# Systematic analysis of jellyfish galaxy candidates in Fornax, Antlia, and
Hydra from the S-PLUS survey: A self-supervised visual identification aid

Yash Gondhalekar1, Ana L. Chies-Santos2 , Rafael S. de Souza3, Carolina
Queiroz4, Amanda R. Lopes5, Fabricio Ferrari6, Gabriel M. Azevedo2, Hellen
Monteiro-Pereira2, Roderik Overzier7,8, Analía V. Smith Castelli5,9,Yara L.
Jaffé10, Rodrigo F. Haack5,9, P.T. Rahna11, Shiyin Shen12, Zihao Mu12, Ciria
Lima-Dias13, Carlos E. Barbosa14, Gustavo B. Oliveira Schwarz14,15, Rogério
Riffel2,16, Yolanda Jimenez-Teja17, Marco Grossi18, Claudia L. Mendes de
Oliveira14, William Schoenell19, Thiago Ribeiro20, Antonio Kanaan21

1Department of CSIS, BITS Pilani K.K Birla Goa Campus, Goa, 403726, Goa, India
2Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Av.
Bento Gonçalves, 9500, Porto Alegre, RS, Brazil
3Centre for Astrophysics Research, University of Hertfordshire, College Lane,
Hatfield, AL10 9AB, UK
4Departamento de Física Matemática, Instituto de Física, Universidade de São
Paulo, Rua do Matão, 1371, CEP 05508-090, São Paulo, Brazil
5Instituto de Astrofísica de La Plata, UNLP-CONICET, Paseo del Bosque s/n,
B1900FWA, Argentina
6Instituto de Matemática Estatística e Física, Universidade Federal do Rio
Grande, Rio Grande, RS, Brazil
7Observatório Nacional, Rua General José Cristino, 77, São Cristóvão,
20921-400 Rio de Janeiro, RJ, Brazil
8Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA, Leiden, The
Netherlands
9Facultad de Ciencias Astrónomicas y Geofísicas, Universidad Nacional de La
Plata, Paseo del Bosque s/n, B1900FWA, Argentina
10Departamento de Física, Universidad Técnica Federico Santa María, Avenida
España 1600, Valparaíso, Chile
11 Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan,
1, 44001 Teruel, Spain.
12Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai,
China
13Instituto Multidisciplinario de Investigación y Postgrado, Universidad de La
Serena, Raúl Bitrán 1305, La Serena, Chile
14Universidade de São Paulo, IAG, Rua do Mato 1225, Sao Paulo, SP, Brazil
15Universidade Presbiteriana Mackenzie, R. da Consolação, 930 - Consolação,
São Paulo, Brazil
16Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, E-38205 La
Laguna, Tenerife, Spain
17Instituto de Astrofísica de Andalucía–CSIC, Glorieta de la Astronomía s/n,
E–18008 Granada, Spain
18 Observatório do Valongo, Universidade Federal do Rio de Janeiro, Rio de
Janeiro, RJ, Brazil
19GMTO Corporation 465 N. Halstead Street, Suite 250 Pasadena, CA 91107, USA
20Rubin Observatory Project Office, 950 N. Cherry Ave., Tucson, AZ 85719, USA
21Departamento de Física - CFM - Universidade Federal de Santa Catarina, PO
BOx 476, 88040-900, Florianópolis, SC, Brazil
yashgondhalekar567@gmail.comana.chies<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We study 51 jellyfish galaxy candidates in the Fornax, Antlia, and Hydra
clusters. These candidates are identified using the JClass scheme based on the
visual classification of wide-field, twelve-band optical images obtained from
the Southern Photometric Local Universe Survey. A comprehensive astrophysical
analysis of the jellyfish (JClass > 0), non-jellyfish (JClass = 0), and
independently organized control samples is undertaken. We develop a semi-
automated pipeline using self-supervised learning and similarity search to
detect jellyfish galaxies. The proposed framework is designed to assist visual
classifiers by providing more reliable JClasses for galaxies. We find that
jellyfish candidates exhibit a lower Gini coefficient, higher entropy, and a
lower 2D Sérsic index as the jellyfish features in these galaxies become more
pronounced. Jellyfish candidates show elevated star formation rates (including
contributions from the main body and tails) by $\sim$1.75 dex, suggesting a
significant increase in the SFR caused by the ram-pressure stripping
phenomenon. Galaxies in the Antlia and Fornax clusters preferentially fall
towards the cluster’s centre, whereas only a mild preference is observed for
Hydra galaxies. Our self-supervised pipeline, applied in visually challenging
cases, offers two main advantages: it reduces human visual biases and scales
effectively for large datasets. This versatile framework promises substantial
enhancements in morphology studies for future galaxy image surveys.

###### keywords:

surveys – techniques: photometric – galaxies: clusters: general – galaxies:
evolution – methods: statistical

††pubyear: 2023††pagerange: Systematic analysis of jellyfish galaxy candidates
in Fornax, Antlia, and Hydra from the S-PLUS survey: A self-supervised visual
identification aid–E

##  1 Introduction

The distribution of galaxies of different morphological types is not uniform
through space. Most galaxies are in groups and clusters, while a smaller
fraction are isolated in the field and voids. The density of the environment
influences immensely the morphological types that are dominant in that region
of the Universe. The morphology-density relation shows that the fractions of
ellipticals and lenticular galaxies increase with environmental density, while
the fractions of spirals and irregular decrease (Dressler, 1980; Goto et al.,
2003; Houghton, 2015; Pfeffer et al., 2023).

Galaxies in dense environments are more subjected to environmental
interaction, both gravitational (with neighbouring galaxies or the cluster
gravitational potential) and hydrodynamical (with the intracluster gas). Such
interactions may end up suppressing the star formation of late-type galaxies
and changing their morphology, turning spirals and irregulars into ellipticals
and S0s. The primary hydrodynamical process that takes place in clusters and
groups is the ram pressure stripping (RPS, Gunn & Gott, 1972), which strips
out the interstellar gas from the galaxies’ disks and may form a unique type
of galaxy called jellyfish.

Jellyfish galaxies, distinguished by their tentacle-like features composed of
ionised gas and star-forming regions, represent a distinctive category of
galaxies undergoing transformation (see Boselli et al., 2022, and references
therein). These galaxies are subject to RPS, which significantly affects their
morphology and may enhance their star formation (Vulcani et al., 2018; Roman-
Oliveira et al., 2019; Azevedo et al., 2023). RPS involves the removal of the
galaxy’s cold interstellar gas by the hot intracluster medium, generally
opposing the galaxy’s movement (e.g., Abadi et al., 1999). Although RPS is
more prevalent in spiral galaxies (Kenney & Koopmann, 1999; Poggianti et al.,
2016b; Fossati et al., 2018; Roman-Oliveira et al., 2019; Roberts et al.,
2021a; Roberts et al., 2021b), it can also occur in elliptical (Sheen et al.,
2017), dwarf (Kenney et al., 2014), and ring galaxies (Moretti et al., 2018).
Consequently, studying jellyfish galaxies and their formation provides
essential insights into galaxy interactions, their environmental effects, and
overall evolution.

RPS galaxies were first observed several decades ago (Haynes et al., 1984).
However, recent advances in observational surveys and cosmological simulations
have enabled more comprehensive and detailed investigations into these
objects. Using the high-resolution TNG100 (i.e., box size of $100\,h^{-1}$Mpc)
simulations, Yun et al. (2018) identified satellite galaxies in massive groups
and clusters exhibiting asymmetric gas distributions and tails,
characteristics indicative of ram pressure stripping. Their findings suggest
that approximately 13 per cent of cluster satellites at redshifts $z<0.6$ bear
the signatures of ram pressure stripping and associated gaseous tails. When
the analysis was confined to gas-rich galaxies, this proportion escalated to
31 per cent. Additionally, Yun et al. (2018) pointed out that these estimates
could be considered conservative lower limits, as potential jellyfish
candidates could be overlooked due to their random orientation, possibly
missing approximately 30 per cent of them. Recently, Zinger et al. (2023)
extended Yun et al. (2018)’s study to incorporate TNG50 with TNG100
simulations to present a richer sample of jellyfish candidates residing in
hosts at the lower mass end, outskirts of groups or clusters, and at the
higher redshift regime.Rohr et al. (2023); Göller et al. (2023) further
investigated their evolution and loss of cold gas. They find that while
jellyfish candidates undergo dominating star formation in their main bodies
(i.e., discs), no significant overall enhancement was observed in their star
formation rates compared to the control sample consisting of satellite and
field galaxies with similar properties known to affect star formation
(redshift, stellar mass, host mass, gas content).

From an observational perspective, galaxies undergoing ram pressure stripping
have been scrutinised using photometry and integral field spectroscopy (IFS)
over a wide spectral range, extending from the ultraviolet to radio
frequencies (Jaffé et al., 2015; Poggianti et al., 2017; Fossati et al., 2018;
George et al., 2018; Roman-Oliveira et al., 2019; Roberts et al., 2021a).
These studies have led to the detection of significant amounts of ionised,
atomic, and molecular gas in the tails and discs of these galaxies (Jaffé et
al., 2015; Poggianti et al., 2017; Fossati et al., 2018; Poggianti et al.,
2019a; Roman-Oliveira et al., 2019; Ramatsoku et al., 2019, 2020; Deb et al.,
2020; Moretti et al., 2020). Many dedicated works have been performed in the
past decade, focusing specifically on these galaxies and probing them in
diverse environments at different redshifts. Such efforts have resulted in the
discovery of dozens to hundreds of jellyfish galaxy candidates in both low-
redshift ($z\lesssim 0.1$) and medium-redshift ($0.2<z<0.9$) clusters and
groups (Poggianti et al., 2016a, 2017; Roberts et al., 2021a; Roberts et al.,
2021b; Durret et al., 2021, 2022). Notably, over 70 jellyfish candidates have
been found within the A901/2 multi-cluster system alone (Roman-Oliveira et
al., 2019; Roman-Oliveira et al., 2021; Ruggiero et al., 2019).

A defining feature of jellyfish galaxies is their enhanced star formation
activity. These galaxies have been observed to possess higher star formation
rates (SFRs) compared to other star-forming galaxies within clusters, with
SFRs often exceeding even those of starburst galaxies (Merluzzi et al., 2013;
Vulcani et al., 2018; Roman-Oliveira et al., 2019; Roberts et al., 2021a),
with a notable enhancement within their ‘tentacle’ structures (Gullieuszik et
al., 2020). This intensified activity is believed to result from compression
and shock waves generated as the galaxy traverses through the surrounding
intracluster medium (Vulcani et al., 2020). However, the enhancement of SFRs
for jellyfish candidates belonging to galaxy groups is yet to be fully
understood since some studies find an enhancement (e.g., Kolcu et al., 2022)
while some do not (e.g., Oman et al., 2021; Roberts et al., 2021b). This
elevated star formation rate in cluster jellyfish candidates points to a phase
of active evolution in these galaxies, shedding light on the potential
mechanisms driving galaxy evolution. However, the ultimate fate of these
dynamically evolving galaxies remains uncertain. One possibility is that RPS
could transform spiral and irregular galaxies into lenticular and elliptical
galaxies, as removing gas could eventually lead to quenching (Larson et al.,
1980). Additionally, spirals may undergo a process termed ‘diffusion’,
culminating in their transformation into dwarf galaxies (Roman-Oliveira et
al., 2021). Another intriguing possibility is that the observed ultra-compact
dwarfs (UCDs) and intracluster globular clusters (GCs) in low-redshift
clusters may originate from H ii regions formed in the tails of jellyfish
candidates, given the observed similarities in their mass (Poggianti et al.,
2019a; Giunchi et al., 2023).

Traditionally, jellyfish candidates have been identified through visual
inspection in optical wavelengths, which has resulted in a classification
scheme based on observed stripping signatures in the optical bands, known as
JClass (Poggianti et al., 2016b). This scheme encompasses a spectrum of cases
ranging from the most extreme (JClass 5) to progressively milder (JClass 1)
instances. For example, Fig. 1 of Roman-Oliveira et al. (2019) and Figs. 1–3
of Poggianti et al. (2016b) show visual examples of different JClass
candidates. IFS data can be used to categorise jellyfish candidates into
various stages of stripping to complement this idea by contrasting H$\alpha$
emission images with those of continuum emission (Poggianti et al., 2017;
Jaffé et al., 2018; Azevedo et al., 2023). Nonetheless, this approach is also
reliant on visual criteria.

Despite its popularity, human visual inspection possesses a few drawbacks. It
is time-consuming and can be susceptible to errors due to biases introduced by
disturbed morphology, bright knots of star formation, and debris tails. Given
the importance of jellyfish classification in understanding their
astrophysical properties and evolution, it is important to inspect alternative
approaches to visual classification. Machine learning techniques present a
complementary strategy to identify these objects and mitigate these
challenges. The application of machine learning has gained prominence in
recent years as a powerful tool to automate image classification in astronomy
(e.g., Moore et al., 2006; Selim & Abd El Aziz, 2017; Goddard & Shamir, 2020;
Teimoorinia et al., 2020; Vega-Ferrero et al., 2021; Xu et al., 2023).

In the realm of machine learning methods, self-supervised learning (SSL)
representation has recently gained significant attention due to its ability to
learn generalisable and semantically meaningful data representations without
manual labelling (Liu et al., 2021; Albelwi, 2022; Ericsson et al., 2022,
e.g.). SSL does not necessarily require large datasets to perform well, which
makes it beneficial for scenarios where only a small sample of objects is
known (El-Nouby et al., 2021). Various SSL approaches have been proposed,
including Momentum Contrast (MoCo; He et al., 2020), Bootstrap Your Own Latent
(BYOL; Grill et al., 2020), and Augmented Multiscale Deep InfoMax (AMDIM;
Bachman et al., 2019).

Hayat et al. (2021) applied SSL to multi-band galaxy images from the Sloan
Digital Sky Survey (SDSS), demonstrating that it could achieve performance
comparable to or better than supervised learning with half or fewer labels for
galaxy morphology classification and redshift estimation tasks. Sarmiento et
al. (2021) found that SSL representations were more resilient to non-physical
properties, such as instrumental effects, and more closely tied to physical
properties than Principal Component Analysis (PCA) representations. Detailed
astrophysical studies revealed that SSL representations closely relate to
galaxies’ physical properties, such as velocity dispersion, stellar mass, and
metallicity. Public-access tools developed by Stein et al. (2021), as well as
work by Stein et al. (2022), have further illustrated how SSL can be employed
for large-scale similarity searches to identify rare astronomical objects,
explicitly showcasing its utility in detecting strong gravitationally lensed
galaxies.

In this study, we use the S-PLUS multi-band survey data (Mendes de Oliveira et
al. 2019) to identify instances of RPS. Specifically, we employ the narrow-
band filter $J0660$ to detect H$\alpha$ emitters within three nearby galaxy
clusters: Fornax, Antlia, and Hydra. Logroño-García et al. (2019) has shown
that H$\alpha$ will fall within the $J0660$ filter for sources up to $z\leq
0.015$ for the J-PLUS survey (Cenarro et al., 2019), which has an identical
filter set to S-PLUS. The S-PLUS survey offers a suitable dataset because of
its extensive coverage of these three nearby clusters. This work uses broad-
band optical combined with the $J0660$ classifications, which can better view
RPS than just optical images (e.g., Poggianti et al. (2016b); McPartland et
al. (2016). We visually classify these RPS candidates based on their stripping
strength (JClass) and subsequently develop a semi-automated detection pipeline
using SSL, demonstrating it as a concept validation. For the pipeline, we
learn representations of the galaxy images using SSL and perform a similarity
search on these representations to yield the most similar galaxies to a given
‘query’ galaxy to assist visual inspection. We use two downstream tasks, query
by example and supervised classification using the SSL representations, to
evaluate the SSL representation quality. This work primarily focuses on
applying SSL methods in computer vision, particularly for galaxy images that
are widely accessible yet often require further labelling. Distinguishing this
work from prior studies, we apply these techniques to a relatively small
dataset of approximately 200 images. This approach holds significant interest
due to the frequent underperformance of supervised learning methods in the
context of limited data.

This paper is organised as follows. Section 2 outlines the S-PLUS data
employed in this work, providing details on the selection criteria and data
preprocessing. Our methodology, discussing the visual inspection of H$\alpha$
emitters and the SSL training details for classification, is detailed in
Section 3. In Sections 4 and 5, we validate our semi-automated detection
approach, present the astrophysical properties of the jellyfish candidates,
and discuss the implications of our findings, respectively. We then summarise
our main findings in Section 6, leading to our concluding remarks and
potential future work in Section 7. All magnitudes presented in this paper are
in the AB system.

##  2 Data

The Southern-Photometric Local Universe Survey (S-PLUS; Mendes de Oliveira et
al. 2019) has already observed approximately 3,200 deg2 of the southern
hemisphere. Its goal is to map an extensive area exceeding 9,000 deg2 using an
optimised photometric system (Cenarro et al. 2019). This system incorporates
five broad-band (BB) filters ($g,r,i,z$ being SDSS-like and $u$ being
Javalambre) and seven narrow-band (NB) filters, covering a wide spectral range
from 3700 to 9000 Å. The NB filters offer unparalleled insights into nearby
galaxies because of their ability to detect prominent stellar features such as
[OII], Ca H+K, H$\delta$, H$\alpha$, Mgb, and Ca triplets. Furthermore, S-PLUS
reaches about one magnitude deeper than the SDSS (Alam et al. 2015), providing
strong constraints on the star formation histories and photometric redshifts
of galaxies. Observations for the project are made using a 2 deg2 field of
view camera fitted with a 9k $\times$ 9k CCD at a 0.55 arcsec/pixel scale.
This equipment is mounted on a fully robotic 0.8-m diameter telescope
(T80-South) located at Cerro Tololo, Chile.

The photometric data from S-PLUS are calibrated according to the methodology
described by Almeida-Fernandes et al. (2022). The calibrated magnitudes for
all 12 bands are measured in six distinct apertures in addition to the
astrometry and other photometric parameters. The entire catalogue of images
and data is available through the S-PLUS web portal111https://splus.cloud,
which provides various tools for querying and visualising the data. For this
study, we have chosen to focus our analysis on the photometric data

obtained using SExtractor (Bertin & Arnouts, 1996), employing the so-called
“dual-mode” and selecting AUTO magnitudes.

###  2.1 Data selection

To ensure that the H$\alpha$ emission from our candidates falls within the
$J0660$ filter, a visual inspection was performed of all galaxies from three
nearby clusters (at redshift $z\leq 0.015$) included in the S-PLUS Data
Release 1 (DR1; Mendes de Oliveira et al., 2019). Galaxies that exhibited an
excess in H$\alpha$ emission were explicitly sought. Six S-PLUS fields were
analysed in Antlia, 23 in Fornax from DR1 and iDR3, and four in Hydra. An
additional twenty fields on the outskirts of Fornax were also inspected as
they became available at the time of the start of the visual inspection. We
obtained a sample of candidate H$\alpha$-excess objects by subtracting the
$r_{\mathrm{SDSS}}$ band image from the narrow H$\alpha$ filter. Before
subtraction, the $r_{\mathrm{SDSS}}$ band was scaled to match the global count
rates between the objects in common on the two images. Following this
selection process, we identified 158 H$\alpha$ emitting candidate galaxies,
with 38, 47, and 73 originating from Antlia, Fornax, and Hydra, respectively.
This set constitutes our primary sample.

We assembled a control sample of 75 additional galaxies from the Fornax
cluster for visual inspection. These galaxies were not previously identified
as exhibiting H$\alpha$ emission excess and exhibited a magnitude distribution
in the $r_{SDSS}$ band similar to that of our selected candidates. In Fig. 1,
we present the magnitude distributions in the $i_{SDSS}$ band, which does not
contain H$\alpha$ emission excess, for both the primary and control samples.

Figure 1: Comparison of $i_{SDSS}$-band magnitudes between the main and
control samples used for visual inspection. The solid blue histogram
represents the main sample, while the black curve represents the control
sample.

##  3 Methodology

Having discussed the potential of self-supervised learning, we now discuss the
implementation details. Our approach consists of two key stages: first, we
pre-select jellyfish candidates based on a visual inspection of S-PLUS multi-
band images. Subsequently, we benchmark SSL as a means to assist visual
classification in future applications.

###  3.1 Visual inspection

Stripping galaxy candidates are typically classified through visual inspection
based on the evidence of stripping signatures in optical bands, ranging from
the most extreme (JClass 5) to the weakest (JClass 1) cases (Poggianti et al.,
2016b; Roman-Oliveira et al., 2019). These classifications are determined by
the formation of tentacles of ripped gas, which occur because of the
interaction between the galaxy’s interstellar medium and the intracluster
medium (ICM).

In this study, we performed the visual classification of the main and control
samples internally in a private project using the Zooniverse
platform222https://www.zooniverse.org/. This task was accomplished by six
classifiers 333Carolina Queiroz, Ana L. Chies Santos, Yash Gondhalekar, Yara
Jaffé, Rahna P.T., and Mu Zihao., who categorised galaxies with no visual
stripping evidence as JClass 0 and flagged galaxies with merger evidence. The
assignment of the final JClass to galaxies disregards JClasses from visual
classifiers who flagged the galaxy as a merger. To aid the classification
process, we provided a composite image consisting of three panels: an image
displaying only H$\alpha$ emission (J0660 narrow-band), an RGI image generated
using Trilogy (Coe et al., 2012) with $r_{SDSS}$, $g_{SDSS}$, and $i_{SDSS}$,
and a colour image (RGI) combined with H$\alpha$ emission to accentuate the
star-forming regions, depicted in pink.

These star-forming regions, typically bright in H$\alpha$, resemble
irregularly distributed star-formation clumps, often called debris.
Occasionally, no image was available for one or more broad bands. In such
cases, neighbouring bands were selected to compose the images (e.g.,
$u_{JAVA}$ or $z_{SDSS}$). However, this did not rectify the problem for a few
galaxies, in which case we either obtained a dark or no image. We then
replaced the $\rm RGI$ \+ H$\alpha$ image with the full 12-band image or
omitted this frame.

If more than one galaxy was present in the field, the classifiers were
instructed to classify only the galaxy positioned at the centre of the frames.
The final JClass designation corresponds to the median of all classifications.
The visual inspection and classification workflow is described in Fig. 3. In
Fig. 2, we present an example of a composite image for the galaxy NGC1437A
(Serra et al., 2023) from the Fornax cluster, as inspected in Zooniverse. Note
the pink clumps of star formation in the right panel; this galaxy was
classified as JClass 3.

Figure 2: Example of composite image inspected in Zooniverse. Upper left
panel: $J0660$ narrow-band image. Bottom left panel: $RGI$ coloured image.
Right panel: $RGI$ \+ H$\alpha$ image. The central galaxy is NGC1437A from the
Fornax cluster, classified as JClass 3. The zoomed inset highlights the pink
clumps denoting star-forming regions for visual clarity.

Following the visual inspection, we identified 51 jellyfish candidates with
JClass ranging from 1 to 4 (no example with JClass 5 was found in the
dataset). These include 13 galaxies from Antlia, 25 from Fornax, and 13 from
Hydra. Notably, four of the 25 galaxies from Fornax belong to the control
sample. Four jellyfish candidates are included in the control sample because
the data selection, which relied only on H$\alpha$ emission as discussed in
Sect. 2.1, is independent of visual inspection that identified jellyfish
candidates. The distribution of JClass across each cluster is presented in
Fig. 4.

Figure 3: Workflow of visual inspection consisting of $n$ human classifiers
for assigning a JClass to a galaxy.

Thus, $\sim$30% of the H$\alpha$ emitters are jellyfish candidates (excluding
the four jellyfish candidates from the control sample). Yun et al. (2019)
analysed 2600 satellites in the IllustrisTNG simulation, selecting galaxies
with some gas, stellar masses higher than $10^{9.5}\,M_{\odot}$ and in
clusters, and massive groups with halo masses
$10^{13}<M_{200c}/M_{\odot}<10^{14.6}$. They found that $\sim$31% of the
galaxies were jellyfish at $z<0.6$. Observationally, Roman-Oliveira et al.
(2019) finds $\sim$ 16% of the star-forming galaxies in A901/2 at $z=0.0165$
to be jellyfish candidates. Vulcani et al. (2022) studied a sample of late-
type, blue, and bright ($B<18.2$) galaxies in clusters from the WINGS and
OmegaWINGS surveys ($0.04<z<0.07$) within two virial radii. Their study found
$\sim$15% of the sample as stripping candidates and $\sim$20% of galaxies with
“unwinding arms", which could be attributed to jellyfish seen face-on.
Although the sample selection criteria and type of data are different from
previous works, our fraction of stripping candidates falls in a similar range
of values compared to recent literature values.

Figure 4: Frequency of jellyfish candidates based on their respective JClass
rankings for each galaxy cluster and the control group, arranged in descending
order from the strongest to the weakest.

###  3.2 Image pre-processing for machine learning

Although convolutional neural networks (CNNs) possess the ability to pinpoint
objects within an image, deliberately steering their attention towards the
foreground object can significantly enhance their performance (Cao & Wu,
2021). Observational datasets comprise several point sources and extended
sources with sizes akin to galaxies, which could potentially confuse the
network. In Appendix D, we use the Grad-CAM visualisation method to illustrate
that SSL representations may dominantly encode information about the
background sources instead of the galaxy, which is undesirable. Thus, we
preprocessed the S-PLUS images in our study to mitigate any prospective bias
during the learning procedure by removing background sources from our galaxy
image dataset.

For this purpose, we employ the galmask (v0.2.0) Python package (Gondhalekar
et al., 2022), designed to eliminate background sources from our images.
galmask is applied independently to each band. Before its utilisation for
background source removal, we first generate a segmentation map using
NoiseChisel (Akhlaghi, 2019), followed by the Segment program from Gnuastro
(Akhlaghi & Ichikawa, 2015). We found NoiseChisel to be particularly well
suited to detect the dim, dispersed tails characteristically seen in jellyfish
signatures, which has proved challenging for traditional signal-based
threshold methods. To avoid inadvertently eliminating the peripheries of
galaxies, such as the extended tails, we opted for a slightly conservative set
of parameters within galmask. Segmentation is followed by optional deblending
and connected-component labelling, which selects the connected component
closest to the centre to isolate the central galaxy region from background
sources. An example visualisation of the galaxy image before and after the
application of galmask is shown in Fig. 5, which demonstrates that background
sources present in the original image are masked.

In our dataset of 51 jellyfish and 183 non-jellyfish images, galmask yielded
successful outputs for 46 and 171 images, respectively. The failure of galmask
to process a handful of images is attributed to the extreme faintness of the
galaxies (some of which were undetectable by NoiseChisel) or difficulties
encountered during the extraction of the galaxy cutouts. As galmask operates
separately on each band, we discarded any galaxy images that did not yield a
successful output across all 12 bands. After this, we manually inspected all
galmask outputs to identify any failures in the masking process. Any images
showing portions of the galaxy that were erroneously removed during the
masking stage within galmask were also discarded. This results in 43 jellyfish
and 140 non-jellyfish images to carry forward in our analysis. We also
estimate the background level in the central galaxy and subtract it from the
outputs of galmask. In addition, we apply an arcsinh transformation to all
images to enhance contrast. Although this procedure results in a reduced
dataset size in our already small dataset, SSL is data-rich in that it can
learn meaningful representations even with less data. Thus, we opt for a
‘stricter’ selection of galaxies to include in our final dataset.
Additionally, our data set has a high imbalance, with jellyfish examples
constituting only approximately 22% of the total (this fraction of jellyfish
candidates is similar to the values found in the literature; see Sect. 3.1).

Figure 5: An example application of galmask on the jellyfish candidate IC1885
having JClass = 2. galmask is used during preprocessing to remove unwanted
background sources.

###  3.3 Self-supervised Learning using SimCLR

Our self-supervised approach is based on the SimCLR framework (e.g., Chen et
al., 2020a), which is a contrastive method and offers an elegant, end-to-end
solution for learning generalised feature representations from unlabelled
data. We have modified certain aspects of SimCLR, such as the base encoder
network and data augmentation, to suit our requirements better (details of our
modification in the architecture and hyperparameters are described in Appendix
A.1). A batch of $N$ images from the training dataset is sampled at each
training iteration. For each sampled image $\boldsymbol{x}$, two independent
augmentation functions are applied to produce $\tilde{\boldsymbol{x}}_{i}$ and
$\tilde{\boldsymbol{x}}_{j}$. This doubles the batch size to $2N$ images.

Both $\tilde{\boldsymbol{x}}_{i}$ and $\tilde{\boldsymbol{x}}_{j}$ are passed
through the base encoder network, denoted as $f(\cdot)$ (often a convolutional
network for image data), which extracts a one-dimensional representation
vector, $\boldsymbol{h}_{i}=f(\tilde{\boldsymbol{x_{i}}})$. Subsequently, a
projection head network, usually a single hidden layer multilayer perceptron
(MLP), denoted as $g(\cdot)$, projects the representation vector onto a space
where a contrastive loss function is applied, i.e.,
$z_{i}=g(\boldsymbol{h}_{i})$. Instead of directly applying the contrastive
loss function to the representations, using a projection head during training
promotes learning more potent representations (Chen et al., 2020a).

A ‘positive’ pair, denoted as
($\tilde{\boldsymbol{x}}_{i},\tilde{\boldsymbol{x}}_{j}$), consists of two
distinct augmented views derived from the same original image
$\boldsymbol{x}$. Conversely, a ‘negative’ pair comprises two images not
derived from the same original image. In contrastive learning, these negative
pairs are essential to learning differentiable feature representations by
enforcing the model to learn distinct representations for different images.
The contrastive loss function, or NT-Xent loss, is formulated as follows:

$l_{i,j}=-\log{\dfrac{\exp({\textrm{sim}(z_{i},z_{j})/\tau})}{\sum_{k=1}^{2N}\mathbbm{1}_{[k\neq
i]}\exp{(\mathrm{sim}(z_{i},z_{k})/\tau})}}$ (1)

where
$\textrm{sim}(\boldsymbol{p},\boldsymbol{q})=\dfrac{\boldsymbol{p}\cdot\boldsymbol{q}}{\|\boldsymbol{p}\|\|\boldsymbol{q}\|}$
is the similarity function, $\tau$ is a temperature hyperparameter controlling
the sensitivity of the loss function (Zhang et al. 2021), and
$\mathbbm{1}_{[k\neq i]}\in{0,1}$ is the indicator function that equals one
only if $k\neq i$. The loss is averaged over all positive pairs in the sampled
mini-batch, and the weights of networks $f$ and $g$ are adjusted to minimise
it.

One defining feature of SimCLR is its use of large batch sizes (as high as
8192) to keep track of negative examples, bypassing the need for more complex
structures like memory banks (Wu et al., 2018; He et al., 2020). It harnesses
the robustness of data augmentations and allows multiple negative examples for
each positive pair instead of the traditional single negative example per
positive pair (see, e.g. Liu et al., 2021). Such an approach enhances the
effectiveness of the contrastive loss function and improves the quality of the
learnt representations.

Data augmentation is vital for learning valuable representations. A good data
augmentation pipeline is particularly important, given the small size of our
dataset. They must maintain the semantic meaning of the images (Hayat et al.,
2021), compelling the model to learn features that persist through
transformations. Ultimately, this results in learnt representations invariant
to these transformations (Tian et al., 2020; Xiao et al., 2020; Wang & Qi,
2021), enhancing the generalisability of these representations. Our data
augmentation pipeline encompasses the following procedures:

  * •

Centre crop: Each image is centre-cropped to a size of $200\times 200$ pixels
($\sim 9\times 10^{-3}$ pc). As the galaxies often reside near the centre of
the image, centre-cropping can be beneficial.

  * •

Random-crop-and-resize: After centre-cropping, we randomly crop a section from
the image and resize it to $72\times 72$ pixels. This is done for a few
reasons. First, in contrastive learning, we only need to determine if two
image patches are from the same image, not necessarily requiring the whole
image. Second, smaller images not only expedite training but have also been
shown to improve performance in SSL scenarios (Cao & Wu, 2021).

  * •

Random horizontal and vertical flip: We apply each flip with a 0.5
probability. Horizontal flips help the model to be invariant to the galaxy’s
horizontal mirror-image transformation. Although less common, vertical flips
are also useful, as we want the learnt representation to be unaffected even if
the galaxy appears inverted.

  * •

Custom Colour Jitter: As this study does not deal with RGB images, the
conventional colour jitter technique (randomly adjusting the brightness,
contrast, saturation, and hue of an image) cannot be used. To introduce colour
jitter into our multi-channel images, we multiply pixel values by a uniformly
sampled value in the $[0.8,1.2]$ range, keeping it fixed for a particular
channel (Illarionova et al., 2021). This effect scales the channel-wise mean
and standard deviation by the sampled value, introducing an element of
randomness. This transformation is randomly applied with a probability of 0.8.

  * •

Random rotation: Each image is rotated by a random angle sampled from
$[0\degree,360\degree]$ to ensure invariance with the spatial orientation of
the galaxy in the image, as done in Hayat et al. (2021). Although this
rotation includes horizontal and vertical flips as a special case, random
rotation provides more flexibility.

  * •

Gaussian Blur: With a probability of 0.5, we blur an image with a Gaussian
kernel of size $9\times 9$ pixels, selecting the standard deviation, $\sigma$,
uniformly at random in the $[0.1,2.0]$ range, akin to Chen et al. (2020a).
This step enables the representations to remain largely unaffected by varied
levels of image smoothing. To some degree, this also serves as a way to
achieve invariance with the Point Spread Function (PSF), even though the
standard deviation of the Gaussian blurring kernel is not explicitly scaled
using the PSF Full Width at Half Maximum (Hayat et al., 2021; Stein et al.,
2021).

The augmentation techniques we employ enhance those used in the initial SimCLR
model, tailored to offset the limitations posed by our small training dataset.
Introducing variety into the training images can induce the model to learn
more robust and invariant features. We argue that applying a centre-cropping
operation before a random-resize-and-crop, instead of a standalone random-
resize-and-crop, is more advantageous for our dataset. This assertion stems
from the preprocessing step, which substantially reduces background objects.
By prioritising a centre-cropping operation, we are tilting the odds in our
favour to extract random crops from the central galaxy instead of from the
background areas. An ablation study that examines the significance of these
augmentations is presented in Appendix C.

###  3.4 Model implementation

First, the encoder is pretrained. Following the pretraining phase, the
projection head is discarded as the representations of the encoder are
considered more meaningful than the projection head since the latter is found
to lose critical information necessary for downstream tasks (Chen et al.,
2020a). As a result, the pretrained encoder is used as a fixed-feature
extractor to obtain image representations. Since the augmentations described
in Section 3.3 were explicitly designed only for contrastive learning, these
augmentations were discarded for deriving representations from the fixed
feature extractor (Chen et al., 2020a). The images are standardised before
feeding into the model using the channel-wise mean and standard deviation
calculated across the training dataset. Instead of pretraining the encoder on
a large dataset and then fine-tuning it on our small dataset, the pretraining
is performed directly on the target dataset, a strategy that has also recently
shown promise in the low-data regime (El-Nouby et al. 2021; Cao & Wu 2021).
The extremely small size of our dataset is used to test whether (a) SSL can
learn meaningful representations of galaxies and (b) SSL representations can
encode important features for downstream tasks such as classification, which
was previously unexplored in an astronomical context for small data.

Contrastive learning approaches often benefit from a longer training duration
and larger batch sizes, as they expose the model to more negative examples
(Chen et al., 2020a). Given RAM limitations, we select a batch size of 128,
the maximum feasible size for our application. Furthermore, smaller resolution
images pave the way for larger batch sizes, as noted in (Cao & Wu, 2021). The
model undergoes training with the contrastive loss function for 1000 epochs,
with optimisation using the Adam with decoupled weight decay method (AdamW;
Loshchilov & Hutter, 2019), featuring a weight decay of $10^{-4}$ and a
learning rate, $lr=10^{-4}$. A large number of epochs ensures better
convergence on our small dataset. We adopt a cosine annealing schedule to
regulate the learning rate, with the minimum learning rate set to $lr/50$ and
without restarts (Loshchilov & Hutter, 2016). The maximum number of epochs for
the scheduler is set to the number of epochs in our training run, i.e., 1000.
The temperature parameter, $\tau$, is set to 0.05. Hyperparameter tuning was
performed using $K$-Fold cross-validation, with more details provided in
Appendix A.2.1. Weights & Biases (Biewald, 2020) was used for tracking mode
training and validation experiments.

##  4 Self-supervised learning results

In this section, we discuss the results of the SSL for similarity search and
provide an example application to assist and improve subjective visual
classification. Due to limited examples in our dataset, we combine the
training and testing sets for the analysis in this section.

###  4.1 Query by example

We conduct a query by example (or similarity search), similar to the works of
Stein et al. (2021); Hayat et al. (2021) to inspect what types of galaxies are
clustered closely in the self-supervised representation space. To conduct this
experiment, cosine similarities are calculated between the representation
vectors of a chosen query galaxy image and all other galaxy images in the
dataset, and the similarities are ordered in decreasing order to select the
four closest representation vectors (and the corresponding images) to the
representation of the query galaxy. The query galaxy image is then visually
compared for any morphological similarities with the selected closest images
to gain insights into the clustering in the self-supervised representation
space.

Figure 6: Illustration of the query by example returning the four closest
images to the query image (outlined in red) as obtained by the similarity
search. The JClass obtained from visual classification, and the cosine
similarity values are marked on the images. The galaxy’s name is shown on top
of each image. Various cases are shown, such as non-jellyfish (JClass 0) query
images or jellyfish (JClass 1, 3) query images. While we use galmask during
preprocessing, the images shown here are without the use of galmask.

Figure 7: (continued)

Fig. 6 shows the results of our similarity search. It can be observed that the
similarity search returns semantically similar images to the query image. In
particular, the query search returns galaxies with similar colours and visual
morphological characteristics. The query search is unaffected by the rotation
of galaxies by any arbitrary angle and robust to the number and shape of
background sources within the images. The former is likely because of the
random rotation data augmentation used during self-supervised pretraining. We
hypothesise the latter is mainly due to the use of galmask in our internal
preprocessing pipeline, which conveniently removes many unwanted sources from
the background. Slight correspondence is observed between the JClass of the
query galaxy and the JClass of the most similar images to the query galaxy.
Jellyfish (non-jellyfish) query galaxies tend to have jellyfish (non-
jellyfish) galaxies as the most similar galaxies to the query (jellyfish:
$\textrm{JClass}>0$; non-jellyfish: $\textrm{JClass}=0$). However, since these
JClasses are based on visual classification rather than SSL, it is challenging
to interpret these correlations. Overall, we conclude that the self-supervised
representations encode important information about the galaxies, which allows
the clustering of the galaxies in a morphologically meaningful manner.

###  4.2 Re-calibrating visual classification

During visual inspection, each visual classifier individually assigns labels
to an image, with no measurable boundaries between different JClasses. Such a
methodology largely hinges on the classifier’s prior domain knowledge and the
guidelines provided before the image assessment. Fig. 8 demonstrates this
behaviour. Even though taking the median of visual classifications of
different classifiers attempts to minimize individual human biases, it would
be affected if there is a large disagreement among the visual classifiers.
Therefore, strategies that counteract human biases can improve this subjective
classification procedure. As discussed in Sect. 4.1, self-supervised
representations present a morphologically significant structure, with
analogous galaxies closely clustered. This finding serves as the basis for our
proof-of-concept application, which shows how SSL can increase the quality of
visual classification in a data-efficient way. This section thus examines the
potential of using self-supervised representations to refine visually labelled
JClasses.

Figure 8: Illustration of the subjectiveness of visual classification. As
denoted in the image, five of the six visual classifiers assigned a JClass to
this galaxy, while one classifier did not assign any JClass (denoted by “NA").
Out of the five classifiers, one assigned a JClass 3, two assigned a JClass 2,
one assigned a JClass 1, and the other classifier assigned a JClass 0. Thus,
considerable uncertainty prevails in the visual analysis since different
visual classifiers assigned various JClasses. As described in Sect. 3.1, the
final visual JClass is the median across all the JClasses, i.e., JClass 2,
which might not be reliable due to the significant uncertainty across visual
classifiers.

Since the JClass assigned by visual inspection is based on a subjective
assessment of jellyfish-ness, a linear evaluation protocol (see Appendix. B)
in which a supervised logistic regression classifier is employed on the self-
supervised representations using the JClasses as ground-truth labels will be
affected by the quality of these labels. The linear evaluation will not yield
a precise disturbance strength estimate, either, since it is only a binary
classification (jellyfish vs. non-jellyfish). A multi-label classification
(with ground-truth categories $\textrm{JClass}=0,1,2,3,4$) will degrade due to
the increased severity of the class imbalance. Thus, a supervised regressor
trained on self-supervised representations is not ideal for improving JClass.
To mitigate these issues, we develop a new downstream task to assign JClass to
galaxies leveraging self-supervised representations to assist visual
classifiers in their classification.

Since we propose not to rely solely on visual inspection and aim to improve
estimates of visual JClasses, this section focuses only on galaxies with high
uncertainty in the JClass among the visual classifiers. Hence, our initial
step involves identifying galaxies that present a visual classification
challenge. If a galaxy receives more than $\lceil N/2\rceil$ unique visually
assigned JClasses from $N$ visual classifiers (where $\lceil\rceil$ denotes
the ceiling function), it signifies a considerable classification uncertainty,
which renders the galaxy visually complex. We refer to this set of galaxies as
our “target” sample. Here, $N=6$ (see Sect. 3.1). Notably, around 85% of the
galaxies in our target sample are jellyfish candidates, suggesting a more
considerable disparity among visual classifiers in assigning JClass to
jellyfish than non-jellyfish galaxies. Since our goal is to yield precise
JClass estimates for identifying novel instances of galaxies exhibiting
jellyfish characteristics, we limit our self-supervised application to the
target sample.

We predict JClass using the self-supervised representations as follows: given
a target galaxy, $K$-nearest neighbours to it are found in the representation
space, and the mean of JClasses of the nearby galaxies, weighted by their
cosine similarities, is assigned as the JClass of the target galaxy. The
nearby galaxies are chosen such that they are not already in the target
sample. We have chosen to use $K=4$. The JClass assigned using SSL is
determined by the following relationship:

$\textrm{JClass}_{ss}=\dfrac{\sum_{i=1}^{K}s_{i}\,\textrm{JClass}_{v_{i}}}{\sum_{i=1}^{K}s_{i}}$
(2)

Here, $\textrm{JClass}_{v}$ and $\textrm{JClass}_{ss}$ represent the visually
assigned and the self-supervised predicted JClass, respectively. $s_{i}$
denotes the cosine similarity between the query image and the $i^{th}$ image
similar to the query. Such a weighted scheme enables assigning more weightage
to more similar galaxies. We emphasise that we do not train a $k$-nearest
neighbour classifier on the representations to predict the JClass since the
self-supervised model is already trained to encode relevant information about
the galaxies.

A similarity search is then conducted using the target galaxy as the query,
similar to Sect. 4.1. Fig. 9 illustrates our framework to assign JClass to
galaxies based on the similarity search on the representations of galaxies.
Although our proposed approach uses visual JClasses for the final prediction
after the self-supervised learning is performed, these visual JClasses are not
used as ground-truth labels in training our self-supervised model. This means
that our self-supervised approach learns patterns in the galaxy images based
on the observed data alone and does not use the visual JClasses to learn to
distinguish between jellyfish and non-jellyfish galaxies. This characteristic
feature of our self-supervised approach alleviates human biases and thus
provides benefits over approaches such as training a supervised CNN on the
galaxy images or training a supervised classifier on the self-supervised
representations.

An example application of our framework is provided in Fig. 10. The top two
rows show two weak jellyfish query images (JClass 2 and 1, respectively),
whereas the self-supervised approach predicted it to be a non-jellyfish
galaxy. This occurs because galaxies most similar to the query had a JClass 0.
The third and fourth rows show two cases where the self-supervised approach
predicted a milder jellyfish signature, i.e., a lower JClass, than visual
classification (JClass 2 instead of JClass 4 and JClass 1 instead of JClass
2). We assume that the visual JClasses of all non-query images (not outlined
in red) are fairly accurate since we have only selected cases where the
majority of the visual classifiers agreed on a common JClass. Hence, for the
third and fourth rows, the fact that similar galaxies to the query image
contain a mix of jellyfish and non-jellyfish galaxies suggests that the
corresponding query image likely contained some features similar to non-
jellyfish galaxies and some features similar to jellyfish candidates. As a
result, cases where similar images to the query contain both jellyfish and
non-jellyfish galaxies might be the most complex to classify visually.
JClasses predicted using SSL could be the most beneficial for visual
inspection for such cases.

In the second-last row, visual and self-supervised approaches match their
JClass predictions – such cases are relatively less complex for visual
classification. In the last row, the self-supervised approach predicted the
query galaxy to be a stronger jellyfish candidate, resulting from all similar
galaxies also being jellyfish. In this case, the visual similarity of
morphological signatures between the query and the similar images is not
entirely apparent. Despite jellyfish candidates being rare in the dataset, all
four similar galaxies are jellyfish, which could strongly indicate jellyfish
signatures in the query. However, we note that the query was identified as a
merger by visual classification444 A galaxy is classified as a merger if more
than half of the classifiers visually classified it as a merger.. Hence, it is
possible that the self-supervised model could not distinguish well between
jellyfish and merger galaxies; instead, it predicted a higher JClass.

Figure 9: Workflow demonstrating the use of SSL to assign JClass to a galaxy
solely based on the similarity search on the extracted representations of
galaxies. Before training the self-supervised encoder, we find it crucial to
account for background sources to prevent affecting the similarity search, as
discussed in Sect. 3.2 and demonstrated in Appendix. D.

Figure 10: An example application of our framework to assign a JClass to
galaxies that are visually confusing to classify. The images outlined in red
are the query images and have significant deviations in their visual JClass
(see text for details). The four images closest to each query image are shown
as obtained by SSL. The JClass predicted by SSL (see text for details) is also
shown for each query image. The JClasses mentioned in images not outlined in
red are obtained from visual classification. Cosine similarity values are
indicated. Visual classification also predicts whether a given galaxy shows
merger signatures, shown in each image’s bottom-right. A galaxy is considered
a merger only when more than half of the visual classifiers voted in favour of
a merger.

As part of a complementary validation test, we assessed the agreement between
the self-supervised and visual JClasses for cases with confident visual
classification (i.e., those with a maximum of two distinct visual JClasses
across all visual classifiers). This criterion identified 34 non-jellyfish
(JClass 0) galaxies555Applying this criterion yielded only one JClass = 1
example. Although not utilised here, this example further underscores the
uncertainty in visually classifying jellyfish candidates.. Among these, 33
galaxies identified visually as JClass 0 were also predicted as JClass 0 using
the self-supervised approach, while the remaining galaxy was classified as
JClass 1 by the self-supervised method. Consequently, a high level of
agreement is observed between the visual and self-supervised JClasses for
these cases. This experiment suggests that the self-supervised model
effectively captures abstract features that align with human inspection in
classifying a galaxy as a non-jellyfish. However, the limited number of
jellyfish examples in this test restricts our ability to fully assess the
model’s accuracy in identifying jellyfish galaxies, indicating a need for
further investigation with a more balanced dataset.

The experiments in this section show that SSL can help visual inspectors
classify visually complex cases to improve the JClass prediction. We call this
an “improvement” since the JClasses predicted based on the nearest neighbour
search in the self-supervised representation space alleviates human-level
uncertainties associated with visual-only inspection, primarily because
learning to distinguish jellyfish from non-jellyfish galaxies does not use
labels but is majorly learnt from the data itself. A practical application of
our method is to train a self-supervised model on a larger galaxy dataset
containing secure jellyfish candidates based on visual inspection and use it
for fast JClass assignment on any new galaxy. Unlike pure visual inspection,
such an approach may scale to large astronomical datasets better. See Sect. 6
for more discussion.

##  5 Astrophysical analysis

This section explores the astrophysical properties of the jellyfish candidates
as labelled by the visual inspection. We present the morphological features of
the jellyfish candidates and their spatial distribution around the three
cluster systems. We also estimate their star formation rates and stellar
masses and analyse their distributions on the phase-space diagrams. It is
important to note that although candidates in JClass 1 and 2 are considered
jellyfish galaxy candidates in the study, they are weak examples of jellyfish
galaxies. Therefore, they may represent ’disturbed’ morphologies rather than
exhibiting true jellyfish signatures.

###  5.1 Morphological properties via Morfometryka

We perform a morphometrical analysis of the galaxies to look for possible
correlations in the JClass–morphology space, using the Morfometryka code
(Ferrari et al., 2015). We select two non-parametric and one parametric
morphological indicator: i) The normalised information entropy $H$, which
summarises the distribution of pixel values in the galaxy region in the images
– smooth (clumpy) galaxies have low (high) $H$; ii) the Gini coefficient $G$
as used by Lotz et al. (2004), which is another measure of the flux
distribution across pixels; iii) the best-fit Sérsic index from the two-
dimensional Sérsic fit to the galaxy images, nFit2D, which quantifies the
curvature of the radially centred light distribution (which would be the
brightness profile in 1D case). We rely solely on $r$-band statistics due to
their comparatively high signal-to-noise ratio (S/N). All measurements are
performed considering pixels inside the Petrosian region (see Ferrari et al.,
2015, for details)

Fig. 11 shows the joint distributions of $H-G$ and $H-\textrm{nFit2D}$, along
with the marginal distributions of each morphological parameter, coloured by
the JClass. The most extreme jellyfish candidates in our dataset (with
$\textrm{JClass}=4$) were not considered due to insufficient examples for
their kernel density estimate (KDE) calculation. We note that JClass 1
candidates are the weakest examples of RPS, so they nearly overlap with JClass
0 in the distribution of the three morphological parameters considered. The
$H-G$ plot shows a non-trivial correlation between the position in the $H-G$
space and the JClass of the increasingly stronger JClasses (JClass = 2, 3). In
particular, JClass 2 and 3 galaxies have higher entropy than other galaxies,
suggesting that galaxies with strong RPS evidence are clumpier than galaxies
with weak or no evidence of RPS. A similar pattern is observed with $G$, where
JClass 2 and 3 candidates have lower $G$, suggesting that the flux in such
galaxies is spread across more pixels than in galaxies with weak or no RPS
evidence, which is in contrast to Bellhouse et al. (2022) who found $G$ alone
to be an insufficient indicator to separate ram-pressure stripping galaxies
from the general population of galaxies. The $H-\textrm{nFit2D}$ plot
additionally shows that JClass 3 candidates have lower Sérsic indices than
lower JClass candidates in the plot, which indicates the former are more disc-
like than galaxies with weaker or no RPS evidence (JClass 0, 1, and 2). From
an astrophysical perspective, this observation is expected as jellyfish
galaxies generally possess a disc component (e.g., Poggianti et al., 2016b).

Although the small sample size limits the conclusions from our analysis here,
we find hints that the clumpiness of galaxies increases, and their “disc-ness"
increases as the JClass increases, as suggested by the marginal distribution
of the morphological parameters. Repeating this study on larger datasets would
allow deducing more meaningful conclusions. We also note that mergers may
share a morphology parameter space similar to jellyfish candidates, which is
observed in several studies (e.g., McPartland et al., 2016; Bellhouse et al.,
2022; Krabbe et al., 2023), but this is not discussed here.

Figure 11: Distribution of the morphological parameters considered in this
study ($G$, $H$, and nFit2D), coloured by the JClass. The data points and the
bivariate KDE curves are shown in the main plot, whereas the univariate KDE
curves are shown on the top and right of the figures. The univariate KDEs are
normalized independently of each other. Cases with unusual conditions during
the morphometry calculations were excluded, as indicated by the quality flag
(see Table 3 of Ferrari et al. (2015) for more details).

###  5.2 SFR vs. mass

The star formation rates (SFR) of the jellyfish candidates are derived from
the H$\alpha$ fluxes. Such flux measurements are obtained using the Three
Filter Method (3FM; Pascual et al., 2007; Vilella-Rojo et al., 2015) applied
to $r$, $J660$ and $i$-band images. This approach creates emission line maps
by assuming that the two broad-band filters can trace the continuum of the
galaxy within the narrow-band filter, where the emission line is located. The
3FM is based on colour relations, so the images must be calibrated and PSF-
corrected. Moreover, a low pass (Butterworth) filter is applied to all images
to decrease noise. A Voronoi binning is performed to reach an S/N of 20 in the
$J0660$ image. The S/N limit was chosen after several tests to ascertain
artefacts or bad pixels are excluded. Details of the pre-processing procedures
will be discussed in Lopes et al. (in prep)666Examples of H$\alpha$ maps and
the main code used to derive the SFR can be found at
https://github.com/amanda-lopes/Halpha-SPLUS-Jelly. We integrated the
resulting H$\alpha$ map to estimate the H$\alpha$ flux within a radius
encompassing 90% of the flux ($r_{90}$) in the $r$-band for each galaxy. The
choice of $r_{90}$ aims to maximise the inclusion of the emission structure in
the analysis. From the H$\alpha$ flux, we derived the H$\alpha$ luminosity,
which is converted to SFR following the relation given by Kennicutt (1998).
The SFRs are corrected for dust and [NII] following the relation proposed by
Kouroumpatzakis et al. (2021). This procedure computes the total integrated
star formation rates for the entire galaxy region. SFR errors are derived by a
simple propagation of errors.

The stellar masses ($M_{\star}$) are obtained by fitting the galaxy spectral
energy distributions (SEDs) with the CIGALE code (Boquien et al. 2019; version
2020.0). SED modelling was performed for only 84 galaxies from the main and
control samples (15, 46, and 23 from Antlia, Fornax, and Hydra, respectively),
which had their photometry measured in the S-PLUS filters (Haack et al. 2024;
Smith Castelli et al. 2024) using SExtractor. The spectroscopic redshifts and
distances were obtained from the NASA/IPAC Extragalactic Database (NED)777The
NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the
National Aeronautics and Space Administration..

In Fig. 12, we compare the star formation rate (SFR) as a function of
$M_{\star}$ of all jellyfish candidates (JClass > 0) vs. normal (i.e., non-
jellyfish; JClass 0) or star-forming galaxies, combined from the three
clusters. Comparison between each JClass is not performed due to the low
number of examples for each JClass. It can be observed that no significant
trends are observed in the SFR vs. $M_{\star}$ relation for the jellyfish
candidates. The SFRs of the jellyfish candidates generally tend to possess
elevated star formation compared to non-jellyfish candidates; however, this
elevation is not apparent at the high stellar mass end. The jellyfish
candidates are skewed towards lower stellar masses, as seen in the lower
panel. Thus, one possible reason for the non-elevation could be the rarity of
jellyfish candidates at higher stellar masses. Possible implications of these
observations are discussed in Sect. 6.

We perform a two-sample Kolmogorov-Smirnov (KS) test to statistically quantify
the SFR comparison, similar to Roman-Oliveira et al. (2019). The p-values for
the SFR comparison of jellyfish vs. non-jellyfish galaxies and the main vs.
control sample galaxies are lower than $10^{-4}$. For any reasonable
confidence level (e.g., 95%, 99%), we thus reject the null hypothesis that the
SFRs of the two samples are drawn from the same distribution for the jellyfish
vs. non-jellyfish and the main vs. control comparison. These findings are
qualitatively in line with the results of other studies (e.g., Poggianti et
al., 2016b; Vulcani et al., 2018; Roman-Oliveira et al., 2019), which found
increased star formation in jellyfish candidates compared to other normal or
star-forming galaxies.

Figure 12: Star formation rate versus stellar mass for varying JClass
candidates. Dots (squares) indicate galaxies from the main (control) sample.
The lower panel shows the distribution of the stellar masses for non-jellyfish
and jellyfish candidates. Examples with significant errors in the SFR
calculation
$\Big{(}\dfrac{\textrm{SFR}_{\textrm{error}}}{\textrm{SFR}}>50\%\Big{)}$ are
excluded. Typical errors in the SFR are $\lesssim 30\%$.

###  5.3 Direction of infalling

Jellyfish galaxies leave a trail of RPS gas in the opposite direction of
motion (Roberts et al., 2021b; Poggianti et al., 2017; Fumagalli et al.,
2014). Thus, the trail direction provides information about the most probable
direction of the galaxy’s motion in the cluster system (e.g., McPartland et
al., 2016; Smith et al., 2010; Smith et al., 2022). We discuss the projected
motion of the jellyfish candidates in each cluster: Antlia, Hydra, and Fornax,
shown by trail vectors (e.g., Roman-Oliveira et al., 2019; Roman-Oliveira et
al., 2021).

Roman-Oliveira et al. (2021) found that the shift between the peak and the
centre of light of galaxies (calculated using Morfometryka) is a better proxy
for the motion direction than visual inspection, especially for disturbed
morphologies. The motivation for using such an approach lies in the fact that
while the centre of light of the galaxy is sensitive, the peak of light is
resilient to perturbations in the galaxy morphology due to ram pressure
stripping so that the difference between them can be used as a tracer of the
galaxy’s motion. As a result, we derive the trail vectors using Morfometryka
measurements, where the direction is based on the following relation:
$(x,y)_{\rm peak}-(x,y)_{\rm col}$. Similar to Sect. 5.1, calculations are
performed only on $r$-band images.

Fig. 13 shows the spatial distribution of the jellyfish candidates from each
galaxy cluster, with the trail vectors shown by the arrows. Similar to Roman-
Oliveira et al. (2019), we calculate the angle between the trailing vector and
the line joining the galaxy to the cluster’s centre to identify whether the
galaxy moves towards or away from the cluster centre. The galaxy is considered
infalling towards the centre if the angle is less than 90 degrees and
outfalling if the angle is greater than 90 degrees. Table 1 shows the
distribution of the number of galaxies falling inwards or outwards from the
respective cluster system. We consider galaxies in a cluster to preferentially
fall toward the cluster when more than half of the galaxies are found to be
infalling. Thus, galaxies from Antlia and Fornax preferentially fall toward
the cluster, whereas there seems to be mild or no specific preference for
galaxies from Hydra to infall. However, we note that our analysis is affected
by the limited sample size.

Figure 13: Spatial distribution of jellyfish candidates in each galaxy cluster: Antlia, Fornax, and Hydra, along with their trail vectors shown by arrows. Since only the direction is considered in this study, all trail vectors are shown with the same length. Galaxies with a failed trail vector calculation were excluded. The black cross marks the centre of the cluster. The red dashed circle indicates the virial radius. Table 1:  No. of infalling and outfalling galaxies, categorised by the JClass, in each galaxy cluster, as indicated by the trail vector directions. See Fig. 13 for the trail directions. Cluster | Direction | JClass 1 | JClass 2 | JClass 3 | JClass 4 | Total
---|---|---|---|---|---|---
Antlia | Infalling | 2 | 2 | 1 | 1 | 6
| Outfalling | 1 | 1 | 0 | 0 | 2
Hydra | Infalling | 3 | 3 | 0 | 1 | 7
| Outfalling | 2 | 1 | 2 | 1 | 6
Fornax | Infalling | 5 | 5 | 2 | 2 | 14
| Outfalling | 3 | 1 | 3 | 0 | 7

###  5.4 Phase-space analysis

The environment where a galaxy resides within a group or cluster may pose
noteworthy morphological and physical transformations. In addition, the
position and velocity of the galaxy with respect to the cluster centre are
determinants for our understanding of the different dynamical effects at play.
In particular, the phase-space diagram (Jaffé et al. 2015) relates the
peculiar line-of-sight (LOS) velocity $\Delta\mathrm{V_{los}}$ of each galaxy
and their projected radial position $\mathrm{R_{p}}$ from the cluster centre.
The line-of-sight velocity can be determined by

$\displaystyle{\frac{\Delta\mathrm{V_{los}}}{\sigma_{\mathrm{v}}}=\frac{c(z-z_{cl})}{(1+z_{cl})\sigma_{\mathrm{v}}}},$
(3)

where $\sigma_{\mathrm{v}}$ is the velocity dispersion of the cluster, $c$ the
speed of light, $z$ the spectroscopic redshift of a given galaxy, and $z_{cl}$
the redshift of the cluster. For the projected distance, we converted each
angular distance in arcsec to a kpc scale based on the distance to the cluster
(e.g., 1$\arcsec$ = 0.247 kpc in Hydra, as discussed in Arnaboldi et al.
2012).

The spectroscopic properties of the jellyfish candidates were obtained from
NED. However, for three candidates from Hydra, we did not find their
spectroscopic properties in NED, for which we made use of the catalogue of ram
pressure targets from Hydra published by the WALLABY survey (Wang et al.,
2021). The coordinates (RA, DEC) of these galaxies are: (159.854∘, -27.9125∘),
(159.192∘, -28.1672∘) and (159.337∘, -28.2372∘). The properties of the three
clusters are shown in Table 2. In the case of Fornax, we consider the cluster
centre at NGC1399.

Table 2: Cluster properties: distance to the cluster, $D_{cl}$ (Mpc), virial radius, $\mathrm{R_{200}}$ (Mpc), virial mass, $\mathrm{M_{200}}$ ($\mathrm{M_{\odot}}$), velocity dispersion, $\sigma_{\mathrm{v}}$ (km s-1), and spectroscopic redshift ($z_{cl}$). References: (a) Wong et al. (2016); (b) Sarkar et al. (2022); (c) Ragusa et al. (2023); (d) Hopp & Materne (1985); (e)Sarkar et al. (2022); (f) Tonry et al. (2001); (g) Iodice et al. (2019); (h) Drinkwater et al. (2001); (i) Reiprich & Böhringer (2002); (j) Arnaboldi et al. (2012); (k) Wang et al. 2021; (l) Lima-Dias et al. (2021).  Cluster | $D_{cl}$ | $\mathrm{R_{200}}$ | $\mathrm{M_{200}}$ | $\sigma_{\mathrm{v}}$ | $z_{cl}$
---|---|---|---|---|---
Antlia | 39.8(a) | 0.887(b) | $10^{14\,(c)}$ | 591(c) | 0.009(a)
Fornax | 19.9(e) | 0.7(f) | $7\times 10^{13\,(g)}$ | 370(g) | 0.0046(h)
Hydra | 50(i) | 1.4(j) | $3\times 10^{14\,(k)}$ | 690(l) | 0.012(l)

In Fig. 14, we show the distributions of the most secure jellyfish candidates
from each cluster in the projected phase-space diagram. The x-axis shows the
projected distance normalised by the virial radius $\mathrm{R_{200}}$.
Following Roman-Oliveira et al. (2019), we define two boundaries: $(B1)$
$\displaystyle{|\Delta V_{los}/\sigma_{v}|\leq
1.5-(1.5/1.2)\times\mathrm{R_{p}/R_{200}}}$ (Jaffé et al. 2015) and $(B2)$
$\displaystyle{|\Delta V_{los}/\sigma_{v}|\leq
2.0-(2.0/0.5)\times\mathrm{R_{p}/R_{200}}}$ (Weinzirl et al., 2017) (see also
Rhee et al. 2017; Pasquali et al. 2019). The areas within the defined
boundaries represent virialized galaxies. The purpose of segmenting the phase
space into regions is to determine the most likely stage of the galaxy’s
orbit, such as recent infalling, backsplashing, or having already undergone
virialization.

Figure 14: Projected phase-space diagram for the jellyfish candidates from
Antlia, Fornax, and Hydra. The cluster centre for Fornax considered is
NGC1399. The colour bar shows the JClass. In the case of Fornax, dots
(squares) indicate candidates from the main (control) samples. The dotted and
dashed lines indicate boundaries $B1$ and $B2$, respectively.

In the case of Antlia, some of the JClass 1 and 2 candidates are under the
influence of the cluster, and have peculiar velocities of the order of the
velocity dispersion of the cluster. Two candidates are close to boundary $B2$
(one of them being a JClass 3). However, the remaining candidates (including a
JClass 4) are outside the influence of the cluster and exhibit relatively high
LOS velocities. For Hydra, most of the candidates are found within the
influence of the cluster. On the other hand, most of the Fornax candidates are
located in the outskirts ($\mathrm{R_{p}>2\times R_{200}}$), which is also
confirmed by the spatial distribution of Fornax galaxies in Fig. 13. This is
not unexpected since Fornax’s outskirts up to large radii are covered in this
study. These candidates also exhibit high velocities with respect to the
cluster velocity dispersion. Two JClass 4 candidates are located at
$R_{p}>3R_{\textrm{200}}$. Further inspection of these candidates can reveal
whether ram-pressure stripping is acting out to these large outskirts, which
is a possible phenomenon (Bahé et al., 2013).

To better investigate the distribution of candidates in Fornax, we plotted the
phase space diagram by considering the centre at NGC1316, a lenticular galaxy
from an in-falling subgroup. However, as shown in Fig. 15, the jellyfish
candidates are even further away from the influence of this subgroup. Finally,
since Fornax is surrounded by three other groups (NGC1225, Eridanus, and
NGC1532), another hypothesis is that they may influence these candidates.
However, this conjecture is refuted by the spatial distribution map shown in
Fig. 16.Therefore, more investigation is needed to determine whether this
gravitational influence of Fornax is causing RPS in these candidates. We note
that, another significant influence of the cluster environment on a galaxy,
which reaches beyond the virialized region, is the extent of the virial shock
surrounding the cluster. This shock boundary can extend several times beyond
the virial radius (e.g. Bahé et al., 2013; Zinger et al., 2018) and once a
galaxy crosses the virial shock, the surrounding gas density increases and
consequently there is a rise in ram pressure.

Figure 15: Projected phase-space diagram similar to the one for Fornax in Fig.
14, but considering the centre at NGC1316. Figure 16: Spatial distribution of
galaxies from Fornax. The dots (squares) indicate candidates from the main
(control) samples. The colour bar indicates the JClass. The pink dashed circle
indicates the virial radius. The black cross (star) shows the location of
NGC1399 (NGC1316). The black diamonds indicate the locations of three nearby
groups (NGC1225, Eridanus, and NGC1532).

##  6 Discussion

This paper analyses 51 jellyfish galaxy candidates from three nearby galaxy
clusters: Fornax, Antlia, and Hydra, observed in the S-PLUS survey. These
candidates were derived using the traditional visual inspection approach,
which produced a categorical RPS measure, the JClass, ranging from 1 to 4,
representing the weakest to strongest RPS evidence. We have not recovered any
JClass = 5 cases in our hunt for jellyfish candidates in these three clusters.
It is possible that these clusters do not harbour extreme ram-pressure
stripping galaxies, or that such stripped structures may be revealed by other
observational methods that are beyond the parameters probed by this study; see
Serra et al. (2023) for an example of a prominent tail in HI gas observed by
MeerKAT in NGC1437A, which received a JClass = 3 in our study.

Following the identification of jellyfish candidates, we analysed their
astrophysical properties. A morphological study revealed that moderate to
extreme jellyfish candidates (JClass 2 and 3; JClass 4 was not studied for
morphology due to scarcity of JClass 4 examples) are clumpier (higher entropy,
$H$) and have more scattered flux (smaller Gini coefficient, $G$) than
galaxies with weak or no evidence of RPS (JClass 0 and 1). The JClass 2 and 3
galaxies are more disc-like than JClass 0 and 1 galaxies, quantified by the
lower Sérsic indices of the former. The increasing “disc-ness" as the
jellyfish signatures become more prominent is expected since jellyfish
galaxies are known to have a prominent galactic disc. The majority of the
jellyfish candidates with JClass 2 and 3 are low stellar mass galaxies
($M_{*}<10^{10}$ M⊙), with most of them having $10^{7}$
M${}_{\odot}<M_{*}<10^{9}$ M⊙ (see Fig. 12). Low-mass star-forming galaxies
are usually pure-disc systems with surface brightness profiles well described
by an exponential law ($n\sim 1$; Hunter & Elmegreen, 2006; Lange et al.,
2015; Salo et al., 2015). These galaxies are the ones that are more easily
perturbed in a dense environment (Boselli & Gavazzi, 2006; Boselli et al.,
2022; Kleiner et al., 2023). Thus the jellyfish candidates with a higher
JClass might be associated with lower mass cluster members that are more
sensitive to the surrounding environment compared to JClass 0 galaxies,
characterised by a larger range of stellar masses that extends above $10^{10}$
M⊙ (Fig. 12).

An essential finding through this analysis is that high JClass galaxies
($\textrm{JClass}\geq 2$, are not entirely distinct from the others (JClass 0,
1). Instead, they prefer a specific sub-region of the morphological parameter
space of the JClass 0 and 1 galaxies, as aptly demonstrated by Fig. 11. This
overlap in space occupation could be because the employed morphological
parameters produce degeneracies between extreme RPS galaxies and a specific
type of non-jellyfish galaxies. These observations demonstrate that jellyfish
candidates have complicated morphological characteristics that likely cannot
be sufficiently described by a single morphological indicator. Thus, a
combination of these morphological characteristics can be used to perform
morphological cuts for candidate jellyfish sample selection in the future.
Simulations studying the evolution of jellyfish galaxies (its different stages
such as cluster infall, stripping of gas from its disc, and late-stage
evolution) can allow tracking its position in the morphology space (e.g., the
two-dimensional space of Fig. 11) to get direct insights into morphological
evolution of jellyfish galaxies. Also, interpreting weak jellyfish candidates
(JClass 1 and 2) as examples of ‘disturbed’ morphologies rather than jellyfish
could also help explain why these candidates largely overlap with the non-
jellyfish population.

The star formation activity analysis suggested that galaxies with
$\textrm{JClass}\geq 1$ have a higher SFR than normal, star-forming galaxies
(with JClass 0). This observation is expected since RPS is known to cause a
temporary starburst in jellyfish galaxies before eventually quenching its cold
gas (e.g., Gullieuszik et al., 2017; Vulcani et al., 2018; Poggianti et al.,
2019b; Roman-Oliveira et al., 2019; Gullieuszik et al., 2020). The SFR vs.
stellar mass plot trends suggest that this effect can become less pronounced
for high-mass galaxies ($M_{\star}\gtrsim 10^{9}\,M_{\odot}$). However, it is
not possible to make definitive conclusions since selection effects can be at
play: our sample consists of few examples of low-mass normal, star-forming
galaxies, and many jellyfish candidates have a low stellar mass, as seen in
Fig. 12. Such a disproportionate distribution of stellar mass of the galaxy
candidates poses difficulties in comparing SFRs at any given mass in this
study.

By analysing the tail direction of galaxies with $\textrm{JClass}>1$ in their
respective cluster systems, we find that galaxies from the Antlia and Fornax
clusters have tails preferentially pointing away from the cluster centre,
which suggests they are falling towards it probably for the first time.
However, only a mild preference is observed for galaxies in the Hydra cluster
since around half of the galaxies in Hydra indicate infall, whereas the other
half indicate outfall. We find insufficient evidence that nearby groups could
affect the ram pressure stripping in galaxies from Fornax.

Further insights might require more extensive analyses due to potential
selection effects influenced by the galaxies’ projected radii from the cluster
centre. For instance, comparing our calculated trail vector directions with Hi
tail directions from studies such as Wang et al. (2021); Kleiner et al. (2023)
could be insightful but lies beyond the scope of this paper.

The properties of jellyfish candidates are generally compared with non-
jellyfish galaxies to gain insights into the differing physics between the two
types of galaxies. Naturally, the astrophysics and the subsequent scientific
implications depend on how the JClasses are assigned. The traditional visual
classification used to separate jellyfish from non-jellyfish galaxies is
highly dependent on human visual biases, which makes the classification
subjective. In our visual classification, we often observed disagreement
between different classifiers. It is also impractical to manually vet large
datasets (comprising $\gtrsim 10^{6-7}$ galaxies) to identify rare jellyfish
galaxies.

To mitigate these challenges, we proposed a semi-automated pipeline using SSL
and demonstrated a proof-of-concept application of our pipeline. We pretrained
an encoder network aimed at extracting generalised feature representations of
galaxies without relying on human-based JClass for learning. Thus, SSL
pretraining is ideal for learning morphologies from large, unlabelled galaxy
datasets, a common theme in astronomy. The encoder is then used as a feature
extractor on galaxies unseen during the pretraining. Noting the limitations of
fully supervised learning or supervised learning on self-supervised
representations in providing JClass estimates, we developed a novel downstream
task based on the self-supervised representations. We assign a self-
supervised-based JClass to refine the visually-assigned JClass using a
weighted nearest-neighbor search on the self-supervised representations. For
any given galaxy, we assign the refined JClass as the weighted mean of visual
JClasses of the $k$ nearest neighbours in the self-supervised representation
space. We demonstrated the application of this framework to a few galaxies
having uncertain visual JClass classification, which in this study refers to
the case where more than half of the visual classifiers predict different
JClasses. Care was taken to ensure that the nearby galaxies used to assign the
JClass to the concerned galaxy were not themselves uncertain for visual
classification. The astrophysical analysis presented in Sect. 5 studied
possible patterns in the changing astrophysics as the JClass increases;
however, the JClass was obtained only by visual inspection. Our self-
supervised pipeline can be integrated with visual classification to improve
JClass estimates of uncertain visual classifications, which could reveal new
patterns or improve the reliability of observed patterns.

Due to our limited dataset, it is difficult to reliably quantitatively assess
how much disagreement exists between the visual and self-supervised JClasses.
However, we have found many cases where SSL predicted weak and intermediate
jellyfish candidates based on visual classification (JClass 1, 2) as non-
jellyfish (JClass 0). This may help mitigate false-positive cases. We have
also found cases where both approaches agree in their JClass estimate,
particularly for visual non-jellyfish galaxies. Cases where the self-
supervised predicted a stronger jellyfish signature were also present. Such
cases could pave the way for detecting new jellyfish galaxies. We have
validated our framework by finding that the self-supervised and visual
JClasses agree well for visually confident JClass predictions, which was the
expectation.

A current limitation of our self-supervised pipeline is based on the fact that
jellyfish galaxies and non-jellyfish galaxies, even the most pronounced ones,
have overlapping morphological features, such as extended emission or diffuse
regions at their edges. Since the self-supervised representations are of high
dimensionality (512 in this study), such similarity searches may highlight
similarities based on features that do not help distinguish jellyfish from
non-jellyfish galaxies. In other words, although the learned features are
useful for classification, we can not guarantee that they directly correspond
to fundamental astrophysical properties that are immediately interpretable. As
a result, we speculate that differentiating between merger and jellyfish
galaxies will be difficult based on the current approach.

As seen in Sect. 4.2, cases where the self-supervised JClass is greater than
the visual JClass can be studied in more detail, such as their astrophysical
and morphological characteristics, which is another potential application of
SSL. Such studies can also differentiate true ram pressure stripping
candidates from merger galaxies. Another research direction is identifying and
disentangling features or learning a similarity metric (instead of fixing it
to cosine similarity) that helps distinguish jellyfish from non-jellyfish
galaxies, which could alleviate these issues. A larger pretraining dataset can
also prove beneficial.

Although this study aimed to improve the JClass obtained from visual
classification, there are several possible extensions of our study. The
strongest jellyfish candidates based on visual classification can be used as
queries for similarity search so that the resulting similar images output by
the SSL pipeline can be further inspected for jellyfish identification. An
advantage is that only the strongest jellyfish signatures need to be
classified visually (which generally happens quickly and reliably), and our
pipeline may automatically identify other strong, intermediate, or weak
jellyfish signatures. Once identified by our pipeline, these jellyfish
candidates can be inspected in more detail. Such an approach is helpful for
swiftly identifying new jellyfish candidates from future galaxy surveys.
Another research direction is to pre-train the self-supervised encoder on a
large, unlabelled galaxy dataset and then perform fine-tuning of the model for
the specific task of JClass assignment. The fine-tuning approach can
significantly improve the generalisability of the learnt representations and
has been shown to surpass fully supervised methods (e.g., Liu et al., 2019;
Hayat et al., 2021; Abul Hayat et al., 2021). The loss function for fine-
tuning could be based on a representation similarity metric.

##  7 Conclusions

This study catalogues and analyses the astrophysical properties of 51
jellyfish candidates (possessing visual evidence of ram pressure stripping)
within the Fornax, Antlia, and Hydra clusters from the S-PLUS survey data.
Based on the Gini coefficient ($G$), entropy ($H$), and best-fit 2D Sérsic
index (nFit2D) morphological parameters, we find that galaxies possessing
extreme ram pressure stripping prefer the following regions in the morphology
space: low $G$, high $H$, and low nFit2D. However, the region where such
galaxies are located overlaps with the overall span of normal, star-forming
galaxies in the morphology space. We have found that galaxies with
$\textrm{JClass}\geq 1$ possess an overall higher SFR compared to the sample
of normal, star-forming galaxies. While we observe a strong preference for
galaxies in the Antlia and Fornax clusters to infall toward the cluster
centre, galaxies from Hydra possess a relatively weaker preference for infall.
According to our study, the order of virialisation of the clusters is Hydra,
Antlia, and Fornax, with Hydra being the most likely virialised system.

Another crucial contribution of our study is to present a semi-automated
pipeline based on a branch of machine learning called self-supervised learning
(SSL) to assist in visually classifying galaxies. The primary motivation to
use our designed pipeline for identifying jellyfish galaxies is because,
traditionally, their identification in optical wavelengths has predominantly
depended on visual inspection, which is a time-consuming endeavour.

Our study analyses the capabilities of SSL to assist visual morphological
classification of galaxies in the low-data regime ($\sim$200 galaxies only),
which has been previously largely unexplored in an astronomical context.
Despite the paucity of data, a similarity search using SSL revealed that the
learnt representations of our galaxies are robust to orientation and noise.
Our study thus shows that SSL can learn meaningful feature representations of
galaxies even with limited data, likely due to its non-dependence on any
labels during training. There are two immediate advantages of our self-
supervised pipeline used to refine the visual JClasses. First, unlike
laborious visual inspection, it is scalable to large datasets. Once the self-
supervised encoder network is pretrained, it can be used for swift JClass
assignment for new galaxies based on a simple, weighted nearest neighbour
search. Second, although our pipeline uses the visually assigned JClasses for
the final JClass prediction, the self-supervised encoder is trained agnostic
to the visual JClass labels. Thus, the training is unaffected by the quality
of visual JClass predictions. Furthermore, our pipeline relies only on
confident visual classifications, significantly reducing misclassifications
arising from human biases. Traditional approaches of supervised learning or
training a supervised classifier on the extracted feature representations
(i.e., the linear evaluation protocol) rely entirely on the quality of the
visual JClass since these labels are used as ground truths in the learning
process.

Our pipeline can also be used as a guide to train human classifiers to assist
in their visual classification. Another application of our pipeline is
identifying false positives and negatives during follow-up analysis after
human classification. Our self-supervised strategy is designed to lay the
groundwork for a more comprehensive search in the future. For example, with
large astronomical datasets, more powerful semantic embeddings can be
obtained, further improving the performance. It will then be possible to
leverage our self-supervised pipeline to produce more reliable JClass
estimates and thus pave the way for better constraining the properties of
these rare jellyfish galaxies. Finally, the idea of a task-agnostic nearest
neighbour search in the self-supervised representation space makes our
pipeline highly adaptable for the seamless identification of any rare
astronomical signatures within astronomical datasets of future astronomical
surveys.

## Acknowledgements

The S-PLUS project, including the T80-South robotic telescope and the S-PLUS
scientific survey, was founded as a partnership between the Fundação de Amparo
à Pesquisa do Estado de São Paulo (FAPESP), the Observatório Nacional (ON),
the Federal University of Sergipe (UFS), and the Federal University of Santa
Catarina (UFSC), with important financial and practical contributions from
other collaborating institutes in Brazil, Chile (Universidad de La Serena),
and Spain (Centro de Estudios de Física del Cosmos de Aragón, CEFCA). We
further acknowledge financial support from the São Paulo Research Foundation
(FAPESP), the Brazilian National Research Council (CNPq), the Coordination for
the Improvement of Higher Education Personnel (CAPES), the Carlos Chagas Filho
Rio de Janeiro State Research Foundation (FAPERJ), and the Brazilian
Innovation Agency (FINEP). We acknowledge useful discussions with Angela
Krabbe, Cristina Furlanetto, Karín Menéndez-Delmestre and Alvaro Alvarez-
Candal. ACS acknowledges funding from CNPq and the Rio Grande do Sul Research
Foundation (FAPERGS) through grants CNPq-403580/2016-1, CNPq-11153/2018-6,
PqG/FAPERGS-17/2551-0001, FAPERGS/CAPES 19/2551-0000696-9. This work was
partially supported by the CAS PIFI programme 2021VMC0005. RSS and SS
acknowledge the support from the China Manned Space Project with NO. CMS-
CSST-2021-A07. Y.J. acknowledges financial support from ANID BASAL project No.
FB210003 and FONDECYT Regular No. 1230441. RR acknowledges support from the
Fundación Jesús Serra and the Instituto de Astrofísica de Canarias under the
Visiting Researcher Programme 2023-2025 agreed between both institutions. RR,
also acknowledges support from the ACIISI, Consejería de Economía,
Conocimiento y Empleo del Gobierno de Canarias and the European Regional
Development Fund (ERDF) under grant with reference ProID2021010079, and the
support through the RAVET project by the grant PID2019-107427GB-C32 from the
Spanish Ministry of Science, Innovation and Universities MCIU. This work has
also been supported through the IAC project TRACES, which is partially
supported through the state budget and the regional budget of the Consejería
de Economía, Industria, Comercio y Conocimiento of the Canary Islands
Autonomous Community. RR also thanks to CNPq 311223/2020-6, 304927/2017-1 and
400352/2016-8, FAPERGS 16/2551-0000251-7 and 19/1750-2, CAPES/0001. This work
was partly done using GNU Astronomy Utilities (Gnuastro, ascl.net/1801.009)
version 0.19. Work on Gnuastro has been funded by the Japanese Ministry of
Education, Culture, Sports, Science, and Technology (MEXT) scholarship and its
Grant-in-Aid for Scientific Research (21244012, 24253003), the European
Research Council (ERC) advanced grant 339659-MUSICOS, the Spanish Ministry of
Economy and Competitiveness (MINECO, grant number AYA2016-76219-P) and the
NextGenerationEU grant through the Recovery and Resilience Facility project
ICTS-MRR-2021-03-CEFCA. This research has made use of the NASA/IPAC
Extragalactic Database (NED), which is funded by the National Aeronautics and
Space Administration and operated by the California Institute of Technology.
This research made use of the following python packages: Astropy (Astropy
Collaboration et al. 2013, 2018), Matplotlib (Hunter 2007), NumPy (Harris et
al. 2020) and SciPy (Virtanen et al. 2020).

## Data Availability

Part of the data can be found at the S-PLUS cloud at https://splus.cloud/. The
complete dataset underlying this paper will be shared upon a reasonable
request to the corresponding authors. We make the codes used in this study
publicly available at https://github.com/Yash-10/jellyfish_self_supervised.

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##  Appendix A Model training details

###  A.1 Implementation details

All experiments are conducted using the pytorch-lightning library (Falcon et
al. 2019; version 1.6.0), and our SimCLR implementation is motivated by the
SimCLR tutorial888https://uvadlc-
notebooks.readthedocs.io/en/latest/tutorial_notebooks/tutorial17/SimCLR.html
in Lippe (2022). We use ResNet-34 as our base encoder instead of the Resnet-50
used in the original SimCLR approach (He et al., 2016) since larger models
tend to overfit on small datasets (Cao & Wu, 2021). The ResNet-34 architecture
is modified to accept our 12-channel input. To handle the relatively low-
resolution images in our case as compared to typical images used for ResNet,
such as those from ImageNet (Deng et al., 2009), we also change the stride
from 2 to 1 in the first convolutional layer and reduce the amount of pooling
by removing the first max pooling layer (Newell & Deng 2020; Hayat et al.
2021). We use the default weight initialisation in PyTorch for all the models
considered in our study. This choice of architecture yields a 512-dimensional
representation vector for each image. Although increasing the dimensionality
of the representations enhances their quality, higher dimensional
representations may degrade the quality of the representations for smaller
datasets (Kolesnikov et al., 2019). Hence, we refrain from experimenting with
different representation sizes. Further studies can investigate the potential
benefits of increasing representation dimensions for smaller datasets.

The projection head in our self-supervised model is a two-layer MLP with a
ReLU activation function, mapping the representation vector onto a
128-dimensional space. Taking a cue from the observation by Chen et al.
(2020b) that a wider projection head improves performance, we opt for a four-
fold wider hidden layer. We do not, however, increase the depth of the MLP,
given that the benefits of deeper MLPs tend to saturate for already-wide
projection heads.

###  A.2 Hyperparameter tuning

####  A.2.1 For self-supervised pretraining

For pretraining, the following hyperparameters are tuned: learning rate,
weight decay, temperature, and number of epochs. As mentioned in the main
text, the batch size is fixed to 128. $K$-fold cross-validation is used to
optimise the hyperparameters by dividing the training dataset into $K$ folds.
We note that such an approach is less commonly used in the SSL context since
pretraining datasets are generally sufficiently large, unlike the case here.
The study by Suzuki et al. (e.g., 2022), for example, utilised $K$-fold cross-
validation in SSL. We adopt such a validation procedure for two main reasons.
First, our dataset size is too small to assume that a simple train-validation-
test split would estimate the model performance reliably. Second, it would
mean a part of the training data is set aside for validation, thus reducing
the amount of training data.

The hyperparameters are tuned using a combination of contrastive loss (defined
in Section 3.3) and top-5 accuracy (the number of times the desired patch is
within the top five most similar examples to the original image in the sampled
batch) on the validation split. For computational reasons, $K=3$ is used
instead of the common choices ($K=5$ or $10$), which means the scores are
averaged across three folds. We remind the reader that the top-5 accuracy is
not the accuracy in the downstream classification task. The similarity is
computed using the cosine similarity metric. The top-5 accuracy is used
instead of top-1 since the former is less noisy. Even though there are two
classes, jellyfish and non-jellyfish, here, the use of top-5 accuracy is
valid, unlike traditional supervised classification, since the similarity is
compared across all images from a given batch. The hyperparameters could be
selected based on the downstream classification performance. However, such an
approach is not used here since we are more concerned with image similarity
than the final classification performance.

A progressive grid-search approach is used to select the optimal set of
hyperparameters. First, a coarse search is performed on a wide range of
hyperparameter values: three learning rate values uniformly selected from
logarithmically spaced values in the range $10^{-5}$ to $10^{-2}$, weight
decay uniformly selected from three logarithmically spaced values in the range
$10^{-6}$ to $10^{-3}$, and temperature selected from 0.1, 0.5, 1.0. Such a
wide search informs of each hyperparameter’s approximate optimal
hyperparameter intervals. The optimal region found was around $3\times
10^{-4}$ for learning rate, $3\times 10^{-5}$ for weight decay, and 0.1 for
temperature. A finer search is then performed around these values. In all
cases till now, training was performed for 100 epochs to keep the
computational costs low. We separately list the top five approaches based on
top-5 accuracy and contrastive loss and only select the hyperparameter sets
that appeared in both lists. This makes the hyperparameter selection less
noisy. Six sets of hyperparameters appeared on both lists. Each case was then
trained for longer, i.e., 300 and 500 epochs, to yield the optimal
hyperparameter set: learning rate = $10^{-4}$, weight decay = $10^{-4}$, and
temperature = 0.05, again decided based on the combination of top-5 accuracy
and contrastive loss. As mentioned in the main text, training the model longer
often helps contrastive learning. To test this, we trained the model using the
optimal learning rate, weight decay, and temperature defined above for longer
epochs, i.e. 700 and 1000 epochs. We found the performance to improve by
training longer, which corroborates the fact. Hence, we use 1000 epochs for
pretraining.

Fig. 17 compares the top-5 accuracy and contrastive loss, averaged across
three folds, corresponding to the optimal hyperparameters obtained using the
above procedure. The figure shows that training for 1000 epochs yields the
highest accuracy and lowest contrastive loss. We have observed the standard
deviation across the folds to be $<2.5\%$. This difference is non-trivial,
which may be due to our extremely small dataset that makes the individual
folds not fully representative of the entire dataset.

Figure 17: Averaged top-5 accuracy and contrastive loss, across the three
folds, for the optimal hyperparameters (learning rate = $10^{-4}$, weight
decay = $10^{-4}$, and temperature = 0.05), obtained during hyperparameter
tuning of the self-supervised pretraining, as a function of the number of
epochs.

####  A.2.2 For supervised learning

The following hyperparameters are tuned: learning rate, weight decay, and
number of epochs. As in Section A.2.1, $K=3$ is used for the $K$-fold cross-
validation. The learning rate is selected from {$10^{-5}$, $10^{-4}$,
$10^{-3}$}, weight decay from {$10^{-5}$, $10^{-4}$, $10^{-3}$}, and number of
epochs from {50, 70, 90}. The macro-averaged precision and recall scores are
used for selecting the optimal hyperparameter set. A similar grid search
approach is used as in Section A.2.1. This results in 27 different sets of
hyperparameters. $K$-fold cross-validation is performed on each hyperparameter
set, and the corresponding precision, recall, and accuracy scores are averaged
across the three folds. The optimal hyperparameter set is chosen by selecting
those that appear in the top three positions for all three metrics. In our
case, two hyperparameter sets appeared in the top three positions. The tie was
broken by selecting the set that ranked better across all three metrics. This
procedure yielded the optimal hyperparameter set: learning rate = $10^{-5}$,
weight decay = $10^{-3}$, and number of epochs = 90.

Fig. 18 shows the classification metrics averaged across the three folds as a
function of the number of epochs. Overall, 90 epochs training performs better
than 50 or 70 epochs training. Hence, we choose 90 epochs for comparison with
the self-supervised approach.

Figure 18: Averaged precision, recall, and top-1 accuracy, across the three
folds, for the supervised classification using the optimal hyperparameters
(learning rate = $10^{-5}$, weight decay = $10^{-3}$), obtained during
hyperparameter tuning, as a function of the number of epochs.

####  A.2.3 For linear evaluation

Linear evaluation results are discussed in Appendix. B. Here, the tuning is
performed on the following hyperparameters: learning rate, batch size, and
number of epochs. The representations from the training set (obtained during
the train-test split during the linear evaluation) were divided into $K$
folds. Since the 512-dimensional representations are dealt with here rather
than images, the hyperparameter tuning poses relatively less computational
burden than the experiments in Section A.2.1 and A.2.2. Hence, $K=10$ is used
here.

Similar to the hyperparameter tuning procedure of Sect. A.2.2, the macro-
averaged precision and recall over the folds are compared. However, several
ties were observed in this case while ranking different hyperparameter sets
based on precision and recall scores. Hence, the logistic loss (also called
the cross-entropy loss) was used to break the ties. The set that yielded the
least loss was then selected. The optimal hyperparameter set we obtained is:
batch size = 16, learning rate = $5\times 10^{-3}$, and number of epochs =
350. As seen from Fig. 19, the number of epochs = 350 is optimal.

Figure 19: Averaged precision, recall, and logistic loss, across ten folds,
for the linear evaluation using the optimal hyperparameters (learning rate =
$5\times 10^{-3}$ and batch size = 16) as a function of the number of epochs.

##  Appendix B Self-supervised vs. supervised learning

We use the Resnet-34 architecture for the supervised CNN to match the encoder
architecture of SSL. Since supervised approaches benefit from having the
entire object within the image, we use all augmentations as in the self-
supervised case except random-resize-and-crop. Moreover, to ensure the
learning is not affected by class imbalance, we use weighted random sampling
wherein images from the minority class (i.e., jellyfish) are oversampled in
each sampled batch. We also reduce the learning rate by a factor of 0.1 after
70% and 90% of the total epochs during training for both approaches. For
linear evaluation, we train the logistic regression classifier using the SGD
optimiser with initial learning rate = $5\times 10^{-3}$, batch size = 16, and
the number of epochs = 350 but do not use weight decay.

It is widely acknowledged that supervised learning methods tend to exhibit
subpar performance as the size of the dataset decreases. This is mainly due to
their vulnerability to overfitting (Ying, 2019), unless certain regularisation
techniques, such as dropout (Srivastava et al., 2014), are employed. On the
contrary, SSL demonstrates relative resilience to fluctuations in the training
data size, as it does not rely on labels during the learning process but
instead self-generates supervision from the data itself. We assess these
claims by contrasting (a) the classification performance of a supervised
logistic regression classifier, trained on self-supervised representations,
with (b) vanilla supervised CNN. The former strategy is often called the
‘linear evaluation protocol’ and is one of the common ways to evaluate self-
supervised representation quality. Both methods use the ground-truth labels
derived from visual classification results, with the only difference being
that the former only uses labels during the supervised logistic regression
classifier training but not for pretraining the encoder. The hyperparameter
tuning details are described in Appendix A.2. For comparison purposes, we
framed the problem as a binary classification. As stated in the main text,
such a binary classification task greatly simplifies the comparison since a
multi-label classification scheme (JClass 0, 1, 2, 3, and 4) exacerbates the
class-imbalance issue due to the rareness of extreme jellyfish candidates.
Moreover, to ascertain the robustness of the self-supervised representations
to variations in seeing conditions, celestial locations, and other systematic
factors, training is performed on galaxies from the Antlia and Hydra clusters,
whereas the testing set includes images only from the Fornax cluster. For
completeness, we discuss the other two cases (testing the model on the Hydra
and Antlia cluster galaxies) in Appendix E

Fig. 20 illustrates the comparison between the two approaches. Figs. 20(a) and
20(b) suggest that the supervised approach leans more towards classifying
galaxies as jellyfish than the self-supervised approach, as evidenced by the
misclassification of eight non-jellyfish galaxies as jellyfish. This bias
occurs despite adjustments made for class imbalance during the supervised
learning process (Appendix A.1). Conversely, when trained on self-supervised
representations, a logistic regression classifier demonstrates enhanced
robustness to imbalance, as it does not depend on labels for learning the
representations. This finding indicates that self-supervised representations
have successfully captured meaningful information regarding the galaxies’
jellyfish-ness. This, in turn, enables the downstream classifier to
differentiate more accurately between jellyfish and non-jellyfish galaxies.
Overall, SSL demonstrates an improvement in classification performance over
supervised learning.

In the context of this study, an effective classification scheme should
generate a robust recall rate ($\dfrac{\textrm{TP}}{\textrm{TP}+\textrm{FN}}$;
TP: True positive, FN: False negative; positive denotes the jellyfish
category) for jellyfish candidates while maintaining high precision
($\dfrac{\textrm{TP}}{\textrm{TP}+\textrm{FP}}$) for non-jellyfish galaxies.
Considering the rarity of jellyfish candidates, a certain level of false
positives can be tolerated. Provided these inaccuracies are infrequent, manual
re-inspection and refinement of these galaxies by human classifiers is
feasible. In contrast, overlooking jellyfish candidates can compromise the
utility of such a model. Figs. 20(a) and 20(b) indicate that both self-
supervised and supervised methodologies achieve identical recall scores for
the jellyfish category (83%). The precision scores for the non-jellyfish
category are also identical (94% and 93% for self-supervised and supervised
learning, respectively). Thus, self-supervised and supervised learning provide
similar performances in such a context.

We note that in our study, a threshold probability of 0.5 is used for
classification in both the self-supervised and supervised methods. Alternative
threshold choices were not experimented with. Figs. 20(d) and 20(e), which
display the predicted probabilities, can serve as a general guide for
hypothesising how results might shift with the application of different
thresholds. Given the rarity of jellyfish candidates, one might consider a
higher probability threshold (analogous to the 0.8 threshold used for the
visually classified raw score in Zinger et al. 2023). If a higher threshold is
used, even more significant improvements can be obtained using the self-
supervised approach, as suggested by the probabilities observed in Figs. 20(d)
and 20(e).

(a)

(b)

(c)

(d)

(e)

Figure 20: Classification performance comparison between the supervised and
self-supervised approaches. Panels (a) and (b) show the confusion matrices,
(c) compares the macro-averaged precision, recall, and area under the Receiver
operating characteristic (ROC) curve (AUC), and (d) and (e) show the
prediction probabilities output by the supervised ResNet and the logistic
regression classifier on the self-supervised representations. By definition,
AUC lies in the $[0,\,1]$ range, but here we show it as a percentage only for
visualisation purposes.

##  Appendix C Data augmentation ablation study

Data augmentation is critical in learning good-quality representations for the
contrastive learning framework used here (Chen et al., 2020a). Ablation
studies are an indirect way to understand which augmentations (or combinations
of augmentations) are critical or relatively unhelpful for learning good
representations. Such ablation studies are commonplace in SSL approaches and
have been studied by many works (see, e.g., Hayat et al. 2021; Kinakh et al.
2021).

The procedure is as follows: certain augmentation(s) from the pipeline are
turned off, pretraining is performed by learning representations of images
using images from the training dataset, and the linear evaluation protocol
from Appendix. B is employed on the test dataset. The ‘baseline’ denotes the
case where all augmentations described in the main text are used. An
augmentation or a set of augmentations is considered important for the
downstream classification task if the test performance decreases compared to
the baseline after removing that augmentation or set of augmentations. Similar
to the main text, training is performed on galaxy images from the Antlia and
Hydra galaxy clusters, and testing is done on images from the Fornax cluster.

Fig. 21 shows the F1 scores of the classification under different sets of
augmentations. Accuracy is not used due to the class imbalance. It can be
observed that the F1 score decreases from the baseline score, 81.7, to 50.7
when random resized crop and colour jitter are omitted. Thus, this combination
of augmentations is vital for classification performance. Since the F1 score
is the least among all F1 scores in the plot, we conclude that random resized
crop and colour jitter is the most important set of augmentations. This also
confirms the observation in Chen et al. (2020a). Even though our colour jitter
implementation differs from theirs, it is noteworthy that the result still
holds. The figure also shows that random resized crop is the most important
augmentation in our case, followed by colour jitter, following a similar
logic. All other augmentations are also important for the classification task,
except when horizontal flip, vertical flip, and random rotation augmentations
are removed (Approach 10 in the figure), since the performance improves when
these three augmentations are removed from the augmentation pipeline. A
possible reason for this is that, since flips are a special case of rotation
augmentation, incorporating both kinds of augmentations leads to redundancy,
which could reduce the quality of the learnt representations. For approaches 1
and 2 in Fig. 21, we used a smaller batch size of 16 instead of 128 for self-
supervised training due to memory constraints when not using cropping.

Figure 21: Classification F1 scores under various omission combinations of
data augmentations. The labels on each bar describe which augmentations were
removed from the pipeline. For example,
no_horizontal_and_vertical_flip_and_rotation means that horizontal flip,
vertical flip, and random rotation augmentations were removed. The ‘baseline’
approach is marked by orange colour.

##  Appendix D Importance of accounting for background/nearby sources for
effective similarity search

We use the Grad-CAM pixel attribution method on the self-supervised
representations extracted by the trained model to visualise how background or
nearby astronomical sources can affect the similarity search. Implementation
is taken from the grad-cam Python library (Gildenblat & contributors,
2021)999The tutorial can be found here: https://jacobgil.github.io/pytorch-
gradcam-book/Pixel%20Attribution%20for%20embeddings.html.

To demonstrate the effects due to background sources, we select a few cases in
which galmask could not effectively remove sources near the galaxy of
interest. We seek to find whether the similarity search can inadvertently find