*natbibCitation

11institutetext: 1Division of Particle and Astrophysical Science, Nagoya
University, Furo-cho, Chikusa-ku, Nagoya 464–8602, Japan
2The Research Centre for Statistical Machine Learning, the Institute of
Statistical Mathematics, 10–3 Midori-cho, Tachikawa, Tokyo 190–8562, Japan
3Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS,
University of Tokyo, Kashiwa, Chiba 277-8583, Japan
4International Centre for Radio Astronomy Research, University of Western
Australia, 35 Stirling Hwy, Crawley, WA6009, Australia
5Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of
Tokyo, Kashiwa, Chiba 277-8583, Japan
6Jodrell Bank Centre for Astrophysics, Department of Physics & Astronomy,
University of Manchester, Oxford Road, Manchester M13 9PL, UK
7Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing
100871, People’s Republic of China
8Department of Astrophysical Sciences, Princeton University,Princeton, NJ
08544, USA
9Department of Astronomy, School of Science, The University of Tokyo, 7-3-1
Hongo, Bunkyo, Tokyo 113-0033, Japan
10National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan
11Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astronomy-
Mathematics Building, AS/NTU, No.1, Section 4, Roosevelt Road, Taipei 10617,
Taiwan
12Research Center for Space and Cosmic Evolution, Ehime University, 2-5
Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan
13European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748, Garching,
Germany

# Galaxy mergers in Subaru HSC-SSP: a deep representation learning approach
for identification and the role of environment on merger incidence

Kiyoaki Christopher Omori 11 Connor Bottrell 334455 Mike Walmsley 66 Hassen M.
Yesuf 33 7 7 Andy D. Goulding 88 Xuheng Ding 33 Gergö Popping 1313 John D.
Silverman 33 9 9 Tsutomu T. Takeuchi 11 2 2 Yoshiki Toba 101011111212

(Received September , 2023; accepted September, 2023)

###### Abstract

Context. Galaxy mergers and interactions are an important process within the
context of galaxy evolution, however a method which identifies pure and
complete merger samples is still not definitive. A method to create such a
merger sample is required, so that studies can be conducted to deepen our
understanding on the merger process and its impact on galaxy evolution.

Aims. In this work, we take a deep learning-based approach for galaxy merger
identification in Subaru HSC-SSP, specifically through the use of deep
representation learning and fine-tuning, with the aim of creating a pure and
complete merger sample within the HSC-SSP survey. We can use this merger
sample to conduct studies on how mergers affect galaxy evolution.

Methods. We use Zoobot, a deep learning representation learning model pre-
trained on citizen science votes on Galaxy Zoo DeCALS images. We fine-tune
Zoobot for the purpose of merger classification of images of SDSS and GAMA
galaxies in HSC-SSP public data release 3. Fine-tuning is done using $\sim
1200$ synthetic HSC-SSP images of galaxies from the TNG simulation. We then
find merger probabilities on observed HSC images using the fine-tuned model.
Using our merger probabilities, we examine the relationship between merger
activity and environment.

Results. We find that our fine-tuned model returns an accuracy on the
synthetic validation data of $\sim 76\%$. This number is comparable to those
of previous studies where convolutional neural networks were trained with
simulation images, but with our work requiring a far smaller number of
training samples. For our synthetic data, our model is able to achieve
completeness and precision values of $\sim 80\%$. In addition, our model is
able to correctly classify both mergers and non-mergers of diverse
morphologies and structures, including those at various stages and mass
ratios, while distinguishing between projections and merger pairs. For the
relation between galaxy mergers and environment, we find two distinct trends.
Using stellar mass overdensity estimates for TNG simulations and observations
using SDSS and GAMA, we find that galaxies with higher merger scores favor
lower density environments on scales of 0.5 to 8 $h^{-1}$Mpc. However, below
these scales in the simulations, we find that galaxies with higher merger
scores favor higher density environments.

Conclusions. We fine-tuned a citizen-science trained deep representation
learning model for purpose of merger galaxy classification in HSC-SSP, and
make our merger probability catalogue available to the public. Using our
morphology-based catalogue, we find that mergers are more prevalent in lower
density environments on scales of 0.5 - 8 $h^{-1}$Mpc.

###### Key Words.:

galaxies:evolution – galaxies:interactions – methods: data analysis –
galaxies: abundances – galaxies: statistics

##  1 Introduction

Galaxy evolution involves many processes that can affect the physical
properties of the involved galaxies. Galaxy interactions and mergers are
considered to be an important driver of physical phenomena and evolution in
galaxies. For example, galaxy interactions and mergers can drive inflow of gas
towards the centers of galaxies (Hernquist, 1989; Barnes & Hernquist, 1992;
Mihos & Hernquist, 1996; Naab & Burkert, 2001; Hopkins & Quataert, 2010;
Blumenthal & Barnes, 2018). These inflows can enhance star formation activity
(Beckman et al., 2008; Ellison et al., 2008; Patton et al., 2011, 2013;
Hopkins et al., 2013; Moreno et al., 2015; Sparre & Springel, 2016; Thorp et
al., 2019), dilute central gas phase metallicities (Ellison et al., 2008;
Rupke et al., 2010; Montuori, M. et al., 2010; Sol Alonso et al., 2010; Perez
et al., 2011; Torrey et al., 2012; Sparre & Springel, 2016; Thorp et al.,
2019), trigger accretion onto supermassive blackholes (Keel et al., 1985;
Sanders et al., 1988; Matteo et al., 2005; Koss et al., 2010; Ellison et al.,
2011; Satyapal et al., 2014; Ellison et al., 2015; Goulding et al., 2018;
Ellison et al., 2019), and trigger quasars (Urrutia et al., 2008). More
broadly, in the $\Lambda$-dominated cold dark matter ($\Lambda$CDM) framework
for structure formation in the Universe, accretion of stellar material though
galaxy mergers (ex-situ assembly) is a key process by which massive galaxies
grow their stellar mass.

Despite its importance, we do not have a full understanding of galaxy
interactions and mergers. While studies have been able to quantify the role of
mergers as a driver of stellar mass growth (Robotham et al., 2014; Rodriguez-
Gomez et al., 2016), the specific role of mergers in driving stellar mass
growth, enhancement of star formation and active galactic nuclei (AGN)
activity, and morphological transformations is still contentious. Even the
environment in which galaxy mergers are prevalent does not have a definitive
conclusion. Some dark matter halo simulations predict that mergers are more
likely to happen in lower mass density regions (Ghigna et al., 1998), however
other simulation results (Fakhouri & Ma, 2009; Hester & Tasitsiomi, 2010), as
well as observational studies (Jian et al., 2012) do not necessarily agree
with this prediction, stating that mergers occur in denser environments. A
major reason for the lack of clear understanding of the role of mergers and
interactions in galaxy evolution or their environments is the difficulty of
precise identification of merger galaxies in observational data.

There have been numerous studies employing several different methods for
merger identification. One approach is the close-pairs method. This method
searches for binary pairs in the sky using imaging and photometry or
spectroscopy (e.g., Lin et al., 2004; Soares, 2007). This method has a number
of issues. First, this approach misses galaxies in the post-coalescence phase
of a merger, as there is only access to single-galaxy characteristics. Second,
this approach requires spectroscopic redshifts, which also may be impacted by
spectroscopic incompleteness. Third, merger rates in observations may be
overestimated compared to those in simulations, even if the same criteria is
used, due to reasons such as chance projections, as well as the difficulty of
obtaining accurate merging timescales (Kitzbichler & White, 2008). The
criteria for pair selection, such as exact velocity and separation cuts, have
undergone significant refinement to register fewer interlopers in merging pair
samples (Zepf & Koo, 1989; Burkey et al., 1994; Carlberg et al., 1994; Yee &
Ellingson, 1995; Woods et al., 1995; Patton et al., 1997; Wu & Keel, 1998).
Also, some mergers may not be detected by this method, as there may be merging
galaxy pairs with a pair distance greater than the maximum projected distance
adopted for a study.

Other methods rely on galaxy imaging data and their morphologies. Galaxy
interactions can cause disturbances to the morphology of a galaxy (Toomre &
Toomre, 1972; Toomre, 1977; Negroponte & White, 1983; Hernquist, 1992; Naab &
Burkert, 2003; Hopkins et al., 2008; Berg et al., 2014), which can be
quantified into non-parametric statistics. An example of these statistics are
the CAS parameters (Concentration (Bershady et al., 2000), Asymmetry
(Conselice et al., 2000), Smoothness (Conselice, 2003)), Gini and $M_{20}$
(Lotz et al., 2004). An n number of these parameters can be combined to create
a criteria for merger classification in the n-dimensional feature space (e.g.,
Goulding et al., 2018; Snyder et al., 2019; Rose et al., 2023; Thibert et al.,
2021; Guzmán-Ortega et al., 2023). Using these statistics can reduce the
dimensionality of data being used. As a result, the required number of
training samples can be reduced compared to image classification methods such
as convolutional neural networks. The issue with this method is that merger-
driven morphological disturbances are low surface brightness features
(Conselice et al., 2000; Bottrell et al., 2019b; Thorp et al., 2021; Wilkinson
et al., 2022) which require high quality imaging, both in terms of depth and
resolution, to identify. Modern day imaging surveys, such as the multi-tiered,
wide-field, multi-band imaging survey Hyper Suprime-Cam Subaru Strategic
Program (HSC-SSP, Aihara et al. 2018, see Section 3.1), can allow for such
imaging where these features are visible. However, the issue still remains
that these non-parametric statistics do not capture the complexity in high-
quality imaging data provided by modern wide-field galaxy surveys, and as
such, not all information from images can be extracted from these statistics
and the n-dimensional feature spaces using them.

There have also been methods relying on visual inspection of galaxy images.
When conducting morphological studies, visual classification by experts is
largely considered the gold standard (Nair & Abraham, 2010). Foremost, the
visual approach can incorporate domain-specific human knowledge in the
classification of galaxies, i.e., human knowledge of what is visually a merger
can be used to purify any classification results, particularly in
classifications done by machine learning methods. Indeed, visual follow-ups by
human classifiers is often employed to purify merger ‘candidate’ samples
produced by automated and quantitative approaches (e.g., Bickley et al., 2022;
Pearson et al., 2022). The visually distilled samples yield more robust
scientific outcomes on merger properties. Therefore, it is clear that domain
knowledge provided by human classifiers is valuable. Second, visual
classifications, in principle, use all of the morphological information
encoded in high-quality galaxy images, and is not restricted to a set of
summary statistics (Blumenthal et al., 2020). However, this method also has
its weaknesses. First, the criteria for what is considered a merger can differ
depending on the individual carrying out the visual inspection: so the same
galaxy may be assigned a different label by different people. Additionally,
visual inspection by humans can be very time-consuming, and not realistic for
large datasets in modern day galaxy surveys. The Galaxy Zoo Project (Lintott
et al., 2008, 2011, hereinafter referred to as GZ1) overcame these issues to
an extent. GZ1 is a catalogue (Darg et al., 2010a) offering morphology
probabilities for over 1 million Sloan Digital Sky Survey (SDSS) galaxies,
with citizen scientists assigning labels for morphological features. The
labels assigned in this catalogue are weighted in accordance with the
‘correctness’ of the scientists. Merger probabilities are part of this
catalogue, and have been used in many merger-related studies, such as
Holincheck et al. (2016); Weigel et al. (2017). However, while citizen science
can be more time efficient than classifications made by expert scientists, it
may not be as reliable.

Recent advents in deep learning technology for image-based galaxy
characterization have made the visual inspection process less time- and human-
resource consuming. Convolutional neural networks (CNNs) and deep learning
models have achieved performances greater than other computer imaging methods
(Krizhevsky et al., 2017), even surpassing the performance of some human
classifications (He et al., 2015). CNNs have already been used in a number of
studies, both in galaxy morphology classification as a whole (e.g., Dieleman
et al., 2015; Domínguez Sánchez et al., 2018; Jacobs et al., 2019; Zhu et al.,
2019; Ghosh et al., 2020; Cheng et al., 2021; Domínguez Sánchez et al., 2022;
Walmsley et al., 2022a; Cavanagh et al., 2023; Huertas-Company & Lanusse,
2023), and the specific task of galaxy merger classification, with varying
levels of accuracy (e.g., Walmsley et al., 2019; Pearson et al., 2019b;
Bottrell et al., 2019a; Bickley et al., 2021; Ćiprijanović et al., 2020;
Ferreira et al., 2020; Ćiprijanović et al., 2021; Bickley et al., 2022;
Bottrell et al., 2022; Pearson et al., 2022; Ferreira et al., 2022).

In this work, we investigate a particular approach of the training process in
CNNs, in the form of transfer learning. Training a CNN from scratch requires a
very large labeled training set, and preparing such a dataset for each
classification task can be very time- and human-resource expensive, as
highlighted in the issues with visual classification above. This step can be
potentially streamlined and made more efficient through transfer learning, or
transferring the knowledge from a previous study and adapting it to a new
dataset. The approach of using transfer learning for galaxy merger
identification was conducted in Ackermann et al. (2018), which found that
transfer learning using the diverse ImageNet dataset can lead to improvements
over conventional machine learning methods. In Domínguez Sánchez et al.
(2019), transfer learning and fine-tuning using astronomical data was
conducted. This study found that knowledge can be transferred between
astronomical surveys, and that combining transfer learning and fine-tuning can
boost model performance and reduce training sample size. This work will
combine the approaches of the above works. We will use the techniques of
transfer learning and fine-tuning, through the use of the pre-trained model
Zoobot (Walmsley et al., 2023). Zoobot is a pre-trained model trained on
diverse astronomical images, using human knowledge in its pre-trained weights
as a foundation. In Walmsley et al. (2022b), ring galaxies were correctly
classified using a fine-tuning sample size of $\sim 100$, finding that galaxy
morphological classification problems can be solved through a transfer-
learning and fine-tuning approach. Our approach is to use the weights of
Zoobot as a foundation, and fine-tuned the model for the purpose of galaxy
merger identification. The model is fine-tuned to classify HSC-SSP images,
using a small sample of survey-realistic HSC-SSP images from the TNG50
cosmological magneto-hydrodynamical simulation (Pillepich et al., 2019; Nelson
et al., 2019) and corresponding ground truth merger status labels. This
approach is able to construct a model combining a) human domain knowledge on
galaxy morphology and b) ground truth merger labels accessible only from
simulations.

This work is broadly divided into two portions. In the first portion,
encompassing from Section 2 to Section 4, we discuss our machine-learning
based approach for classification, and evaluate the performance of our
classifier. In the second portion of this work, composed of Section 5 and
Section 6, we conduct investigations on galaxies we identified using our fine-
tuned model, particularly the relationship between galaxy mergers and
environment. Specifically, we investigate whether mergers are found more
frequently in higher density or lower density environments. We study the
relationship between galaxy merger probability and their overdensities by
using multiscale environmental parameters, ranging from 0.05 M$h^{-1}$Mpc to 8
$h^{-1}$Mpc, computed by Yesuf (2022). We compare the findings of the
relationship found in the observational galaxies with those in simulations,
and discuss the results.

##  2 Method

In this section, we describe the Zoobot deep representation model from
(Walmsley et al., 2022a, b, 2023). We then describe our approach to fine-
tuning the model using survey realistic HSC-SSP images constructed from
galaxies from the TNG50 cosmological hydrodynamical simulation.

###  2.1 Zoobot

Zoobot (Walmsley et al., 2023) is a publicly available pretrained model that
can be fine-tuned for use in galaxy morphology classification problems. The
initial deep learning model is trained with the methods written in Walmsley et
al. (2022a), using data and labels from Galaxy Zoo DECaLS (hereinafter
referred to as GZ DECaLS). GZ DECaLS is a project where volunteers visually
classified galaxies in the deep, low-redshift images of the Dark Energy Camera
Legacy Survey (DECaLS, Dey et al., 2019). Zoobot uses DECaLS imagery due to
its superior depth and seeing compared to that in the imagery used in previous
GZ projects. For example, in GZ 2 (Darg et al., 2010a), which is often used
for machine learning architecture in astronomical imaging classification
(e.g., Banerji et al., 2010; Ackermann et al., 2018), SDSS images are used.
This imaging survey has a median $5\sigma$ point source depth of $r=22.7$ mag
with a median seeing of $1\aas@@fstack{\prime\prime}4$ and a plate scale of
$0\aas@@fstack{\prime\prime}396$ per pixel (York et al., 2000). The DeCALS
survey has a median $5\sigma$ point source depth of $r=23.6$ mag, and seeing
better than $1\aas@@fstack{\prime\prime}3$, and a plate scale of
$0\aas@@fstack{\prime\prime}262$ per pixel (Dey et al., 2019), offering
improved imaging quality. This not only allows for fainter and low surface
brightness merger features to be revealed, but also is closer to the depth of
the images we conduct training and make predictions on, which we explain in
Section 3.

The classifications made in the GZ DECaLS dataset were for galaxy features
such as bars, bulges, spiral arms, and merger indicators. A total of
approximately 7.5 million classifications were given for over 310,000 galaxies
in GZ DeCALS. These classifications were then used to train a deep
representation learning model. Predictions made by the trained model achieved
99% accuracy when measured against confident volunteer classification for a
variety of features, such as spiral arms, bars, and merger status. The results
of Walmsley et al. (2022b) showed that this trained model was able to find
similar galaxies and anomalies without any modification, even for tasks that
it was never trained for. Further, the model can be fine-tuned for specific
morphological classification tasks.

The technique of fine-tuning consists of training an initial model (usually
with a large amount of data), then adapting the model to a different task
(usually with a smaller amount of training data). Once the initial model is
trained and representations learned, the ‘head’ layer (i.e. the upper layer)
is removed, and the weights of the remaining layers, or ‘base’ layers, frozen.
A ‘new head’ model with outputs appropriate for the different task is added,
then trained with data and labels for the new task. The characteristic of this
method is that a far smaller training sample for the specific task is required
compared to training a model from scratch.

Walmsley et al. (2022b) found that when using a small training sample
($\sim$1000 samples), this fine-tuning approach can yield higher accuracies
compared to training a dataset from scratch. Further, fine-tuning using a
‘base’ model trained on generic galaxy morphology data and labels (Zoobot)
yielded higher accuracies than fine-tuning a model trained with a generic
terrestrial set of representations (ImageNet). Further detailed descriptions
and methods used in Galaxy Zoo DeCALS and Zoobot are available in Walmsley et
al. (2022a), Walmsley et al. (2022b), and Walmsley et al. (2023).

###  2.2 Fine-tuning Zoobot using simulation images

####  2.2.1 Training data

Training a classifier, whether it be from scratch or through transfer
learning, requires training data consisting of image data and corresponding
ground truth labels. For this work, we require galaxy image data with labels
of either merger or non-merger. We obtain images with ground-truth merger
labels by using synthetic HSC-SSP images of galaxies from the TNG50
simulation. The use of simulations allows us access to information about a
galaxy that is generally unavailable in observations, such as when the galaxy
underwent or will undergo its previous or next merger, as well as properties
of the merger activity itself, such as the mass ratio between the galaxies
involved.

####  2.2.2 IllustrisTNG50

We use data available from simulation data to acquire galaxy samples for
mergers and non-mergers. Specifically, we use a suite of large-volume
cosmological magneto-hydrodynamical simulation data in the form of
IllustrisTNG simulation data. The IllustrisTNG simulations (Springel et al.,
2018; Pillepich et al., 2018a; Naiman et al., 2018; Nelson et al., 2018;
Marinacci et al., 2018), performed with with the moving mesh code AREPO
(Springel, 2010), includes a comprehensive model for galaxy formation
(Weinberger et al., 2017; Pillepich et al., 2018b). This model includes
treatments for stellar formation and evolution, black hole growth, magnetic
fields, stellar and black hole feedback, and radiative cooling. TNG
simulations track the evolution of dark matter, gas, stars, and supermassive
blackholes ranging from the very early universe up to redshift $z=0$. TNG
simulations include three runs spanning a range of volume and resolution,
TNG50, TNG100 and TNG300, in order of ascending volume and descending
resolution. For this work we use simulation data from TNG50 (Pillepich et al.,
2019; Nelson et al., 2019), which offers the highest resolution, with evolving
$2\times 2160^{3}$ dark matter particles and gas cells in a 50 Mpc box.

We use survey-realistic synthetic HSC images from the TNG50 data, with the
imaging to come in Bottrell et al. (2023). The galaxies from the TNG
simulations go through a multiple steps to produce these synthetic images.

First, the images are forward-modelled into idealized synthetic images in HSC
grizy bands (Kawanomoto et al., 2018) using the Monte Carlo Radiative transfer
code SKIRT (Camps & Baes, 2020). For each galaxy in our sample, stellar and
gaseous particle data taken from its friends-of-friends (FoF) group within a
spherical volume is used to run the radiative transfer simulation. The radius
captured within this spherical volume is sufficiently large that extended
structures, satellites, and nearby groups and clusters are included in the
transfer simulations.

SKIRT models the spectral energy distribution (SED) of stellar populations
using the Bruzual & Charlot (2003) template spectra and Chabrier (2003)
initial mass function for stellar populations older than 10 Myr, and with the
MAPPINGS III SED photo-ionisation code (Groves et al., 2008) for younger
stellar populations (¡ 10 Myr). The MAPPINGS III library accounts for emission
from HII regions, surrounding photodissociation regions, gas and dust
absorptions in birth clouds around young stars, nebular and dust continuum and
line emission.

Next, as TNG simulations do not explicitly track dust evolution, a dust model
is required to account for the relationship between dust and gas properties.
The model used follows Popping et al. (2022), which takes into account the
empirical scaling relation between the dust-to-metal mass ratio (DTM) and
metallicity within gas (Rémy-Ruyer et al., 2014). Following the empirical
broken power law, Rémy-Ruyer et al. (2014), the metallicity in each gas cell
can be converted in to a dust-to-gas mass density ratio, which then in turn
can be used to compute the dust density (abundances). As in Schulz et al.
(2020) and Popping et al. (2022), the dust abundances is set to zero for cells
that are not star forming or temperatures greater than 75000 K. Dust self-
absorption is not accounted for in the transfer simulations.

Finally, RealSim (Bottrell et al., 2019a) in conjunction with HSC Data Access
Tools, is used for a) assignment of insertion location within HSC and flux
calibration, b) spatial rebinning to HSC angular scale, and c) reconstruction
of a HSC PSF and convolusion of the idealized image, and the final injection
into HSC-SSP. The full-color images created using these steps visually
resemble those of real galaxies in the HSC-SSP (Eisert et al. in prep).
Detailed descriptions on the synthetic images and how they are processed will
be provided in Bottrell et al. (2023). We use synthetic images at 3 snapshots,
78, 84, and 91, corresponding to redshifts $z=0.3$, $0.2$, and $0.1$,
respectively. We also constrain the subhalo stellar mass to be
$\log{(\mathrm{M_{*}/M_{\odot}})}>9$, which is approximately the lowest limit
for stellar structures in TNG data to be well resolved.

####  2.2.3 Merger and non-merger selection

We select galaxy mergers based on the time to the closest merger event, either
the most recent merger event or the next merger event. We define a merger
event to be the snapshot within a simulation galaxy’s merger tree where two
halos from the previous snapshot merge and become a single halo. The
observability timescale for galaxy interaction signatures in imaging data is
difficult to constrain, as it can depend on a wide range of properties. These
range from the method used for merger identification (pair identification,
nonparametric statistics), physical properties of the interacting galaxies
themselves (gas mass, pair mass ratio, dust) to the properties of the
observations (wavelength, viewing angle, resolution). Studies have been
conducted using hydrodynamical simulations (Lotz et al., 2008, 2010a, 2010b)
to constrain the observability timescale for various merger identification
methods and merger properties. Timescales found from these works can be as low
as $0.2-0.4$ Gyr, and can exceed 1 Gyr, depending on the signature used, such
as galaxy asymmetry or Gini - $M_{20}$ metric.

For this work, we apply a $0.5$ Gyr cut since or until the closest merger
event to select a merger sample. This cutoff will allow for most merger
signatures to be detected. As we would like to make the model agnostic to a
diverse scope of mergers, we do not place any constraints on the physical
properties of the galaxies such as gas mass or star formation rate, and
include mergers of varying mass ratios: major (mass ratio ¡ 1:4), minor (mass
ratio ¡ 1:10), and mini (mass ratio ¡ 1:20). Mass ratios are defined comparing
the maximum stellar masses of the composing galaxies of the merger pair. These
restrictions leave us with 291 mergers, with 104 at snapshot 78, 111 at
snapshot 84, and 76 at snapshot 91.

For non-merger selection, we adopt a cutoff so that visual merger signatures
should not be visible in the images. For this work, the non-mergers have the
most recent or next merger event to be $>3$ Gyr, sufficiently greater than the
observability timescales found in the works above. These cutoffs give us 1472
non-mergers. We do not use all of these non-mergers, as it is preferable that
the size of classes are balanced when training models. Further, to ensure that
we do not have stellar mass biases between the merger and non-merger samples,
for each merger galaxy we select a non-merger galaxy belonging to the same
snapshot (redshift) with a stellar mass within $0.1$ dex. The stellar mass
distributions of the merger and non-merger galaxies are shown in Fig 1.
Conducting a two-sample KS test on the merger and non-merger stellar mass
distribution returns a statistic of 0.01, and a p-value of 0.99.

Figure 1: The stellar mass distributions for the simulated TNG50 merger and
non-merger galaxies used for fine-tuning Zoobot. There are 291 each of mergers
and non-mergers, with 104 at $z=0.3$. 111 at $z=0.2$, and 76 at $z=0.1$. Each
merger galaxy used in the fine-tuning process has a corresponding non-merger
galaxy at the same snapshot with a stellar mass within 0.1 dex.

The sample used for fine-tuning includes 291 mergers and non-mergers of
similar stellar mass distribution, and as each galaxy in the image catalogue
is processed by SKIRT along 4 lines of sight, we have $\sim$1200 synthetic HSC
gri images each for mergers (assigned with a class label of 1) and non-mergers
(assigned with a class label of 0). A sample size of this order can achieve
greater accuracies through fine-tuning using Zoobot as opposed to training a
model from scratch, or from transfer learning using ImageNet, as shown in
Walmsley et al. (2022b). We note that while our merger sample includes mergers
at varying mass ratios and stages, they are all given the same class label. As
such, the output of our model will only predict whether or not a galaxy is a
merger, and will not make classifications on merger mass ratio or stage.

Cutouts are made for the $\sim 2400$ galaxy images as a final pre-processing
step. These cutouts encompass $10\times$ Sersic $R_{\textrm{eff}}$ of each
galaxy, and are re-sized to 300 $\times$ 300 pixels for input into the model.

####  2.2.4 Training procedure

As highlighted in the previous sections, the ’head’ trained on GZ DeCALS is
removed, and the ‘base’ model is frozen. Detailed architecture of the Zoobot
‘base’ model are available in Walmsley et al. (2022a). We summarize the newly
added ’head’ layer for the merger identification task in Table 1.

Layer (type) | Output Shape | Num. Parameters
---|---|---
GlobalAveragePooling2D | (None, 1280) | 0
Dropout | (None, 1280) | 0
Dense | (None, 64) | 81984
Dropout | (None, 64) | 0
Dense | (None, 64) | 4160
Dropout | (None, 64) | 0
Dense | (None, 64) | 1

Table 1: Architecture of the new ’head’ model we attach to the Zoobot ‘base’
model. The output shape and the number of free parameters are also shown.

We train our new head using binary cross-entropy loss, with a maximum of 150
epochs available for training. However this maximum number of epochs may not
necessarily be reached, as we follow Walmsley et al. (2022b) and adopt an
early stopping algorithm, which ends training when the validation loss stops
decreasing. The training time is dependant on the dataset size. For the small
datasets used in this work, each epoch takes about 50 seconds, with the
longest training taking 48 epochs and the shortest 18 epochs.

Before we conduct tests on observational data, we first evaluate the
performance of the model on simulation data alone. We split the TNG50 dataset
into training, validation, and testing datasets. To prevent train/test
contamination, we make sure that all 4 viewing angles of a single galaxy are
contained in a single dataset, i.e. if a galaxy with viewing angle 1 is
included in the training dataset, the other 3 viewing angles are also included
in the training dataset, and no angles of the same galaxy are in the testing
or validation datasets. We create 10 independent training/validation/testing
subsets through 10-fold cross validation so that each galaxy will be assigned
a merger probability. The split for each dataset is 63% training, 27%
validation, and 10% testing. We record the accuracy, loss, validation accuracy
and validation loss of each run.

Class | Precision | Recall | F1-Score
---|---|---|---
Non-merger | 0.74 | 0.83 | 0.75
Merger | 0.80 | 0.70 | 0.80
Table 2: Means of metrics of 10 individual Zoobot fine-tuning runs, assuming a
complete binary class split (non-merger class (class 0): merger probability ¡
0.5, merger class (class 1): merger probability ¿ 0.5). Each run split the
TNG50 dataset into different 63% training, 27% validation, and 10% testing
datasets. The metrics are based on the validation dataset.

Table 2 reports the mean precision, recall, and f1-score for each class
(merger and non-merger). A summary of the confusion matrices for each run are
available in Appendix A. We note a stochasticity in validation accuracy and
validation loss in the confusion matrices, likely resulting from the variation
in the training/validation/testing dataset splits.

The mean accuracy obtained from the 10 runs is 76%. These results are
comparable to or greater than previous works that trained CNNs from scratch
using simulation images of galaxy mergers (e.g. Pearson et al., 2019b), with
this work using a far smaller set of training data. For example, Pearson et
al. (2019b) uses $\sim$ 7000 images to train their simulation network, and
achieves an accuracy of 65.2%. We can expect a further increase in training
data by incorporating mergers and non-mergers from more TNG snapshots when the
images become available, which should further improve accuracies.

Making predictions on galaxies returns a merger probability between 0 and 1,
with 0 indicating a non-merger galaxy and 1 indicating a merger galaxy ,
independent of merger mass ratio or merger stage. Figure 2 shows histograms of
these probabilities for the 10 runs. In Fig. 2(a) we see that the
probabilities are peaked in a range between 0.4 - 0.5, indicating that many
galaxies have unclear classifications, and not as many galaxies are
‘confidently’ labeled mergers or non-mergers. However, we find that more
mergers are given a probability ¿ 0.5, and more non-mergers are given a
probability ¡ 0.5. We further investigate what type of mergers are given
unclear merger probabilities. Figure 2(b) shows the merger probability
distributions on ground truth pre-merger (within 0.5 Gyr until the merger
event) and post-merger (within 0.5 Gyr since the merger event) galaxy images.
We find that while the model most frequently gives pre-mergers a probability ¿
0.8, post-mergers are found to be most frequently given a probability between
0.4 - 0.5. Figure 2(c) shows the merger probability distributions on ground
truth major merger (mass ratio ¿ 1:4), minor merger (1:4 ¿ mass ratio ¿ 1:10),
and mini merger (1:10 ¿ mass ratio ¿ 1:20) images. We find that while the
model is able to give high merger probabilities to mergers of all mass ratios,
more minor and mini mergers are given lower probabilities (0.5 ¡ merger
probability ¡ 0.8) compared to major mergers. As such, the galaxies given
unclear merger probabilities are likely to be minor and mini post-mergers.

(a) All galaxies, mergers, and non-mergers

(b) Non-mergers, pre-mergers, and post-mergers

(c) Non-mergers, major mergers, minor mergers, and mini mergers

Figure 2: Merger probability distributions for TNG50 synthetic galaxy images
predicted using our fine-tuned model. We used 10-fold cross-validation during
training for 10 independent testing samples to find probabilities for all
galaxies., i.e. each galaxy was given one probability during the process. Each
subfigure shows the merger probability distributions for different types of
ground-truth mergers. a) All galaxies, mergers, and non-mergers. b) Non-
mergers, pre-mergers (0.5 Gyr ¿ time until merger ¿ 0 Gyr), and post-mergers
(0.5 Gyr ¿ time since merger ¿ 0 Gyr). c) Non-mergers, major mergers (mass
ratio ¿ 1:4), minor mergers (1:4 ¿ mass ratio ¿ 1:10), mini mergers (1:10 ¿
mass ratio ¿ 1:20).

We next evaluate the model’s performance at various thresholds using an ROC
curve. The ROC curve plots the true positive ($\frac{TP}{TP+FN}$) against the
false positive ($\frac{FP}{FP+TN}$) rates at all probability thresholds
between 0 and 1. Figure 3 shows the ROC curve. The area under the ROC curve
(AUC) measures the ability of the model, returning a value between 0 and 1.
This value is the probability that a randomly selected merger has a merger
probability greater than that of a randomly selected non-merger. An AUC of 1
indicates a perfect classifier. Our AUC is 0.84.

Figure 3: The trained model’s ROC curve. The numbers overlayed on the curve
indicate thresholds where the false positive and true positive rates along the
curve are recorded. The dotted diagonal line is the performance of a
completely random model which outputs a random probability for any image. An
ROC curve is preferred to be above this dotted diagonal, and the curve
generated from our model is above this line. We also find an AUC value of
0.84.

(a) The trained model’s performance, with mean completeness and precision as a
function of merger probability. The blue curve indicates completeness, and the
orange curve indicates precision. Vertical error bars indicate the maximum and
minimum values for the metric from the 10 runs at each probability bin.

(b) Same as Fig. 4(a) but metrics are split by merger mass ratio (major,
minor, mini). We find mini and minor mergers are predicted at an equivalent,
if not greater precision compared to major mergers. We also find that the
completeness at any fixed merger probability decreases with decreasing merger
mass ratio.

Figure 4: Precision and completeness curves of the TNG images. Figure 4(a)
shows the curves assuming a complete binary split, and Fig. 4(b) investigates
the curves taking into consideration differing merger mass ratios.

We further show the model’s performance as a function of merger probability in
Fig. 4(a), in the form of mean completeness and precision curves of the 10
runs. The completeness is obtained by the dividing the number of ground truth
mergers with a greater merger probability than the probability bin, by the
total number of ground truth mergers in the testing dataset:

$\textrm{Completeness}(p_{\textrm{merg}})\\\ =\frac{(\textrm{Num. GT
Mergers}>p_{\textrm{merg}})-\textrm{Total GT Mergers}}{\textrm{Total GT
Mergers}}$ (1)

where GT means ground truth. The precision is obtained by the dividing the
number of ground truth mergers with a greater merger probability than the
probability bin by the total number of objects with a greater merger
probability than the probability bin:

$\textrm{Precision}(p_{\textrm{merg}})\\\ =\frac{\textrm{Num. GT
Mergers}>p_{\textrm{merg}}}{\textrm{Num. Objects}>p_{\textrm{merg}}}$ (2)

The model has values of 80% for both completeness and precision for mergers on
the testing dataset if we adopt a complete binary split, that is, any galaxy
with a merger probability $>0.5$ is classified as a merger, and any $<0.5$ is
classified as a non-merger. This accuracy can be considered a reasonable
result ($>80\%$). However, if we adopt a merger/non-merger split based on
‘confident’ predictions, i.e., merger probability $>0.8$, our mean accuracy
increases to 91%.

We further investigate the role of mass ratio in the completeness and
precision curves. Fig. 4(b) shows the mean precision and completeness as a
function of the same merger probabilities, however this time separating the
major, minor, and mini mergers. We find that the mean precision at a binary
split is 59% for major mergers, 63% for minor mergers, and 62% for mini
mergers. These metrics increase to 80% for major mergers, 82% for minor
mergers, and 79% for mini mergers for ‘confident’ merger probabilities. The
precision values are lower when the mergers are split by mass ratio as opposed
to a 2-class split due to the method of computing the metrics. There are an
equal number of overall mergers and non-mergers, however the respective number
of major, minor, and mini mergers are lower than the number of non-mergers in
each test dataset. As a result while the numerator in Equation 2 accounts only
for mergers of the labeled mass ratio, the denominator includes all non-
mergers and mergers regardless of mass ratio. As such, our findings with
respect to the precisions shown in Fig. 4(b) are more relevant in a
qualitative manner rather than quantitative. Noting the gradients for the
metric curves, we find that the completeness curve for major mergers drops off
most gradually, indicating that our model is most confident in classifying
major mergers. We also note that the precision for mini mergers (mass ratio ¡
1:20) is the highest between the 3 mass ratios at a binary split, and remains
the highest at the ‘confident’ probabilities, indicating that the model is
able to predict mini mergers at an equivalent or greater precision compared to
major and minor mergers. This precision will allow for studies using large,
precise samples of sub-major mergers, which have adverse effects on galaxy
properties such as size growth (Bédorf & Portegies Zwart, 2013; Lang et al.,
2014; Martin et al., 2018; Bottrell et al., 2023).

We provide some examples of true positive, true negative, false positive and
false negative galaxy classifications from the 10 runs in Appendix B, in
Figures 17 \- 20, respectively, adopting a completely binary split. With this
split, the model seems to be able to identify mergers of diverse morphologies,
ranging from interacting pairs to merger remnants with visual signatures. We
also find that the model is able to identify non-mergers of diverse
morphologies, including projections, overlaps, and isolated galaxies, as shown
in the varying appearances of true negative predictions in Fig. 18. The model
seems to have mixed results on galaxy projections, as there are examples in
both Fig. 19 (false positives) and Fig. 18 (true negatives). For incorrectly
classified mergers (false negatives), many of the mergers with low
probabilities (merger probability $<0.3$) are those with large mass ratios
($\mu<0.25$) whose times since or until the nearest merger event are close to
the selection threshold of 0.5 Gyr ($>0.3$ Gyr), meaning that potential merger
indicators may not be visible, for example 84-569599_v0 (merger probability
0.05) in row 4, column 5 of Fig. 20 is a mini merger that is $0.31$ Gyr until
its merger event, and look visually very similar to non-mergers. Many of these
galaxies would also likely not be classified as mergers by human-based visual
classification methods. However, we also note there are also
misclassifications with major mergers, for example 84-577873_v0 (merger
probability 0.40) in row 3, column 4 of Fig. 20 is a major merger that is
$0.49$ Gyr until its merger event, which would likely be labeled as a merger
by human-based methods. For misclassified non-mergers (false positives),
galaxies with high merger probabilities (¿0.8) are likely to be classified as
merging by human-based methods, as they show merger-like disturbances, and may
also have projections. As such, our machine-learning based approach may
encounter similar issues as previous human-based visual approaches.
Nevertheless, even with its misclassifications, we find that the model is able
to correctly classify a diverse range of mergers and non-mergers, which should
be useful for merger galaxy sciences.

##  3 Predictions on observations

In this section, we describe the work we do to make predictions on
observational images using the fine-tuned model. For the work conducted in
this section, we trained a new head model using a 70% training and 30%
validation split of the simulation dataset used in the previous section, and
no further split of testing data, and attached it to the original Zoobot base
model. Armed with our fine-tuned Zoobot model, we apply it to SDSS and GAMA
spectroscopically confirmed galaxies in the HSC-SSP public data release 3
(Aihara et al., 2022).The training with this split lasted 37 epochs, with a
duration of 23 minutes using GPU (NVIDIA Quadro P400).

###  3.1 Data; The Subaru Hyper Suprime-Cam Subaru Strategic Program

The HSC-SSP is a multi-tiered, wide-field, multi-band imaging survey on the
Subaru 8.2 m telescope on Maunakea in Hawaii. Detailed information about the
survey, its instrumentation, and its techniques are available in Aihara et al.
(2018) and relevant papers (Bosch et al., 2018; Miyazaki et al., 2018;
Komiyama et al., 2018; Furusawa et al., 2018). We use data from HSC-SSP due to
its wide field of observation and exceptional ground-based depth and
resolution. In its widest component (Wide layer), HSC-SSP covers about 600
deg2 of the sky in five broad band filters (grizy), with observations from 330
nights coadded. The depth of the HSC survey is $r\approx 26$ mags ($5\sigma$,
point source) for the Wide layer. The coverage and depth of HSC-SSP will give
us access to high quality imaging data of several million galaxies. We plan to
make merger probabilities for all of HSC-SSP Wide in future works, a catalogue
of which will be made publicly available for the benefit of the galaxy
astronomy community. This merger probability catalogue is expected to be one
of the largest catalogues of its kind.

For the work conducted in Section 5, we use a subsample of galaxies from the
HSC-SSP Wide internal data release S21A catalogue to conduct predictions on
with our trained model. To select a galaxy sample, we cross-match HSC-SSP S21A
galaxies to SDSS Data Release 17 (Abdurro’uf et al., 2022) and Galaxy And Mass
Assembly Data Release 4 (GAMA DR4, Driver et al., 2022) galaxies within 1 sky
arcsec. We are left with 145,544 matches in SDSS and 156,604 matches in GAMA,
for a total of 302,148 galaxies. All galaxies matched have spec-z measurements
from their respective catalogues. We only use spectroscopic redshifts, due to
photometric redshift errors. The galaxies have a magnitude limit of r ¡ 17.7
mag for SDSS galaxies and r ¡ 19.8 for GAMA galaxies. The galaxies lie within
a redshift range of $z=0.01-0.35$ and have $M_{*}=3\times 10^{9}-3\times
10^{11}M_{\odot}$. $M_{*}$ values are obtained following Chen et al. (2012)
for the SDSS galaxies and its own catalogue for the GAMA galaxies. The SDSS
galaxy stellar masses, using a principal component analysis method on SDSS
spectra. First, a model spectra is created based on Bruzual & Charlot (2003)
stellar population synthesis model. Next, principal components are identified
from the model library. Finally, the SDSS spectra are fitted to the model and
physical properties estimated. The masses obtained are consistent with the
GALEX-SDSS-WISE Catalog (Salim et al., 2016, 2018). The GAMA galaxy stellar
masses are obtained using the SED fitting code MAGPHYS (Driver et al., 2018).
MAGPHYS also uses a library based on Bruzual & Charlot (2003). Sets of optical
and infrared spectra are regressed towards flux measurements and errors to
find a best-fit SED and physical parameters, including stellar mass.

Each galaxy in the catalogue also has several environmental parameters related
to its local mass density, studied in Yesuf (2022). The stellar mass
overdensities within radii of 0.5, 1, and 8 $h^{-1}$Mpc, as well as within the
radii determined by the projected distance to the 5th nearest neighbor are
calculated. Only galaxies within $|\Delta v|<1000\mathrm{kms^{-1}}$ relative
to the primary source are considered in this calculation. This cutoff prevents
unrelated foreground or background galaxies from being included. The densities
are normalized by the median densities of all galaxies within a given mass
range and redshift bin, making them overdensities relative to the median in
the redshift bin. Details on how the densities are calculated are written in
Yesuf (2022) and the papers referenced within.

We make predictions on gri images for each HSC galaxy, with the images having
the same dimensions as the synthetic HSC images of the TNG50 galaxies -
cutouts encompassing $10\times R_{\textrm{eff}}$, re-sized to 300 $\times$ 300
pixels. For each input image, our model will output a merger probability
between 0 and 1, with 0 indicating non-merger and 1 indicating a merger, again
independent of merger mass ratio or merger stage.

We note that some HSC galaxy identifications are susceptible to ”bright galaxy
shredding”, discussed in Aihara et al. (2018). Bright $(i<19)$ galaxies,
especially of late-type, are deblended into multiple objects, with the
debelending seen even after cross-matching with a spectroscopic catalogue. An
inspection of the non-cropped image of objects affected by shredding reveals
that that it is part of the spiral arm of a larger galaxy. As much as 15% of
bright galaxies in HSC-SSP suffer from shredding, so it is expected that there
are galaxies suffering from similar effects in our classified samples.
However, these issues are expected to be resolved when making predictions on
future HSC-SSP public data releases. For this work, as we are using the
SDSS/GAMA coordinates and their petrosian radii to make our cutouts, we should
not be as affected by shredding compared to HSC data.

##  4 Results

###  4.1 Prediction results

HSC ID | ra | dec | z | $\log M_{*}$ | $R_{\mathrm{eff}}$ | $p_{\mathrm{m}}$
---|---|---|---|---|---|---
40976904286657178 | 135.21693 | -0.21783 | 0.13429 | 9.94 | 0.9441 | 0.775
40976904286655515 | 135.22422 | -0.25286 | 0.26773 | 10.69 | 1.3761 | 0.748
40976899991693591 | 135.15696 | -0.35011 | 0.25953 | 10.82 | 0.9324 | 0.373
40976899991692475 | 135.17823 | -0.37379 | 0.19888 | 10.50 | 0.6889 | 0.361
40976899991691083 | 135.20912 | -0.40034 | 0.26186 | 10.74 | 1.0056 | 0.525
Table 3: The first 5 rows of the merger probability catalogue, which will be
made publicly available. The columns are, from left to right: HSC ID, right
ascension, declination, redshift, log stellar mass, effective radii in
arcseconds, merger probability.

(a) Merger probability distributions of HSC galaxies cross-matched with SDSS
DR17.

(b) Merger probability distributions of HSC galaxies cross-matched with GAMA
DR4.

Figure 5: Merger probability distributions for HSC-SDSS (upper) and HSC-GAMA
(lower) cross-matched galaxies predicted using our fine-tuned model. Note that
in both cases, more galaxies lie in an unclear range (merger probability
$0.2-0.5$) for non-mergers than ‘confident’ non-mergers (merger probability
$0-0.1$). However, we find that many of the mergers identified are confident
(merger probability $>0.8$).

We plot a histogram of the merger probabilities of the SDSS and GAMA galaxies
in Fig. 5. We see that the outputted probabilities are diverse in range, with
the most galaxies being assigned ‘unconfident’ labels, with the peak being
between 0.1 - 0.5 for the SDSS galaxies and 0.3 - 0.5 for the GAMA galaxies.
This location of the peak is similar to that found in the simulation
predictions in the previous Section, but differs from the probabilities found
by transfer learning in Ackermann et al. (2018); Ferreira et al. (2020), where
very clear probabilities both for mergers and non-mergers were favored. A
possible explanation for the difference in distribution between our results
and previous works, i.e., the peak in the 0.1 - 0.6 merger probability range,
is the inclusion of the substantial number of mini mergers in our training
sample. We will be able to examine this upon the completion of the images in
Bottrell et al. (2023), as we will have many more major and minor mergers to
fine-tune our model with. Many galaxies with similar appearances as the true
mini mergers used in the fine-tuning process could be assigned ‘unconfident’
merger probablities in this range, whether they be merging or non-merging in
ground truth. However, we also note the secondary peak at higher merger
probability ($>0.9$), meaning many mergers are confidently identified. This is
consistent with the above mentioned works, and also allows for a large
‘confident’ merger sample for science purposes.

We show examples of galaxies within various merger probability bins in our
predicted samples in Appendix C, in Figures 21 through 24. We find that in the
low merger probability bins (merger probabilities $0-0.3$, Fig. 21), our model
correctly identifies likely stellar overlaps and projections as non-mergers,
as well as a diverse appearance of non-mergers, similar to the correctly
identified non-mergers in the simulation data. On the high merger probability
end (merger probabilities $>0.8$), similar to as seen in the simulation data,
the model can predict mergers with diverse appearances, including clear
interacting pairs and late or early stage mergers with disturbances.

Figure 6: Merger probability distributions for galaxies with a
spectroscopically identified pair within a 30 kpc radius aperture, binned by
velocity difference of the pair. The vertical axis represents the fraction of
galaxies in each merger probability bin belonging to each velocity difference
bin. We find that the fraction of smaller velocity difference galaxy pairs
increases monotonically with merger probability bin.

As further validation, we confirm our model’s ability to differentiate between
projections and physically connected pairs in observational images. For each
galaxy within our two samples that has a neighbor within a 30 kpc physical
aperture, we calculate the line-of-sight velocity offset between the galaxy
and its neighbor by $\Delta v=c\Delta z/(1+z_{\textrm{target}})$. We plot the
merger probability distribution of these galaxies, binned by the line-of-sight
velocity offset with its neighbor, or in the case of galaxies with multiple
neighbors the minimum line-of-sight velocity offset, in Fig. 6. We find that
pairs with offset $\Delta v<500\mathrm{kms^{-1}}$ makes up the greatest
fraction of galaxies pairs with merger probability ¿ 0.8, and as the velocity
offset increases, a greater distribution of galaxies are given unclear to
lower merger probabilities (merger probability ¡ 0.5). Of the galaxies with
both high merger probability and offset, while a fraction of such may be
projections, there are also likely to be true mergers that coincidentally have
a projection. In particular, there may be post-merger galaxies that are not a
pair but still have high merger probability. Based on our simulation results
in Fig. 2(b), our model identifies 1 post-merger galaxy for every 2 pre-merger
galaxies. Following these results, a fraction of galaxies with $\Delta
v>500\mathrm{kms^{-1}}$ and high merger probabilities in Fig. 6 are likely to
be post-mergers. .

###  4.2 Merger sample selection for science

The results from simulation data show that a complete binary split, i.e.,
merger probability $>0.5$ is a merger and $<0.5$ is a non-merger, gives a
precision that is $\sim 80\%$. However, the merger probability distribution
for both observation and simulation results show that many galaxies lie in a
range between merger probability $0.2-0.6$. As such, while the merger
probabilities we found can be sufficiently useful to investigate trends
between merger probability and physical properties, conducting studies
adopting a complete binary split may suffer from contamination of
‘unconfident’ galaxies. We can see from Fig. 23 that there are many unclear
galaxies in the probability range $0.5-0.8$ that may or may not be real
mergers, thus using galaxies in this range may contaminate both merger and
non-merger samples.

Figure 7: Merger fraction as a function of merger probability for our two
samples. The black vertical dotted line indicates the ‘confident’ merger
probability threshold of 0.8. We also plot the merger fractions found in
Pearson et al. (2019a, red, green, and yellow lines), Nevin et al. (2023,
brown lines), Kim et al. (2021, black lines), Lotz et al. (2011, light blue
dotted line), and Cotini et al. (2013, purple line). We find that our merger
fraction matches those of previous studies at increased merger probabilities.

We plot the merger fraction of our two samples as a function of merger
probability in Fig. 7. We compare our results with previous works calculating
the merger fraction in similar redshift ranges, both in observations and
simulations (Lotz et al., 2011; Cotini et al., 2013; Pearson et al., 2019a;
Kim et al., 2021; Nevin et al., 2023). We find that our merger fractions, in
most cases, become statistically consistent with these works if we consider
‘confident’ classifications (merger probability $>0.8$) as our threshold, with
the threshold indicated by the dotted vertical line. However, we note that
despite the statistical consistency there are likely to be contaminants
regardless of threshold.

We will not set a definite, arbitrary threshold to define a merger in the
catalogue to be released, instead we will just provide the merger
probabilities for every galaxy, as shown in Table 3, and users can determine
their thresholds. However we recommend that a ‘confident’ threshold (merger
probability $>0.8$) is used to determine a merger sample.

##  5 Merger galaxy properties

In this section, we use merger probabilities obtained using our model to
investigate the relationship between galaxy mergers and local galaxy
environments. We evaluate the merger probability distribution in differing
environmental density bins for the various environmental parameters. We also
investigate the relationship between galaxy merging and environment in TNG
simulations, and look for any agreements between observations and simulations.

###  5.1 Environmental overdensities as a function of merger probability

(a) $0.1h^{-1}$ Mpc stellar mass overdensity
$\log(1+\delta_{0.1\textrm{Mpc}/h})$
KS test (SDSS) statistic: 0.394
KS test (GAMA) statistic: 0.238

(b) $0.5h^{-1}$ Mpc stellar mass overdensity
$\log(1+\delta_{0.5\textrm{Mpc}/h})$
KS test (SDSS) statistic: 0.417
KS test (GAMA) statistic: 0.184

(c) $1h^{-1}$ Mpc stellar mass overdensity $\log(1+\delta_{1\textrm{Mpc}/h})$
KS test (SDSS) statistic: 0.341
KS test (GAMA) statistic: 0.143

(d) $8h^{-1}$ Mpc stellar mass overdensity $\log(1+\delta_{8\textrm{Mpc}/h})$
KS test (SDSS) statistic: 0.183
KS test (GAMA) statistic: 0.127

(e) 5th nearest neighbor overdensity $\log(1+\delta_{5})$
KS test (SDSS) statistic: 0.191
KS test (GAMA) statistic: 0.069

Figure 8: Cumulative distribution curves of merger probabilities of HSC
galaxies cross-matched with GAMA (dotted lines) and SDSS (solid lines)
predicted by our fine-tuned model. Each curve represents a different
environmental density bin. The gradients of these curves show that in lower
density environments, there are more higher merger probability galaxies, and
in higher density environments, there are more galaxies with lower merger
probabilities. This trend holds true for each parameter investigated. The
trend also holds qualitatively between the SDSS and GAMA samples. We also
indicate the KS test statistic between the densest and least dense regions in
each figure as reference.

Figure 8 shows the cumulative distributions of merger probability in bins of
various environment metrics described in Section 3. The distributions are
split into separate density bins, depending on the scale of the parameter
used.

The upper left panel of Fig. 8 shows the sensitivity of merger probability to
environmental overdensities at 0.5 $h^{-1}$Mpc scales (1 $h^{-1}$Mpc aperture,
centered on the target galaxy). The upper right panel shows the same at 1
$h^{-1}$Mpc scales (2 $h^{-1}$Mpc aperture). The bottom left panel shows the
same at 8 $h^{-1}$Mpc scales (16 $h^{-1}$Mpc aperture). The bottom right shows
the sensitivity of merger probability to environmental overdensities within
the radii of the target galaxy’s 5th nearest neighbor. From blue to red, the
curves show the cumulative distributions of merger probability in increasingly
dense environments.

We find a clear difference in the distribution curves and histograms between
the lowest density $(\log(1+\delta_{x})<-1.0)$ and highest density
$(\log(1+\delta_{x})>1.0)$ environments, with a similar trend holding across
all 4 environmental parameters investigated. In each panel, we find that the
lowest density environments contain the largest number of galaxies with high
merger probability, as seen by the blue curve in each panel. This is the most
pronounced in the blue curves in the upper left (0.5 $h^{-1}$Mpc) and upper
right (1 $h^{-1}$Mpc) panels, but still qualitatively hold true in the bottom
two panels (8 $h^{-1}$Mpc and 5th nearest neighbor scale).

Conversely, we find that higher density environments contain the largest
number of galaxies with low merger probability, as seen by the red curves.

In higher density environments $(\log(1+\delta_{x})>0.0)$, we find that
galaxies with a lower merger probability tend to be in this environment, as
seen by the red and green curves. For lower density environments
$(\log(1+\delta_{x})<0.0)$, we find that the opposite holds true, that higher
merger probability galaxies tend to be in lower density environments, shown by
the blue and orange curves. We also find that these trends, in general,
qualitatively hold true regardless of stellar mass of the target galaxy, as
shown in Appendix D. In most figures, the most mass overdense regions have
more galaxies with low merger probability, and high merger probability
galaxies are more likely to lie in mass underdense regions. We note that mass
overdense and underdense do not necessarily refer to group members and non-
group members, and we find no differences when investigating these qualitative
trends separately for group and non-group members. Further, as the stellar
mass overdensities have a strong correlation with halo mass (Yesuf, 2022),
these trends also appear at differing halo mass scales.

These results are consistent with the findings of works such as Ghigna et al.
(1998), Lin et al. (2010) and Alonso et al. (2012). These works, with
environments computed at similar scales, suggest that mergers and merging
pairs are more likely to happen in less dense environments. In addition,
spectroscopic pair matching methods with strict spectroscopic cuts are more
likely to produce results similar to our findings (Ellison et al., 2010).

However, we also note that these results contradict with the suggestion that
galaxy interactions are associated with intermediate to higher density
regions, where galaxies have close companions and neighbors (Darg et al.,
2010a; Jian et al., 2012). For example, Darg et al. (2010a) found that at the
$\log(1+\delta_{2\mathrm{h^{-1}Mpc}})$ scale, even though both mergers and
non-mergers peak in an intermediate environment, mergers occupy a slightly
denser environment, which differs from our findings. We will discuss possible
reasons in Section 6.

###  5.2 Comparison with simulation data

(a) Major companions
KS test (Simulation) statistic: 0.226
KS test (Observation) statistic: 0.131

(b) Major and minor companions
KS test (Simulation) statistic: 0.194
KS test (Observation) statistic: 0.131

Figure 9: Environment distribution cumulative histograms of the environmental
densities within a spherical volume including the 5th nearest neighbor to the
target galaxy, for TNG50 and TNG100 mergers and non-mergers. From left to
right: a) environmental mass densities taking into account companions with
mass ratio ¿1:4 (major companions), and b) environmental mass densities taking
into account companions with mass ratio ¿ 1:10 (major and minor companions).
We also make the histograms for the observational data visible as reference
where available, indicated by the dotted lines.KS test statistics between
simulation mergers and non-mergers, as well as between confident mergers
(merger probability ¿0.8) and non-mergers (merger probability ¡0.3) are
indicated.

(a) Major companions
KS test (Simulation) statistic: 0.348

(b) Major and minor companions
KS test (Simulation) statistic: 0.353

Figure 10: Same as Fig. 9, but for stellar mass overdensities within a 50 kpc
radii spherical volume.

(a) Major companions
KS test (Simulation) statistic: 0.285
KS test (Observation) statistic: 0.231

(b) Major and minor companions
KS test (Simulation) statistic: 0.260
KS test (Observation) statistic: 0.231

Figure 11: Same as Fig. 9, but for stellar mass overdensities within a 100 kpc
radii spherical volume.

(a) Major companions
KS test (Simulation) statistic: 0.108
KS test (Observation) statistic: 0.171

(b) Major and minor companions
KS test (Simulation) statistic: 0.100
KS test (Observation) statistic: 0.171

Figure 12: Same as Fig. 9, but for stellar mass overdensities within a 500 kpc
radii spherical volume. Observational data is available for this parameter.

(a) Major companions
KS test (Simulation) statistic: 0.140
KS test (Observation) statistic: 0.168

(b) Major and minor companions
KS test (Simulation) statistic: 0.129
KS test (Observation) statistic: 0.168

Figure 13: Same as Fig. 9, but for stellar mass overdensities within a 1 Mpc
radii spherical volume. Observational data is available for this parameter.

(a) Major companions
KS test (Simulation) statistic: 0.147

(b) Major and minor companions
KS test (Simulation) statistic: 0.131

Figure 14: Same as Fig. 9, but for stellar mass overdensities within a 2 Mpc
radii spherical volume.

(a) Major companions
KS test (Simulation) statistic: 0.153
KS test (Observation) statistic: 0.102

(b) Major and minor companions
KS test (Simulation) statistic: 0.123
KS test (Observation) statistic: 0.102

Figure 15: Same as Fig. 9, but for stellar mass overdensities within a 8 Mpc
radii spherical volume. Observational data is available for this parameter.

Figures 9 through 15 show the cumulative histograms of environmental
distributions of a total of 244,722 TNG50 and TNG100 mergers and non-mergers
between snapshots 59 and 99 (redshifts $0.7>z>0.1$), grouped by redshift,
further split into two subfigures, with the left figure accounting for
companions with mass ratio ¿ 1:4 (major companions) and the right figure
accounting for companions with mass ratio ¿ 1:10 (major and minor companions),
for each parameter. The mergers and non-mergers were selected using the same
timescale criteria used in creating the fine-tuning dataset for Zoobot, for a
total of 17,877 mergers and 226,895 non-mergers. The environmental parameters
used are similar to the observations, being the stellar mass overdensities
within a spherical volume with radii of 0.05, 0.1, 0.5, 1, 2, and 8
$h^{-1}$Mpc, as well as within the radii of the 5th nearest neighbor, and are
calculated through similar computations as the environmental parameters in the
observations in Section 3. We also make the environmental distributions from
the observations visible where the data is available, being the density within
the 0.1 $h^{-1}$Mpc, 0.5 $h^{-1}$Mpc, 1 $h^{-1}$Mpc, 8 $h^{-1}$Mpc radii
spherical volume, and the radii of the 5th nearest neighbor. We split the
observational data in 4 different merger probability bins, with $p_{m}$ ¡0.3,
0.3¡$p_{m}$¡0.5, 0.5¡$p_{m}$¡0.8, and 0.8¡$p_{m}$.

We find 2 differing trends in the simulational data, depending on the scale of
the environmental density parameter. For the environmental density parameters
of the scale of 0.5 $h^{-1}$Mpc and larger, and for 5th nearest neighbor
environments, a greater fraction of mergers lie in mass underdense
environments, and a greater fraction of non-mergers lie in mass overdense
environments, indicating a similar trend as that seen with the predictions on
observational data, as the fraction of mergers in lower density environments
increases with increasing merger probability bin. We also find that there are
very little to no mergers found in the densest environments for each of these
parameters. We also find that these trends are, in general, not sensitive to
mass ratio, and hold true for all investigated redshift bins up to $z=0.7$. As
such, we have a consistency in the relationship between galaxy mergers and
environmental densities between observations and simulations at equivalent
scales.

Conversely, we find that the above trend is reversed for the environmental
density parameters within the spherical volume of 0.05 and 0.1 $h^{-1}$Mpc,
found in Fig. 10 and Fig. 11, respectively. That is, at these scales, we find
that the majority of non-mergers are in the lowest density environments, as
shown by the brown, red, and orange lines, and mergers are found in more dense
environments, as shown by the blue, green, and purple lines. These trends are
also not sensitive to mass ratio or redshift. However, this reversal does not
occur in the observational data, as shown in Fig. 11. While the behavior of
the low merger environment curves show a steeper gradient in underdense
regions $(0.5<\log(1+\delta_{x})<0.0)$, the trend is qualitatively similar as
the larger scales. Further investigation is required on the inconsistency
between the observations and simulations at this scale, particularly as they
are consistent at larger scales. We plan to investigate this in future works.

##  6 Discussion

Based on our merger probabilities and subsequent analysis in the previous
section, our investigation finds that at the scales of 0.5 $h^{-1}$ Mpc and
greater, i.e. close to the cluster scale and larger, merger galaxies are more
prevalent in lower density environments, and higher density environments have
a lower merger incidence, with this trend found both in observations and
simulations. At the 0.1 $h^{-1}$Mpc and lower scales, i.e., close to the
galaxy scale, there are more non-mergers in lower density environments in the
simulations, however this reversal does not occur in our observational data.

Previous studies that have investigated the environmental dependence of merger
activity have found varying results, with some works finding a greater merger
fraction in higher density environments (Jian et al., 2012), and others
finding merger fraction peaks in intermediate environments (Perez et al.,
2009), and others finding that mergers are more likely to occur in lower
density environments (Ghigna et al., 1998). We have results showing that the
merger prevalence can be increased at both high and low density environments,
with the trend differing depending on the scale of the environmental
parameter.

In the richest environments, such as in the center of clusters, velocity
dispersions are high, at scales of $\sim 1000$ km s-1 (Struble & Rood, 1999).
At these speeds, galaxy-galaxy interactions are likely to be elastic
encounters, and mergers and infall are less likely to occur (Kuntschner et
al., 2002). Such encounters can strip the gas required to fuel star formation
events (Gunn & Gott, 1972), and hence be a catalyst for dynamical evolution in
cluster galaxies, but the final product of the interaction will likely not be
a merger, resulting in lower merger incidence. As such, while higher density
regions can have an increased pair fraction, but a lowered merger fraction
(Lin et al., 2010). Conversely, in lower density environments, accretion and
merger events can occur more frequently.

At a smaller scale, such as in the galaxy scale, over 90% of non-merger
galaxies are found in lower density environments, and higher density
environments are mostly populated with mergers. At this scale, galaxies are
likely to be at closer projected separation with its neighbors compared to at
greater scales, and hence be part of a merger. As a result, higher densities
at this scale means there is a greater likelihood of a neighbor being a
physically connected merger, resulting in the reversal of the trend from the
larger scales.

We suggest a possible reason for any disagreements with previous works,
particularly in higher density environments, to be attributed to the
difference in merger sample selection techniques. For example, Darg et al.
(2010a), a work based on visual identification of mergers, finds that while
both mergers and non-mergers peak in intermediate density environments,
mergers occupy slightly denser environments than non-mergers. However, Ellison
et al. (2010), a work using spectroscopic pair selection, finds that a
significant fraction of galaxy pairs are in higher density environments, but
they also suggest that lower density environments are where mergers are likely
to occur, a suggestion which is consistent with our results.

Different merger sample selection methods will lead to different merger
samples, some with very little overlap (De Propris et al., 2007), and as such,
trends in physical properties such as environment may differ. Additionally,
some methods may be susceptible to overestimation of merger galaxies and
contamination.

Spectroscopic pair matching methods can contaminate merger samples with
interlopers. In high velocity dispersion environments, using the line-of-sight
velocities as a proxy for 3 dimensional velocities has limitations, and is
strongly affected by interlopers (Saro et al., 2013), and galaxies may be
considered merging pairs even if they are not physically connected. As such,
merger catalogues created using these methods can overestimate the merger
fraction.

Similarly, image-based classification techniques can also be contaminated with
stellar and galactic chance projections, in both visual identification (Darg
et al., 2010a, b; Pearson et al., 2019b) and quantitative morphologies (De
Propris et al., 2007). In visual identification, the lack of complete
information for objects could lead to projected galaxy pairs and galaxy-star
pairs to be incorrectly classified as mergers. Such projections and galaxy-
star pairs can also pose difficulties when conducting studies with
quantitative morphologies such as asymmetries. The source extraction
algorithms used may incorrectly deblend galaxy images containing projections,
leading to highly asymmetric non-mergers. Contaminations from projections are
likely to be more frequent in higher density environments.

Moreover, we note that our environment parameters discriminate by mass
overdense and underdense regions, with no specification on group or cluster
membership. While number overdense environments, such as groups and clusters,
do have evidence of merger activity, particularly at z ¿ 1 (Lemaux et al.,
2012; Tomczak et al., 2017; Liu et al., 2023), our parameters focus on the
masses of these environments. In mass overdense environments, as our figures
do show, there are still galaxies with high merger probabilities to be found.
These galaxies are likely dry merger systems occurring in groups or cluster
environments, particularly important for the formation of early-type brightest
cluster galaxies (BCGs) in cluster centers (Mulchaey et al., 2006; Rines et
al., 2007; McIntosh et al., 2008; Tran et al., 2008; Liu et al., 2009; Lin et
al., 2010; Burke & Collins, 2013; Lidman et al., 2013; Ascaso et al., 2014).
However, at redshift z ¡ 1, many BCGs have finished their growth, and while
there are BCGs that continue their growth through mergers at these redshifts,
such cases are a minority (Collins et al., 2009; Stott et al., 2010, 2011; Liu
et al., 2015; Runge & Yan, 2018). Further, in the most mass overdense
environments, at z ¡ 1, merger activity is suppressed due to increased
velocity dispersions (Pipino et al., 2014), leading to a lower merger fraction
in these environments. In mass underdense environments, such as in field
environments, or the outskirts of clusters and groups, the likelihood of
finding a merger increases (Ghigna et al., 1998; Oh et al., 2019). This is
also found at higher redshifts, both in the field (Delahaye et al., 2017) and
in outskirt (Koulouridis & Bartalucci, 2019) regions. As such, the fraction of
mergers in mass underdense regions should be greater than that in mass
overdense regions, which is consistent with our results.

Our environmental trends, particularly the decreased fraction of mergers in
higher density environments, show that our morphology-based classification
model is likely able to differentiate and give low merger probabilities to
images of interlopers, i.e., non-merging pairs in higher density environments,
an issue which needs corrections in both spectroscopy-based and image-based
classification methods. We note that our environmental trends on observational
data may harbor an implicit bias due to the morphology-density relation
(Dressler, 1980). The high velocity encounters in higher density environments
can strip gas in galaxies, leading to visual morphologies exhibiting more
smoother, spheroidal features. As such, galaxies in higher density
environments are less likely to exhibit the tidal features that are present in
mergers, resulting in such galaxies to be assigned low merger probabilities by
our morphology-based merger identification model. However, we suggest that
such a bias can be mitigated. First, the findings in Darg et al. (2010a),
based on visual classification, suggest that mergers are more likely found in
higher density environments, which contradicts what is found in comsmological
n-body and hydrodynamical simulations. As the implicit biases due to the
morphology density relation can be overlooked by visual classification
studies, we suggest that a similar overlook is possible in our work. Second,
the ground truth merger selection in our fine-tuning process is based on the
time to the closest merger event, and is not be biased to any environments and
morphlogies.

Investigations on the physical properties of the merger galaxies, such as
projected separation and relative velocity differences with their neighbors,
as well as colors, star formation rates and morphologies, are planned in
future works, to determine if there are any environmental dependences on the
properties of the mergers themselves in addition to merger incidence.

##  7 Conclusion

In this work, we take a deep learning based approach for merger classification
in Subaru HSC-SSP. We fine-tune the pre-trained model Zoobot using synthetic
HSC images of galaxies in the Illustris TNG simulations, then make predictions
using the fine-tuned model on a sample of galaxies in HSC-SSP S21A wide cross-
matched with SDSS and GAMA. We find that the fine-tuning approach can achieve
accuracies comparable to previous merger classification studies using
simulational data, at a 76% accuracy, as well as 80% completion and precision.
We achieved these results requiring a far smaller sample size than previous
studies, sufficing with $\sim 10^{3}$ training samples of each class. We also
find that our morphology-based model is able to correctly predict both mergers
and non-mergers of diverse appearances, mergers of differing mass ratios and
stages, and can also distinguish to a degree between projections and true
merging pairs. The merger rate found by our model is consistent with those of
previous works if we adopt a ‘confident’ threshold.

We will make the merger catalogue we produced in this work publicly available.
We plan to classify all of HSC-SSP in the future and make the results publicly
available as well.

Further, we studied the relationship between merger activity and multi-scale
galaxy environments in both the simulation data of TNG and the observational
data of HSC-SSP, and compared our results. We find two trends in the
simulation data, and one trend in the observational data. Both sets of data
are in agreement that at scales of 0.5 $h^{-1}$Mpc and larger, merger galaxies
favor lower density environments, and non-mergers favor higher density
environments. However, below these scales, the simulation data finds that non-
merger galaxies are most prevalent in lower density environments, and higher
density environments favor mergers. In future works, we plan to investigate in
both observations and simulations where the reversal in trend occurs, as well
as the galaxy properties of the mergers themselves.

###### Acknowledgements.

We would first and foremost like to thank the native Hawaiians for sharing the
Maunakea mountain, a place of cultural, historical, and natural significance,
allowing us access to a beautiful view of the Universe. Next, we would like to
thank the anonymous referee for their comments and feedback in greatly
improving the quality of this work. The Hyper Suprime-Cam (HSC) collaboration
includes the astronomical communities of Japan and Taiwan, and Princeton
University. The HSC instrumentation and software were developed by the
National Astronomical Observatory of Japan (NAOJ), the Kavli Institute for the
Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo,
the High Energy Accelerator Research Organization (KEK), the Academia Sinica
Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton
University. Funding was contributed by the FIRST program from the Japanese
Cabinet Office, the Ministry of Education, Culture, Sports, Science and
Technology (MEXT), the Japan Society for the Promotion of Science (JSPS),
Japan Science and Technology Agency (JST), the Toray Science Foundation, NAOJ,
Kavli IPMU, KEK, ASIAA, and Princeton University. This paper is based [in
part] on data collected at the Subaru Telescope and retrieved from the HSC
data archive system, which is operated by Subaru Telescope and Astronomy Data
Center (ADC) at NAOJ. Data analysis was in part carried out with the
cooperation of Center for Computational Astrophysics (CfCA) at NAOJ. We are
honored and grateful for the opportunity of observing the Universe from
Maunakea, which has the cultural, historical and natural significance in
Hawaii. This paper makes use of software developed for Vera C. Rubin
Observatory. We thank the Rubin Observatory for making their code available as
free software at http://pipelines.lsst.io/. The Pan-STARRS1 Surveys (PS1) and
the PS1 public science archive have been made possible through contributions
by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS
Project Office, the Max Planck Society and its participating institutes, the
Max Planck Institute for Astronomy, Heidelberg, and the Max Planck Institute
for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham
University, the University of Edinburgh, the Queen’s University Belfast, the
Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory
Global Telescope Network Incorporated, the National Central University of
Taiwan, the Space Telescope Science Institute, the National Aeronautics and
Space Administration under grant No. NNX08AR22G issued through the Planetary
Science Division of the NASA Science Mission Directorate, the National Science
Foundation grant No. AST-1238877, the University of Maryland, Eotvos Lorand
University (ELTE), the Los Alamos National Laboratory, and the Gordon and
Betty Moore Foundation. This work has been supported by the Japan Society for
the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research
(21H01128). This work has also been supported in part by the Collaboration
Funding of the Institute of Statistical Mathematics “New Perspective of the
Cosmology Pioneered by the Fusion of Data Science and Physics”. K.O. is
supported by JSPS KAKENHI Grant Number JP23KJ1089. H.Y. was supported by JSPS
KAKENHI Grant Number JP22K14072 and the Research Fund for International Young
Scientists of NSFC (11950410492).

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##  Appendix A Confusion matrices

Figure 16: Total combined confusion matrix for the 10 runs of our Zoobot fine-
tuning process. Each run fine-tuned a new model on a different set of
training/validation data, and the confusion matrices are on 10 different sets
of testing data.he stellar mass distributions for merger and non-merger
galaxies used for fine-tuning Zoobot. The maximum and minimum values for each
cell are also indicated.

##  Appendix B Predictions on simulation images

Figure 17: 20 randomly drawn examples of true positive classifications (merger
probability $>0.5$) from the 10 test sets, in descending order, with the
probabilities indicated in the image, and the identification of the galaxy
indicated below the image in the format [snapshot]-[ID]_[viewing angle]. The
model seems to be able to identify various merger features, including close
companions and merger remnants such as rings.

Figure 18: The same as Fig. 17 but for true negatives. The model seems to be
able to correctly identify some projections/overlaps as non-interacting. More
importantly, a diverse appearance of non-mergers are correctly identified.

Figure 19: The same as Fig. 17 but for false positives. Some close overlaps
are incorrectly classified as a merging. Such galaxies, such as 84-432385_v2
with a merger probability of 0.90, would also likely be classified as mergers
by human visual identification.

Figure 20: The same as Fig. 17 but for false negatives. Many galaxies with
lower probabilities, especially those in the bottom 2 rows are minor or mini
mergers with the most recent/next merger close to the 0.5 Gyr threshold for
merger selection.

##  Appendix C Predictions on observation images

Figure 21: 20 randomly drawn examples of GAMA galaxies with a merger
probability $<0.3$, with merger probabilities in descending order. The merger
probabilities are indicated in the image and the GAMA ID below the image.
Figure 22: The same as Fig. 21 but for merger probability $>0.3$ and $<0.5$.
Figure 23: The same as Fig. 21 but for merger probability $>0.5$ and $<0.8$.
Figure 24: The same as Fig. 21 but for merger probability $>0.8$.

##  Appendix D Mass-fixed environment trends

(a) $9<\log(M_{*})<9.5$
KS test (SDSS) statistic: 0.432
KS test (GAMA) statistic: 0.263

(b) $9.5<\log(M_{*})<10$
KS test (SDSS) statistic: 0.601
KS test (GAMA) statistic: 0.378

(c) $10<\log(M_{*})<10.5$
KS test (SDSS) statistic: 0.757
KS test (GAMA) statistic: 0.053

(d) $10.5<\log(M_{*})<11$
KS test (SDSS) statistic: 0.064 p-value: 0.430
KS test (GAMA) statistic: 0.192

Figure 25: Cumulative distribution curves of merger probabilities of HSC
galaxies cross-matched with GAMA (dotted lines) and SDSS (solid lines)
predicted by our fine-tuned model, similar to Fig. 8, but separated into
different mass bins, as indicated in each figure. The KS test statistic
between the most underdense and most overdense environments are also indicated
for each subplot, with p-values available if ¿ 0.05. Calculated for a 100 kpc
radius aperture.

(a) $9<\log(M_{*})<9.5$
KS test (SDSS) statistic: 0.483
KS test (GAMA) statistic: 0.190

(b) $9.5<\log(M_{*})<10$
KS test (SDSS) statistic: 0.455
KS test (GAMA) statistic: 0.193

(c) $10<\log(M_{*})<10.5$
KS test (SDSS) statistic: 0.492
KS test (GAMA) statistic: 0.434 p-value: 0.503

(d) $10.5<\log(M_{*})<11$
KS test (SDSS) statistic: 0.233
KS test (GAMA) statistic: 0.159

Figure 26: The same as Fig. 25 but for a 500 kpc radius aperture.

(a) $9<\log(M_{*})<9.5$
KS test (SDSS) statistic: 0.436
KS test (GAMA) statistic: 0.211

(b) $9.5<\log(M_{*})<10$
KS test (SDSS) statistic: 0.473
KS test (GAMA) statistic: 0.156

(c) $10<\log(M_{*})<10.5$
KS test (SDSS) statistic: 0.352
KS test (GAMA) statistic: 0.113

(d) $10.5<\log(M_{*})<11$
KS test (SDSS) statistic: 0.241
KS test (GAMA) statistic: 0.137

Figure 27: The same as Fig. 25 but for a 1 Mpc radius aperture

(a) $9<\log(M_{*})<9.5$
KS test (SDSS) statistic: 0.193 p-value: 0.459
KS test (GAMA) statistic: 0.053 p-value: 0.767

(b) $9.5<\log(M_{*})<10$
KS test (SDSS) statistic: 0.170 p-value: 0.111
KS test (GAMA) statistic: 0.036 p-value: 0.822

(c) $10<\log(M_{*})<10.5$
KS test (SDSS) statistic: 0.107 p-value: 0.143
KS test (GAMA) statistic: 0.125 p-value: $7.059\times 10^{-7}$

(d) $10.5<\log(M_{*})<11$
KS test (SDSS) statistic: 0.200
KS test (GAMA) statistic: 0.255

Figure 28: The same as Fig. 25 but for a 8 Mpc radius aperture

(a) $9<\log(M_{*})<9.5$
KS test (SDSS) statistic: 0.423
KS test (GAMA) statistic: 0.094

(b) $9.5<\log(M_{*})<10$
KS test (SDSS) statistic: 0.220
KS test (GAMA) statistic: 0.091

(c) $10<\log(M_{*})<10.5$
KS test (SDSS) statistic: 0.152
KS test (GAMA) statistic: 0.037 p-value: 0.045

(d) $10.5<\log(M_{*})<11$
KS test (SDSS) statistic: 0.190
KS test (GAMA) statistic: 0.075

Figure 29: The same as Fig. 25 but for an aperture of radius up to the 5th
nearest neighbor.