutions

  * •

Offer translation as needed, sensing the environment

An overview of Dona appears in Figure 1. To the best of our knowledge, Dona is
among the first personal agents for voice assistance in course registration.
It impacts human-AI interaction, speech recognition, NLP and app development,
in line with other work including some of our own, e.g. (?), (?), (?), (?),
(?), (?), (?), (?), (?).

## Hey Dona: System Framework

The overall system framework of the intelligent agent Dona is described here.
We mention its system requirements, explain its system architecture, and
outline its system analysis.

### System Requirements

The following hardware and software have been used in order to develop the
Dona application.

  * •

Hardware: A Pentium-pro processor or later is used with a RAM capacity of
512MB or more.

  * •

Software: We use Windows 7(32-bit)+, Python 2.7+, Chrome Driver, Selenium Web
Automation, and SQLite.

### System Architecture

Dona is created in Python as open-source software modules with PyCharm
community backing. Its main modules are described in a nutshell here.

  1. 1.

Speech recognition: This occurs online and offline with Google voice API.
Extensive training via machine learning enables recognition of different
accents and distinguishing intended speech from noise.

  2. 2.

Text-to-speech: We deploy _Pyttsx_ (Python Text to Speech), a cross-platform
Python wrapper with common text-to-speech engines on Mac OS X, Windows, and
Linux. Its _pyttsx3_ module supports 2 voices: female and male (by _sapi5_ for
windows). We choose the “female” voice eponymous with “Dona”.

  3. 3.

KB design: DBpedia is good for Knowledge Base design because it covers many
domains, represents real community agreement, automatically evolves as
Wikipedia changes, and is multilingual. It helps sense the environment for
translation in user conversation, as needed.

  4. 4.

Library support: SQLite (Structured Query Language Lite) is designed for
library support as it has an in-process relational database (RDB) for
efficient storage and querying of small-to-medium data sets. Much of this is
imbibed in Dona’s cache memory. Task dependencies can be modeled in-house.
This is ideal as Dona only stores university-related data (e.g. courses, pre-
requisites). SQLite’s library runs embedded in memory alongside the
application, a reasonable subset of its books are implemented by the standard
library DB driver, feasible for searching user requests. Task dependencies can
be modeled using RDB paradigms as SQLite thrives on SQL.

  5. 5.

Audio: PyAudio offers Python bindings for Port Audio, the cross-platform audio
input-output (I/O) library. It facilitates playing and recording audio on many
platforms with seamless access on desktops, smart devices etc.

  6. 6.

NLP: We harness the NLTK (Natural Language Tool Kit) of Python. It has easy-
to-use interfaces for 50+ corpora and lexical resources, e.g. WordNet, with
text processing suites for classification, tokenization, stemming, tagging,
parsing, semantic reasoning, and an active discussion forum. It is useful in
interpretation and communication for good human-AI interaction.

### System Analysis and Machine Learning (ML)

Dona is trained with vast real data on courses, voices with different accents,
partially noisy settings etc. System analysis occurs to understand the
framework, especially noting where it fails, e.g. various accents, complex
task dependencies. Solutions are discovered to resolve issues.

Since there are modules, their functions and interrelation can easily be
studied with failure diagnosis to propose solutions. These provide the scope
for further learning via ML techniques to improve performance. Neural networks
with deep learning are useful, with the potential for enhancement.

## User Interaction and Evaluation

We highlight the input and output process of Dona, along with a sample of its
user interaction. We outline its system workflow and provide excerpts from its
user evaluation.

### The I/O of Dona

The basic I/O (input-output) process of Dona is synopsized in Algorithm 1.

Algorithm 1: Hey Dona I/O

1\. Procedure RunDona()

2\. VAR chat $\leftarrow$ Predefined chats and inputs

3\. While TRUE;

VAR CMD $\leftarrow$ TakeCommand();

if CMD = = NULL repeat step 2

VAR RESP $\leftarrow$ Response();

Output RESP;

End While

4\. End Procedure RunDona

5\. Procedure TakeCommand()

6\. VAR source $\leftarrow$ microphone input

7\. VAR voice $\leftarrow$ voice heard through a source

8\. VAR CMD $\leftarrow$ command decoded from voice

9\. Output $\leftarrow$ CMD

10\. End Procedure TakeCommand()

Figure 2 provides an illustration of the overall I/O process in Dona. Based on
this I/O process, Listing 1 depicts a sample user interaction.

Figure 2: System I/O process of Dona

Listing 1: User Q&A Interaction Example

Dona: How can I help you?’
Student: I want to register for a course.
Dona: What is your degree and major?
Student: Masters in Computer Science.
Dona: These courses are available… _[Displays courses]_
Student: Register me for HCI (CSIT-535)
Dona: Did you complete prerequisites? _[Displays them]_
Student: Yes.
Dona completes the registration and informs the student.

Figure 3: System workflow illustrating a general activity diagram for Dona

### System workflow

The general system workflow in the Dona application as an intelligent agent is
synopsized with an activity diagram and a use case diagram. The activity
diagram for Dona’s user interaction appears in Figure 3 while its use case
diagram is shown in Figure 4. Initially, the system is in idle mode. As it
receives a wake-up call, it begins execution. The received command is
identified (question / task). Specific action is taken accordingly. After the
question is answered or task performed, the system waits for another command.
This loop continues unless it receives the quit command. At that moment, it
goes back to sleep.

On a further note as per a few implementation details in the system workflow,
the pilot version of Dona demonstrated here has much of its database
functionality coded into the program itself rather than being offline (to
speed up the process), this being seamlessly extendable in ongoing work. Based
on that, a typical user Q&A would involve information retrieval from the MySQL
database as pertinent to the user’s requirements (e.g. pre-requisites,
semester course offerings) via a SQL query, converting that information (query
response) to text via the NLP functionality in an interactive manner,
transforming that response to audio using the text-to-speech functionality
through Pyttsx and communicating the voice response by deploying PyAudio, as
the audio output to the user. Note that multiple conversations from the same
user can be tracked because Dona asks users during a typical Q&A interaction
whether they wish to add more courses, perform any further activities etc.
This is displayed in a live demo video (?).

Figure 4: System workflow depicting a typical use case diagram for Dona

### User evaluation

Dona is assessed by 10+ student users hailing from the continents of Europe,
Asia, Africa, North America and South America, and spanning countries such as
USA, Netherlands, India, China, Nigeria, Brazil etc. These students have
various accents and speeds of talking. Some of them are in indoor settings
while some in outdoor settings. They come from different majors in their
degree education and have different task dependencies based on course
availability in a given semester, pre-requisite courses, and so on. They test
Dona and convey their responses, which serve as the results of user
evaluation.

The evaluation results are summarized in Table 1 with round figures. In sum,
all users indicate that they find the system useful. Some of them provide
feedback with suggestions for improvement, e.g. some users encounter latency
in Dona’s processing, especially in outdoor settings, while others indicate
the need for automated tuition payments to be included in Dona to make course
registration seem like a more realistic experience and be truly complete. Such
feedback can be incorporated in future work. A link for Dona is available on
GitHub & can be provided to interested users upon request. A video of a sample
demo is included here (?) which depicts Dona’s user interaction with multiple
international students from various educational backgrounds.

Dona’s Criteria | Students’ Observation
---|---
Accent Support | 90% of users satisfied
Language Translation | 75% of users satisfied
Task Optimization | 90% of users satisfied
Overall Quality | 80% of users satisfied
Problems | some latency, no tuition payment
Table 1: Assessment by Various Student Users

## Conclusions and Future Work

In this paper, we present an example of a project deployed to contribute our
two cents to the general realm of AI in education. This is a developed
application called _Dona_ that offers virtual voice assistance in student
course registration. User testing of Dona reveals that it is beneficial as an
intelligent personal agent with human-AI interaction, NLP and speech
recognition. It recognizes accents, does translation as needed, models task
dependencies, works well on desktops (as opposed to some apps designed only
for mobile devices), and tunes in with indoor as well as outdoor settings
(e.g. in combating noise). Dona is built with PyCharm community backing to
feasibly accommodate updates.

As future work, we aim to address the following. We will to fix latency issues
encountered by a few users. We intend to incorporate features to automate
paying tuition bills to enrich user experiences. Furthermore, we would
potentially alert students for graduation, analogous to a human advisor or a
registrar office. Analogous to prior work in our research group (?), (?), (?),
(?), our work in this paper relates to smart cities. It makes impacts on the
_smart living_ & _smart people_ characteristics due to its ubiquitous AI-based
assistance, contributing to lifestyle quality & $21^{st}$ century education
respectively.

## Acknowledgments

The authors thank the students who performed user evaluations of Dona,
especially Isabele Bittencourt, Darko Radakovic, Iyanuolowa Shode and Xu Du,
all from Montclair State University, since they provided detailed video
recordings of their demos. Aparna Varde acknowledges NSF grants 2117308 (MRI:
Acquisition of a Multimodal Collaborative Robot System (MCROS) to Support
Cross-Disciplinary Human-Centered Research and Education at Montclair State
University), and 2018575 (MRI: Acquisition of a High-Performance GPU Cluster
for Research and Education). She is a visiting researcher at the Max Planck
Institute for Informatics in Saarbrucken, Germany, ongoing from her
sabbatical, conducting data science related research, spanning NLP and
commonsense knowledge.

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# Kinematical higher-twist corrections in $\gamma^{*}\gamma\to\pi\pi$
111Presented by Qin-Tao Song at DIS2022: XXIX International Workshop on Deep-
Inelastic Scattering and Related Subjects, Santiago de Compostela, Spain, May
2-6 2022

Cédric Lorcé  CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de
Paris, 91128 Palaiseau, France  Bernard Pire  CPHT, CNRS, Ecole Polytechnique,
Institut Polytechnique de Paris, 91128 Palaiseau, France  Qin-Tao Song  CPHT,
CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau,
France  School of Physics and Microelectronics, Zhengzhou University,
Zhengzhou, Henan 450001, China

###### Abstract

We apply the Braun-Manashov technique to improve the description of
$\gamma^{*}(q_{1})\gamma(q_{2})\to M(p_{1})M(p_{2})$ amplitudes at large
$Q^{2}=-q_{1}^{2}$ and small $s=(q_{1}+q_{2})^{2}$. We derive the kinematical
higher-twist contributions of order $s/Q^{2}$ and $m^{2}/Q^{2}$ to the
helicity amplitudes and estimate their sizes in the kinematics accessible at
Belle and Belle II. Since pion GPDs cannot be directly measured by experiment,
$\pi\pi$ GDAs are the best way to investigate the energy-momentum tensor form
factors for pions.

##  I Introduction

Since generalized distribution amplitudes (GDAs) Muller:1994ses ; Diehl:1998dk
; Polyakov:1998ze  are hadronic matrix elements of the same bilocal quark (or
gluon) operator on the light-cone as the operator entering the definition of
generalized parton distributions (GPDs) Diehl:2003ny , the techniques
developed by Braun and Manashov Braun:2011dg ; Braun:2011zr ; Braun:2011th  to
separate kinematical and dynamical contributions in the product of two
electromagnetic currents
$T\\{j_{\mu}^{\text{em}}(z_{1}x)j_{\nu}^{\text{em}}(z_{2}x)\\}$ and applied to
the deeply-virtual Compton scattering (DVCS) reaction Braun:2012bg  can be
used in the description of the reaction

$e(k_{1})\gamma\to e^{\prime}(k_{2})M_{1}(p_{1})M_{2}(p_{2})$ (1)

accessible in $e^{+}e^{-}$ collisions. GDAs can be accessed in these reactions
Diehl:2000uv  in the kinematical range where $Q^{2}=-(k_{2}-k_{1})^{2}$ is
large but $s=(p_{1}+p_{2})^{2}$ is much smaller than $Q^{2}$. They have
already been the subject of careful studies at Belle Belle:2015oin ;
Kumano:2017lhr .

The kinematical corrections considered here come from two types of operators,
namely 1) the subtraction of traces in the leading-twist operators and 2) the
higher-twist operators which can be reduced to the total derivatives of the
leading-twist ones. The kinematical corrections in DVCS can be considered as a
generalization of the target mass corrections in deep inelastic scattering
Nachtmann:1973mr .

##  II Kinematics and generalized distribution amplitudes

Figure 1: Kinematics of the process
$\gamma^{*}(q_{1})\gamma(q_{2})\to\pi(p_{1})\pi(p_{2})$ in the center of mass
of the meson pair; the virtual photon is emitted by the electron,
$q_{1}=k_{1}-k_{2}$.

To describe the process (1), we define the lightlike vectors $n$ and
$\tilde{n}$ as

$\displaystyle\tilde{n}=q_{1}+(1-\tau)q_{2},\qquad n=q_{2},$ (2)

where $\tau=s/(Q^{2}+s)$, $Q^{2}=-q_{1}^{2}$, and
$s=(q_{1}+q_{2})^{2}=(p_{1}+p_{2})^{2}$. The polar angle of the meson
($M_{i}$) momenta $\theta$ is illustrated in Fig. 1 and defined as ($m$ is the
mass of the meson):

$\displaystyle\cos{\theta}=\frac{2q_{1}\cdot(p_{2}-p_{1})}{\beta_{0}\,(Q^{2}+s)},\qquad\beta_{0}=\sqrt{1-\frac{4m^{2}}{s}}.$
(3)

The skewness variable

$\displaystyle\zeta_{0}=\frac{(p_{2}-p_{1})\cdot n}{(p_{2}+p_{1})\cdot n},$
(4)

is related to $\cos\theta$ through $\zeta_{0}=-\beta_{0}\cos{\theta}$. In our
kinematics, only $\Delta=p_{2}-p_{1}$ has a transverse momentum,
$\Delta=\zeta_{0}(\tilde{n}-\tau n)+\Delta_{T}$. Using the on-shell condition,
$\Delta_{T}^{2}=4m^{2}-(1-\zeta_{0}^{2})s$.

The leading-twist amplitude was first presented in Ref. Diehl:2000uv  with the
help of a twist-2 GDA $\Phi(z,\zeta_{0},s)$ for an isoscalar meson pair,

$\displaystyle\langle
M(p_{2})M(p_{1})|\,O_{++}(z_{1}n,z_{2}n)\,|0\rangle=\chi\,2P\cdot n\int
dz\,e^{2i\left[zz_{1}+(1-z)z_{2}\right]P\cdot n}\,\Phi(z,\zeta_{0},s),$ (5)

where $P=(p_{1}+p_{2})/2$, $\chi=5e^{2}/18$ and $\Phi$ is the sum of GDAs of
the quark flavors $u$ and $d$, $\Phi=\Phi_{u}+\Phi_{d}$.
$O_{++}(z_{1}n,z_{2}n)$ is the leading-twist vector operator (a light-like
Wilson line joining the points $z_{1}n$ and $z_{2}n$ is implied),

$\displaystyle
O_{++}(z_{1}n,z_{2}n)=\chi\left[\bar{u}(z_{1}n)\not{n}u(z_{2}n)+\bar{d}(z_{1}n)\not{n}d(z_{2}n)\right].$
(6)

The matrix element of this operator can also be expressed in terms of double
distributions as Teryaev:2001qm

$\displaystyle\langle
M(p_{2})M(p_{1})|\,O_{++}(z_{1}n,z_{2}n)\,|0\rangle=\chi\int
d\beta\,d\alpha\left[f(\beta,\alpha)\,\Delta\cdot n-g(\beta,\alpha)\,2P\cdot
n\right]e^{-il_{z_{1}z_{2}}\cdot n}$ (7)

with $f$ and $g$ having support on the rhombus $|\alpha|+|\beta|\leq 1$ and
assumed to vanish at the boundary, and

$\displaystyle
l_{z_{1}z_{2}}=(z_{2}-z_{1})\left[\beta\,\frac{\Delta}{2}-(\alpha+1)P\right]-2z_{1}P.$
(8)

Then, setting $z_{1}-z_{2}=1$, one can easily relate the GDA to double
distributions

$\displaystyle\Phi(z,\zeta_{0},s)=2\int
d\beta\,d\alpha\,\delta(y+\alpha-\beta\zeta_{0})\left[f(\beta,\alpha)\,\zeta_{0}-g(\beta,\alpha)\right],$
(9)

where $y=2z-1$.

In general, GDAs can be expanded as Diehl:2000uv

$\displaystyle\Phi(z,\cos\theta,s)=6z(1-z)\sum_{n=1,\text{odd}}^{\infty}\sum_{l=0,\text{even}}^{n+1}\tilde{B}_{nl}(s)C_{n}^{(3/2)}(2z-1)P_{l}(\cos\theta).$
(10)

In the asymptotic limit ($Q^{2}\rightarrow\infty$), only the $n=1$ term
survives,

$\displaystyle\Phi(z,\cos\theta,s)=18z(1-z)(2z-1)\left[\tilde{B}_{10}(s)+\tilde{B}_{12}(s)P_{2}(\cos\theta)\right],$
(11)

where the first and second terms indicate the S-wave and D-wave production of
a meson pair, respectively.

##  III Helicity amplitudes

The amplitude for $\gamma^{*}\gamma\to MM$ reads,

$\displaystyle A_{\mu\nu}=i\int d^{4}x\,e^{-ir\cdot x}\langle
M(p_{2})M(p_{1})|\,T\\{j_{\mu}^{\text{em}}(z_{1}x)j_{\nu}^{\text{em}}(z_{2}x)\\}\,|0\rangle,\\!\\!$
(12)

where $r=z_{1}q_{1}+z_{2}q_{2}$, and the constraint $z_{1}-z_{2}=1$ is
imposed. Electromagnetic gauge invariance leads to the decomposition
Braun:2012bg

$\displaystyle
A^{\mu\nu}=-A^{(0)}\,g_{\perp}^{\mu\nu}+A^{(1)}\,\frac{\Delta_{\alpha}g_{\perp}^{\alpha\nu}}{Q}\left(\tilde{n}^{\mu}+(1-\tau)n^{\mu}\right)+\frac{1}{2}\,A^{(2)}\,\Delta_{\alpha}\Delta_{\beta}(g_{\perp}^{\alpha\mu}g_{\perp}^{\beta\nu}-\epsilon_{\perp}^{\alpha\mu}\epsilon_{\perp}^{\beta\nu})+A^{(3)\mu}\,n^{\nu}$
(13)

with $g_{\perp}^{\mu\nu}$ and $\epsilon_{\perp}^{\mu\nu}$ given by

$\displaystyle
g_{\perp}^{\mu\nu}=g^{\mu\nu}-\frac{n^{\mu}\tilde{n}^{\nu}+n^{\nu}\tilde{n}^{\mu}}{n\cdot\tilde{n}},\qquad\epsilon_{\perp}^{\mu\nu}=\epsilon^{\mu\nu\alpha\beta}\,\frac{\tilde{n}_{\alpha}n_{\beta}}{n\cdot\tilde{n}}.$
(14)

The last term in Eq. (13) is of no interest since it does not contribute to
any observable, and the rest of them can be expressed in terms of the GDAs if
the factorization condition $Q^{2}\gg s,\Lambda_{\text{QCD}}^{2}$ is
satisfied.

To calculate the helicity amplitudes, we define the photon polarization
vectors as Diehl:2000uv

$\displaystyle\epsilon_{0}^{\mu}=\frac{1}{Q}(|q_{1}^{3}|,0,0,q_{1}^{0}),\,\,\epsilon_{\pm}^{\mu}=\frac{1}{\sqrt{2}}(0,\mp
1,-i,0),$ (15)

where the lower indices $\pm$ and $0$ indicate the helicities of the photon.
The polarization vectors $\tilde{\epsilon}$ for the real photon only have the
transverse components, and they are related to the ones of the virtual photon
as $\tilde{\epsilon}_{\pm}=-\epsilon_{\mp}$. There are three independent
helicity amplitudes
$A_{ij}=\epsilon_{i}^{\mu}\tilde{\epsilon}_{j}^{\nu}A_{\mu\nu}.$ We choose the
independent helicity amplitudes as $A^{(0)}=A_{++}$,
$A_{0+}=-A^{(1)}(\Delta\cdot\epsilon_{-})$ and
$A_{-+}=-A^{(2)}(\Delta\cdot\epsilon_{-})^{2}$.

We shall not detail here222Details will be given in a forthcoming publication.
our calculation of the helicity amplitudes of $\gamma^{*}\gamma\to MM$; we
adopt (and adapt to our case) the techniques used for the DVCS amplitude in
Ref. Braun:2012bg . Our results for the helicity amplitudes in terms of GDAs
read :

$\displaystyle A^{(0)}=$
$\displaystyle\chi\left\\{(1-\frac{s}{2Q^{2}})\int_{0}^{1}dz\frac{\Phi(z,\eta,s)}{1-z}-\frac{s}{Q^{2}}\int_{0}^{1}dz\frac{\Phi(z,\eta,s)}{z}\ln(1-z)\right.$
$\displaystyle-\left.(\frac{2s}{Q^{2}}\eta+\frac{\Delta_{T}^{2}}{\beta_{0}^{2}Q^{2}}\frac{\partial}{\partial\eta})\frac{\partial}{\partial\eta}\int_{0}^{1}dz\frac{\Phi(z,\eta,s)}{z}\left[\frac{\ln(1-z)}{2}+Li_{2}(1-z)-Li_{2}(1)\right]\right\\},$
$\displaystyle A^{(1)}=$
$\displaystyle\frac{2\chi}{\beta_{0}Q}\frac{\partial}{\partial\eta}\int_{0}^{1}dz\Phi(z,\eta,s)\frac{\ln(1-z)}{z},$
$\displaystyle A^{(2)}=$
$\displaystyle-\frac{2\chi}{\beta_{0}^{2}Q^{2}}\frac{\partial^{2}}{\partial\eta^{2}}\int_{0}^{1}dz\Phi(z,\eta,s)\frac{2z-1}{z}\ln(1-z),$
(16)

where $\eta=\cos\theta$. The target mass correction $m^{2}/Q^{2}$ is implicit
through $\Delta_{T}^{2}=4m^{2}-(1-\zeta_{0}^{2})s$.

##  IV Numerical estimates of kinematical higher-twist corrections to the
cross section

The process $\gamma^{*}\gamma\to MM$ can be measured in $e^{+}e^{-}$
collisions, as demonstrated at KEKB. The cross section for $e\gamma\to eMM$ is
expressed as Diehl:2000uv

$\displaystyle\frac{d\sigma}{dQ^{2}dsd(\cos\theta)d\varphi}=$
$\displaystyle\frac{\alpha_{\text{EM}}^{3}\beta_{0}}{16\pi
s_{e\gamma}}\frac{1}{Q^{2}(1-\epsilon)}\left[|A_{++}|^{2}+|A_{-+}|^{2}+2\epsilon|A_{0+}|^{2}-\cos\varphi\text{Re}(A_{++}^{\ast}A_{0+}-A_{-+}^{\ast}A_{0+})\right.$
$\displaystyle\left.+2\epsilon\cos(2\varphi)\text{Re}(A_{++}^{\ast}A_{-+})\right],$
(17)

where $\varphi$ is the azimuthal angle of the meson pair as illustrated in
Fig. (1) and $s_{e\gamma}$ is center-of-mass energy of $e\gamma$. $\epsilon$
is defined as $\epsilon=\frac{1-y}{1-y+y^{2}/2}$,
$y=\frac{Q^{2}+s}{s_{e\gamma}}$ and $\alpha_{\text{EM}}=\frac{e^{2}}{4\pi}$ .

In 2016, the Belle Collaboration released the measurements of the differential
cross section for $\gamma^{*}+\gamma\rightarrow\pi^{0}+\pi^{0}$Belle:2015oin ,
from which the twist-2 pion GDA Kumano:2017lhr  was extracted by using the
leading-twist amplitude. Now we adopt the pion GDA to estimate the cross
section of $e\gamma\to e\pi\pi$ where the integral of $\varphi$ is performed,
and use this pion GDA to show the size of the kinematical contributions via
Eqs. (16) and (17). Following the kinematics of the Belle measurements, the
values of $Q^{2}$ are chosen as $Q^{2}=9,16,25$ GeV2, $s\in(0.25,4)$ GeV2 and
we temporarily set $s_{e\gamma}=30$ GeV2 which is the typical value at Belle.

In Fig. (2), we present the ratio $d\sigma_{t2+t3+t4}/d\sigma_{t2}$ where
$d\sigma_{ti}$ is the kinematical twist-$i$ cross section for different values
of $\cos\theta$ : black (pink, red, blue) lines denote $\cos\theta=0.2$
($0.4,0.6,0.8)$. In this figure, the contributions of the kinematical higher-
twist corrections are quite clear, and we can infer that the kinematical
corrections cannot be neglected when $\sqrt{s}>1$ GeV. Around $\sqrt{s}\sim
1.5$ GeV, the kinematical corrections are dominant in the cross section with
$\cos\theta=0.8$, but this is mainly due to the fact that the twist-2 cross
section is tiny with the extracted GDA from Belle measurements; however, this
GDA may not be accurate enough since the uncertainties of Belle measurements
are large in these kinematics. As $Q^{2}$ increases, the role of the
kinematical contributions becomes less important, consistently with the fact
that the higher-twist kinematical contributions are suppressed by $1/Q$ or
$1/Q^{2}$.

Figure 2:  Ratio of $d\sigma_{t2+t3+t4}/d\sigma_{t2}$ with the pion GDA
extracted from Belle measurements.

To sum-up this phenomenological study, let us stress that the uncertainties of
Belle measurements Belle:2015oin  are quite large, and the statistical errors
are dominant. However, this situation will be improved substantially soon,
since Belle II collaboration just started taking data at the SuperKEKB with a
much higher luminosity. Precise measurements of $\gamma^{*}+\gamma\rightarrow
M_{1}+M_{2}$ are expected in the near future, and an accurate description of
the amplitudes will require the inclusion of kinematical contributions up to
twist 4. This will be of utmost importance to address the question of the form
factors of the pion energy-momentum tensor Kumano:2017lhr  and of the impact-
parameter picture representation of GDAs Pire:2002ut .

## References

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# VaTEST I: Validation of Sub-Saturn Exoplanet TOI-181b in Narrow Orbit from
its Host Star

Priyashkumar Mistry,1 Kamlesh Pathak,1 Georgios Lekkas,2 Aniket Prasad,3
Surendra Bhattarai,4 Mousam Maity,5 Charles A. Beichman,6 David R. Ciardi,6
Phil Evans$,^{7}$ Allyson Bieryla,8 Jason D. Eastman,8 David W. Latham,8
Gilbert A. Esquerdo8 and Jennifer P. Lucero9

1Department of Physics, Sardar Vallabhbhai National Institute of Technology,
Surat-395007, Gujarat, India
2Department of Physics, University of Ioannina, Ioannina-45110, Greece
3Department of Physics, National Institute of Technology, Agartala-799046,
Tripura, India
4Department of Physical Sciences, Indian Institute of Science Education and
Research Kolkata, Mohanpur-741246, West Bengal, India
5Department of Physics, Presidency University, Kolkata-700073, West Bengal,
India
6NASA Exoplanet Science Institute - Caltech/IPAC Pasadena, CA 91350 USA.
7El Sauce Observatory, Coquimbo Province, Chile.
8Center for Astrophysics, Harvard & Smithsonian, 60 Garden St, Cambridge, MA
02138, USA
9Institute of Astrophysics, Pontificia Universidad Católica de Chile,
Santiago-8331150, Región Metropolitana, Chile E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present here a validation of sub-Saturn exoplanet TOI-181b orbiting a K
spectral type star TOI-181 (Mass: 0.822 $\pm$ 0.04 M☉, Radius: 0.745 $\pm$
0.02 R☉, Temperature: 4994 $\pm$ 50 K) as a part of Validation of Transiting
Exoplanets using Statistical Tools (VaTEST) project. TOI-181b is a planet with
radius 6.95 $\pm$ 0.08 R⊕, mass 46.16 $\pm$ 2.71 M⊕, orbiting in a slightly
eccentric orbit with eccentricity 0.15 $\pm$ 0.06 and semi-major axis of 0.054
$\pm$ 0.004 AU, with an orbital period of 4.5320 $\pm$ 0.000002 days. The
transit photometry data was collected using Transiting Exoplanet Survey
Satellite (TESS) and spectroscopic data for radial velocity analysis was
collected using The European Southern Observatory’s (ESO) High Accuracy Radial
Velocity Planet Searcher (HARPS) telescope. Based on the radial velocity best-
fit model we measured RV semi-amplitude to be 20.56 $\pm$ 2.37 m s-1.
Additionally, we used VESPA and TRICERATOPS to compute the False Positive
Probability (FPP), and the findings were FPP values of $1.68\times 10^{-14}$
and $3.81\times 10^{-04}$, respectively, which are significantly lower than
the 1% threshold. The finding of TOI-181b is significant in the perspective of
future work on the formation and migration history of analogous planetary
systems since warm sub-Saturns are uncommon in the known sample of exoplanets.

###### keywords:

individual: TOI-181, technique: photometry, spectroscopic, radial velocities,
methods: statistical

††pubyear: 2023††pagerange: VaTEST I: Validation of Sub-Saturn Exoplanet
TOI-181b in Narrow Orbit from its Host Star–A

##  1 Introduction

Up to the time of writing a total number of 5054 exoplanets have been
discovered and confirmed 111https://exoplanetarchive.ipac.caltech.edu/. For
the coming years, this amount is expected to experience an even larger growth
with many near and far future missions expected to be launched. Many of these
discovered extra-solar planets are different from the planets of our Solar
System, imposing a wide variety of different exoplanets that can exist. The
very first exoplanet discovery happened 30 years ago, in 1992, by the
discoverers Aleksander Wolszczan and Dale Frail (Wolszczan & Frail, 1992), who
found two exoplanets orbiting a pulsar.

Astronomers have discovered and classified many types of exoplanets. In
addition to super-Earths, which are terrestrial planets composed of rocky
materials and larger than our own, there are also hot-Jupiters. These planets
are comparable in size to or larger than Jupiter, and they orbit their host
star very closely. Sub-Saturns or super-Neptunes is a further classification.
This category of exoplanets is under-explored and incredibly interesting to
investigate due to their unique properties. The exoplanets discovered in this
category have a narrow range of radii (2-8 R⊕) but larger masses (20-100 M⊕).
Sub-Saturns have very little correlation between their masses and radii and
strong relation with the metallicity of their host stars (Petigura et al.,
2017). According to theory, hot Jupiters and sub-Saturns cannot originate
within the ice line because their gaseous envelopes would be torn apart by
stellar wind, leaving only their low-mass rocky cores. According to the
concept of planetary migration, this sort of planet forms outside the ice line
and migrates toward its host star through an exchange of angular momentum
(Lissauer & Stevenson, 2007).

The launch of space missions like Kepler (Borucki et al., 2010a), K2 (Howell
et al., 2014), and TESS (Ricker & TESS Team, 2015) have provided us with
valuable data which resulted in the discovery of a huge number of exoplanets.
However, a pretty common thing, space missions can suffer from, is the
detection of the so-called False Positive events. False positives or false
detection are cases in which a transit signal from the target is not caused by
a true exoplanet transit but rather by any other background source or
eclipsing binaries. False detection in transit space missions can be filtered
out by statistical validation of transit candidates. Hence, concentrated
efforts have been made to develop efficient statistical validation tools that
can be employed for various space missions. BLENDER (Torres et al., 2005) was
one of the first statistical tools utilised for validating exoplanet
candidates from Kepler. It used $\chi^{2}$ statistics on synthetically
generated light curves based on planetary and blended eclipsing binary models
combined with multi-colour photometry calculation to rule out the
possibilities of false positive scenarios. BLENDER’s approach to testing for
false positive astrophysical scenarios provided a framework for exoplanet
validation despite its suffering from long computation times owing to the
simulation of false positive scenarios. A newer validation framework by the
name of VESPA (Morton, 2012) greatly reduced computation time by employing a
simpler trapezoidal model in place of physical transit models, as was the case
with BLENDER. Using the TRILEGAL (Girardi et al., 2005) model of the galaxy,
VESPA simulates a population of stars similar in properties to the target
star. The population is then used to produce a prior distribution for each
astrophysical scenario using the trapezoidal model. It used an MCMC sampling
routine to fit the Kepler light curve and produced a false positive
probability based on the fit. Both VESPA and BLENDER have the capability to
account for follow-up high contrast imaging. The framework was widely used to
statistically validate exoplanets from Kepler as well as TESS. TRICERATOPS
(Giacalone & Dressing, 2020) was developed specifically to utilise the unique
features and requirements of the TESS mission. With a lower resolution than
previous such missions, there is an even greater necessity to account for
multiple star systems and scenarios like diluted transits. VESPA and
TRICERATOPS have been used to successfully validate planet candidates for the
Kepler (Morton et al., 2016), K2 (Dressing et al., 2017; Bhure et al., 2021;
Christiansen et al., 2022) and TESS (Giacalone et al., 2021) missions.

Other tools such as PASTIS (Díaz et al., 2014; Santerne et al., 2015) have
also been alternatively used to validate exoplanet candidates. PASTIS is
unique in the sense that it provides the capability to combine radial velocity
observation with light curve analysis for validation. However, this does make
PASTIS a more robust framework to validate transiting exoplanets at the cost
of being computationally expensive. It also utilises a realistic model of
galactic extinction on top of the TRILEGAL galactic model to better account
for the possible blends, which crucially depends on the frequency of
background star extinction in the line of sight. Using two of these
statistical tools (chosen to independently verify the result and to utilise
the merits of statistical tools, discussed in section 4) along with the TESS
photometry data and radial velocity follow-up data from HARPS (Pepe et al.,
2000), we present here the evidence for the existence of a sub-Saturn planet
orbiting TOI-181 as observed by TESS in sectors 2 and 29.

The statistical validation used in this current study is part of the newly
launched project, Validation of Transiting Exoplanets using Statistical Tools
(VaTEST)222https://sites.google.com/view/project-vatest/home. The aim of this
project is to validate exoplanet signals using statistical tools and
probabilistic algorithms, in combination with other packages mentioned later
in this study (Lightkurve (Lightkurve Collaboration et al., 2018), TLS (Hippke
& Heller, 2019), and Juliet (Espinoza et al., 2019) for photometric and
spectroscopic data analysis. Future work of this project will be aimed at bulk
validation of unconfirmed exoplanets using a variety of statistical
validation, false alarm and false positive diagnostics tests and photometric
and spectroscopic data analysis to calculate the exoplanet properties.

The rest of this paper is organized as follows. In Section 2, we present the
observational transit data from TESS, ground based transit follow-up, high
resolution imaging observation and radial velocity data from HARPS. In section
and 3, we focus our attention to the host star and characterise the star-
planet system using a combined model of transit photometry and RVs. In section
In Section 4, we discussed prominent features of confirmed exoplanet TOI-181b.
Section 5 refers to the summary of this paper and the conclusion.

##  2 Data Reduction

###  2.1 Transit Photometry

TOI-181 (TIC 76923707) can be found at the coordinates RA 23:28:41.41 and Dec
-34:29:29.08, and it was spotted by the Transiting Exoplanet Search Satellite
(TESS) (Ricker & TESS Team, 2015) in sector 2 on August 23rd, 2018 and sector
29 on August 26th, 2020. In sector 2, photometric data for TOI-181 was
collected with a 2-minute cadence, whereas data for sector 29 was collected
with a 2-minute as well as a 20-second cadence. These pixel data were
processed by the TESS Science Processing Operation Centre (TESS-SPOC) pipeline
(Jenkins et al., 2016), and made available the target pixel files (TPF) and
light curve files cleaned from instrumental systematics. The Transiting Planet
Search (TPS) module of SPOC was responsible for the independent recovery of
transit signals for each sector. With a signal-to-noise ratio (SNR) of 86.57,
the SPOC pipeline was successful in recovering a transiting signal for
TOI-181. The transit signal for this specific target is shown in Fig. 1.

Figure 1: Transit light curve of sector 02 (upper panel) and sector 29 (lower
panel). Blue dots represent the non-de-trended light curve and black dots are
for de-trended light curve. De-trended light curve is binned so that
difference can be clearly visible.

With the help of the Lightkurve Python package (Lightkurve Collaboration et
al., 2018), we were able to download these signals from the Mikulski Archive
for Space Telescopes (MAST)333https://archive.stsci.edu/. This light curve
exhibited stellar variability, which was eliminated by de-trending the light
curve using the flatten function of Lightkurve. In order to ensure that the
in-transit portion of a signal was not lost during the de-trending process, we
used a mask that was 0.12-days long and had a period of 4.53 days, starting
from the epoch time 2458358.12. Fig. 1 illustrates the difference that can be
seen between the signal after it has been de-trended and the actual signal.

We determined the duration of the transit event, the time of the epoch, and
the transit depth by applying a Transit Least Squares (TLS) (Hippke & Heller,
2019) model to the light curve after it had been cleaned up and de-trended.
The values that are reported by SPOC on the ExoFOP-
TESS444https://exofop.ipac.caltech.edu/tess/ website are identical to the
values that are calculated by TLS.

###  2.2 Follow-up Transit Photometry

We obtained ground-based time-series photometry in order to precisely collect
the transit features and to comprehend and confirm the nature of the transit
detected by TESS. This follow-up observation was conducted as part of the TESS
Follow-up Observing Program (TFOP; Collins et al. (2018)). We used the TESS
Transit Finder, a customized version of the Tapir software package (Jensen,
2013) to schedule our observations. We observed a full transit in Johnson-
Cousins R-band on UT20181108 using the Evans 0.36m telescope at El Sauce
Observatory in Coquimbo Province, Chile. The telescope was equipped with an
STT 1603-3 CCD camera with 1536 $\times$ 1024 pixels binned 2 $\times$ 2 in-
camera resulting in an image scale of 1.47" /pixel. The photometric data was
obtained from 10 $\times$ 70 seconds followed by 254 $\times$ 60 seconds
exposures, after standard calibration, using a circular 7.4" aperture in
AstroImageJ (Collins et al., 2016). Fig. 2 shows the field of view of El Sauce
Observatory along with the transit light curve obtained by calculating the
relative flux of target star (marked with green circle and T1) with respect to
other comparison stars.

Figure 2: Upper Panel: El Sauce Observatory field of view. Yellow circle shows
2$\arcmin$ region from our target. Green circle marked with T1 is TOI-181, T9
and T11 are stars that lie within 2$\arcmin$ region. Stars marked with red
circles are comparison stars. Lower Panel: Transit light curve of target
TOI-181, relative flux was calculated using comparison stars. Photometry data
was collected using telescope equipped with STT 1603-3 CCD camera at El Sauce
Observatory. Blue filled circles shows the binned data.

###  2.3 High Angular Resolution Imaging

High resolution imaging is an effective tool for reducing the possibility of
blended background objects. We used the archival, high-angular-resolution AO
image data collected by the Keck II/NIRC2 camera. Additionally, ExoFOP makes
this publicly accessible (submitted by David Ciardi). The Keck AO data was
collected on December 06, 2018. The pixel scale for NIRC2 is 9.942 mas per
pixel.

Figure 3: High resolution image of TOI-181 with 5$\sigma$ contrast curve
(uploaded on ExoFOP by David Ciardi). Pink shaded region describes the
uncertainties in the contrast sensitivity estimated by measuring RMS
dispersion. Estimated sensitivity of companion is $\approx$7 $\Delta$mag at
0.5". Curve is saturating $\approx$8 $\Delta$mag, so the point source that has
contrast greater than this value will remain non-detected.

Fig. 3 displays the observed image. The estimated point spread function of the
source is 0.0556". The star looks to be single and doesn’t have any very close
neighbours within a few arcseconds. At a distance of 0.5", the estimated
sensitivity to the companion is $\approx$7 $\Delta$mag. So eventually, it
rules out the possibility of any background blended source affecting the light
curve of our target.

###  2.4 Radial Velocity Observations

The European Southern Observatory’s (ESO) High Accuracy Radial Velocity Planet
Searcher (HARPS) (Pepe et al., 2000) telescope collected spectral data in
order to calculate the radial velocity (RV) of the host star. HARPS is a
3.6-meter telescope that is based at ESO’s La Silla Observatory. HARPS can
achieve radial velocity precision on the order of 1 m/s over very long
timescales. To avoid spectral drift due to temperature and air pressure,
spectrograph was fed with two fibres contained in a vacuum chamber. One of the
fibres collects starlight, while the other simultaneously measures the Th-Ar
reference spectrum. Both fibres have a 1" aperture in the sky. We were able to
recover 23 spectral observations between the dates of June 25th, 2019 and
December 1st, 2020. The spectral range of these observations was 378.2-691.3
nm, and the spectral resolution was 115000. We made use of a pipeline that had
been developed by Nora Eisner (Eisner, 2020) in order to obtain the RV values
from these spectra. The RV data had been extracted and are presented in Table
1.

Table 1: Radial velocity data as extracted from the spectral data collected by HARPS. Based on data obtained from the ESO Science Archive Facility with DOI: https://doi.org/10.18727/archive/33 BJD Time | RV (m s-1) | RV Uncertainty (m s-1)
---|---|---
2458659.85568 | -4766.142504 | 8.435472
2458660.85346 | -4745.218259 | 6.531391
2458670.77969 | -4756.403730 | 4.848487
2458672.86062 | -4752.448405 | 6.362948
2458673.83568 | -4728.360590 | 3.715174
2458674.87044 | -4739.506311 | 5.139311
2458675.81618 | -4755.954379 | 4.945969
2458683.86426 | -4750.973759 | 1.906334
2458683.94273 | -4747.586764 | 6.552498
2458684.79363 | -4772.551952 | 6.258132
2458689.76742 | -4770.629672 | 6.004815
2458690.79475 | -4762.125532 | 4.466280
2458691.77767 | -4738.547657 | 4.140452
2458750.58685 | -4728.338615 | 4.929043
2458752.61872 | -4776.305472 | 4.542711
2458753.60754 | -4790.955086 | 4.069793
2458754.65281 | -4775.853945 | 4.689729
2458755.65078 | -4745.048769 | 3.621645
2459163.62510 | -4733.510345 | 4.777836
2459178.57572 | -4754.916775 | 4.606471
2459181.59995 | -4730.861963 | 4.374840
2459182.59757 | -4747.139606 | 4.972627
2459184.60398 | -4775.425414 | 4.197057

##  3 Analysis and Results

###  3.1 Stellar Parameters

We collected stellar spectra on UT2018-11-16 with the 1.5-metre Tillinghast
Refactor Echelle Spectrograph (TRES) (Mink, 2011) at the Fred Lawrence Whipple
Observatory (FLOW) in southern Arizona. The TRES reconnaissance spectra were
organised by Dave Latham and collected by Gilbert Esquerdo. The spectra (SNR =
28.2) were extracted through a custom pipeline presented in Buchhave et al.
(2010), and stellar parameters were determined using stellar parameter
classification (SPC) tool (Buchhave et al., 2012, 2014). The stellar effective
temperature $T_{eff}$ = 4994 $\pm$ 50 K, logarithmic surface gravity
$logg_{*}$ = 4.685 $\pm$ 0.1, stellar rotational velocity $vsini$ = 2.28 $\pm$
0.5 km $s^{-1}$, and metal abundance [m/H] of 0.272 $\pm$ 0.08 were obtained
via this tool.

We derived stellar parameters by using spectral energy distribution (SED)
(Stassun & Torres, 2016) and MIST isochrones (Choi et al., 2016; Dotter, 2016)
joint fits with EXOFASTv2 (Eastman et al., 2019). This joint fit can precisely
measure the radius, mass, age, and $logg_{*}$ of the star (Eastman et al.,
2022). To perform this framework, we used TESS transit photometry data,
broadband photometry, and Gaia DR2 parallax (Gaia Collaboration et al., 2018).
We placed priors on effective temperature and metallicity, determined using
spectral analysis. We also showed the MIST stellar evolution track for TOI-181
in Fig 4. The best-fit SED model along with broadband photometry is shown in
Fig. 5 Through this analysis, we measured stellar parameters,
$R_{*}=0.745^{+0.024}_{-0.023}R_{\sun}$,
$M_{*}=0.822^{+0.040}_{-0.038}M_{\sun}$, Age = $5.4^{+4.9}_{-3.7}$ Gyr, and
$logg_{*}=4.608^{+0.035}_{-0.034}$. Table 2 shows the adopted parameters.

Figure 4: Stellar evolution track for TOI-181. Black line represents the most probable evolutionary track, black dot is a representation of model effective temperature and logarithmic surface gravity. Red asterisk symbol shows the equal evolutionary point or age of TOI-181. Figure 5: The spectral energy distribution of TOI-181. Red horizontal error bars show the broadband photometry measurements and vertical bars represent the uncertainty in measurements. Black curve shows the best fit Kurcuz stellar atmosphere model with blue circles representing model fluxes over each band. Table 2: Stellar Parameters Parameter | Unit | Value
---|---|---
RA | deg | 352.17${\degr}$
DEC | deg | -34.49${\degr}$
Distance | pc | 96.23 $\pm$ 0.57
Stellar Radius | $R_{\sun}$ | 0.745 $\pm$ 0.024
Stellar Mass | $M_{\sun}$ | 0.822 $\pm$ 0.040
Effective Temperature | K | 4994 $\pm$ 50
Stellar Density | g $cm^{-3}$ | 2.80 $\pm$ 0.31
Luminosity | $L_{\sun}$ | 0.298 $\pm$ 0.011
Gravity | $logg_{*}$ | 4.608 $\pm$ 0.035
Stellar Rotation | km $s^{-1}$ | 2.28 $\pm$ 0.50
Metallicity | [m/H] | 0.272 $\pm$ 0.08
Age | Gyr | 5.4 $\pm$ 4.9
Magnitudes
TESS | 10.46 $\pm$ 0.006 |
B | 12.23 $\pm$ 0.211 |
V | 11.19 $\pm$ 0.019 |
Gaia | 11.08 $\pm$ 0.001 |
J | 9.62 $\pm$ 0.029 |
H | 9.14 $\pm$ 0.022 |
K | 9.05 $\pm$ 0.021 |
WISE 3.4 $\mu m$ | 8.96 $\pm$ 0.02 |
WISE 4.6$\mu m$ | 9.04 $\pm$ 0.02 |
WISE 12$\mu m$ | 8.93 $\pm$ 0.03 |
WISE 22 $\mu m$ | 8.48 |
Other Identifiers
TIC 76923707
2MASS J23284126-3429289
APASS 17429793
Gaia DR2 6552346035980010624
TYC 7517-00248-1
UCAC4 278-232062
WISE J232841.35-342929.0

Because the proper motion for TOI-181 is relatively large
($\mu_{\alpha}=111.3563$, $\mu_{\delta}=-2.6423$ mas/yr), we have checked
archival images to search for a possible line-of-sight star that may currently
be behind the star. Utilizing the Second Palomar Sky Survey (Reid et al.,
1991) and the 2MASS Survey (Skrutskie et al., 2006) and the Finder Chart
service at IRSA linked through the ExoFOP
555https://irsa.ipac.caltech.edu/applications/finderchart/servlet/api?mode=getResult&locstr=352.17254091369102+-34.491409902166303&subsetsize=5&survey=DSS%2CSDSS%2C2MASS%2CWISE,
we searched for possible background contamination. The oldest image is from
the UK Schmidt survey in 1981, which is 40 years before the TESS observations.
In that time, TOI-181 has moved approximately 4″ to the East (and 0.1″ to the
South). The resolution of the 1981 imaging is approximately 5″, which would be
sensitive to another approximately 2-3 magnitudes fainter and would appear as
a shoulder on the point spread function of TOI-181. There is no evidence in
the imaging for the presence of another star at the current location of
TOI-181.

Further, in support of TOI-181 being a single star, the Gaia solution is
consistent with the star being single. Gaia DR3 astrometry (Gaia Collaboration
et al., 2021) provides additional information on the possibility of inner
companions that may have gone undetected by either Gaia or the high resolution
imaging. The Gaia Renormalised Unit Weight Error (RUWE) is a metric, similar
to a reduced chi-square, where values that are $\lesssim 1.4$ indicate that
the Gaia astrometric solution is consistent with the star being single whereas
RUWE values $\gtrsim 1.4$ may indicate an astrometric excess noise, possibly
caused the presence of an unseen companion (e.g., Ziegler et al., 2020).
TOI-181 has a Gaia DR3 RUWE value of 0.88 indicating that the astrometric fits
are consistent with the single star model.

###  3.2 Periodogram Analysis

We generated a Generalized Lomb-Scargle (GLS) periodogram (Zechmeister &
Kürster, 2009) for RVs and residual RVs. Fig. 6 shows the resulting
periodogram. We started by subtracting the corresponding mean RV from RV
values to remove offset. The periodogram is plotted between the lowest
frequency 0.0 $day^{-1}$ and highest frequency measured using Nyquist limit
for unevenly spaced data (VanderPlas, 2018), which resulted in $\approx$ 0.40
$day^{-1}$. We calculated the false alarm probability (FAP) using the equation
presented in the Zechmeister & Kürster (2009). Any significant signal is
considered to have a FAP threshold of 0.1% or smaller. The top panel of Fig. 6
shows that a significant peak is found at $\approx$ 4.53 days (red dashed line
indication) with a FAP of 0.086 %. This period is consistent with the measured
period using transit photometry. Bottom panel of Fig. 6 shows the periodogram
of residual RVs, which has no significant peak above the considered threshold,
which indicates the absence of any other periodic signal in the data, noting
the observation capabilities of the instrument.

Figure 6: The GLS periodogram for RVs (upper panel) and residuals RVs (lower
panel). The primary peak is observed at $\approx$ 4.53 days (red dashed line).
This period is consistent with orbital period derived using transit
photometry. FAP levels of 0.1 %, 1 % and 10 % for the periodogram are shown in
legend.

###  3.3 Validation using FPP

We employed two statistical validation tools, VESPA (Morton, 2012) and
TRICERATOPS (Giacalone & Dressing, 2020) as a preliminary check for the
exoplanet. We make use of VESPA version 0.6 through a virtual machine created
by Kevin Hardegree-Ullman666https://github.com/kevinkhu/vespa-vm. To calculate
FPP for any given target, VESPA requires three input files, star.ini that
contain the parameters (effective temperature, metallicity, logg, magnitude of
the star in different bands, including the TEES band) of the target star.
fpp.ini file contains the orbital period, planet-to-star radius ratio, maximum
aperture radius (in arcsec), maximum permitted secondary depth of a potential
secondary eclipse (secthresh), position of target (RA and DEC), telescope
filter, and cadence (in days). transit.txt file that contains the data from
transit photometry. If the calculated FPP for the target is $<$ 1 % (Morton,
2012; Morton et al., 2016), then it can be validated as a planet. In Table 3,
we have compiled a list of all VESPA outputs.

Table 3: VESPA output for all FP scenarios. Shows the calculated probability of various scenarios. Scenario | Sector 02 | Sector 29 | Combined
---|---|---|---
$\mathcal{P}$(HEB) | 9.04$\times 10^{-10}$ | 6.49$\times 10^{-8}$ | 1.35$\times 10^{-17}$
$\mathcal{P}$(HEB) ($\times$2P) | 2.92$\times 10^{-14}$ | 1.38$\times 10^{-11}$ | 1.67$\times 10^{-14}$
$\mathcal{P}$(EB) | 5.56$\times 10^{-13}$ | 8.05$\times 10^{-20}$ | 2.83$\times 10^{-20}$
$\mathcal{P}$(EB) ($\times$2P) | 7.03$\times 10^{-33}$ | 1.79$\times 10^{-25}$ | 6.78$\times 10^{-33}$
$\mathcal{P}$(BEB) | 9.67$\times 10^{-20}$ | 5.66$\times 10^{-32}$ | 5.66$\times 10^{-17}$
$\mathcal{P}$(BEB) ($\times$2P) | 0.00 | 0.00 | 0.00
$\mathcal{P}$(Planet) | 1.00 | 1.00 | 1.00
FPP | 9.05$\times 10^{-10}$ | 6.50$\times 10^{-8}$ | 1.68$\times 10^{-14}$

The results of the calculations for FPP from VESPA are significantly lower
than the threshold of 1 %. It presents a convincing illustration of a target
being considered a planet.

The TOI-181 signal was put through a different statistical validation software
called TRICERATOPS (Giacalone & Dressing, 2020) so that we could conduct an
independent check. Employing an algorithm similar to VESPA, It investigates a
variety of astrophysical situations that could produce false-positive signals.
TRICERATOPS was developed in particular for the purpose of validating TESS
observations. The aperture mask of a target, the transit depth, and the
orbital period are all required as priors. Based on the parameters provided,
it uses a Bayesian framework to check for the various FP scenarios. The added
advantage over VESPA is that it also performs an analysis not only on the
target star but also on the stars that are located within a 2.5’ radius. And
using this information, it computes both the FPP of the signal as well as the
probability that the planet candidate is a false positive originating from a
known nearby star. This probability is referred to as the nearby FPP (NFPP).

TRICERATOPS is able to confirm that a signal is a planet if the FPP < 0.015
and the NFPP < 0.001, as stated in Giacalone et al. (2021). If the FPP < 0.5
and the NFPP is < 0.001, it is probably a planet; however, if the NFPP is
greater than 0.1, the signal is probably due to a nearby false positive
scenario. Table 4 contains a compilation of the FPP that was calculated for
TOI 181 using TRICERATOPS for each of the different sectors.

Table 4: FPP and NFPP calculated using TRICERATOPS Sector | FPP | NFPP
---|---|---
02 | 0.0006061 $\pm$ 0.0027549 | 4.2022$\times 10^{-28}$ $\pm$ 6.1927$\times 10^{-28}$
29 | 0.0022743 $\pm$ 0.0053222 | 4.0302$\times 10^{-31}$ $\pm$ 8.7789$\times 10^{-28}$
Both | 0.0003812 $\pm$ 0.0009869 | 2.5397$\times 10^{-53}$ $\pm$ 9.1340$\times 10^{-53}$

###  3.4 Planetary Parameters

We employed the Juliet (Espinoza et al., 2019) Python package to model the
transit and radial velocity data. The Juliet is a versatile modelling tool for
extra-solar planetary systems that allows the fast and easy calculation of
parameters from transit photometry, radial velocity, or both using Bayesian
inference and, in particular, Nested Sampling to allow both effective
measurement and suitable model comparisons. Juliet can take various datasets
of transit photometry and radial velocity simultaneously and calculate
systematic trends using linear models or Gaussian Processes (GP). The priors
that we used during the modelling process are displayed in Table 5.

Table 5: Priors provided to Juliet for modeling

$\mathcal{N}$: Normal Distribution
$\mathcal{U}$: Uniform Distribution
$\mathcal{L}$: Log-uniform Distribution

Prior | Description | Distribution
---|---|---
Period (P) | days |  $\mathcal{N}$(4.53193, 0.1)
$T_{0}$ | BJD |  $\mathcal{N}$(2458358.1182, 0.1)
$r_{1}$ | Espinoza (2018) |  $\mathcal{U}$(0.0, 1.0)
$r_{2}$ | Espinoza (2018) |  $\mathcal{U}$(0.0, 1.0)
a/$R_{*}$ |  |  $\mathcal{U}$(10, 20)
K | m s-1 |  $\mathcal{U}$(15, 23)
Eccentricity |  |  $\mathcal{U}$(0.0, 0.7)
$\omega$ | deg |  $\mathcal{U}$(-360, 360)
Instrumental Parameters
$q_{1}$ | Kipping (2013) |  $\mathcal{U}$(0.0, 1.0)
$q_{2}$ | Kipping (2013) |  $\mathcal{U}$(0.0, 1.0)
$m_{flux}$ | ppm |  $\mathcal{N}$(0.0, 0.1)
$m_{dilution}$ |  | 1.0
$\sigma_{w}$ | ppm |  $\mathcal{L}$(0.1, 1000)
$\mu_{instrument}$ | m $s^{-1}$ |  $\mathcal{U}$(a, b)

Figure 7: Phase folded transit light curve centred on T0 (BTJD 2458358.1180).
Blue line suggests the best-fit transit model with log evidence ($lnz$) of
171216.32083 $\pm$ 0.44260 using Juliet. Bottom panel shows the residuals
between the best-fit model and data. Red white-filled markers shows the binned
data. Figure 8: Phase folded radial velocity curve, based on data obtained
from the ESO Science Archive Facility with DOI:
https://doi.org/10.18727/archive/33. Red line suggests the best-fit radial
velocity model using Juliet. Bottom panel shows the residuals between the
best-fit model and data.

From the best-fit model of transit (Fig. 7) and radial velocity (Fig. 8) using
Juliet, we calculated planetary and orbital parameters. Based on this TOI-181b
is a planet having the density 0.75 g cm-3, orbiting its host star in a
slightly eccentric orbit of eccentricity 0.15 having semi-major axis of 0.054
AU with orbital period 4.5320 days. TOI-181b has radius of 0.6339 RJ and mass
of 0.1452 MJ and has equilibrium temperature (assuming Bond Albedo (AB) = 0)
895.10 K. As mentioned mass of TOI-181b is 0.1452 MJ which is well-below the
exoplanet mass-limit of 13 MJ (Lecavelier des Etangs & Lissauer, 2022), so
along with measured FPPs using VESPA and TRICERATOPS, radial velocity
measurements also rules out the possibility of eclipsing binary and confirms
the planetary nature of TOI-181b. Using the Juliet best-fit model we also
derived quadratic limb darkening parameters for TESS infrared band: $u_{1}$ =
0.7259 ${}^{+0.08166}_{-0.1187}$, $u_{2}$ = -0.28075 ${}^{+0.1749}_{-0.0870}$.

Based on the priors provided, all the calculated planetary and orbital
parameters (mean value and 68 % confidence interval of the posterior
probability distribution) are listed in Table 6.

Table 6: Median values and 68% confidence interval for TOI 181 b from Juliet Parameters | Description (Unit) | Values
---|---|---
P | Period (days) | 4.5320 ${}^{+0.000002}_{-0.000002}$
$R_{P}$ | Radius ($R_{J}$) | 0.6339 ${}^{+0.0079}_{-0.0092}$
$R_{P}$ | Radius ($R_{\earth}$) | 6.9559 ${}^{+0.087}_{-0.101}$
$T_{C}$ | Epoch Time (BJD) | 2458358.12 ${}^{+0.00027}_{-0.00026}$
$T_{d}$ | Transit Duration (days) | 0.0829 ${}^{+0.0097}_{-0.0088}$
$a$ | Semi-major Axis (AU) | 0.0539 ${}^{+0.0043}_{-0.0036}$
$i$ | Inclination (Degree) | 88.28 ${}^{+0.32}_{-0.34}$
$e$ | Eccentricity | 0.1543 ${}^{+0.06}_{-0.03}$
$\omega$ | Argument of Periastron (Degree) | -96.91 ${}^{+19.48}_{-28.82}$
$T_{eqq}$ | Equilibrium Temperature (K) | 895.10 ${}^{+32.14}_{-33.86}$
$S$ | Insolation ($S_{\earth}$) | 102.43 ${}^{+15.52}_{-14.64}$
$M_{P}$ | Mass ($M_{J}$) | 0.1452 ${}^{+0.0085}_{-0.024}$
$M_{P}$ | Mass ($M_{\earth}$) | 46.1687 ${}^{+2.71}_{-7.83}$
K | RV Semi-amplitude (m $s^{-1}$) | 20.5610 ${}^{+1.46}_{-2.37}$
$logK$ | Log of RV Semi-amplitude | 1.3130 ${}^{+0.029}_{-0.053}$
$R_{P}/R_{S}$ | Radius of planet in stellar radii | 0.0854 ${}^{+0.001}_{-0.001}$
$a/R_{S}$ | Semi-major axis in stellar radii | 15.5641 ${}^{+1.25}_{-1.06}$
$\delta$ | Transit Depth (Fraction) | 0.0073 ${}^{+0.00018}_{-0.00021}$
$b$ | Impact Parameter | 0.5348 ${}^{+0.05}_{-0.07}$
$\rho$ | Density (cgs) | 0.7562 ${}^{+0.015}_{-0.100}$
$g_{P}$ | Surface Gravity (m $s^{-2}$) | 9.3642 ${}^{+0.30}_{-1.35}$
$M_{P}\sin i$ | Minimum Mass ($M_{J}$) | 0.1452 ${}^{+0.008}_{-0.024}$
$M_{P}/M_{S}$ | Mass Ratio | 0.000169 ${}^{+0.00001}_{-0.00003}$
TESS Infrared Band (Quadratic Limb Darkening Parameters)
$u_{1}$ | Limb Darkening Parameter | 0.6888 ${}^{+0.10}_{-0.13}$
$u_{2}$ | Limb Darkening Parameter | -0.2350 ${}^{+0.21}_{-0.12}$

##  4 Discussion

This paper describes the discovery of TOI-181b, the first exoplanet confirmed
by the VaTEST project. To further our understanding of sub-Saturn planets
orbiting metal-rich stars, precise determination of host star and planet
properties of TOI-181b is invaluable. In our discussion, we focus on derived
planet properties and their prominent features that make the planet
interesting to study.

###  4.1 TOI-181b and other known sub-Saturns

TOI-181b has a radius of 0.6339 RJ and a mass of 0.1452 MJ, which are greater
than Neptune’s radius and mass but smaller than Saturn’s, placing it in the
sub-Saturn or super-Neptune group. The density measured from mass and radius
is 0.75 g cm$-3$, which is comparable with Saturn’s density (0.69 g cm-3).
Petigura et al. (2017) has gathered a sample of 23 sub-Saturns (Table 7) with
densities measured at 50% or better. Further this sample was extended by 7
more sub-Saturns (Table 8) by Nowak et al. (2020). We expanded this sample
with the discovery of TOI-181b and also identified 16 more sub-Saturns (Table
9) with measured densities with a precision of 50% or better. K2-98b (Barragán
et al., 2016), planet having radius 4.3 $R_{\earth}$ and mass 32 $M_{\earth}$,
which is one of the dense sub-Saturns ($\rho$ = 2.15 g $cm^{-3}$) after
Kepler-413b (Kostov et al., 2014, $\rho$ = 3.2 g $cm^{-3}$) and K2-108b
(Petigura et al., 2017, $\rho$ = 2.22 g $cm^{-3}$). TOI-421 c (Carleo et al.,
2020) having radius 5.09 $R_{\earth}$ and mass 16.42 $M_{\earth}$, which is
one of the few sub-Saturns orbiting in multi-planetary system. An ultra-hot
sub-Saturn LTT 9779 b (Jenkins et al., 2020) having equilibrium temperature
1978 K. Other sub-Saturns are listed in Table 9.

Figure 9: Top figure: Scatter plot of planetary radius and mass of all the
known sub-Saturns. Bottom figure: Scatter plot of planetary density (g cm-3)
vs planetary mass ($M_{\earth}$). Colorbar shows the equilibrium planetary
temperature in kelvin. TOI-181b is marked by text. Planets are taken from the
NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/).

The top panel of Fig. 9 shows the scatter plot for radius and mass of all
known sub-Saturns along with TOI-181b. This plot depicts the main
characteristics of sub-Saturns observed by Petigura et al. (2017). There seems
to be no correlation between planetary radius and mass. This type of planets
have a narrow range of radii (4–8 $R_{\earth}$) but is uniformly distributed
throughout its mass. As can be seen from the Fig. 9, there is an absence of
sub-Saturns for radii range 5.5 - 6.5 $R_{\earth}$ and masses of 20 - 30
$M_{\earth}$. TOI-181b is located at the upper edge of this scarcity, which
makes it an interesting object to study the transition between small and
massive sub-Saturns.

The bottom panel of Fig. 9 shows the plot of density vs mass for the known
sample of sub-Saturns. There seems to be little correlation between these
parameters. For this 47 sub-Saturn sample, the Spearman’s rank correlation
coefficient is r = 0.62, which is a little lower than the r = 0.79 measured by
Petigura et al. (2017) and the r = 72 measured by Nowak et al. (2020). This
shows that the association between these two variables would be considered
statistically significant.

###  4.2 Eccentricity and Orbital Circularization

TOI-181b has non-zero eccentricity of 0.15 and a short orbital period of 4.52
days. Based on this it can be expected that tides will damp away the
eccentricity. To check this scenario we calculated orbit circularization rate
(Goldreich & Soter, 1966),

$\tau_{e}=\frac{4}{63}\left(\frac{Q^{\prime}}{n}\right)\left(\frac{M_{P}}{M_{*}}\right)\left(\frac{a}{R_{P}}\right)^{5}$
(1)

where, n is mean motion given by $\sqrt{GM_{*}/a^{3}}$ and Q’ is modified
tidal quality factor which is given by $Q^{\prime}=3Q/2k_{2}$. Q is specific
dissipation function and $k_{2}$ is Love number (Goldreich & Soter, 1966;
Mardling & Lin, 2004). Value for $Q^{\prime}$ is uncertain even for solar
system planets. Petigura et al. (2017) had assumed $Q^{\prime}=10^{5}$ for
sub-Saturns. We are following the same assumption here to measure
circularization rate. As per eq. 1 we measured $\tau_{e}$ = 0.42 Gyr. Because
this timescale is shorter than the age of its host star, the circularization
caused by tides cannot account for the eccentric nature of planetary orbits.
Though if we use $Q^{\prime}=10^{6}$ resultant $\tau_{e}$ is 4.19 Gyr which is
greater than the lower bound of stellar age. So this tension can be alleviated
by adopting $Q^{\prime}=10^{6}$ instead of $10^{5}$. Alternative solutions
include additional undetected exoplanets in the system. This eccentric orbit
can persist by the planet-planet interactions. So if this is true than it is
very plausible that a second planet that is yet to be discovered is causing
continual gravitational perturbations to keep TOI-181b’s eccentricity constant
over very long periods.

###  4.3 Atmospheric Characterization

By taking into account the brightness of the host star, radius, mass and
planetary equilibrium temperature, Kempton et al. (2018) developed a method to
calculate Transmission and Emission Spectroscopy Metrics (TSM and ESM). TSM
and ESM will make it simple to identify the best atmospheric characterization
targets among the TESS planet candidates by calculating the expected James
Webb Space Telescope (JWST) signal-to-noise ratio in transmission and thermal
emission spectroscopy for a given planet. For TOI-181b TSM is measured as
179.17 which is above the threshold of forth quartile suggested by Kempton et
al. (2018), that makes it a good target for transmission spectroscopy. ESM is
measured as 34.76 which is also well above the threshold of 7.5 that makes the
planet amenable to perform atmospheric characterization, with a focus on JWST
capabilities. By assuming H/He atmosphere we calculated atmospheric scale
height ($H=K_{b}T_{eq}/\mu g$ Madhusudhan et al. (2014), where $\mu$ (mean
molecular mass) = 2.4, $K_{b}$ (Boltzmann Constant)) of 331.13 km. Based on
this value we estimated amplitude of spectral features for transmission
spectroscopy (Kreidberg, 2018) which arrived to be 0.023%. This suggest that
TOI-181b may not suitable for ground-based transmission spectroscopy but the
previous results of TSM and ESM suggesting it to be the good target for JWST
spectroscopy. By assessing the elemental compositions and total metal
enrichment of planet’s atmosphere, such studies could directly evaluate our
hypotheses regarding the planet’s bulk composition and creation history.
Future investigations will determine the atmospheric composition of this and
other sub-Saturns with low densities, thereby shedding light on the nature of
these mystery objects.

###  4.4 Planetary Envelope Fraction

Sub-Saturns are structurally distinct from other types of planets. It has both
heavy elements in its core and a gaseous envelope surrounding the planet, both
of which contribute significantly to the overall mass. Having such large radii
imply that the envelopes of H/He make up a significant percentage of their
overall mass (Lopez & Fortney, 2014), with typical envelope fractions
($f_{env}$) ranging from 10% to 50%. The PLATYPOS (PLAneTarY Photoevaporation
Simulator) algorithm (Ketzer & Poppenhaeger, 2022) is used to calculate the
envelope fraction and core mass of TOI-181b. This simulator estimates
$f_{env}$ using the Lopez & Fortney (2014) model, then uses existing
parametrizations of planetary mass-radius relations with an energy-limited
hydrodynamic escape model to estimate the mass-loss rate over time. We used
the grid of core mass, radius, distance, and metallicity to solve for
planetary mass. We interpolated the known planetary mass to estimate the
$f_{env}$. Based on the assumption (Petigura et al., 2016) that the envelope
fractions are unaffected by the detailed structure and composition of the
core, we estimated the $f_{env}$ to be 60.97%, implying that TOI-181b has the
majority of its mass in its H/He envelope. We measured the core mass of 18.02
$M_{\earth}$ and core radius of 2.06 $R_{\earth}$ (super-Earth sized).
Estimated $f_{env}$ for TOI-181b is highest among all known sub-Saturns. We
calculated planetary metal enrichment ($Z_{P}/Z_{*}$ where,
$Z_{*}=Z_{\sun}10^{[Fe/H]}$, $Z_{P}=M_{core}/M_{env}$) to be 17.28. This value
is towards the lower end of the other planets’ metal enrichment fraction
(Thorngren et al., 2016) as the maximum mass of TOI-181b is carried in its
envelope. We calculated the planet’s gravitational binding energy of
$6.85\times 10^{41}$ erg, for which the survival threshold predicted by photo-
evaporation and thermal evolution models is $\approx 7.29\times 10^{40}$ erg
(Lopez et al., 2012). For our target, we measured the lifetime integrated XUV
flux incident to be $1.35\times 10^{36}$ erg, which is well below the
mentioned threshold. As a result, TOI-181b is either sufficiently massive or
in a wide enough orbit to be immune to significant photo-evaporation.

###  4.5 Hot-Neptune Desert

Fig. 10 depicts the relationship between planetary radii and orbital periods
for all known exoplanets. TOI-181b carries a red star indication. The study
demonstrates that Neptune-like planets in tight orbits are uncommon due to
X-ray or Extreme Ultra Violet (EUV) emission from the host rapidly stripping
close-in short-period planets’ atmospheres and leaving behind low-mass rocky
cores (Lopez & Fortney, 2013; Owen & Lai, 2018; Chen & Rogers, 2016). This
region is known as the "Hot Neptune Desert" (Mazeh et al., 2016). The dashed
line in Fig. 10 depicts the Neptune desert. The suggested photoevaporation
mechanism is consistent with the lowest boundary of the hot Neptune desert
(i.e., planets with small radii). In addition to that, tidal disruption of
planets in in eccentric orbit and circularization of the orbit due to tidal
interactions with the host star can explain both upper and lower boundary of
desert (Owen & Lai, 2018). TOI-181b is within this sparsely hot Neptune desert
and is one of the largest planets discovered in this region; hence, it retains
a substantial amount of its volatile envelope. This can be explained as,
TOI-181b has enough gravitational binding energy to hold its massive H/He
envelope against the incident hig energy X-ray or EUV radiation, which is
already discussed in section 4.4.

Figure 10: Distribution of known exoplanets in the graph of radii vs orbital
period. Red star sign shows TOI-181b and region enclosed inside black dashed
line shows the "Hot Neptune Desert". Planets are taken from the NASA Exoplanet
Archive (https://exoplanetarchive.ipac.caltech.edu/)

##  5 Conclusions

In this paper, we describe the validation of the sub-Saturn-like exoplanet
TOI-181b. In order to validate, we obtained spectral information from the ESO
science portal, which was collected by the 3.6-meter HARPS telescope, and
transit photometry data from the MAST archive. We used two different false
positive probability calculating software as an independen check to test the
transit signals. The FPP for VESPA and TRICERATOPS was $1.68\times 10^{-14}$
and $3.81\times 10^{-4}$, respectively, which is significantly less than the 1
% threshold. The high resolution image obtained with the Keck II/NIRC2 camera
further suggests that the target is not being affected by any nearby
companions. Additionally, we used Juliet to fit a transit and radial velocity
model to the data. The calculated planetary parameters based on the best-fit
model are: Orbital period 4.5320 $\pm$ 0.000002 days, Radius 0.63 $\pm$ 0.007
RJ, Transit Duration 0.083 $\pm$ 0.009 days, Equilibrium Temperature 895.10
$\pm$ 33.86 K, Insolation 102.43 $\pm$ 15.52 S⊕, Mass 0.1452 $\pm$ 0.02 MJ,
Density 0.75 $\pm$ 0.1 g cm-3, and surface gravity 9.36 $\pm$ 1.35 m s-2. We
also find out the quadratic limb darkening parameters of the TESS infrared
band and those are 0.6888 $\pm$ 0.13 and -0.2350 $\pm$ 0.21. Based on these
calculated parameters, TOI-181b is characterised as a Sub-Saturn like planet.

## Acknowledgements

This work has made use of the materials provided by Planet Hunters Coffee
Chat, which is funded through NASA. This work made use of a virtual machine
provided and maintained by Kevin Hardegree-Ullman to run the VESPA code. This
research has made use of the Exoplanet Follow-up Observation Program website,
which is operated by the California Institute of Technology, under contract
with the National Aeronautics and Space Administration under the Exoplanet
Exploration Program. We also thank the people who came forward and shared
their experiences throughout the way. The following software were used in this
research: TLS (Hippke & Heller, 2019), Lightkurve (Lightkurve Collaboration et
al., 2018), Juliet (Espinoza et al., 2019), VESPA (Morton, 2012) and
TRICERATOPS (Giacalone & Dressing, 2020), PLATYPOS (Ketzer & Poppenhaeger,
2022).

## Data Availability

The TESS photometry and the high angular resolution imaging data used in this
article are available at the Mikulski Archive for Space Telescope (MAST)
(https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html) and the
ExoFOP-TESS website
(https://exofop.ipac.caltech.edu/tess/target.php?id=76923707) respectively.
Radial velocity data are provided in Table 1. The data underlying this article
will be made available on the reasonable request to the corresponding author.

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##  Appendix A Known Sample of Sub-Saturns

Planet | $N_{P}$ | $N_{S}$ | Radius | Mass | Density | Temperature | Eccentricity | [Fe/H] | Reference
---|---|---|---|---|---|---|---|---|---
|  |  | $R_{\earth}$ | $M_{\earth}$ | g $cm^{-3}$ | K |  | dex |
CoRoT-8 b | 1 | 1 | 6.39${}^{+0.22}_{-0.22}$ | 69.29${}^{+10.49}_{-13.03}$ | 1.45${}^{+0.29}_{-0.29}$ | 844 | — | 0.30 | Bordé et al. (2010)
GJ 436 b | 1 | 1 | 4.09${}^{+0.20}_{-0.20}$ | 23.42${}^{+1.72}_{-1.72}$ | 2.01${}^{+0.25}_{-0.25}$ | 669 | 0.14 | -0.03 | Butler et al. (2004)
HAT-P-11 b | 1 | 1 | 4.45${}^{+0.10}_{-0.10}$ | 26.70${}^{+2.22}_{-2.22}$ | 1.68${}^{+0.16}_{-0.16}$ | 838 | 0.20 | 0.31 | Bakos et al. (2010)
HAT-P-26 b | 1 | 1 | 6.33${}^{+0.81}_{-0.36}$ | 18.75${}^{+2.23}_{-2.23}$ | 0.4${}^{+0.10}_{-0.10}$ | 1001 | 0.12 | -0.04 | Hartman et al. (2011)
HATS-7 b | 1 | 1 | 6.31${}^{+0.52}_{-0.38}$ | 39.09${}^{+4.45}_{-4.45}$ | 0.88${}^{+0.24}_{-0.19}$ | 1070 | — | 0.25 | Bakos et al. (2015)
K2-108 b | 1 | 1 | 5.28${}^{+0.54}_{-0.54}$ | 59.40${}^{+4.40}_{-4.40}$ | 2.22${}^{+0.77}_{-0.55}$ | 1446 | 0.18 | 0.33 | Petigura et al. (2017)
K2-24 b | 2 | 1 | 5.40${}^{+0.20}_{-0.20}$ | 19.00${}^{+2.20}_{-2.10}$ | 0.64${}^{+0.12}_{-0.10}$ | 766 | — | 0.42 | Petigura et al. (2016)
K2-24 c | 2 | 1 | 7.50${}^{+0.30}_{-0.30}$ | 15.40${}^{+1.90}_{-1.80}$ | 0.20${}^{+0.04}_{-0.03}$ | 605 | — | 0.42 | Petigura et al. (2016)
K2-27 b | 1 | 3 | 4.45${}^{+0.33}_{-0.33}$ | 29.10${}^{+7.50}_{-7.40}$ | 1.80${}^{+0.70}_{-0.55}$ | 910 | 0.25 | 0.13 | Petigura et al. (2017)
K2-32 b | 3 | 2 | 5.13${}^{+0.28}_{-0.28}$ | 16.50${}^{+2.70}_{-2.70}$ | 0.67${}^{+0.16}_{-0.16}$ | 817 | — | -0.02 | Petigura et al. (2017)
K2-39 b | 1 | 1 | 5.71${}^{+0.63}_{-0.63}$ | 39.80${}^{+4.40}_{-4.40}$ | 1.17${}^{+0.47}_{-0.32}$ | 1670 | 0.15 | 0.43 | Petigura et al. (2017)
Kepler-101 b | 2 | 1 | 5.77${}^{+0.85}_{-0.79}$ | 51.10${}^{+5.10}_{-4.70}$ | 1.45${}^{+0.83}_{-0.48}$ | 1513 | 0.09 | 0.33 | Rowe et al. (2014)
Kepler-11 e | 6 | 1 | 4.00${}^{+0.20}_{-0.30}$ | 6.70${}^{+1.20}_{-1.00}$ | 0.60${}^{+0.20}_{-0.10}$ | 630 | 0.01 | -0.04 | Lissauer et al. (2011)
Kepler-18 c | 3 | 1 | 5.22${}^{+0.36}_{-0.34}$ | 18.40${}^{+2.70}_{-1.90}$ | 0.57${}^{+0.12}_{-0.10}$ | 979 | — | 0.19 | Cochran et al. (2011)
Kepler-18 d | 3 | 1 | 6.00${}^{+0.40}_{-0.40}$ | 14.90${}^{+1.80}_{-4.20}$ | 0.30${}^{+0.10}_{-0.10}$ | 784 | — | 0.19 | Cochran et al. (2011)
Kepler-223 d | 4 | 1 | 5.24${}^{+0.26}_{-0.45}$ | 8.00${}^{+1.50}_{-1.30}$ | 0.31${}^{+0.12}_{-0.07}$ | 1040 | 0.04 | 0.06 | Rowe et al. (2014)
Kepler-223 e | 4 | 1 | 4.60${}^{+0.27}_{-0.41}$ | 4.80${}^{+1.40}_{-1.20}$ | 0.28${}^{+0.12}_{-0.08}$ | 944 | 0.05 | 0.06 | Rowe et al. (2014)
Kepler-25 c | 3 | 2 | 4.50${}^{+0.08}_{-0.08}$ | 14.30${}^{+2.70}_{-2.50}$ | 0.96${}^{+0.24}_{-0.23}$ | 1080 | — | -0.04 | Steffen et al. (2012)
Kepler-4 b | 1 | 1 | 4.00${}^{+0.21}_{-0.21}$ | 24.47${}^{+3.81}_{-3.81}$ | 1.91${}^{+0.36}_{-0.47}$ | 1650 | — | 0.17 | Borucki et al. (2010b)
Kepler-413 b | 1 | 2 | 4.35${}^{+0.10}_{-0.10}$ | 67.00${}^{+22.0}_{-21.0}$ | 3.20${}^{+1.00}_{-1.00}$ | 348 | 0.12 | -0.20 | Kostov et al. (2014)
Kepler-56 b | 3 | 1 | 5.10${}^{+0.50}_{-0.70}$ | 32.00${}^{+11.20}_{-0.50}$ | 1.40${}^{+0.50}_{-0.50}$ | 1479 | — | 0.37 | Steffen et al. (2013)
Kepler-79 d | 4 | 1 | 6.91${}^{+0.01}_{-0.01}$ | 11.30${}^{+2.20}_{-2.20}$ | 0.09${}^{+0.03}_{-0.03}$ | 626 | 0.03 | -0.02 | Rowe et al. (2014)
Kepler-87 c | 2 | 1 | 6.14${}^{+0.29}_{-0.29}$ | 6.40${}^{+0.80}_{-0.80}$ | 0.15${}^{+0.02}_{-0.02}$ | 403 | 0.04 | -0.17 | Ofir et al. (2014)
Table 7: Sample of sub-Saturns from Petigura et al. (2017). $N_{P}$: Number of Planets, $N_{S}$: Number of Stars. Planet | $N_{P}$ | $N_{S}$ | Radius | Mass | Density | Temperature | Eccentricity | [Fe/H] | Reference
---|---|---|---|---|---|---|---|---|---
|  |  | $R_{\earth}$ | $M_{\earth}$ | g $cm^{-3}$ | K |  | dex |
GJ-3470 b | 1 | 1 | 4.57${}^{+0.18}_{-0.18}$ | 13.90${}^{+1.50}_{-1.50}$ | 0.80${}^{+0.13}_{-0.13}$ | 594 | — | 0.20 | Bonfils et al. (2012)
HD 219666 b | 1 | 1 | 4.71${}^{+0.17}_{-0.17}$ | 16.60${}^{+1.30}_{-1.30}$ | 0.87${}^{+0.12}_{-0.11}$ | 1073 | 0.00 | 0.04 | Esposito et al. (2019)
HD 89345 b | 1 | 1 | 6.86${}^{+0.14}_{-0.14}$ | 35.70${}^{+3.30}_{-3.30}$ | 0.61${}^{+0.07}_{-0.07}$ | 1053 | 0.20 | 0.45 | Van Eylen et al. (2018)
K2-280 b | 1 | 1 | 7.50${}^{+0.44}_{-0.44}$ | 37.10${}^{+5.60}_{-5.60}$ | 0.48${}^{+0.13}_{-0.10}$ | 787 | 0.35 | 0.33 | Livingston et al. (2018)
K2-60 b | 1 | 1 | 7.66${}^{+0.42}_{-0.42}$ | 135.4${}^{+11.76}_{-11.76}$ | 1.7${}^{+0.30}_{-0.30}$ | 1400 | 0.00 | 0.01 | Crossfield et al. (2016)
Kepler-1656 b | 2 | 1 | 5.02${}^{+0.53}_{-0.53}$ | 48.60${}^{+4.20}_{-3.80}$ | 2.13${}^{+0.87}_{-0.57}$ | 651 | 0.84 | 0.19 | Brady et al. (2018)
WASP-156 b | 1 | 1 | 5.72${}^{+0.22}_{-0.22}$ | 40.68${}^{+3.18}_{-2.86}$ | 1.30${}^{+0.10}_{-0.10}$ | 970 | 0.01 | 0.24 | Demangeon et al. (2018)
Table 8: Extension of previous sample by Nowak et al. (2020). Planet | $N_{P}$ | $N_{S}$ | Radius | Mass | Density | Temperature | Eccentricity | [Fe/H] | Reference
---|---|---|---|---|---|---|---|---|---
|  |  | $R_{\earth}$ | $M_{\earth}$ | g $cm^{-3}$ | K |  | dex |
AU Mic b | 2 | 1 | 4.07${}^{+0.17}_{-0.17}$ | 17.00${}^{+5.00}_{-5.00}$ | 1.40${}^{+0.40}_{-0.40}$ | 593 | 0.00 | — | Plavchan et al. (2020)
HATS-37 A b | 1 | 2 | 6.79${}^{+0.18}_{-0.18}$ | 31.47${}^{+13.35}_{-13.35}$ | 0.55${}^{+0.24}_{-0.24}$ | 1085 | 0.00 | 0.05 | Jordán et al. (2020)
HATS-38 b | 1 | 1 | 6.88${}^{+0.19}_{-0.19}$ | 23.52${}^{+3.50}_{-3.50}$ | 0.40${}^{+0.07}_{-0.07}$ | 1294 | 0.00 | -0.10 | Jordán et al. (2020)
K2-98 b | 1 | 1 | 4.30${}^{+0.30}_{-0.20}$ | 32.20${}^{+8.10}_{-8.10}$ | 2.15${}^{+0.67}_{-0.60}$ | 1102 | 0.00 | -0.20 | Barragán et al. (2016)
KOI-1783.02 | 2 | 1 | 5.44${}^{+0.52}_{-0.30}$ | 15.00${}^{+4.30}_{-3.60}$ | 0.51${}^{+0.21}_{-0.15}$ | — | 0.00 | 0.11 | Vissapragada et al. (2020)
LP 714-47 b | 1 | 1 | 4.70${}^{+0.30}_{-0.30}$ | 30.80${}^{+1.50}_{-1.50}$ | 1.70${}^{+0.30}_{-0.30}$ | 700 | 0.04 | 0.41 | Dreizler et al. (2020)
LTT 9779 b | 1 | 1 | 4.72${}^{+0.23}_{-0.23}$ | 29.32${}^{+0.78}_{-0.81}$ | 1.54${}^{+0.12}_{-0.12}$ | 1978 | 0.00 | 0.27 | Jenkins et al. (2020)
NGTS-14 A b | 1 | 2 | 4.98${}^{+0.34}_{-0.34}$ | 29.24${}^{+3.81}_{-3.81}$ | 1.40${}^{+0.33}_{-0.33}$ | 1143 | 0.00 | 0.10 | Smith et al. (2021)
TOI-1710 b | 1 | 1 | 5.34${}^{+0.11}_{-0.11}$ | 28.30${}^{+4.70}_{-4.70}$ | 0.94${}^{+0.22}_{-0.22}$ | 687 | 0.16 | 0.10 | König et al. (2022)
TOI-1728 b | 1 | 1 | 5.05${}^{+0.16}_{-0.17}$ | 26.78${}^{+5.43}_{-5.13}$ | 1.14${}^{+0.26}_{-0.24}$ | 767 | 0.06 | 0.25 | Kanodia et al. (2020)
TOI-181 b | 1 | 1 | 6.96${}^{+0.09}_{-0.10}$ | 46.17${}^{+2.71}_{-7.83}$ | 0.76${}^{+0.02}_{-0.10}$ | 895 | 0.15 | 0.27 | This Work
TOI-257 b | 1 | 1 | 7.16${}^{+0.15}_{-0.15}$ | 43.86${}^{+7.31}_{-7.31}$ | 0.65${}^{+0.12}_{-0.11}$ | 1027 | 0.00 | 0.17 | Addison et al. (2021)
TOI-3884 b | 1 | 1 | 6.00${}^{+0.18}_{-0.18}$ | 16.50${}^{+3.50}_{-1.80}$ | 0.42${}^{+0.10}_{-0.06}$ | 463 | — | 0.23 | Almenara et al. (2022)
TOI-421 c | 2 | 2 | 5.09${}^{+0.16}_{-0.15}$ | 16.42${}^{+1.06}_{-1.04}$ | 0.69${}^{+0.08}_{-0.07}$ | 674 | 0.15 | -0.02 | Carleo et al. (2020)
TOI-532 b | 1 | 1 | 5.82${}^{+0.19}_{-0.19}$ | 61.50${}^{+9.70}_{-9.30}$ | 1.72${}^{+0.31}_{-0.31}$ | 867 | 0.00 | 0.34 | Kanodia et al. (2021)
TOI-674 b | 1 | 1 | 5.25${}^{+0.17}_{-0.17}$ | 23.60${}^{+3.30}_{-3.30}$ | 0.91${}^{+0.15}_{-0.15}$ | 635 | 0.00 | 0.17 | Murgas et al. (2021)
WASP-166 b | 1 | 1 | 7.06${}^{+0.34}_{-0.34}$ | 32.10${}^{+1.59}_{-1.59}$ | 0.54${}^{+0.09}_{-0.09}$ | 1270 | 0.00 | 0.19 | Hellier et al. (2019)
Table 9: Extension of previous list by this paper.