# Tidal features and disc thicknesses of edge-on galaxies in the SDSS Stripe
82

Maria N. Skryabina,1 Kyle R. Adams,2 and Aleksandr V. Mosenkov2
1St.Petersburg State University, 7/9 Universitetskaya nab., St.Petersburg,
199034, Russia
2Physics and Astronomy, Brigham Young University Provo, UT 84606, United
States E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We examine deep optical images of edge-on galaxies selected from the Sloan
Digital Sky Survey (SDSS) Stripe 82. The entire sample consists of over 800
genuine edge-on galaxies with spectroscopic redshifts out to $z\sim 0.2$. To
discern the faintest details around the galaxies, we use three different data
sources with a photometric depth of down to 30 mag arcsec-2 in the $r$ band:
SDSS Stripe 82, Hyper Suprime-Cam Strategic Program, and DESI Legacy Imaging
Surveys. Our analysis of the deep images reveals a variety of low surface
brightness features. 49 galaxies exhibit prominent tidal structures, including
tidal tails, stellar streams, bridges, and diffuse shells. Additionally, 56
galaxies demonstrate peculiar structural features such as lopsided discs,
faint warps, and dim polar rings. Overall, we detect low surface brightness
structures in 94 galaxies out of 838, accounting for 11% of the sample.
Notably, the fraction of tidal structures is only 5.8%, which is significantly
lower than that obtained in modern cosmological simulations and observations.
Previous studies have shown that strongly interacting galaxies have stellar
discs about 1.5–2 times thicker than those without apparent interactions. In
an analysis where tidal features are carefully masked for precise disc axis
ratio measurements, we show that discs of galaxies with tidal features are
1.33 times thicker, on average, than control galaxies that do not have visible
tidal features. Furthermore, we find that edge-on galaxies with tidal
structures tend to have a higher fraction of oval and boxy discs than galaxies
without tidal features.

###### keywords:

Galaxies: evolution - formation - halos - interactions - photometry -
structure

††pubyear: 2023††pagerange: Tidal features and disc thicknesses of edge-on
galaxies in the SDSS Stripe 82–Appendix A

##  1 INTRODUCTION

Knowing how galaxies form and evolve over time is essential in our
understanding of how the Universe appears currently. Multiple studies have
found that major mergers of galaxies or minor galaxy interactions produce low
surface brightness (LSB) tidal features (see e.g. Toomre & Toomre 1972,
Schwarzkopf & Dettmar 2000, Ibata et al. 2001, Majewski et al. 2003, Martínez-
Delgado et al. 2010, Reshetnikov & Mosenkov 2019). The presence of LSB
structures is also confirmed in numerous simulations (e.g. York et al. 2000,
Chilingarian et al. 2010, Schaye et al. 2015, Pillepich et al. 2019, Mancillas
et al. 2019a). Therefore, tracing LSB features around galaxies can help
identify possible ways these galaxies have interacted and evolved over time
(see e.g. Janowiecki et al. 2010, Duc et al. 2015, Rich et al. 2019, Mosenkov
et al. 2022a). Specifically, in Johnston et al. (2001), $\Lambda$CDM
cosmological galaxy formation simulations predict that from a sample of
galaxies, approximately 20-40% are expected to have tidal features at $z\sim
0$. This percentage is further constrained to 25% by Martin et al. (2022) for
a similar limiting surface brightness of 28 mag arcsec-2. Additionally,
Valenzuela & Remus (2022) measured a tidal feature fraction of 23%.

In the past, LSB features around galaxies were difficult to identify because
they are usually too dim (fainter than $\sim 25-26$ mag arcsec-2 in the $r$
band) to be seen on regular photometric exposures. To add to the difficulty,
some filaments of Galactic cirrus can be mistakenly identified as
extragalactic LSB features (Sollima et al., 2010). Cirrus clouds are typically
found at galactic latitudes greater than 20 degrees and represent dusty
filaments that do not have a particular shape. These clouds derive their name
due to their similarity in appearance to the cirrus clouds of Earth. Milky Way
cirrus clouds can be well-seen in deep optical images and, thus, can hinder
the detection and study of LSB galaxy structures. On the other hand, deep
imaging is of high importance for studying the properties of Galactic cirrus
(see e.g. Miville-Deschênes et al. 2016, Román et al. 2020, Marchuk et al.
2021, Smirnov et al. 2023).

Due to the difficulties discussed above and many others (e.g. sky background
contamination, instrumental scattered light, observational issues related to
long exposures), deep optical observations of galaxies were problematic.
However, improvements in CCD and telescope technology have now made it
possible to discern structures whose surface brightness reaches 29-30 mag
arcsec-2 (see e.g. Martínez-Delgado et al. 2010, Abraham & van Dokkum 2014,
Duc et al. 2014, Rich et al. 2019). New techniques in processing deep images,
such as, for example, using a non-aggressive sky subtraction method (Fliri &
Trujillo, 2016) and taking into account the point spread function (PSF, Jiang
et al. 2014a, Annis et al. 2014, Trujillo & Fliri 2016), have become useful
methods for combining images that give better depth and resolution. Because of
the development of this field of deep photometry over the past 15-20 years,
studies based on deep and ultra deep images of space objects have begun to
play a relevant role in the study of the Universe (see e.g. Mihos et al. 2005,
Illingworth et al. 2013, Abraham & van Dokkum 2014, van Dokkum et al. 2015,
Koda et al. 2015, Poliakov et al. 2021).

Modern sky surveys, such as, for example, the Sloan Digital Sky Survey (SDSS,
York et al. 2000) and the much deeper DESI Legacy Imaging Surveys (Dey et al.,
2019) have provided a plethora of data for extragalactic studies. The
derivation of such a large amount of observational data has created a huge
scope for new studies of objects that were previously inaccessible for
observations. The upcoming Legacy Survey of Space and Time (LSST, Ivezić et
al. 2019) will further enhance our ability to image galaxies, promising even
deeper and more comprehensive observations that could unveil extremely faint
extragalactic structures.

In particular, one region of the sky most interesting for studying is the SDSS
Stripe 82 (Jiang et al., 2014b). This stripe has a width of 2.5 degrees along
the celestial equator with the following coordinates: -50$\degree$$<$R.A.$<$
60$\degree$, -1.25$\degree$$<$Dec.$<$1.25$\degree$. The total area of the
stripe is 275 square degrees in all five SDSS bands. Specifically for our
study, the SDSS Stripe 82 has an advantage in its depth. For instance,
ordinary SDSS exposures reach a depth of 26.5 mag arcsec-2 in the SDSS $r$
band, but in the Stripe 82 the average value is 28.6 mag arcsec-2, as provided
by the IAC Stripe 82 Legacy
Project111http://research.iac.es/proyecto/stripe82/. The photometric depth of
images in the SDSS Stripe 82, as we show in this paper, is sufficient to
explore the prominent low-surface brightness structures around galaxies (see
also Fliri & Trujillo 2016, Martínez-Lombilla & Knapen 2019, Yesuf et al.
2021, Zaritsky et al. 2021).

Optical observations of edge-on galaxies provide an unprecedented view of the
luminous matter distribution in galaxies (van der Kruit & Searle 1981, de
Grijs 1998, Dalcanton & Bernstein 2002, Kregel et al. 2002, Mosenkov et al.
2010, Bizyaev et al. 2014). This view allows LSB features to be seen with
increased visual clarity, especially above and below the galaxy mid-plane,
unlike face-on galaxies where faint structures are much less apparent over the
galaxy body and only become discernible far beyond the optical radius (Fry et
al. 1999, van Dokkum et al. 2019, Mosenkov et al. 2020a, Gilhuly et al. 2020,
Mosenkov et al. 2020b, Martínez-Delgado et al. 2021, Gilhuly et al. 2022,
Mosenkov et al. 2022b).

Using machine learning or automated parametric or non-parametric methods is
helpful in identifying the morphology of galaxies (e.g. Kado-Fong et al. 2018,
Sola et al. 2022) and possibly tidal features (Domínguez Sánchez et al. 2023).
In addition, neural networks have identified cirrus clouds in deep optical
images, specifically, in Stripe 82 (Smirnov et al., 2023). When it comes to
galaxy LSB structures themselves, machine learning has not yet been trained to
identify and separate them from galactic cirrus, extended halos of bright,
saturated stars, and image artefacts (especially, artefacts of sky background
subtraction). Also, our training sample of LSB features is still
insufficiently large for developing such an automated classification. Even
with automated classification methods, studies still use human identification
to ensure avoiding improper classifications (Bílek et al. 2020; Martínez-
Delgado et al. 2023; Mosenkov et al. 2024).

In this study, we create a new catalogue of edge-on galaxies selected from the
deep Stripe 82, ES82 for short. This work is aimed at identifying and studying
LSB features around the selected edge-on galaxies while taking into account
cirrus contamination based on the recent study by Smirnov et al. (2023) and by
using complementary sources of deep imaging to exclude false identifications.
We look at the percentage of tidal features from our catalogue to compare
these statistics with those in recent papers, where galaxies at random
orientations were explored, and with modern cosmological hydrodynamical
simulations.

In numerous studies, it has been found that galaxy interactions cause a
thickening of the disc (see e.g. Statler 1988, Quinn et al. 1993, Walker et
al. 1996, Abadi et al. 2003, Qu et al. 2011, Villalobos & Helmi 2008,
Villalobos & Helmi 2009). In Reshetnikov & Combes (1997), it is shown by the
ratio of the radial and vertical scales $h_{\mathrm{R}}/z_{0}$ that
interacting galaxies, on average, have about 1.5-2 times thicker discs than
non-interacting galaxies (see also Schwarzkopf & Dettmar, 2001). This fact can
be explained by the influence of the gravitational forces exerted during
interactions with other galaxies. Such interactions can lead to significant
disturbances in a galaxies stellar disc, such as warping, heating, or flaring
of the disc material (Bournaud et al., 2009; Qu et al., 2011; Comerón et al.,
2011; Reshetnikov et al., 2016). These disturbances increase the velocity
dispersion among the stars in the disc, essentially stirring them up, and
causing the disc to thicken as stars move further from the galactic plane.
Also, as recently found by Kumar et al. (2021) through N-body simulations of
minor galaxy flybys (which can create warps, stellar streams, and tidal
bridges), such fast encounters can increase the disc scale height $z_{0}$ by
only a maximum of $\sim$ 4%, but the reduction of the disc scale length
$h_{\mathrm{R}}$ leads to a thickening of the stellar disc. The relationship
between interactions, which produce tidal structures and a thickened disc, is
still not well studied. Therefore, in our work, our secondary aim is to shed
more light on this issue. To this end, we compare the mean value of the galaxy
disc thicknesses for two samples of galaxies: a sample of objects with LSB
features and those without them.

This paper is organised as follows. In Section 2, we discuss the sample
selection, describe the process of image preparation, determine the
inclination of galaxies in the sample, and the sample completeness is
calculated. In Section 3, we provide definitions for each type of tidal
structure and prominent structural feature, accompanied by examples from our
sample and statistics. In Section 4, the method of photometric decomposition
is outlined and the results on the disc thickness and diskyness/boxyness
$C_{0}$ parameter are presented. In Section 5, we discuss the results
obtained. We summarise our findings in Section 6.

##  2 The sample and data

There have been numerous projects dedicated to processing or reprocessing SDSS
Stripe 82 images. One such project is the IAC Stripe 82 Legacy Project (Fliri
& Trujillo, 2016). This project employs a non-aggressive technique for sky
background subtraction to preserve low-surface brightness structures across
different spatial and intensity scales. We have leveraged data from the IAC
Stripe 82 Legacy Project to develop a comprehensive catalogue of edge-on
galaxies within the deep Stripe 82 region, referred to as ES82 (Edge-on
galaxies in SDSS Stripe 82). This catalogue provides an excellent opportunity
for further analysis of these galaxies, enabling the detection and
characterisation of low-surface brightness features such as tidal tales,
stellar streams, arcs, diffuse shells, bridges, and disc deformations. These
structures serve as compelling evidence of galaxy interactions with their
surrounding environments.

###  2.1 Selection of galaxies

To create our catalogue of edge-on galaxies, we used several sources to
identify flat galaxies in Stripe 82. First, we utilised existing SExtractor
(Bertin & Arnouts, 1996) catalogues of objects in the $r$ band provided by
Fliri & Trujillo (2016) for this sky region. Our aim is to select galaxies
with a relatively large angular size and small apparent axis ratio. Since
SExtractor does not list the optical diameter of galaxies, we used the Kron
radius ($r_{Kron}$) for size filtering. Our selection criteria, based on the
analysis results from the EGIS and EGIPS catalogues (see Bizyaev et al. 2014
and Makarov et al. 2022, respectively), include a Kron radius ($r_{Kron}$)
greater than 15 arcsec and an SExtractor axis ratio B_IMAGE/A_IMAGE of less
than 0.3. These simple criteria should help identify sufficiently large edge-
on or nearly edge-on galaxies, enabling detailed resolution of their vertical
structures.

Figure 1: Kron radius distribution for galaxies from the catalogue.

Additionally, we referred to the EGIS (Bizyaev et al., 2014) and Galaxy Zoo
(Hart et al., 2016) catalogues (for the latter, we considered the fraction of
votes for the “edge-on” response to be >80%) to ensure that all edge-on
galaxies are selected according to our automated criteria. Finally, we
visually examined the catalogue of $\sim$17,000 galaxies in Stripe 82 from
Bottrell et al. (2019) to identify edge-on galaxies and eliminate duplicates
from the pre-final sample by comparing the coordinates of all objects among
themselves.

Next, we used the SDSS Stripe 82 (Fliri & Trujillo, 2016), the Hyper Suprime-
Cam Subaru Strategic Program (HSC-SSP) PDR3 (Aihara et al., 2022), and DESI
Legacy Imaging Surveys (Dey et al., 2019) to create RGB images for each
selected galaxy using these three different sources (the image creation
process is discussed in detail in Sect. 2.2). Note that SDSS Stripe 82 is not
completely covered by the HSC-SSP and DESI Legacy surveys, as also described
in Sect. 2.2. By visual inspection of these images for all the selected
galaxies, we eliminated objects that did not appear to be real edge-on
galaxies due to the presence of image artefacts that resembled an edge-on
disc, spikes of very bright stars, or regions of spiral structure. We also
removed galaxies with inclinations that are not sufficiently large (i.e.,
$i\lesssim 80\degree$), as evidenced by visible spiral arms, a discernible
stellar disc plane, or noticeably shifted dust lanes. After conducting a
thorough visual inspection of the prepared RGB images for a sample of 1167
galaxies, we selected the final version of the catalogue consisting of 838
genuine edge-on or nearly edge-on galaxies the inclinations of these galaxies
are considered in Sect. 2.3). The size distribution for the catalogue galaxies
is presented in Fig. 1.

###  2.2 Data and Preparation

All fits images of the selected galaxies are taken from the IAC Stripe 82
Legacy Project222http://research.iac.es/proyecto/stripe82/ (Fliri & Trujillo,
2016). Specifically, we use sky-rectified images in the $g$, $r$, $i$, and
$r$-deep wavebands, along with the corresponding empirical Point Spread
Function (PSF) images and weight images. These are utilised in the galaxy
photometric decomposition described in Sect. 4. For the coadded data set, the
mean surface brightness limit reaches $\mu$[3$\sigma$, $10\times$ 10 arcsec2]
= 28.6 mag arcsec-2 for the $r$ band333Using the 3$\sigma$ level in square
boxes of $10\times 10$ arcsec2 has become one of the standard definitions for
photometric depth, facilitating comparisons between results obtained with
different telescopes and instruments. The median value of the FWHM for the
same $r$ band is 1.10 arcsec, with a pixel size of 0.396 arcsec.

To enhance the classification process of the sample galaxies, we utilise the
most recent releases of two additional deep sky surveys: DESI Legacy Imaging
Surveys (Dey et al., 2019) and the HSC-SSP (Aihara et al., 2022).

The HSC-SSP survey utilises the Hyper Suprime-Cam (HSC) on the 8.2m Subaru
Telescope, featuring three layers: wide (1400 deg2, $5\sigma$ limit $r\sim 26$
mag), deep (27 deg2, $5\sigma$ limit $r\sim 27$ mag), and ultradeep (3.5 deg2,
$5\sigma$ limit $r\sim 28$ mag). The HSC employs 104 science CCDs and covers a
1.5-degree diameter field of view with a pixel scale of 0.168 arcsec. Notably,
the coadded data from the HSC-SSP offers improved resolution, enhancing the
visualisation of low surface brightness structures, with an average surface
brightness depth of $29.6\pm 0.4$ mag arcsec-2 in the $r$ band.

The DESI Legacy Imaging Surveys, combining the Dark Energy Camera Legacy
Survey (DECaLS), the Beijing-Arisona Sky Survey (BASS), and the Mayall
$z$-band Legacy Survey (MzLS), cover approximately 14,000 deg2 of the
extragalactic sky across both the Northern and Southern celestial hemispheres
in the $g$, $r$, and $z$ bands. The average surface brightness depth in the
$r$ band for our sample galaxies is $28.4\pm 0.3$ mag arcsec-2.

As the observed fields overlap partially in the IAC Stripe 82, DESI Legacy,
and HSC-SSP, not all galaxies in SDSS Stripe 82 have observations in all three
surveys: 539 out of 838 galaxies in our catalogue have HSC-SSP images and 827
galaxies have data in DESI Legacy. This means that for at least 65% of the
galaxy sample, we have three different data sources for more reliable
structure classification.

For a quantitative analysis of galaxy images, we use the SDSS Stripe 82
images, which have been specially prepared by the IAC Stripe 82 Legacy Project
for the accurate treatment of low-surface brightness structures. To enhance
galaxy images, we employ a semi-automatic image preparation pipeline (IMage
ANalysis or IMAN)444https://bitbucket.org/mosenkov/iman_new/src/master/ and
additional Python scripts. Below, we briefly describe our methodology for
preparing stacked cut-outs of the sample galaxies.

First, we make initial image cropping and rotation using the galaxy centre
coordinates and position angles from the SExtractor catalogue files provided
in Fliri & Trujillo (2016). After visual inspection, position angles for about
40% of the galaxies are corrected by inscribing an ellipse to fit the outer
isophotes of the galaxy and determining its position angle. After that, the
first step with cropping and rotation is performed again. By final cropping,
we fix the size of each image as a square with sides equal to 6 semi-major
galaxy axes. The rotation and cropping procedures are also applied to the
error maps which contain information about the weight of each pixel as a
measure of the photometric quality. Employing the Python package
photutils555https://photutils.readthedocs.io/en/stable/, masks for all objects
that do not belong to the target galaxy are created. Sky subtraction is not
executed as our images have already been sky-rectified. We carry out the
procedures, described above, for all bands to obtain cropped and rotated
coadds (using the deep $r$-band images) and colour RGB images to exploit the
Stripe 82 data to its fullest. This aids in unveiling low-surface brightness
structures around the galaxies. The mosaic of SDSS coadded images of the edge-
on disc sample is available online
666https://physics.byu.edu/faculty/mosenkov/docs/Edge-on_Stripe82.pdf.
Supplementary material also contains additional imagery of the galaxies
sourced from the different surveys.

###  2.3 Inclinations of the selected galaxies

Determining the exact orientation of a disc galaxy can often be problematic,
especially for angularly small galaxies where we cannot clearly see the
orientation of the dust lane. Therefore, we classify the selected galaxies
into the following groups, which we will use in further analysis:

  1. 1.

True edge-on galaxies. This group includes objects that have clear, well-
resolved signs indicating the inclination of the object. These signs include
the presence of a dust lane that dissects the galaxy body into two
approximately equal parts under and above the dust lane, the shape of the disc
isophotes (round isophotes often signify that the galaxy is not seen purely
edge-on Mosenkov et al. 2020a), the absence of visible in-plane rings, spiral
arms, and other global non-axially symmetric components such as a bar
(Mosenkov et al., 2020b). In this subsample, we do not include pure edge-on
galaxies that exhibit prominent structural features in or around the galaxy
that would affect the quality of our photometric fitting (see Sect. 4) and
determination of the disc thickening (all such galaxies are moved to the
fourth group described below). In total, this subsample comprises 242
galaxies.

  2. 2.

The second group consists of galaxies without obvious signs of their
inclination. These objects are presumably visible to us from the edge, but
there are no clear signs of this. In particular, these are angularly small
objects, for which the resolution of our images (even in the HSC-SSP where the
PSF FWHM is the best among the surveys used, about 0.6 arcsec) is not
sufficient to determine the galaxy inclination. In this group, we have 409
objects.

  3. 3.

The third group contains objects whose orientation is close to edge-on. For
them, the inclination angle is most likely $80\degree<i<85\degree$. We can
suppose this by the shifted central dust lane relative to the galaxy plane
(see Mosenkov et al. 2015) or the barely visible ends of the spiral arms. This
sample consists of 73 objects.

  4. 4.

The fourth group contains objects that did not fall into the first group: they
are seen edge-on but demonstrate prominent structural and tidal features, that
can affect the determination of the disc thickening. In this group, we also
include galaxies in the vicinity of which there are very bright sources that
can outshine the target galaxy. This sample comprises 115 objects.

The main reason for creating this classification is to compare the thickness
of the galaxy discs, and take into account the inclination effects which is
important for making reliable conclusions. To determine the apparent axis
ratio $q$ more accurately, we perform a simple Sérsic photometric
decomposition described in Sect. 4.

###  2.4 Sample Completeness and the Catalogue

To evaluate the sample’s completeness, we employ a straightforward $V/V_{m}$
test outlined in Thuan & Seitzer (1979). This test involves calculating the
volume of a sphere ($V$) with a radius equivalent to the distance to the
galaxy ($D$). The formula for $D$ is given by $D=d/\theta$, where $d$
represents the linear diameter of the galaxy and $\theta$ denotes the angular
diameter. Additionally, we determine the volume of another sphere ($V_{m}$),
which has a radius equal to the maximum distance ($D_{m}$) at which the galaxy
can still be considered part of our sample. In our scenario,
$D_{m}=d/\theta_{L}$, where $\theta_{L}$ signifies the smallest angular size
observed in our sample object. For our calculations, we use $\theta_{L}=22.33$
arcsec, considering the angular size as the value of the galaxy’s Kron radius.
The volume ratio, denoted as $V/V_{m}$, is given by $(\theta_{L}/\theta)^{3}$.
If objects in Euclidean space are distributed uniformly and the sample is
complete, then the volume ratio ($\langle V/V_{m}\rangle$) will be equal to
0.5.

Calculating this $V/V_{m}$ value for the catalogue of objects, successively
excluding objects with small angular sizes, we conclude that for objects with
$r_{Kron}$ > 61 arcsec (45% of the sample), our sample is essentially complete
with an average volume ratio of $\langle V/V_{m}\rangle=0.49$ in the $r$
waveband.

The whole catalogue is available in the online journal. The catalogue’s core
table is our Table 5 (with R.A., Dec., PA, $q$, $C_{0}$, redshift, the total
magnitude in the $r$ band, etc.). In Fig. 2 we show the distribution of our
galaxies by redshift, with and without prominent structural features. As one
can see, both subsamples have very similar distributions which peak at
$z\simeq 0.06$. The quartiles for both subsamples are
0.06${}^{+0.03}_{-0.02}$. The galaxies in our catalogue span a typical range
of absolute magnitudes, with a median value of -20.7${}^{+0.8}_{-0.7}$ (see
Fig. 2).

Figure 2: Redshift distribution for galaxies from the catalogue.
Figure 3: Absolute magnitude distribution for galaxies from the catalogue.

##  3 STRUCTURE CLASSIFICATION AND STATISTICS

We carry out an LSB structure classification by visual inspection of images
from the three independent deep surveys. Using four images, namely the stacked
and colour RGB images based on the SDSS Stripe 82, DESI Legacy, and HSC-SSP
data, we reveal low surface brightness structures near some galaxies from the
catalogue. All the structures are divided into two categories: tidal
structures and distinctive structural features. In the first category, we
include:

  1. 1.

Tidally Distorted Satellites or Satellite Debris: The remnants of satellites
that were disrupted in the process of tidal interaction (see Mateo et al.
1998, Majewski et al. 1999, Johnston et al. 2001, Sanders et al. 2018, Rich et
al. 2012).

  2. 2.

Tidal Tails and Stellar Streams: Elongated structures of stars and
interstellar gas (manifesting itself in the optical through star-forming
regions) that extend into space from a galaxy due to tidal interactions.
Stellar streams are created by the tidal disruption of low-mass satellites
interacting with the host galaxy (Johnston et al. 1996, Majewski et al. 1999,
McConnachie et al. 2009). Tidal tails result from the merging and interaction
of galaxies, typically through major mergers (Byrd & Howard, 1992; Duc &
Renaud, 2013; Oh et al., 2015).

  3. 3.

Diffuse Shells, Plumes, or Asymmetric Stellar Halos: These diffuse or
concenctric ring-like structures can be produced by major mergers or multiple
minor merger events. They are often associated with the accretion of
satellites on nearly radial orbits (Prieur 1990, Cooper et al. 2011, Ebrova
2013, Pop et al. 2018).

  4. 4.

Bridges: Extended structures consisting of stars and gas representing the flow
of matter from one object to another (Toomre & Toomre, 1972; Smith et al.,
2010; Barrabés et al., 2017).

  5. 5.

Single Arcs and Loops: Elongated structures around galaxies also produced by
tidal effects (see e.g. Morales et al., 2018, and references therein),
specifically by dynamical friction (Boylan-Kolchin et al., 2008) and tidal
stripping (Peñarrubia et al., 2008).

  6. 6.

Disc Deformations: These include thick tidal warps (Semczuk et al., 2020) and
deformed or distorted stellar discs (Dillamore et al., 2022; Dodge et al.,
2023).

Fig. 4 displays typical examples of galaxies with tidal structures from our
sample. In this section, we present a concise overview of each galaxy from
Fig. 4, offering valuable details about its structural characteristics derived
from our personal examination of images from the three different deep surveys:

ES82_18.624_0.215

Also known as SDSS J011429.85+001254.7 (SDSS spectral redshift $z=0.046$),
according to (Moretti et al., 2017) this edge-on galaxy is contained in a
compact group with the mean redshift $z=0.045$. In Fig. 4, one can see a tidal
tail or streams in northwestern and southeastern directions. It can be
reasoned that this galaxy had a tidal interaction with neighbouring object
SDSS J011429.79+001216.0 with SDSS spectral redshift $z=0.045$ and other
galaxies from the cluster. In turn, other neighbouring galaxies do not show
obvious signs of interaction with the object under study.

ES82_21.171_0.081

This edge-on galaxy ($z=0.056$) is also known as SDSS J012440.99+000452.1.
According to HyperLeda (Makarov et al., 2014), it has the SBd morphological
type. Kautsch et al. (2006) determined the object morphological class as Sd.
In all four deep images, we clearly see a bridge that connects the object with
its neighbour SDSS J012437.41+000513.9 which is confirmed by its neighbour’s
SDSS spectral redshift $z=0.056$. The bridge connects the north-west outskirts
of ES82_21.171_0.081 with SDSS J012437.41+000513.9 to the east. Both objects
have warped discs which also points to their tidal interaction.

ES82_315.137_0.294

ES82_315.137_0.294 or SDSS J210032.89+001739.9 has the SBb morphological type
and redshift $z=0.050$. This object demonstrates an arc-shaped structure on
the west side of the galaxy. The structure is seen in three images (HSC image
is not available). The arc extends to the north and after that bends sharply
in the opposite direction. It is noteworthy that there are no objects in the
vicinity of the galaxy for tidal interaction (Nair & Abraham 2010). This arc
can be a dwarf satellite stretched by the tidal forces of the host galaxy.

ES82_24.765_0.437

Another name for this object is SDSS J013903.59+002611.2. The galaxy has an
SBc HyperLeda morphological type or Scd type determined by Kautsch et al.
(2006) and redshift $z=0.100$. The galaxy demonstrates a tidally disrupted
low-mass satellite orbiting the body of the host galaxy that can finally be
ingested by it. According to Yang et al. (2007), the object is located in a
group. The neighbouring galaxy in a northeast direction does not have a
spectroscopic redshift, but its photometric redshift is far greater (0.157)
than that of the target galaxy.

ES82_19.434_0.254

Also known as SDSS J011744.15+001515.5, has a redshift of $z=0.076$. It does
not have a detailed morphological classification in HyperLeda, but its
geometry and colour suggest that this is an S0 galaxy. A distinctive feature
of this object is its pronounced shell that is a clear sign of a minor merger,
which is when a small galaxy is swallowed by a larger one. There are no
clearly seen galaxies in the vicinity to claim that the galaxy is located
within a compact group.

ES82_41.525_0.564

This edge-on galaxy, also known as 2MASX J02460608+0033487, exhibits distinct
features of tidally distorted spirals and/or disc warp. This peculiar
morphology suggests a potential interaction scenario with the neighbouring
galaxy 2MASX J02460531+0036297, situated within a close proximity of 3
arcminutes from ES82_41.525_0.564. Notably, both galaxies share the same
redshift value of $z=0.075$ as determined from SDSS spectroscopic analysis.
This concordance in redshift values further supports the hypothesis of a
physical association or ongoing interaction between these two galactic
systems.

Figure 4: Examples of observed tidal structures are demonstrated in three
independent surveys: first two columns are Stripe 82 coadds and Stripe 82 RGB
images (created using g,r,i filters), the third and fourth columns are images
from HSC-SSP (coadds) and DESI Legacy surveys respectively. The first line
demonstrates a galaxy with a tidal tail, the second line – with a bridge, the
third line – with an arc structure, the fourth line – with a satellite
remnant, the fifth line – with a shell, and the sixth line – with the disc
deformations. The scales of object images from different surveys may vary.

In the second category of distinctive structural features, we include such
structures as:

  1. 1.

Lopsided Discs: significant disc asymmetries along the plane relative to the
centre (Baldwin et al. 1980, Bournaud et al. 2005, Sancisi et al. 2008).

  2. 2.

Thin Warps: a slight departure of the disc matter from the mean galactic plane
which becomes especially prominent at the galaxy periphery (Sánchez-Saavedra
et al. 1990, Reshetnikov & Combes 1998, Reshetnikov et al. 2002, Gómez et al.
2017). The disc warps are typically much more pronounced in HI, outside of the
optical disc, but optical warps can be quite prominent as well (van der Kruit,
1979; Reshetnikov et al., 2016). A disc warp may arise from a misalignment
between the disc and its surrounding dark halo, which can vary over time due
to precession (Weinberg & Blitz 2006. Alternatively, the warp could result
from interactions with satellites (Zee et al. 2022). We subjectively divide
these two types by the prominence and thickness of the warp and classify them
into tidal (thick) warps and thin warps which may be produced by other
mechanisms.

  3. 3.

Polar Structures: large-scale outer rings or discs of gas, dust and stars,
orbiting in the plane approximately perpendicular to the disc of the main or
host galaxy (Whitmore et al. 1990, Reshetnikov & Sotnikova 1997, Moiseev et
al. 2011, Reshetnikov & Combes 2015).

Examples of structural features that we classified in our catalogue are
illustrated in Fig. 5.

ES82_331.378_0.077

In this galaxy, the main prominent feature is the thin disc warp. Galactic
warps may often be a consequence of galaxy-galaxy tidal interactions (López-
Corredoira et al., 2002). In our deep images, there are no close objects that
could gravitationally interact with this object. Verley et al. (2007) included
this galaxy in their catalogue of isolated objects, so the warp was probably
generated by some other mechanism. For example, dark matter halos can play a
role in the formation of disc warps (Sparke & Casertano 1988, Corbelli et al.
2014, Han et al. 2023b, Han et al. 2023a).

ES82_29.743_-0.490

Another example of a galaxy with a prominent structural feature is the polar
ring galaxy candidate ES82_29.743_-0.490 which is also called SPRC-77. Moiseev
et al. (2011) included this object in their catalogue of PRGs as a good
candidate based on the galaxy’s appearance. There are different mechanisms for
PRG formation, such as major mergers, minor mergers, or gas accretion. On our
deep images, this galaxy has a distinctive oval central component and a blue
ring. This PRG also demonstrates a small south-eastern arc that can be
satellite debris stretched during tidal interaction (Mosenkov et al., 2022a).

ES82_1.870_0.902

Another structural feature that is demonstrated in Fig. 5 is disc
lopsidedness. We can clearly see that the disc in ES82_1.870_0.902 is severely
disrupted: the galaxy’s centre of symmetry is shifted in the northwest
direction. It is believed that such non-asymmetry may originate from galaxy
mergers (Zaritsky & Rix, 1997). We suppose that the lopsidedness of this
galaxy is caused by the tidal interactions with its neighbour, PGC 170824,
located north-west of the studied object (their redshifts are 0.100 and 0.102,
respectively). It is not clear if there is a stellar bridge between these
galaxies. Additionally, the centre of symmetry of ES82_1.870_0.902 is shifted
towards PGC 170824.

Figure 5: Examples of observed structural features are demonstrated in three
independent surveys: first two columns are Stripe 82 coadds and Stripe 82 RGB
images, the third and fourth columns are images from HSC-SSP (coadds) and DESI
Legacy surveys respectively. The upper row displays a galaxy with a warp, the
middle row — a candidate for polar-ring galaxy (PRG), and the bottom row — a
galaxy with a lopsided distorted disc.

In total, tidal structures and distinctive structural features are observed in
49 and 56 galaxies out of 838, respectively (taking into account Galactic
cirrus, see below). Quantitative statistics by tidal structures are as
follows:

  1. 1.

Tidal tails and streams (15)

  2. 2.

Diffuse shells (6)

  3. 3.

Bridges (9)

  4. 4.

Arcs (7)

  5. 5.

Satellite debris (7)

  6. 6.

Disc deformations (8)

In general, types of tidal structures are not limited to those listed above.
These LSB structures are the most frequently encountered in our study (we
refer the interested reader to, for example, Martínez-Delgado et al. 2010,
Mancillas et al. 2019b, Sola et al. 2022). The parameters of galaxies with
tidal structures are given in Table 3.

The numbers of galaxies with different structural features are as follows:

  1. 1.

Lopsided discs (11)

  2. 2.

Warps (45)

  3. 3.

Polar rings (3)

As discussed briefly at the beginning, if a galaxy is contained within the
Milky Way’s cirrus clouds or filaments, then it can appear as if it has an LSB
feature. To verify the results of our classification, we must ensure that the
identified LSB features are not corrupted by Galactic cirrus. Smirnov et al.
(2023) used SDSS Stripe 82 images to search for cirrus clouds with a surface
brightness < 29 mag arcsec-2 and compiled a cirrus map using a neural network
that spans the entire Stripe 82. Fig. 10 in the Appendix shows where our
sample of galaxies is located along the cirrus map. We determined that 72
galaxies in our whole catalogue are within 3 times their radius to a cirrus
filament or are directly contained within one. Out of those 72 galaxies, 16
are directly contained within a cirrus filament. There are 8 galaxies with
tidal features that have cirrus filaments within close proximity, and upon
inspection, it was concluded that 7 of those galaxies had minimal
contamination and contained legitimate tidal features. In contrast, the galaxy
ES82_2.265_-0.583 (an apparent tail), was highly contaminated and its effect
could not be ruled out and therefore had to be removed as a tidal feature
candidate. Therefore, cirrus has no appreciable effect on the results of our
classifications.

##  4 Photometric Decomposition

The axis scales of galaxies in our sample that had been determined using
SExtractor appeared to be incorrect for many of them. To redefine disc
thickening, we carry out simple Sérsic (Sersic, 1968) fitting to compare the
values of apparent axis ratio for galaxies with and without LSB structures:

$I(r)=I_{\mathrm{e}}\,\exp\Bigg{[}-k\bigg{(}\Big{(}\frac{r}{r_{\mathrm{e}}}\Big{)}^{\frac{1}{n}}-1\bigg{)}\Bigg{]}\,,$
(1)

where $I_{\mathrm{e}}$ denotes the surface brightness at the effective radius
$r_{\mathrm{e}}$, the parameter $n$ is the Sérsic index, and $k$ is a function
of $n$ that ensures half of the total flux is enclosed within
$r_{\mathrm{e}}$.

The decomposition is performed using the Python wrapper
IMAN777https://bitbucket.org/mosenkov/iman_new/src/master/ which utilises the
GALFIT (Peng et al., 2002) code. In turn, GALFIT uses a Levenberg-Marquardt
algorithm for $\chi^{2}$ minimisation. Utilising pre-existing images of
galaxies in the $r$-deep filter (as detailed in Sect. 2.2), alongside masks
and PSF images, we employ these inputs as data for our analysis. Consequently,
we successfully retrieve essential model parameters for all but 3 galaxies
within our sample, including the apparent axis ratios $q$, effective surface
brightness levels, effective radii, Sérsic index, integrated magnitude, and
the diskyness/boxyness parameter $C_{0}$. When the value of $C_{0}$ is less
than zero, the isophotes exhibit a disc-like appearance. On the other hand,
they appear boxy when $C_{0}$ is greater than zero. If the isophotes can be
accurately represented by pure ellipses, then $C_{0}$ equals zero. In cases
where it was not possible to build an adequate model on the first try, we
perform additional cropping or reduce the image region to fit, minimising the
impact of masking inaccuracies. Three objects for which models have not been
built (mostly because of starlight) are excluded from further analysis. The
proportion of such galaxies is less than 1 per cent of the entire catalogue,
so this aspect should not significantly affect the results. Additionally, we
perform galaxy fitting with tidal structures masked to ensure that the
interpretation of disc thickening does not strictly arise from the systematics
in measuring $q$ for galaxies with tidal features. This procedure helps us
answer the question, whether the light of tidal features affects the
measurements of the axis ratio.

Since we are interested in an investigation of outer isophotes of sample
galaxies with structures and without them, which are described by apparent
axis ratio and $C_{0}$ parameter, we will dwell on them in more detail below.

###  4.1 The disc thickening

In Tables 3 and 4 in the Appendix, we list the model thickening $q$ for
galaxies with observed tidal structures and structural features. To gain more
reliable results, we divide catalogue objects into four groups, which are
described in detail at the end of Sect. 2.2. In this section, we have excluded
group 3 from the analysis to take into account the inclination effects. As
shown in Fig. 6(a), the distributions of galaxies based on their axis ratios
are not normal, therefore lower and upper quartiles are used to compare the
disc thicknesses for subsamples combining the different groups. Table 1
presents the results of the analysis:

Table 1: The statistics for galaxy apparent axis ratio of subsamples with
tidal structures (with and without structure masking), structural features,
and without any visible structures for objects from different groups and their
combinations, where $q$ is the disc axis ratio

obtained in the decomposition process.  Tidal structures Tidal masked All
structures No structures Group $q$ Number $q$ Number $q$ Number $q$ Number 1
$0.17_{-0.01}^{+0.05}$ 5 $0.17_{-0.01}^{+0.05}$ 5 $0.2_{-0.05}^{+0.05}$ 25
$0.19_{-0.03}^{+0.05}$ 216 2 $0.29_{-0.03}^{+0.06}$ 14 $0.28_{-0.03}^{+0.06}$
14 $0.28_{-0.05}^{+0.07}$ 25 $0.25_{-0.05}^{+0.05}$ 382 4
$0.29_{-0.04}^{+0.02}$ 26 $0.28_{-0.04}^{+0.02}$ 26 $0.3_{-0.04}^{+0.07}$ 44
$0.28_{-0.05}^{+0.1}$ 71 1 + 4 $0.28_{-0.06}^{+0.02}$ 31
$0.28_{-0.06}^{+0.03}$ 31 $0.28_{-0.07}^{+0.03}$ 69 $0.21_{-0.04}^{+0.06}$ 287
1 + 2 + 4 $0.28_{-0.05}^{+0.03}$ 45 $0.28_{-0.06}^{+0.03}$ 45
$0.28_{-0.06}^{+0.05}$ 94 $0.23_{-0.05}^{+0.05}$ 669

Regardless of which groups are used to analyse disc thickening, the subsample
of galaxies without structures are still flatter than the subsample with tidal
structures (see Table 1). For a numerical assessment, we focus on the fourth
row of the table, which presents the results based on galaxies from groups 1
and 4 as the inclusion of objects from the second group may influence the
result due to the inclination effects. In groups individually, there may not
be enough objects to obtain a reliable estimation. The median values in Table
1 show that galaxies with tidal structures and with all identified distinctive
features (LSB and others) have about 1.33 times greater disc thickening than
galaxies without them.

To distinguish between the actual disc thickening and potential measurement
errors when $q$ can be affected by present tidal feature light along the minor
axis of the galaxy, we additionally utilise tidal structure masking during the
fitting process. This allows us to quantify the level of enhancement in $q$
specifically attributable to genuine disc axis ratio. The results are
presented in Fig. 6(a) and Table 1. Indeed, we can see in the distributions
that there is some systematic effect of additional disc thickening due to
tidal structures’ light, but the real thickening of the galaxy disc is also
present. In cases of fitting with and without structure masking, galaxies with
tidal structures have about 1.33 times thicker discs than galaxies without
them.

A control matching test is implemented to take into account the magnitude
difference for the subsample of galaxies with tidal structures and without
them. There is a probability that some galaxies without visible structures are
fainter than galaxies with tidal LSB features. Therefore the first subsample
may include galaxies whose discs are thickened by interactions, but whose
features are too faint to be detected. To control for this possibility, a
best-matching control is selected for each tidal feature object. The matching
is performed using the values of the Kron radius (from the SExtracor
catalogue) and model magnitudes in the $r$-band (from the SDSS database). The
algorithm of the matching test is as follows:

Initially, the Kron radius and magnitudes are normalised. Subsequently, the
square root of the sum of squared differences between corresponding parameters
is computed for each galaxy pair. Ultimately, the total sum of these
differences is evaluated:

$Q=\frac{1}{N}\sum_{i=1}^{N}\frac{q_{ts}}{q_{ns}}$

where $q_{ts}$ is a model thickness of galaxy with tidal structures, $q_{ns}$
is a matched galaxy without structures. $N$ is the number of galaxies with
tidal structures in the sample. $Q$ shows how many times, on average, the disc
thickening of galaxies with tidal structures differs from their best-matching
controls. As a result of this test, we get that $Q=1.46$ for model quantities
obtained as a result of fitting without structure masking, and $Q=1.39$ — with
structure masking. This test confirms the accuracy of the obtained results
regarding disc thickening. Furthermore, the results from this test reveal even
greater discrepancies in disc thickness among the subsamples under study.

Let us note that some galaxies in our sample exhibit an apparent axis ratio
value $q$ greater than 0.3, which appears to contradict the criteria used for
cataloging galaxies based on the SExtractor semi-major and semi-minor axes
(denoted as the A_IMAGE and B_IMAGE parameters, respectively). This
discrepancy can be attributed to the inaccuracies in the SExtractor
measurements, which, in turn, affect the $q$ values used for the galaxy
selection. While outliers that are clearly not edge-on galaxies have been
manually filtered out, our sample still includes edge-on galaxies with $q$
values measured by GALFIT that exceed 0.3. This can be attributed to prominent
galaxy bulges, bright halos, shells, thick stellar discs, and the contribution
of the light from LSB structures or external objects.

In general, galaxies with structures do have thicker discs than galaxies
without them. This difference is more significant when considering a subset of
galaxies with only tidal structures. In our study, the difference in relative
thickness is not as significant as in other works. For example, Reshetnikov &
Combes (1997) reported that galaxies undergoing merging have a relative
thickness that is, on average, twice that of non-interacting ones. Similarly,
Schwarzkopf & Dettmar (2000) found this value to be approximately 1.7 times
greater for interacting galaxies compared to non-interacting galaxies.
However, these studies focused on real galaxy mergers in the midst of
collision, whereas our research mostly involves galaxies that are either still
too distant from each other to be considered colliding or are involved in
minor mergers.

(a) * Figure 6: The left figure represents the axis ratio distribution of
galaxies with tidal structures calculated using images with masked and
unmasked structures and images of galaxies without any structural features. p1
is a p-value obtained from the Mann-Whitney test of the null hypothesis that
the distribution underlying the sample of galaxies with tidal structures is
the same as the distribution underlying the sample of galaxies without them.
p2 is the p-value corresponding to the sample of galaxies with masked tidal
structures and the sample of galaxies without structures. The right figure
represents the axis ratio distribution of galaxies with structural features. p
is a p-value obtained from the Mann-Whitney test of the null hypothesis that
the distribution underlying the sample of galaxies with structural features is
the same as the distribution underlying the sample of galaxies without them.

[.45][.45]

(b) *

###  4.2 The diskyness/boxyness parameter $C_{0}$

The tidal interaction of galaxies with their environment can impact the shape
of galactic outer isophotes, which in our investigation is characterised by
the $C_{0}$ value. Galaxies with positive $C_{0}$ values demonstrate oval or
boxy outer isophotes. In turn, galaxies with negative $C_{0}$ values have
disky (diamond-like) external isophotes. In Mosenkov et al. (2020a), it was
shown that the mean value of $C_{0}$ for objects with LSB structures from the
study sample is $\langle C_{0}\rangle=0.37\pm 0.32$ versus $\langle
C_{0}\rangle=-0.29\pm 0.40$ for the remaining ones. However, the sample from
Mosenkov et al. (2020a) consists of only 35 galaxies, and the results of this
paper should be taken with caution. We explored this issue in our catalogue
that consists of 838 objects and can provide us with more reliable results. As
in the part with the analysis of disc thickening, tidal structures are masked
to avoid their influence on the resulting model. Fig. 7(a) shows the
distribution of our galaxies by $C_{0}$. We can see that there is no
significant difference in distributions for galaxies with structural features
and galaxies without any structures. If we compare the diskyness/boxyness
parameters for objects only with tidal structures and without them, we can see
that the median of the distribution of galaxies with tidal structures is
shifted towards positive $C_{0}$. In this case, the fraction of galaxies with
tidal structures that have oval/boxy isophotes is larger which can also be
seen in Fig. 7(a).

Table 2 shows the statistics for parameter $C_{0}$ calculated for different
groups and their combinations like it was done for apparent axis ratios. Here
we also focus on the results described for the totality of groups 1 and 4. We
can see from the table that for galaxies without any structures, the outer
isophotes of the disc are indeed, on average, more oval/boxy than for galaxies
with any kind of structures.

Table 2: The statistics for galaxy $C_{0}$ value of subsamples with tidal structures (with and without structure masking), structural features, and without any observable structures for objects from different groups and their combinations.  | Tidal structures | Tidal masked | Structural features | No structures
---|---|---|---|---
Group |  $C_{0}$ |  Number |  $C_{0}$ |  Number |  $C_{0}$ |  Number |  $C_{0}$ |  Number
1 |  $-0.19_{-0.21}^{+0.3}$ |  5 |  $-0.19_{-0.21}^{+0.3}$ |  5 |  $-0.32_{-0.41}^{+0.2}$ |  25 |  $-0.49_{-0.2}^{+0.29}$ |  216
2 |  $-0.15_{-0.3}^{+0.16}$ |  14 |  $-0.15_{-0.3}^{+0.16}$ |  14 |  $-0.3_{-0.22}^{+0.12}$ |  25 |  $-0.28_{-0.21}^{+0.35}$ |  382
4 |  $-0.15_{-0.1}^{+0.54}$ |  26 |  $-0.17_{-0.23}^{+0.26}$ |  26 |  $-0.43_{-0.21}^{+0.21}$ |  44 |  $-0.52_{-0.18}^{+0.21}$ |  71
1 + 4 |  $-0.15_{-0.19}^{+0.48}$ |  31 |  $-0.18_{-0.23}^{+0.29}$ |  31 |  $-0.4_{-0.28}^{+0.27}$ |  69 |  $-0.5_{-0.2}^{+0.29}$ |  287
1 + 2 + 4 |  $-0.15_{-0.23}^{+0.28}$ |  45 |  $-0.17_{-0.26}^{+0.24}$ |  45 |  $-0.38_{-0.29}^{+0.24}$ |  94 |  $-0.36_{-0.22}^{+0.31}$ |  669

(a) * Figure 7: The left figure represents the $C_{0}$ distribution of
galaxies with tidal structures calculated using images with masked and
unmasked structures and images of galaxies without any structural features. p1
is a p-value obtained from the Mann-Whitney test of the null hypothesis that
the distribution underlying the sample of galaxies with tidal structures is
the same as the distribution underlying the sample of galaxies without them.
p2 is the p-value corresponding to the sample of galaxies with masked tidal
structures and the sample of galaxies without structures.

[.45][.45] The right figure represents the $C_{0}$ of galaxies with structural
features. p is a p-value obtained from the Mann-Whitney test of the null
hypothesis that the distribution underlying the sample of galaxies with
structural features is the same as the distribution underlying the sample of
galaxies without them.

(b) *

##  5 Discussion

###  5.1 The Occurrence Rate of LSB Structures

The main result of Sect. 3 with the classification and statistics of LSB and
other distinctive features is that as compared to other works investigating
galaxy formation models within the standard $\Lambda$CDM cosmological paradigm
(Johnston et al. 2001, Martin et al. 2022), we observe an insufficient number
of galaxies with tidal structures in our catalogue. Interacting galaxies are a
common phenomenon in the local Universe, as evidenced even by our own Galaxy
(Putman et al. 1998, Lee et al. 1999, Belokurov et al. 2006). Cosmological
simulations within the standard $\Lambda$CDM model predict that a significant
number of coherent tidal structures may be detected with sufficiently deep
observations in the outskirts of the majority of nearby massive galaxies (Font
et al. 2011, Cooper et al. 2013, Pillepich et al. 2015). Also, in Johnston et
al. (2001) where $\sim$100 parent galaxies are considered, it is shown (see
their figure 8) that reaching a surface brightness limit $\sim$29 mag arcsec-2
would reveal many tens of tidal features. Specifically, 20-40% of galaxies
from the sample should have approximately one detectable feature. In a recent
study by Martin et al. (2022), in preparation for the 10-year Legacy Survey of
Space and Time (LSST) at the Vera C. Rubin Observatory, the ability to detect
tidal features using the NEWHORIZONS cosmological simulation (Dubois et al.,
2021) is investigated. As shown in figure 17 of Martin et al. (2022), varying
the limiting surface brightness in the $r$ band (28–31 mag arcsec-2) affects
the detection of tidal features across different redshifts. Using this figure
and the mean redshift of our sample, we find that at a limiting surface
brightness of 28 mag arcsec-2 in the $r$ band, approximately 25% of our sample
should exhibit tidal features. Furthermore, Valenzuela & Remus (2022) utilised
the Magneticum simulation to measure a tidal feature fraction of 23%, which is
only 2% lower than that found by Martin et al. (2022). This comparison further
demonstrates the insufficient number of galaxies with tidal features in our
sample compared to those predicted by cosmological simulations.

We further seek to compare our results with those in the literature. It is
important to note that none of the studies discussed below use the same method
as this study to calculate the limiting photometric depth. Given the
substantial differences in methodology, recalibrating the limiting surface
brightness of our sample to align with those of the cited studies would
require an extensive, time-intensive recalibration process. Consequently, such
recalibration was deemed impractical and was not undertaken. In an
observational study using HSC-SSP data, Kado-Fong et al. (2018) obtained the
following result: tidal features were found in 1,201 out of 21,208 sample
galaxies (5.6%), which is consistent with our complete data set (galaxies with
$R_{Kron}>61$ arcsec) confirming the presence of tidal structures in 26
galaxies out of 374 galaxies (7%). However, their sample of galaxies at a
surface brightness of $\mu_{r}=28.1$ mag arcsec-2 is incomplete. For our
incomplete data set (galaxies with $R_{Kron}<61$ arcsec), the presence of
tidal features has a ratio of 24 galaxies out of 464 galaxies (5.2%). Kado-
Fong et al. (2018) used various methods obtained from the literature (see
references therein) to calculate the limiting depth of their sample, but none
of these methods match with our own. In Morales et al. (2018), it is detected
that tidal features are found around $\sim 10$% of a mass-selected sample of
isolated Milky Way analogues at a limiting surface brightness of 28 mag
arcsec-2. Unlike the previous study, Morales et al. (2018) has a complete
sample. To estimate the depth of their study, Morales et al. (2018) used
5$\sigma$ fluctuations with 3 arcscec diameter apertures. In a more recent
study, Sola et al. (2022) found tidal features in 127 galaxies out of a sample
of 352 galaxies (36%, private communication), with features not extending
beyond a photometric depth of 27.5 mag arcsec-2.

There could be numerous reasons why our statistics do not match with other
observations and simulations. Reasons such as visual bias, projection effects,
redshift and mass selection biases, insufficient image depth, contamination by
Galactic cirrus clouds, and the reliability of cosmological hydrodynamic
simulations can all play a role. Below, we briefly consider all of these.

As noted, visual classification was used to categorize the types of tidal and
structural features within our sample. However, visual classification can be
subjective, depending on the individual classifier, and can lead to
disagreements among different classifiers (Bridge et al. 2010, Blumenthal et
al. 2020). For example, in Martin et al. (2022),five experienced classifiers
participated in categorizing tidal features in mock images, where some
classifiers marked an image as having a feature, while others marked it as
featureless. When reviewing the images again, many revised their original
answers. This shows that even classifiers with experience can face uncertainty
in their classifications and that classifications should be revisited numerous
times to ensure accuracy. In the case of our sample, it is likely that some
galaxy images might be overlooked and not included as having tidal features.
For this reason, the entire catalogue was examined by several classifiers to
mitigate this subjective factor, but it is still difficult to estimate to what
extent this has impacted our classification results. In Bridge et al. (2010),
a blind study found that classifications among different classifiers varied by
only 3%. These classifications were done on strong tidal signatures and,
therefore, this percentage would be a lower estimate for our own study.
Another method used to help eliminate visual bias is the method of applying
weights to different classifiers and their classifications. Citizen science
projects such as Galaxy Zoo and Galaxy Cruise use this method with great
success, assigning greater weight to the most consistent classifications
(Simmons et al. 2017, Tanaka et al. 2023). In this study, we do not use this
approach since we have only three well-trained classifiers.

In addition to that, by using multiple survey images in conjunction with those
from the SDSS to identify tidal structures, galaxies were cross-referenced to
ensure that structures are not image artefacts or any other non-extragalactic
structures. This has not been extensively done in other studies and can serve
as a way to curb visual bias. For example, the HSC-SSP, with its higher
resolution images, helped us identify 10 more galaxies with tidal features.
Unfortunately, only 64% of the galaxies from our catalogue are covered by the
HSC-SSP. Based on the additional galaxies identified among the 539 HSC-SSP
galaxies, if we had HSC-SSP data for all catalogue galaxies, we could have
found an additional $\sim 6$ galaxies with tidal features, increasing our
tidal fraction to about $7$%.

Another factor that plays a role in visual classification bias is projection
effects. A vast majority of studies done on tidal features use samples of
galaxies with varying inclination angles, including the studies discussed
above. The varying inclination angles can hide or change the shape of tidal
features, making it difficult to provide accurate classifications (Martin et
al., 2022). In Martin et al. (2022), it was found that for deep imaging, the
uncertainty from projection is dominant for their images. In the case of this
paper, only edge-on galaxies are used, which helps to eliminate some
projection effects and keeps the tidal classifications consistent. Due to
this, projection effects do not play a significant role in our results.

As shown in Fig. 2 for galaxies with structures, the spectroscopic redshift
distribution peaks at $z\simeq 0.06$. Specifically, for tidal structures, the
mean is $z=0.07$ and it peaks at $z\approx 0.04$. This is in agreement with
observations and simulations (Kado-Fong et al. 2018, Martin et al. 2022,
Domínguez Sánchez et al. 2023), which show that more tidal structures are
identified at lower redshifts. This can be attributed to a combination of a
loss of spatial resolution and cosmological dimming of the surface brightness
at higher redshifts, which leads to greater difficulty in identifying LSB
tidal structures (Kado-Fong et al., 2018). We performed a Mann-Whitney test to
assess the null hypothesis that the distribution underlying the sample of
redshifts from galaxies with structures is the same as that of the sample
without structures. The p-value obtained from this test is $p=0.07$.
Therefore, we cannot reject the null hypothesis, concluding that the two sub-
samples are similar. Analysing the redshifts from our sample using $(1+z)^{3}$
for AB magnitudes (see Whitney et al. 2020) to account for cosmological
dimming, the average is found to be 1.2 with a standard deviation of 0.15.
This is not a significant enough change in the surface brightness; therefore,
cosmological dimming should not play a significant role in our sample. Further
evidence can be seen in Fig. 9 where the average offset between the measured
tidal feature surface brightness and their intrinsic surface brightness before
cosmological dimming is $\sim$ 0.09, which is not a significant offset. It is
worth noting that the highest value for cosmological dimming occurs for a
galaxy with a substructure. Looking at cosmological dimming values greater
than or equal to 1.5, it is found that two galaxies with substructures met
these criteria. Specifically, one of the two has a tidal structure and a
cosmological dimming of $\sim 2.3$ ($\Delta\mu=0.36$), while the other has a
dimming of 1.5. Therefore, cosmological dimming does not play a significant
role in detecting tidal structures around our sample of galaxies and does not
explain the lack of tidal structures in galaxy images.

Figure 8: Histogram comparing the masses of galaxies with tidal features and
to the rest of our sample, including those with interesting features. Mass was
calculated using the $g-r$ colour and the absolute magnitude in the $r$ band.

It has been found that the classification of tidal structures is mass-biased
(Atkinson et al. 2013, Kado-Fong et al. 2018, Bílek et al. 2020, Jackson et
al. 2023). That is, more structures are found around larger mass galaxies.
This is expected, as more massive galaxies tend to be more luminous as will
the structures produced by minor/major interactions with these larger mass
galaxies, making them easier to identify. Additionally, the number of major
mergers that occur are expected to scale with the stellar mass of a galaxy,
which means the number of substructures also scales with mass (Guzmán-Ortega
et al. 2023). The study by Bílek et al. (2020) found that galaxies with
stellar masses above $10^{11}\,M_{\odot}$ had 1.7 times more tidal structures
than those below this value. Furthermore, in comparison with Bílek et al.
(2020), Jackson et al. (2023) had 1.2 times more tidal structures. Our study
suggests that the galaxies with more than one tidal feature have, on average,
a stellar mass of $10^{10.6}\,M_{\odot}$. In Fig. 8, galaxies with structures
peak at $\sim 10^{11}\,M_{\odot}$, in agreement with Jackson et al. (2023). We
performed a Mann-Whitney test of the null hypothesis that the distribution
underlying the sample of galaxy masses with tidal structures is the same as
the distribution underlying the sample of galaxy masses without tidal
structures. The p-value obtained from this test is $p=0.04$. Therefore, we can
reject the null hypothesis and conclude that the two sub-samples are not
similar. Therefore, there is a correlation between the stellar mass and the
presence of tidal structures for our sample galaxies. The equation

$\log_{10}\left(\frac{M}{L}\right)=a_{\lambda}+(b_{\lambda}\times\textrm{colour)}$
(2)

was used to find the stellar masses of our galaxies. The $a_{\lambda}$ and the
$b_{\lambda}$ are -0.306 and 1.097, respectively, for the $r$ band and for the
$g-r$ colour. The table of values and the equation above can be found in Bell
et al. (2003). It is important to note that the mass values calculated for our
sample do not take into account dust attenuation in the galaxies but they are
accurate enough for our general purposes.

Figure 9: Histogram of the median surface brightness of all tidal structures
for the r-deep filter. This is overlaid with another histogram of the
intrinsic surface brightness calculated using the cosmological dimming values
for each galaxy. A small offset can be seen between the plots.

Another possible reason for the lack of tidal structures in the current study
could be that our data is still not deep enough to detect the faintest LSB
features. In Johnston et al. (2008), it is shown that the majority of tidal
structures are expected to have a peak surface brightness higher than $\sim
30$ mag arcsec-2. However, as discussed above, Sola et al. (2022) found that
the tidal features in their sample did not extend beyond the depth of a median
value of 27.5 mag arcsec-2. We conducted a similar investigation into the
depth of the tidal structures within our sample. By creating polygon regions
around the structures themselves using SAO DS9, we were able to find that our
sample of tidal structures does not extend beyond the photometric depth of a
median value of 27.1 mag arcsec-2 in the r-deep band (see Fig. 9). This result
is similar to Sola et al. (2022) and could mean that these structures have not
had enough time to accrete onto their host galaxy and dissipate, therefore
remaining luminous. The mass of the galaxies may also play a role as all tidal
structures in our sample have large masses and therefore are more luminous.
This could also mean that our sample is still not deep enough, as only the
more luminous structures are discernible, whereas the deeper structures are
overlooked and missed completely. As shown in Fig. 9, the measured surface
brightness of the tidal structures has a peak at 26.5 mag arcsec-2 and an
average of 26.1 mag arcsec-2 with a standard deviation of 0.7. In Sola et al.
(2022), their average is 25.6 mag arcsec-2 and a standard deviation of 0.7
which matches our measurements.

In summary, our catalogue of edge-on galaxies primarily contains high mass,
low-redshift galaxies, examined in sufficiently deep images. Studies and
cosmological simulations all agree that each of these parameters should
produce the best chance of identifying a large fraction of tidal structures.
Therefore, the reason for this study’s low percentage could be a combination
of some visual bias and our sample not being complete enough. Another reason
not mentioned earlier could be that the predicted fraction of tidal structures
that should be observed from cosmological simulations could be inaccurate.
Even though cosmological simulations have had great success at producing
observed characteristics of galaxies such as hierarchical structure formation
and reproducing the general properties of galaxies (Somerville & Davé 2015,
Ward et al. 2022, Baes et al. 2024) they are not infallible and can produce
discrepancies between prediction and observation. For example, the
longstanding discrepancy of the star formation rate vs. stellar mass relation
that gives a steeper slope than observed for lower mass galaxies at
intermediate redshifts (Daddi et al. 2007, Christensen et al. 2012, Somerville
& Davé 2015). More recent discrepancies have been found such as the
disparities in metallicity recycling and mixing history for larger galaxies
(Jara-Ferreira et al., 2024). Discrepancies such as these possibly arise from
not having a clear understanding of the mechanisms that govern specific
physical processes such as star formation and stellar feedback (Somerville &
Davé 2015). This lack of understanding could explain why the few studies
discussed above and our own do not match cosmological simulations.

Additionally, simulations such as the one used in Martin et al. (2022) produce
‘smooth’ images or images that do not contain contaminants,
background/foreground objects (stars and galaxies), sky subtraction residuals,
imaging artefacts, etc. (Domínguez Sánchez et al., 2023). This allows the
classifiers to know that the structures seen in the mock images are true
structures, leading to higher fraction counts. Another point to consider is
the morphology of the galaxies being produced in simulations. Disc galaxies or
late-type galaxies (LTGs) have been found to be more easily disrupted and will
produce tidal features more easily than compact spheroids (Kormendy et al.
2009, Pedrosa et al. 2014). If a simulation produces more disc galaxies than
spheroidal galaxies, then it is possible that the simulation would produce a
higher fraction of tidal features. Looking specifically at the IllustrisTNG
(Marinacci et al. 2018, Naiman et al. 2018, Nelson et al. 2018, Pillepich et
al. 2018, Springel et al. 2018, Nelson et al. 2019) and EAGLE (Crain et al.
2015, Schaye et al. 2015) simulations, it was found that the morphology of the
simulated galaxies matched observations, where only the asymmetry is larger
for the simulated galaxies (Bignone et al. 2020, Guzmán-Ortega et al. 2023).
The NEWHORIZON simulation used by Martin et al. (2022) also agrees well with
the observed morphology (Dubois et al., 2021). This means that the morphology
in simulations does not account for the observed discrepancy.

This discussion prompted us to look at the morphology of the galaxies in our
sample using the HyperLeda database. For the entire sample, 519 (62%) are
LTGs, 295 (35.2%) are early-type galaxies (ETGs), and 24 (2.9%) have an
unknown morphology. Looking at only tidal structures, 32 galaxies (65.3%) are
LTGs, and 17 (21.1%) are ETGs. Eleven of the LTGs had uncertain
classifications and were further classified by eye. Of the three galaxies that
contain more than one tidal structure, two are ETGs and one is a LTG. It is
known that more tidal features are found around ETGs due to their formation
and evolution mechanism being minor and major mergers which produce more
easily visible features such as plumes (Duc, 2017) and shells (Yoon & Lim,
2020). With the majority of our sample consisting of LTGs, another reason for
the discrepancy could be that our sample lacks ETGs. Many of the studies
mentioned focus either solely on ETGs or have a more balanced split between
ETGs and LTGs. Additionally, these studies often have varying surface
brightness limits. Both effects may lead to different tidal feature fractions.

It is difficult to pinpoint the exact reason for the discrepancy between the
simulations and observations, but our discussion above suggests that further
investigation is needed. Deep photometric studies of large, complete samples
of galaxies should better describe the statistics of tidal structures in the
local Universe for a more appropriate comparison with cosmological
simulations. In one such future study, we will examine almost 6,000 true edge-
on galaxies from the Catalogue of Edge-on Disc Galaxies from SDSS (Bizyaev et
al., 2014). This will be the largest catalogue of edge-on galaxies with
tidal/structural features ever compiled. Further statistical analysis will be
performed and compared with the results from this study.

###  5.2 Disc thickening

Galaxy mergers are believed to be the main drivers for significant kinematic
perturbations of galaxies (Toomre & Toomre 1972, Barrera-Ballesteros et al.
2015). This fact is confirmed in theoretical (e.g Hernquist 1992) and
observational (e.g., Woods et al. 2006, Woods & Geller 2007) studies. Major
mergers, in particular, can significantly change the morphology of a galaxy
(Sales et al., 2012). However, such events are not as common as minor mergers
or interactions of satellite galaxies, which can also impact the disc
structure (Kazantzidis et al., 2008).

One of the types of deformations caused by perturbations in the disc as a
result of tidal interactions is the thickening of the disc. Many simulations
show that these tidal interactions trigger instabilities in the disc and lead
to its fattening (e.g., Moore et al. 1999). Important results from galaxy-
galaxy encounters, even those not leading to a merger, are obtained in N-body
simulations by, for example, Gerin et al. (1990). The authors demonstrate that
interactions with a neighbour, orbiting perpendicular to the plane of the
target galaxy, produce a bending and subsequent disc thickening. Such
interactions lead to a greater effect than in-plane interactions. For the most
part, early simulations predict disc thickening by a factor of 2–4 (Ostriker
1990, Toth & Ostriker 1992, Quinn et al. 1993, Mihos et al. 1995). At the same
time, in the work of Velazquez & White (1999), it is shown that the impact of
tidal heating is overestimated. The increase of the vertical scale height
associated with this effect is greater by a factor of 1.5–2, which is closer
to the results obtained in observations.

In discussing the results obtained in observational studies, one can refer,
for example, to the works of Reshetnikov & Combes (1996) and Reshetnikov &
Combes (1997). These authors investigate the effects of tidally-triggered disc
thickening between galaxies of comparable mass. Using optical photometric data
for a sample of 24 interacting galaxies and a control sample of 7 non-
interacting disc galaxies, they find that the radial-to-vertical scales ratio
$h/z_{0}$ for the first sample is twice as small as that for the second one,
which confirms the simulation results. In Schwarzkopf & Dettmar (2000), the
authors also observe differences in $h/z_{0}$ values for interacting and non-
interacting galaxies. In this study, the apparent axis ratio value of galaxies
for the first group is found to be $\approx 1.7$ times smaller than that for
the second group.

In accordance with the results of our work described in Sect. 4, the discs of
galaxies with observable low-surface brightness structures are 1.33 times
thicker than those of galaxies without observable structures. This value is
slightly less than those obtained in the aforementioned studies. This
difference is due to the fact that those works focused on major interactions,
while our sample consists mostly of minor interactions, which do not
contribute as significantly to the thickening of the discs. Minor interactions
leave specific tidal tracers and, in the context of this article, include
streams/arcs, shells, bridges, and satellite debris (Duc et al. 2014, Hendel &
Johnston 2015). Such tidal structures are found around 86% of the galaxies
that exhibit tidal structures; therefore, it is safe to say that our sample of
LSB structures consists mostly of minor interactions.

##  6 SUMMARY AND CONCLUSIONS

In this paper, we created a catalogue of edge-on galaxies in deep SDSS Stripe
82. Also, we identified and classified LSB and other distinctive structures
near or in these galaxies based on data from three independent deep sky
surveys: SDSS Stripe 82, HSC-SSP DR3, and DESI Legacy Imaging Surveys DR9. 539
out of 838 galaxies in our catalogue have HSC-SSP images and 827 galaxies have
data in DESI Legacy. This means that for at least 65% of the galaxy sample, we
have three different data sources for structure classification. Also, we
investigated the thickening and boxyness/discyness of the galaxy discs
depending on the structure’s presence or absence. The conclusions of this
study can be summarised as follows:

  1. 1.

A catalogue of 838 edge-on galaxies in the SDSS Stripe 82 (ES82) has been
created. The main characteristics of the galaxies have been obtained. The mean
redshift of the galaxies we have considered is $\langle
z_{\mathrm{spec}}\rangle$ = 0.06${}^{+0.03}_{-0.02}$ (Fig. 2). The mean value
of absolute magnitude for the sample galaxies is $\langle M_{r}\rangle$ =
-20.7${}^{+0.8}_{-0.7}$ (Fig. 3), which is consistent with the results of
Bizyaev et al. (2014) for the EGIS catalogue.

  2. 2.

The classification of galaxies by the presence of structures has been
performed. It is important to note that the use of the three independent
surveys played a significant role not only in classifying structures but also
in determining the inclination of galaxies, especially due to the better
angular resolution of HSC-SSP. The coadded and RGB images of SDSS Stripe 82
were useful for selecting a primary sample of galaxies by their disc
flattening and for marking those with unusual structures. Comparing images
from SDSS Stripe 82 with those from HSC-SSP and DESI Legacy allowed us to
identify the presence of spiral structures in the discs and allocate such
objects to a separate category, as galaxies close to an edge-on orientation
affect the accuracy of the results obtained in Sect. 4. The use of the three
surveys also increases the reliability of the fact that the observed features
of galaxies are indeed real structures and not artefacts in the image.

  3. 3.

There are 49 (5.8% of the sample) galaxies with LSB tidal structures (tails,
bridges, arcs, shells, satellite remnants, disc deformations) and 56 (6.7% of
the sample) galaxies with distinctive structural features (thin disc warps,
lopsided discs, and polar structures) are selected and classified. An
important result of this work is that, despite the depth of the studied
images, the number of galaxies with LSB structures in the sample is much lower
than in other studies considering galaxy formation models that adopt the
$\Lambda$CDM paradigm. A possible reason may be the mean size of galaxies in
our catalogue. Our galaxies are mostly small, and possible faint small-
size/thin structures can be difficult to distinguish in them. Another reason
could be that our imaging is not deep enough and there could be visual bias.
We also came to the conclusion that cirrus clouds and cosmological dimming do
not play a significant role in our structure statistics.

  4. 4.

Simple Sérsic fitting is performed for the entire sample. It is shown that
galaxies with observed tidal structures are, on average, thicker (by 1.33
times) than the galaxies without these structures (Fig. 6(a)). Also, the discs
of galaxies with tidal structures or structural features, on average, have
more of a boxy-like shape of the outer isophotes than objects without any
visible structures (Fig. 7(a)).

Based on the results and discussion of this paper, a large portion of studies
done on LSB tidal features have small sample sizes, and larger studies are
needed to get a better representation of the population of tidal features. In
a future paper, we will continue to investigate the statistics, structure, and
surface brightness of LSB tidal and structural features around edge-on
galaxies using a large sample size of almost 6,000 edge-on galaxies. We hope
this will provide new insights into these structures.

## Acknowledgements

We thank Elisabeth Sola for providing the statistics for their tidal
structures from their study Sola et al. (2022), which will be included in a
future paper.

This research has made use of the NASA/IPAC Extragalactic Database (NED;
https://ned.ipac.caltech.edu/) operated by the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National
Aeronautics and Space Administration. This research has made use of the
HyperLEDA database (http://leda.univ-lyon1.fr/; Makarov et al., 2014).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Centre for High-Performance Computing at the University of Utah. The SDSS
website is www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS Collaboration including the Brazilian
Participation Group, the Carnegie Institution for Science, Carnegie Mellon
University, the Chilean Participation Group, the French Participation Group,
Harvard-Smithsonian Centre for Astrophysics, Instituto de Astrofísica de
Canarias, The Johns Hopkins University, Kavli Institute for the Physics and
Mathematics of the Universe (IPMU) / University of Tokyo, the Korean
Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut
für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA
Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-
Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatário Nacional / MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arisona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University.

The Legacy Surveys consist of three individual and complementary projects: the
Dark Energy Camera Legacy Survey (DECaLS; NOAO Proposal ID # 2014B-0404; PIs:
David Schlegel and Arjun Dey), the Beijing-Arisona Sky Survey (BASS; NOAO
Proposal ID # 2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band
Legacy Survey (MzLS; NOAO Proposal ID # 2016A-0453; PI: Arjun Dey). DECaLS,
BASS and MzLS together include data obtained, respectively, at the Blanco
telescope, Cerro Tololo Inter-American Observatory, National Optical Astronomy
Observatory (NOAO); the Bok telescope, Steward Observatory, University of
Arisona; and the Mayall telescope, Kitt Peak National Observatory, NOAO. The
Legacy Surveys project is honored to be permitted to conduct astronomical
research on Iolkam Du’ag (Kitt Peak), a mountain with particular significance
to the Tohono O’odham Nation.

NOAO is operated by the Association of Universities for Research in Astronomy
(AURA) under a cooperative agreement with the National Science Foundation.

This project used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Centre for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, Centre for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho
de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de
Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia,
Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Energeticas, Medioambientales y Tecnologicas-Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the Institut de
Fisica d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-
Maximilians Universitat Munchen and the associated Excellence Cluster
Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, the Ohio State University, the
University of Pennsylvania, the University of Portsmouth, SLAC National
Accelerator Laboratory, Stanford University, the University of Sussex, and
Texas A&M University.

BASS is a key project of the Telescope Access Program (TAP), which has been
funded by the National Astronomical Observatories of China, the Chinese
Academy of Sciences (the Strategic Priority Research Program "The Emergence of
Cosmological Structures" Grant # XDB09000000), and the Special Fund for
Astronomy from the Ministry of Finance. The BASS is also supported by the
External Cooperation Program of Chinese Academy of Sciences (Grant #
114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant #
11433005).

The Legacy Survey team makes use of data products from the Near-Earth Object
Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet
Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by
the National Aeronautics and Space Administration.

The Legacy Surveys imaging of the DESI footprint is supported by the Director,
Office of Science, Office of High Energy Physics of the U.S. Department of
Energy under Contract No. DE-AC02-05CH1123, by the National Energy Research
Scientific Computing Centre, a DOE Office of Science User Facility under the
same contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOAO.

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 Organisation (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 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/.

This paper is based on data collected at the Subaru Telescope and retrieved
from the HSC data archive system, which is operated by the Subaru Telescope
and Astronomy Data Centre (ADC) at NAOJ. Data analysis was in part carried out
with the cooperation of Centre for Computational Astrophysics (CfCA), NAOJ. We
are honoured and grateful for the opportunity of observing the Universe from
Maunakea, which has the cultural, historical, and natural significance in
Hawaii.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

## References

  * Abadi et al. (2003) Abadi M. G., Navarro J. F., Steinmetz M., Eke V. R., 2003, ApJ, 597, 21
  * Abraham & van Dokkum (2014) Abraham R. G., van Dokkum P. G., 2014, PASP, 126, 55
  * Aihara et al. (2022) Aihara H., et al., 2022, PASJ, 74, 247
  * Annis et al. (2014) Annis J., et al., 2014, ApJ, 794, 120
  * Atkinson et al. (2013) Atkinson A. M., Abraham R. G., Ferguson A. M. N., 2013, ApJ, 765, 28
  * Baes et al. (2024) Baes M., et al., 2024, A&A, 683, A182
  * Baldwin et al. (1980) Baldwin J. E., Lynden-Bell D., Sancisi R., 1980, MNRAS, 193, 313
  * Barrabés et al. (2017) Barrabés E., Cors J. M., Garcia-Taberner L., Ollé M., 2017, MNRAS, 472, 2554
  * Barrera-Ballesteros et al. (2015) Barrera-Ballesteros J. K., et al., 2015, A&A, 582, A21
  * Bell et al. (2003) Bell E. F., McIntosh D. H., Katz N., Weinberg M. D., 2003, ApJS, 149, 289
  * Belokurov et al. (2006) Belokurov V., et al., 2006, ApJ, 642, L137
  * Bertin & Arnouts (1996) Bertin E., Arnouts S., 1996, A&AS, 117, 393
  * Bignone et al. (2020) Bignone L. A., Pedrosa S. E., Trayford J. W., Tissera P. B., Pellizza L. J., 2020, MNRAS, 491, 3624
  * Bílek et al. (2020) Bílek M., et al., 2020, MNRAS, 498, 2138
  * Bizyaev et al. (2014) Bizyaev D. V., Kautsch S. J., Mosenkov A. V., Reshetnikov V. P., Sotnikova N. Y., Yablokova N. V., Hillyer R. W., 2014, ApJ, 787, 24
  * Blumenthal et al. (2020) Blumenthal K. A., et al., 2020, MNRAS, 492, 2075
  * Bottrell et al. (2019) Bottrell C., Simard L., Mendel J. T., Ellison S. L., 2019, MNRAS, 486, 390
  * Bournaud et al. (2005) Bournaud F., Combes F., Jog C. J., Puerari I., 2005, A&A, 438, 507
  * Bournaud et al. (2009) Bournaud F., Elmegreen B. G., Martig M., 2009, ApJ, 707, L1
  * Boylan-Kolchin et al. (2008) Boylan-Kolchin M., Ma C.-P., Quataert E., 2008, MNRAS, 383, 93
  * Bridge et al. (2010) Bridge C. R., Carlberg R. G., Sullivan M., 2010, ApJ, 709, 1067
  * Byrd & Howard (1992) Byrd G. G., Howard S., 1992, AJ, 103, 1089
  * Chilingarian et al. (2010) Chilingarian I. V., Di Matteo P., Combes F., Melchior A. L., Semelin B., 2010, A&A, 518, A61
  * Christensen et al. (2012) Christensen C., Quinn T., Governato F., Stilp A., Shen S., Wadsley J., 2012, MNRAS, 425, 3058
  * Comerón et al. (2011) Comerón S., et al., 2011, ApJ, 741, 28
  * Cooper et al. (2011) Cooper A. P., et al., 2011, ApJ, 743, L21
  * Cooper et al. (2013) Cooper A. P., D’Souza R., Kauffmann G., Wang J., Boylan-Kolchin M., Guo Q., Frenk C. S., White S. D. M., 2013, MNRAS, 434, 3348
  * Corbelli et al. (2014) Corbelli E., Thilker D., Zibetti S., Giovanardi C., Salucci P., 2014, A&A, 572, A23
  * Crain et al. (2015) Crain R. A., et al., 2015, MNRAS, 450, 1937
  * Daddi et al. (2007) Daddi E., et al., 2007, ApJ, 670, 156
  * Dalcanton & Bernstein (2002) Dalcanton J. J., Bernstein R. A., 2002, AJ, 124, 1328
  * Dey et al. (2019) Dey A., Schlegel D. J., Lang 2019, AJ, 157, 168
  * Dillamore et al. (2022) Dillamore A. M., Belokurov V., Font A. S., McCarthy I. G., 2022, MNRAS, 513, 1867
  * Dodge et al. (2023) Dodge B. C., Slone O., Lisanti M., Cohen T., 2023, MNRAS, 518, 2870
  * Domínguez Sánchez et al. (2023) Domínguez Sánchez H., et al., 2023, MNRAS, 521, 3861
  * Dubois et al. (2021) Dubois Y., et al., 2021, A&A, 651, A109
  * Duc (2017) Duc P.-A., 2017, in IAU Symposium. pp 180–182
  * Duc & Renaud (2013) Duc P.-A., Renaud F., 2013, in Souchay J., Mathis S., Tokieda T., eds, , Vol. 861, Lecture Notes in Physics, Berlin Springer Verlag. p. 327
  * Duc et al. (2014) Duc P. A., Cuillandre J. C., Karabal E., Cappellari M., Alatalo K., Blitz L., Bournaud F., 2014, MNRAS, 446, 120
  * Duc et al. (2015) Duc P.-A., et al., 2015, MNRAS, 446, 120
  * Ebrova (2013) Ebrova I., 2013, Phd thesis, Charles University in Prague
  * Fliri & Trujillo (2016) Fliri J., Trujillo I., 2016, MNRAS, 456, 1359
  * Font et al. (2011) Font A. S., et al., 2011, MNRAS, 417, 1260
  * Fry et al. (1999) Fry A. M., Morrison H. L., Harding P., Boroson T. A., 1999, AJ, 118, 1209
  * Gerin et al. (1990) Gerin M., Combes F., Athanassoula E., 1990, A&A, 230, 37
  * Gilhuly et al. (2020) Gilhuly C., et al., 2020, ApJ, 897, 108
  * Gilhuly et al. (2022) Gilhuly C., et al., 2022, ApJ, 932, 44
  * Gómez et al. (2017) Gómez F. A., White S. D. M., Grand R. J. J., Marinacci F., Springel V., Pakmor R., 2017, MNRAS, 465, 3446
  * Guzmán-Ortega et al. (2023) Guzmán-Ortega A., Rodriguez-Gomez V., Snyder G. F., Chamberlain K., Hernquist L., 2023, MNRAS, 519, 4920
  * Han et al. (2023a) Han J. J., Conroy C., Hernquist L., 2023a, Nature Astronomy, 7, 1481
  * Han et al. (2023b) Han J. J., Semenov V., Conroy C., Hernquist L., 2023b, ApJ, 957, L24
  * Hart et al. (2016) Hart R. E., et al., 2016, MNRAS, 461, 3663
  * Hendel & Johnston (2015) Hendel D., Johnston K. V., 2015, MNRAS, 454, 2472
  * Hernquist (1992) Hernquist L., 1992, ApJ, 400, 460
  * Ibata et al. (2001) Ibata R., Irwin M., Lewis G., Ferguson A. M. N., Tanvir N., 2001, Nature, 412, 49
  * Illingworth et al. (2013) Illingworth G. D., et al., 2013, ApJS, 209, 6
  * Ivezić et al. (2019) Ivezić Ž., et al., 2019, ApJ, 873, 111
  * Jackson et al. (2023) Jackson T. M., Pasquali A., La Barbera F., More S., Grebel E. K., 2023, MNRAS, 520, 1155
  * Janowiecki et al. (2010) Janowiecki S., Mihos J. C., Harding P., Feldmeier J. J., Rudick C., Morrison H., 2010, ApJ, 715, 972
  * Jara-Ferreira et al. (2024) Jara-Ferreira F., Tissera P. B., Sillero E., Rosas-Guevara Y., Pedrosa S. E., De Rossi M. E., Theuns T., Bignone L., 2024, MNRAS, 530, 1369
  * Jiang et al. (2014a) Jiang L., et al., 2014a, ApJS, 213, 12
  * Jiang et al. (2014b) Jiang L., et al., 2014b, ApJS, 213, 12
  * Johnston et al. (1996) Johnston K. V., Hernquist L., Bolte M., 1996, ApJ, 465, 278
  * Johnston et al. (2001) Johnston K. V., Sackett P. D., Bullock J. S., 2001, ApJ, 557, 137
  * Johnston et al. (2008) Johnston K. V., Bullock J. S., Sharma S., Font A., Robertson B. E., Leitner S. N., 2008, ApJ, 689, 936
  * Kado-Fong et al. (2018) Kado-Fong E., et al., 2018, ApJ, 866, 103
  * Kautsch et al. (2006) Kautsch S. J., Grebel E. K., Barazza F. D., Gallagher J. S. I., 2006, A&A, 445, 765
  * Kazantzidis et al. (2008) Kazantzidis S., Bullock J. S., Zentner A. R., Kravtsov A. V., Moustakas L. A., 2008, ApJ, 688, 254
  * Koda et al. (2015) Koda J., Yagi M., Yamanoi H., Komiyama Y., 2015, ApJ, 807, L2
  * Kormendy et al. (2009) Kormendy J., Fisher D. B., Cornell M. E., Bender R., 2009, ApJS, 182, 216
  * Kregel et al. (2002) Kregel M., van der Kruit P. C., de Grijs R., 2002, MNRAS, 334, 646
  * Kumar et al. (2021) Kumar A., Das M., Kataria S. K., 2021, MNRAS, 506, 98
  * Lee et al. (1999) Lee Y. W., Joo J. M., Sohn Y. J., Rey S. C., Lee H. C., Walker A. R., 1999, Nature, 402, 55
  * López-Corredoira et al. (2002) López-Corredoira M., Betancort-Rijo J., Beckman J. E., 2002, A&A, 386, 169
  * Majewski et al. (1999) Majewski S. R., Siegel M. H., Kunkel W. E., Reid I. N., Johnston K. V., Thompson I. B., Landolt A. U., Palma C., 1999, AJ, 118, 1709
  * Majewski et al. (2003) Majewski S. R., Skrutskie M. F., Weinberg M. D., Ostheimer J. C., 2003, ApJ, 599, 1082
  * Makarov et al. (2014) Makarov D., Prugniel P., Terekhova N., Courtois H., Vauglin I., 2014, A&A, 570, A13
  * Makarov et al. (2022) Makarov D., et al., 2022, MNRAS, 511, 3063
  * Mancillas et al. (2019a) Mancillas B., Duc P.-A., Combes F., Bournaud F., Emsellem E., Martig M., Michel-Dansac L., 2019a, A&A, 632, A122
  * Mancillas et al. (2019b) Mancillas B., Duc P.-A., Combes F., Bournaud F., Emsellem E., Martig M., Michel-Dansac L., 2019b, A&A, 632, A122
  * Marchuk et al. (2021) Marchuk A. A., Smirnov A. A., Mosenkov A. V., Il’in V. B., Gontcharov G. A., Savchenko S. S., Román J., 2021, MNRAS, 508, 5825
  * Marinacci et al. (2018) Marinacci F., et al., 2018, MNRAS, 480, 5113
  * Martin et al. (2022) Martin G., et al., 2022, MNRAS, 513, 1459
  * Martínez-Delgado et al. (2010) Martínez-Delgado D., et al., 2010, AJ, 140, 962
  * Martínez-Delgado et al. (2021) Martínez-Delgado D., et al., 2021, MNRAS, 506, 5030
  * Martínez-Delgado et al. (2023) Martínez-Delgado D., et al., 2023, A&A, 671, A141
  * Martínez-Lombilla & Knapen (2019) Martínez-Lombilla C., Knapen J. H., 2019, A&A, 629, A12
  * Mateo et al. (1998) Mateo M., Olszewski E. W., Morrison H. L., 1998, ApJ, 508, L55
  * McConnachie et al. (2009) McConnachie A. W., et al., 2009, Nature, 461, 66
  * Mihos et al. (1995) Mihos J. C., Walker I. R., Hernquist L., Mendes de Oliveira C., Bolte M., 1995, ApJ, 447, L87
  * Mihos et al. (2005) Mihos J. C., Harding P., Feldmeier J., Morrison H., 2005, ApJ, 631, L41
  * Miville-Deschênes et al. (2016) Miville-Deschênes M. A., Duc P. A., Marleau F., Cuillandre J. C., Didelon P., Gwyn S., Karabal E., 2016, A&A, 593, A4
  * Moiseev et al. (2011) Moiseev A. V., Smirnova K. I., Smirnova A. A., Reshetnikov V. P., 2011, MNRAS, 418, 244
  * Moore et al. (1999) Moore B., Ghigna S., Governato F., Lake G., Quinn T., Stadel J., Tozzi P., 1999, ApJ, 524, L19
  * Morales et al. (2018) Morales G., Martínez-Delgado D., Grebel E. K., Cooper A. P., Javanmardi B., Miskolczi A., 2018, A&A, 614, A143
  * Moretti et al. (2017) Moretti A., et al., 2017, A&A, 599, A81
  * Mosenkov et al. (2010) Mosenkov A. V., Sotnikova N. Y., Reshetnikov V. P., 2010, MNRAS, 401, 559
  * Mosenkov et al. (2015) Mosenkov A. V., Sotnikova N. Y., Reshetnikov V. P., Bizyaev D. V., Kautsch S. J., 2015, MNRAS, 451, 2376
  * Mosenkov et al. (2020a) Mosenkov A., et al., 2020a, MNRAS, 494, 1751
  * Mosenkov et al. (2020b) Mosenkov A. V., Smirnov A. A., Sil’chenko O. K., Rich R. M., Reshetnikov V. P., Kormendy J., 2020b, MNRAS, 497, 2039
  * Mosenkov et al. (2022a) Mosenkov A. V., Reshetnikov V. P., Skryabina M. N., Shakespear Z., 2022a, Research in Astronomy and Astrophysics, 22, 115003
  * Mosenkov et al. (2022b) Mosenkov A. V., et al., 2022b, MNRAS, 515, 5698
  * Mosenkov et al. (2024) Mosenkov A. V., Bahr S. K. H., Reshetnikov V. P., Shakespear Z., Smirnov D. V., 2024, A&A, 681, L15
  * Naiman et al. (2018) Naiman J. P., et al., 2018, MNRAS, 477, 1206
  * Nair & Abraham (2010) Nair P. B., Abraham R. G., 2010, ApJS, 186, 427
  * Nelson et al. (2018) Nelson D., et al., 2018, MNRAS, 475, 624
  * Nelson et al. (2019) Nelson D., et al., 2019, Computational Astrophysics and Cosmology, 6, 2
  * Oh et al. (2015) Oh S. H., Kim W.-T., Lee H. M., 2015, ApJ, 807, 73
  * Ostriker (1990) Ostriker J. P., 1990, in Kron R. G., ed., Astronomical Society of the Pacific Conference Series Vol. 10, Evolution of the Universe of Galaxies. pp 25–29
  * Peñarrubia et al. (2008) Peñarrubia J., Navarro J. F., McConnachie A. W., 2008, ApJ, 673, 226
  * Pedrosa et al. (2014) Pedrosa S. E., Tissera P. B., De Rossi M. E., 2014, A&A, 567, A47
  * Peng et al. (2002) Peng C. Y., Ho L. C., Impey C. D., Rix H.-W., 2002, AJ, 124, 266
  * Pillepich et al. (2015) Pillepich A., Madau P., Mayer L., 2015, ApJ, 799, 184
  * Pillepich et al. (2018) Pillepich A., et al., 2018, MNRAS, 475, 648
  * Pillepich et al. (2019) Pillepich A., et al., 2019, MNRAS, 490, 3196
  * Poliakov et al. (2021) Poliakov D., Mosenkov A. V., Brosch N., Koriski S., Rich R. M., 2021, MNRAS, 503, 6059
  * Pop et al. (2018) Pop A.-R., Pillepich A., Amorisco N. C., Hernquist L., 2018, MNRAS, 480, 1715
  * Prieur (1990) Prieur J. L., 1990, in Wielen R., ed., , Dynamics and Interactions of Galaxies. Berlin, pp 72–83
  * Putman et al. (1998) Putman M. E., et al., 1998, Nature, 394, 752
  * Qu et al. (2011) Qu Y., Di Matteo P., Lehnert M. D., van Driel W., 2011, A&A, 530, A10
  * Quinn et al. (1993) Quinn P. J., Hernquist L., Fullagar D. P., 1993, ApJ, 403, 74
  * Reshetnikov & Combes (1996) Reshetnikov V., Combes F., 1996, A&AS, 116, 417
  * Reshetnikov & Combes (1997) Reshetnikov V., Combes F., 1997, A&A, 324, 80
  * Reshetnikov & Combes (1998) Reshetnikov V., Combes F., 1998, A&A, 337, 9
  * Reshetnikov & Combes (2015) Reshetnikov V., Combes F., 2015, MNRAS, 447, 2287
  * Reshetnikov & Mosenkov (2019) Reshetnikov V. P., Mosenkov A. V., 2019, MNRAS, 483, 1470
  * Reshetnikov & Sotnikova (1997) Reshetnikov V., Sotnikova N., 1997, A&A, 325, 933
  * Reshetnikov et al. (2002) Reshetnikov V., Battaner E., Combes F., Jiménez-Vicente J., 2002, A&A, 382, 513
  * Reshetnikov et al. (2016) Reshetnikov V. P., Mosenkov A. V., Moiseev A. V., Kotov S. S., Savchenko S. S., 2016, MNRAS, 461, 4233
  * Rich et al. (2012) Rich R. M., Collins M. L. M., Black C. M., Longstaff F. A., Koch A., Benson A., Reitzel D. B., 2012, Nature, 482, 192
  * Rich et al. (2019) Rich R. M., et al., 2019, MNRAS, 490, 1539
  * Román et al. (2020) Román J., Trujillo I., Montes M., 2020, A&A, 644, A42
  * Sales et al. (2012) Sales L. V., Navarro J. F., Theuns T., Schaye J., White S. D. M., Frenk C. S., Crain R. A., Dalla Vecchia C., 2012, MNRAS, 423, 1544
  * Sánchez-Saavedra et al. (1990) Sánchez-Saavedra M. L., Battaner E., Florido E., 1990, MNRAS, 246, 458
  * Sancisi et al. (2008) Sancisi R., Fraternali F., Oosterloo T., van der Hulst T., 2008, A&ARv, 15, 189
  * Sanders et al. (2018) Sanders J. L., Evans N. W., Dehnen W., 2018, MNRAS, 478, 3879
  * Schaye et al. (2015) Schaye J., et al., 2015, MNRAS, 446, 521
  * Schwarzkopf & Dettmar (2000) Schwarzkopf U., Dettmar R. J., 2000, A&AS, 144, 85
  * Schwarzkopf & Dettmar (2001) Schwarzkopf U., Dettmar R. J., 2001, A&A, 373, 402
  * Semczuk et al. (2020) Semczuk M., Łokas E. L., D’Onghia E., Athanassoula E., Debattista V. P., Hernquist L., 2020, MNRAS, 498, 3535
  * Sersic (1968) Sersic J. L., 1968, Atlas de Galaxias Australes. Córdoba: Obs. Astronómico
  * Simmons et al. (2017) Simmons B. D., et al., 2017, MNRAS, 464, 4420
  * Smirnov et al. (2023) Smirnov A. A., et al., 2023, MNRAS, 519, 4735
  * Smith et al. (2010) Smith B. J., Giroux M. L., Struck C., Hancock M., 2010, AJ, 139, 1212
  * Sola et al. (2022) Sola E., et al., 2022, A&A, 662, A124
  * Sollima et al. (2010) Sollima A., Gil de Paz A., Martinez-Delgado D., Gabany R. J., Gallego-Laborda J. J., Hallas T., 2010, A&A, 516, A83
  * Somerville & Davé (2015) Somerville R. S., Davé R., 2015, ARA&A, 53, 51
  * Sparke & Casertano (1988) Sparke L. S., Casertano S., 1988, MNRAS, 234, 873
  * Springel et al. (2018) Springel V., et al., 2018, MNRAS, 475, 676
  * Statler (1988) Statler T. S., 1988, ApJ, 331, 71
  * Tanaka et al. (2023) Tanaka M., et al., 2023, PASJ, 75, 986
  * Thuan & Seitzer (1979) Thuan T. X., Seitzer P. O., 1979, ApJ, 231, 680
  * Toomre & Toomre (1972) Toomre A., Toomre J., 1972, ApJ, 178, 623
  * Toth & Ostriker (1992) Toth G., Ostriker J. P., 1992, ApJ, 389, 5
  * Trujillo & Fliri (2016) Trujillo I., Fliri J., 2016, ApJ, 823, 123
  * Valenzuela & Remus (2022) Valenzuela L. M., Remus R.-S., 2022, arXiv e-prints, p. arXiv:2208.08443
  * Velazquez & White (1999) Velazquez H., White S. D. M., 1999, MNRAS, 304, 254
  * Verley et al. (2007) Verley S., et al., 2007, A&A, 470, 505
  * Villalobos & Helmi (2008) Villalobos Á., Helmi A., 2008, MNRAS, 391, 1806
  * Villalobos & Helmi (2009) Villalobos Á., Helmi A., 2009, MNRAS, 399, 166
  * Walker et al. (1996) Walker I. R., Mihos J. C., Hernquist L., 1996, ApJ, 460, 121
  * Ward et al. (2022) Ward S. R., Harrison C. M., Costa T., Mainieri V., 2022, MNRAS, 514, 2936
  * Weinberg & Blitz (2006) Weinberg M. D., Blitz L., 2006, ApJ, 641, L33
  * Whitmore et al. (1990) Whitmore B. C., Lucas R. A., McElroy D. B., Steiman-Cameron T. Y., Sackett P. D., Olling R. P., 1990, AJ, 100, 1489
  * Whitney et al. (2020) Whitney A., Conselice C. J., Duncan K., Spitler L. R., 2020, ApJ, 903, 14
  * Woods & Geller (2007) Woods D. F., Geller M. J., 2007, AJ, 134, 527
  * Woods et al. (2006) Woods D. F., Geller M. J., Barton E. J., 2006, AJ, 132, 197
  * Yang et al. (2007) Yang X., Mo H. J., van den Bosch F. C., Pasquali A., Li C., Barden M., 2007, ApJ, 671, 153
  * Yesuf et al. (2021) Yesuf H. M., Ho L. C., Faber S. M., 2021, ApJ, 923, 205
  * Yoon & Lim (2020) Yoon Y., Lim G., 2020, ApJ, 905, 154
  * York et al. (2000) York D. G., et al., 2000, AJ, 120, 1579
  * Zaritsky & Rix (1997) Zaritsky D., Rix H.-W., 1997, ApJ, 477, 118
  * Zaritsky et al. (2021) Zaritsky D., Donnerstein R., Karunakaran A., Barbosa C. E., Dey A., Kadowaki J., Spekkens K., Zhang H., 2021, ApJS, 257, 60
  * Zee et al. (2022) Zee W.-B. G., Yoon S.-J., Moon J.-S., An S.-H., Paudel S., Yun K., 2022, ApJ, 935, 48
  * de Grijs (1998) de Grijs R., 1998, MNRAS, 299, 595
  * van Dokkum et al. (2015) van Dokkum P. G., Abraham R., Merritt A., Zhang J., Geha M., Conroy C., 2015, ApJ, 798, L45
  * van Dokkum et al. (2019) van Dokkum P., et al., 2019, ApJ, 883, L32
  * van der Kruit (1979) van der Kruit P. C., 1979, A&AS, 38, 15
  * van der Kruit & Searle (1981) van der Kruit P. C., Searle L., 1981, A&A, 95, 105

## Appendix A

Table 3:  Sub-sample of galaxies with tidal structures.

Name | R.A. | Dec. | PA | Structure | $q$ | $C_{0}$
---|---|---|---|---|---|---
| $\degree$ | $\degree$ | $\degree$ |  |  |
ES_0.756_-0.317 | 0.75613 | -0.31716 | 1.6 | 6 | 0.22 | -0.19
ES_1.870_0.902 | 1.87010 | 0.90169 | 24.0 | 6 | 0.35 | -0.65
ES_2.265_-0.583⋆ | 2.26488 | -0.58253 | -32.2 | 1 | 0.25 | 1.54
ES_7.350_0.316 | 7.35044 | 0.31575 | 22.6 | 5 | 0.21 | -0.52
ES_13.728_0.434 | 13.72821 | 0.43372 | 77.9 | 5 | 0.18 | 0.93
ES_14.082_-0.126 | 14.08171 | -0.12576 | -14.1 | 6 | 0.29 | 0.13
ES_15.846_-0.469 | 15.84552 | -0.46923 | -82.9 | 2 | 0.30 | 0.28
ES_17.089_0.044 | 17.08944 | 0.04368 | -14.8 | 1 | 0.28 | -0.15
ES_18.239_-0.345⋆ | 18.23926 | -0.34500 | -73.6 | 1, 2 | 0.31 | -0.10
ES_18.624_0.215 | 18.62440 | 0.21522 | 53.0 | 1 | 0.25 | 0.09
ES_19.434_0.254 | 19.43399 | 0.25434 | -64.7 | 2 | 0.43 | 0.05
ES_19.677_1.135 | 19.67695 | 1.13460 | -69.2 | 6 | 0.29 | 0.6
ES_20.130_0.786 | 20.13038 | 0.78572 | -28.7 | 5 | 0.20 | -0.72
ES_20.271_0.103 | 20.27080 | 0.10292 | 33.0 | 1 | 0.22 | 0.62
ES_21.171_0.081 | 21.17076 | 0.08109 | -50.6 | 3, 6 | 0.15 | 0.83
ES_23.504_-0.537 | 23.50383 | -0.53683 | -73.8 | 4 | 0.30 | -0.16
ES_24.765_0.437 | 24.76539 | 0.43667 | -20.7 | 5 | 0.21 | -0.15
ES_28.265_1.023 | 28.26460 | 1.02305 | 75.0 | 1 | 0.28 | 0.64
ES_29.743_-0.490 | 29.74327 | -0.48984 | -38.9 | 3 | 0.51 | -0.94
ES_30.191_-0.908 | 30.19102 | -0.90786 | 57.3 | 3 | 0.18 | 0.37
ES_30.259_0.031 | 30.25862 | 0.03129 | 50.4 | 3 | 0.16 | 0.46
ES_31.960_-0.384 | 31.96020 | -0.38421 | 2.8 | 1 | 0.28 | -0.51
ES_31.972_-0.028 | 31.97232 | -0.02835 | -34.6 | 1 | 0.31 | -0.58
ES_32.794_-0.517 | 32.79416 | -0.51687 | -52.2 | 1 | 0.22 | -0.11
ES_37.936_-0.945⋆ | 37.93556 | -0.94535 | -48.6 | 2 | 0.38 | -0.49
ES_38.657_-0.980 | 38.65716 | -0.97985 | -36.1 | 4 | 0.31 | -0.15
ES_41.525_0.564 | 41.52514 | 0.56355 | 46.7 | 6 | 0.28 | -0.25
ES_43.963_0.564 | 43.96324 | 0.56408 | 39.5 | 3 | 0.30 | -0.37
ES_47.102_-0.559 | 47.10241 | -0.55866 | 14.0 | 5 | 0.15 | -0.72
ES_49.360_-0.094⋆ | 49.36040 | -0.09421 | 117.0 | 5 | 0.28 | 0.39
ES_52.605_0.274 | 52.60547 | 0.27378 | -90.4 | 3 | 0.40 | -0.56
ES_53.382_0.699⋆ | 53.38157 | 0.69928 | 14.5 | 4 | 0.33 | 0.40
ES_311.043_-0.415 | 311.04300 | -0.41547 | 327.0 | 1 | 0.20 | -0.57
ES_314.206_-0.238⋆ | 314.20637 | -0.23774 | -5.2 | 1 | 0.29 | -0.15
ES_315.137_0.294 | 315.13693 | 0.29442 | 16.4 | 4 | 0.26 | -0.65
ES_316.508_-0.504⋆ | 316.50807 | -0.50361 | 36.9 | 4 | 0.32 | -0.62
ES_319.092_-0.730 | 319.09166 | -0.73014 | -35.1 | 1 | 0.17 | 0.10
ES_323.211_1.153 | 323.21103 | 1.15324 | 15.8 | 6 | 0.31 | -0.43
ES_325.543_-0.288 | 325.54260 | -0.28770 | 65.3 | 1,3 | 0.44 | 0.02
ES_327.676_0.912⋆ | 327.67642 | 0.91201 | -59.1 | 6 | 0.52 | 0.14
ES_330.520_-0.382 | 330.52009 | -0.38229 | -40.6 | 4 | 0.25 | -0.23
ES_336.825_-0.682 | 336.82471 | -0.68212 | 4.3 | 1 | 0.24 | 0.54
ES_337.223_0.771 | 337.22315 | 0.77054 | -27.3 | 2 | 0.35 | -0.72
ES_339.889_0.411 | 339.88871 | 0.41084 | -82.9 | 4 | 0.25 | -0.03
ES_344.086_0.487 | 344.08555 | 0.48698 | 82.8 | 4 | 0.25 | -0.24
ES_344.174_0.162 | 344.17380 | 0.16169 | 99.2 | 3 | 0.36 | -0.33
ES_350.008_-0.102 | 350.00776 | -0.10197 | 38.6 | 1 | 0.26 | -0.40
ES_350.832_-0.500 | 350.83207 | -0.49982 | -5.6 | 3 | 0.19 | -0.19
ES_353.011_1.223 | 353.01133 | 1.22329 | 13.5 | 5 | 0.24 | -0.17
ES_354.826_-0.643 | 354.82611 | -0.64319 | 80.5 | 2 | 0.29 | -0.44

Notes: Parameters of the galaxies in the table are Galaxy name, Right
ascension (J2000), Declination (J2000), Position angle, the type of structures
in accordance with the classification (1 – tidal tails, 2 – diffuse shells, 3
– bridges, 4 – arcs, 5 – satellites or satellite remnants, 6 – disk
deformations), the apparent axis ratio of the modelling disk, the model disk
boxyness/diskyness parameter. A star symbol ⋆ marks a galaxy which is
contained within or near the Milky Way’s cirrus cloud or filaments.

Table 4:  Sub-sample of galaxies with structural features.

Name | R.A. | Dec. | PA | Structure | $q$ | $C_{0}$
---|---|---|---|---|---|---
| $\degree$ | $\degree$ | $\degree$ |  |  |
ES82_1.870_0.902 | 1.8701 | 0.90169 | 24 | 1 | 0.35 | -0.66
ES82_5.724_-0.997 | 5.72384 | -0.99712 | -53 | 1, 2 | 0.49 | -0.65
ES82_6.036_0.379 | 6.03629 | 0.37913 | 61.3 | 1 | 0.25 | -0.97
ES82_10.574_0.371 | 10.57439 | 0.3707 | 63.16 | 2 | 0.28 | -0.39
ES82_13.396_0.596 | 13.3955 | 0.59626 | -43.9 | 2 | 0.38 | -0.55
ES82_16.599_-0.170 | 16.59915 | -0.16965 | 43.1 | 2 | 0.33 | -0.76
ES82_17.693_0.793 | 17.69276 | 0.79335 | 9.7 | 2 | 0.24 | -0.51
ES82_17.898_0.462 | 17.898 | 0.46228 | 88.29 | 2 | 0.19 | 0.07
ES82_19.468_0.781 | 19.46848 | 0.78079 | 3.7 | 2 | 0.28 | -0.4
ES82_22.977_0.492 | 22.97732 | 0.49202 | 15.5 | 2 | 0.17 | -0.34
ES82_23.639_-0.430 | 23.6386 | -0.4303 | 40.4 | 2 | 0.3 | -0.89
ES82_23.752_-0.451 | 23.75164 | -0.45117 | 14.7 | 2 | 0.33 | -0.56
ES82_24.469_1.043 | 24.46947 | 1.04303 | -57.4 | 2 | 0.32 | -0.59
ES82_25.149_0.259 | 25.14949 | 0.25854 | 45.96 | 1 | 0.16 | 0
ES82_27.115_0.394 | 27.11468 | 0.39393 | 2 | 2 | 0.41 | -0.79
ES82_27.561_0.062 | 27.56087 | 0.06211 | 21.6 | 2 | 0.24 | -0.46
ES82_28.265_1.023 | 28.2646 | 1.02305 | 74.99 | 1 | 0.28 | -0.04
ES82_28.698_-0.724 | 28.69831 | -0.7235 | -49.7 | 2 | 0.42 | -0.64
ES82_29.237_1.168 | 29.23671 | 1.16805 | 54.4 | 2 | 0.31 | -0.3
ES82_29.743_-0.490 | 29.74327 | -0.48984 | -38.9 | 3 | 0.51 | -0.94
ES82_30.181_1.019 | 30.18109 | 1.01942 | 15.7 | 2 | 0.25 | -1.13
ES82_30.569_-0.533 | 30.56906 | -0.53304 | 64.4 | 2 | 0.15 | -0.41
ES82_31.245_-0.264 | 31.24546 | -0.26359 | 89 | 2 | 0.17 | -0.78
ES82_32.722_-0.921 | 32.72181 | -0.92063 | 2.44 | 2 | 0.11 | 0.44
ES82_32.777_-0.655 | 32.77656 | -0.65528 | 17.38 | 1, 2 | 0.21 | 0.04
ES82_33.789_-0.704 | 33.78917 | -0.70357 | -26 | 2 | 0.15 | -0.69
ES82_36.641_-1.108 | 36.64127 | -1.10789 | 49.1 | 1 | 0.25 | 0.12
ES82_37.911_-1.083 | 37.9107 | -1.08262 | 84.17 | 2 | 0.33 | -0.42
ES82_39.177_-0.017 | 39.17708 | -0.01708 | 70.1 | 2 | 0.28 | -0.67
ES82_40.079_0.440 | 40.0789 | 0.43967 | 22 | 1 | 0.22 | -0.02
ES82_42.143_-0.993 | 42.14331 | -0.99324 | -1.5 | 2 | 0.3 | -0.93
ES82_46.894_-1.049 | 46.89375 | -1.04942 | -21.9 | 2 | 0.45 | -0.4
ES82_49.642_-0.362 | 49.64189 | -0.36224 | 25.6 | 2 | 0.38 | -0.85
ES82_56.608_-0.599 | 56.60797 | -0.59911 | -14.7 | 2 | 0.26 | -1.04
ES82_313.353_0.652 | 313.3526 | 0.65198 | 18.69 | 2 | 0.19 | -0.55
ES82_314.393_0.341 | 314.39313 | 0.34109 | -84.1 | 2 | 0.22 | -0.88
ES82_319.276_-0.627 | 319.276 | -0.62669 | 76 | 1 | 0.2 | -0.8
ES82_320.078_-1.093 | 320.07803 | -1.09339 | 81.5 | 1 | 0.4 | -0.48
ES82_320.151_1.212 | 320.15142 | 1.21234 | 32.52 | 2 | 0.3311 | -0.58
ES82_326.305_-0.186 | 326.30545 | -0.18557 | -84.68 | 2 | 0.29 | 0.17
ES82_326.580_-0.208 | 326.57991 | -0.20788 | 29.5 | 3 | 0.39 | -0.77
ES82_331.378_0.077 | 331.37818 | 0.07724 | 25.59 | 2 | 0.31 | -0.75
ES82_333.748_1.020 | 333.7481 | 1.01956 | -17.15 | 3 | 0.51 | -0.67
ES82_336.167_-0.897 | 336.16729 | -0.89715 | -23.1 | 2 | 0.42 | -0.59
ES82_336.384_0.039 | 336.38395 | 0.03903 | -5.7 | 2 | 0.35 | -0.52
ES82_339.008_-0.560 | 339.0076 | -0.56015 | 68.3 | 2 | 0.26 | -0.43
ES82_340.030_-0.818 | 340.03024 | -0.81837 | -33.8 | 2 | 0.29 | -0.01
ES82_341.096_-0.114 | 341.09551 | -0.11431 | -0.1 | 2 | 0.21 | -0.44
ES82_346.594_-0.822 | 346.59386 | -0.82193 | 16.26 | 2 | 0.12 | -0.09
ES82_347.324_0.064 | 347.32405 | 0.06416 | -55.3 | 2 | 0.23 | -0.86
ES82_347.624_0.273 | 347.62387 | 0.27306 | 84.5 | 2 | 0.27 | -0.38
ES82_349.019_-0.123 | 349.01868 | -0.12261 | 7.99 | 2 | 0.13 | 0.05
ES82_351.140_-0.731 | 351.13954 | -0.73058 | -30.2 | 2 | 0.36 | -0.42
ES82_352.972_-0.827 | 352.97156 | -0.8265 | 108 | 2 | 0.16 | -0.62
ES82_353.011_1.223 | 353.01133 | 1.22329 | 13.5 | 1 | 0.25 | -0.41
ES82_355.229_-1.074 | 355.22855 | -1.07404 | 33.7 | 2 | 0.3 | -0.56

Notes: Parameters of the galaxies in the table: Galaxy name, Right ascension
(J2000), Declination (J2000), Position angle, The type of structures in
accordance with the classification of structures given in the chapter of the
same name (1 - lopsided discs , 2 - disks with warps, 3 - polar rings), the
apparent axis ratio of the modelling disk, the model disk boxyness/diskyness.

Table 5:  The structural parameters of edge-on galaxies from ES82.

Name | R.A. | Dec. | PA | $z$ | $M_{r}$ | Structure | Tidal | is_edge_on | isoA_r | isoB_r | $q$ | $C_{0}$
---|---|---|---|---|---|---|---|---|---|---|---|---
| $\degree$ | $\degree$ | $\degree$ |  | mag |  |  |  | arcsec | arcsec |  |
ES82_0.048_-0.644 | 0.04837 | -0.64402 | -62.7 | 0.14 | -22.094 | False | False | 2 | 10.29 | 3.48 | 0.25 | -0.1
ES82_0.418_1.092 | 0.41752 | 1.09196 | 18.6 | 0.061 | -21.451 | False | False | 4 | 18.54 | 9.19 | 0.49 | -0.35
ES82_0.679_-0.409 | 0.67949 | -0.40948 | -51.5 | 0.084 | -20.522 | False | False | 2 | 16.91 | 2.88 | 0.17 | -0.1
ES82_0.722_0.947 | 0.72167 | 0.94712 | -66.88 | 0.054 | -19.47 | False | False | 2 | 18.48 | 2.8 | 0.2 | 0.14
ES82_0.756_-0.317 | 0.75613 | -0.31716 | 1.6 | 0.084 | -21.493 | True | True | 1 | 16.91 | 4.43 | 0.25 | -0.19
ES82_0.836_-0.527 | 0.83576 | -0.52669 | -8 | 0.076 | -20.559 | False | False | 4 | 7.45 | 5.04 | 0.53 | -0.51
… |  |  |  |  |  |  |  |  |  |  |  |

Notes: Parameters of galaxies from the catalog ES 82: Galaxy id in the
catalog, R.A. (J2000) in decimal degrees, Dec. (J2000) in decimal degrees,
position angle, SDSS redshift, absolute magnitude in the $r$ band, boolean
parameter characterizing the presence of any distinctive structures (see text)
in the galaxy, boolean parameter characterizing the presence of tidal
structures (see text) in the galaxy, galaxy group (1–4, see text), SDSS
isophotal major axis in the $r$ band in arcseconds, SDSS isophotal minor axis
in the $r$ band in arcseconds, disk apparent axis ratio, boxyness/diskyness
parameter. Table is published in its entirety in the electronic edition.

Figure 10: A series of six stacked strips showing the Milky Way’s cirrus
clouds where the purple boxed circles show where each galaxy within our
catalogue is located. Each strip, going from left to right, covers
approximately 18 degrees of the sky. This covers a total of 110 degrees in
R.A. The R.A. ranges from 60$\degree$ to 0$\degree$ which includes the first
three strips and then 360$\degree$ to 310$\degree$ which includes the last
three strips. The Dec. ranges from -1.25$\degree$ to 1.25$\degree$. These
images are constructed from a single image (available on
https://physics.byu.edu/faculty/mosenkov/docs/cirrus_wcs.fits) that spans the
entire SDSS Stripe 82 (Smirnov et al., 2023). 64 (red circles) out of 838
galaxies fall within or near a cirrus cloud. The seven green circles represent
the galaxies that have tidal features. The one green diamond represents the
galaxy that was removed as a tidal feature candidate.