11institutetext: Instituto de Astrofísica de Canarias, c/ Vía Láctea s/n,
E-38205, La Laguna, Tenerife, Spain 22institutetext: Departamento de
Astrofísica, Universidad de La Laguna, E-38206, La Laguna, Tenerife, Spain
33institutetext: Instituto de Astrofísica de Andalucía (CSIC), Granada, Spain
44institutetext: Kapteyn Astronomical Institute, University of Groningen, PO
Box 800, NL-9700 AV Groningen, the Netherlands 55institutetext: Department of
Physics & Astronomy, University of California Los Angeles, 430 Portola Plaza,
Los Angeles, CA 90095-1547, USA 66institutetext: Departamento de Física
Teórica y del Cosmos Universidad de Granada, 18071 Granada, Spain
77institutetext: Instituto Universitario Carlos I de Física Teórica y
Computacional, Universidad de Granada, 18071 Granada, Spain 88institutetext:
ESA NEO Coordination Centre, Via Galileo Galilei, 00044 Frascati (RM), Italy
99institutetext: GMV, Isaac Newton 11, Tres Cantos, 28760 Madrid, Spain
1010institutetext: Centro de Astronomía (CITEVA), Universidad de Antofagasta,
Avda. U. de Antofagasta 02800, Antofagasta, Chile

# The AMIGA sample of isolated galaxies

XIV. Disc breaks and interactions through ultra-deep optical imaging

P. M. Sánchez-Alarcón , 1122<EMAIL_ADDRESS>J. Román , 11223344
<EMAIL_ADDRESS>J. H. Knapen 1122 L. Verdes-Montenegro 33 S. Comerón
2211 R. M. Rich 55 J. E. Beckman 1122 M. Argudo-Fernández 6677 P. Ramírez-
Moreta 8899 J. Blasco 66 E. Unda-Sanzana 1010 J. Garrido 33 S. Sánchez-
Exposito 33

###### Abstract

Context. In the standard cosmological model of galaxy evolution, mergers and
interactions play a fundamental role in shaping galaxies. Galaxies that are
currently isolated are thus interesting, allowing us to distinguish between
internal and external processes affecting the galactic structure. However,
current observational limits may obscure crucial information in the low-mass
or low-brightness regime.

Aims. We use optical imaging of a subsample of the AMIGA catalogue of isolated
galaxies to explore the impact of different factors on the structure of these
galaxies. In particular, we study the type of disc break as a function of the
degree of isolation and the presence of interaction indicators like tidal
streams or plumes which are only detectable in the ultra-low surface
brightness regime.

Methods. We present ultra-deep optical imaging in the r-band of a sample of 25
low-redshift ($z<0.035$) isolated galaxies. Through careful data processing
and analysis techniques, the nominal surface brightness limits achieved are
comparable to those to be obtained on the 10-year LSST coadds
($\mu_{r,\textrm{lim}}$ $\gtrsim$ 29.5 $\textrm{mag\leavevmode\nobreak\
arcsec}^{-2}$ [3$\sigma$; 10”$\times$10”]). We place special emphasis on
preserving the low surface brightness features throughout the processing.

Results. The extreme depth of our imaging allows us to study the interaction
signatures of 20 galaxies, given that the presence of Galactic cirrus is a
strong limiting factor in the characterisation of interactions for the
remaining 5 of them. We detect previously unreported interaction features in 8
(40%$\pm$14%) galaxies in our sample. We identify 9 galaxies (36%$\pm$10%)
showing an exponential disc (Type I), 14 galaxies (56%$\pm$10%) with down-
bending (Type II) profile and only 2 galaxies (8%$\pm$5%) with up-bending
(Type III) profiles. Isolated galaxies have considerably more purely
exponential discs and fewer up-bending surface brightness profiles than field
or cluster galaxies. We find clear minor merger activity in some of the
galaxies with single exponential or down-bending profiles, and both of the
galaxies with up-bending profiles show signatures of a past interaction.

Conclusions. We show the importance of ultra-deep optical imaging in revealing
the presence of faint external features in galaxies which indicate a probable
history of interaction. We confirm that up-bending profiles are likely
produced by major mergers while down-bending profiles are probably formed by a
threshold in star formation. Unperturbed galaxies, evolving slowly with a low
star formation rate could induce the high rate of Type I discs in isolated
galaxies.

###### Key Words.:

galaxies: evolution - galaxies: photometry - galaxies: spiral - galaxies:
structure - galaxies: interactions

##  1 Introduction

Present-day galactic discs are snapshots of galaxy evolution resulting from
galaxy formation and evolution through cosmic time. The study of galaxies with
a variety of morphologies, evolutionary stages, and environments helps us to
assemble a global picture to explain all the observed features. One of the
simplest, yet most effective ways to classify galactic structures is through
their surface brightness profiles. These profiles were initially characterised
with a single exponential decay by Patterson (1940) and de Vaucouleurs (1958),
but the current view is considerably more complex. Following the observation
of breaks in profiles by van der Kruit (1979) and van der Kruit & Searle
(1981, 1981b) at the outer regions of the edge-on galaxies, work by Erwin et
al. (2005) and Pohlen & Trujillo (2006) considered breaks over a range of
galactocentric radii and in less-inclined galaxies. They established a
classification based on the global shape of the disk profile: Type I or pure
exponential for profiles with no breaks, Type II or down-bending profiles with
outer slopes steeper than the inner ones (e.g. Freeman, 1970; Pohlen et al.,
2002) and Type III or up-bending profiles where the exponential decline is
steeper in the inner part of the disc that in the outer part (e.g. Erwin et
al., 2005). This classification has been helpful since galaxies show different
average properties for each type, suggesting a different origin or evolution.

One of the most characteristic features in discs is the drastic change in age
around the break radius, noticed as a ”U-shape” in the colour profiles, while
the mass surface density profile remains relatively constant (e.g. Azzollini
et al., 2008; Bakos et al., 2008; Bakos & Trujillo, 2012; Martín-Navarro et
al, 2012; Zheng et al., 2015; Watkins et al., 2016; Ruiz-Lara et al., 2016).
This observational feature has been tentatively explained as the result of gas
accretion plus a density threshold in the star formation, and subsequent
redistribution of mass by radial migration (e.g Debattista et al., 2006;
Roškar et al., 2008; Martínez-Serrano et al, 2009) which has been described as
inside-out formation of the disc (Sánchez-Blázquez et al., 2009).

The environment appears to play a key role in the frequency of each break type
(e.g. Pranger et al., 2017; Watkins et al., 2019). In general, high-density
environments favour up-bending Type III profiles (see Maltby et al, 2012).
This is not surprising, given that the environment is one of the most
influential factors in shaping galactic morphology (e.g., Balogh et al., 2004;
Thomas et al., 2005; Baldry et al., 2006; Erwin et al., 2012). However,
internal processes (e.g., Kormendy & Kennicutt, 2004) or the accretion of cold
gas (Bosma, 2017) are also capable of transforming the characteristics of the
galaxies. Correlations between the type of break (in particular the Type III
fraction) with internal parameters (Herpich et al., 2017; Wang et al., 2018),
and possible interactions (Eliche-Moral et al., 2015; Borlaff et al., 2018)
are also found. Adding more complexity, instrumental effects including
background subtraction or scattered light can have a significant effect on the
photometric profiles, especially at extremely low surface brightness (Sandin,
2014). This means that determining the specific impact of different processes
is not a straightforward task. A possible approach is to study isolated
galaxies, excluding or diminishing the impact of environmental processes
(e.g., Karachentseva, 1973; Huchra & Thuan, 1977; Arakelian & Magtesian, 1981;
Schwarzkopf & Dettmar, 2001; Varela et al., 2004).

Determining and quantifying the isolation of a galaxy is not a simple task.
The Analysis of the interstellar Medium of Isolated GAlaxies (AMIGA) Project
(Verdes-Montenegro et al., 2005) is an exhaustive study of galaxies isolated
from major companions, based on the original catalogue of isolated galaxies
(CIG) presented by Karachentseva (1973) and later revised and quantified by
Verley et al. (2007a, b) and Argudo-Fernández et al. (2013). Despite the
efforts shown in these works to quantify minor interaction features, low
signal-to-noise spectroscopic and imaging surveys may fail to identify the
presence of faint surface brightness satellites around galaxies classified as
isolated. In fact, numerical simulations based on the $\Lambda$-CDM
cosmological paradigm predict an average of one low surface brightness feature
per galaxy due to minor interactions at a surface brightness level of $\mu$ =
29 $\textrm{mag\,arcsec}^{-2}$ (Johnston et al., 2001) and we can expect many
galaxy features fainter than $\mu=30\,\textrm{mag\,arcsec}^{-2}$ (Johnston et
al., 2008).

The interest in low surface brightness science is confronted with significant
challenges due to numerous observational limitations. Advances have been made
in recent years in developing deep optical surveys (e.g., Laine et al., 2014;
Abraham & van Dokkum, 2014; Fliri & Trujillo, 2016; Dark Energy Survey
Collaboration et al., 2016; Román & Trujillo, 2018; Aihara et al., 2018;
Martínez-Delgado, 2019; Trujillo et al., 2021), characterising scattered light
(e.g., Slater et al., 2009; Karabal et al., 2017; Infante-Sainz et al., 2020),
improving observational (Jablonka et al., 2010; Duc et al., 2015; Mihos et
al., 2017; Trujillo & Fliri, 2016; Staudaher et al., 2019) and data processing
techniques (Jiang et al., 2014; Trujillo & Fliri, 2016; Borlaff et al., 2019;
Haigh et al., 2021), and more (see review by Mihos, 2019). Indeed,
increasingly sophisticated studies are able to reveal the presence of
satellites (Laine et al., 2014; Mihos et al., 2015; Román et al., 2021) and
tidal features (Laine et al., 2014; Martínez-Delgado, 2019; Martínez-Delgado
et al., 2023; Huang & Fan, 2022; Román et al., 2023) at increasingly lower
surface brightness, but a long way remains to correctly detect and classify
all the structures predicted by simulations (see Martin et al., 2022, and
references therein).

In this work, we carry out an ultra-deep imaging study of isolated galaxies
from the AMIGA catalogue in order to shed light on the structural differences
between these isolated galaxies and galaxies in higher-density environments.
In particular, we are interested in: 1) the types of breaks in the discs of
isolated galaxies in comparison with those in higher-density environments.
This is something not yet done in the literature for isolated galaxies, and so
far has only been carried out comparing higher-density environments such as
clusters, and groups with simply the ”field”. 2) Using low surface brightness
imaging to explore the presence of minor interactions in these isolated
galaxies. 3) Explore possible correlations between the type of break, presence
of minor interactions and density, that can help elucidate the dominant
factors in shaping the disc of galaxies.

This work is structured as follows: In Section 2 we describe the data sample
and the reduction procedure followed. In Section 3 we explain the methods used
to measure the surface brightness profiles, classify the profiles by type and
detect signs of interaction. In Section 4 we present the results that are
discussed in Section 5. The conclusions of our work are summarised in Section
6. We adopt the values of the cosmological constants
$H_{0}=70\,\textrm{km\,s}^{-1}\,\textrm{Mpc}^{-1}$, $T_{0}=2.725\,\textrm{K}$,
and $\Omega_{m}=0.3$. Galactic extinction is corrected following Schlafly &
Finkbeiner (2011). We use the AB photometric system.

##  2 Sample, data and processing

Table 1: Observational and physical properties of the 25 galaxies studied in
this work.

Galaxy | ID | $V_{\textrm{rad}}$ | $L_{B}$ | Telescope/Survey | Integration time | Depth $\mu_{\textrm{lim}}$ | FOV |
---|---|---|---|---|---|---|---|---
|  | [km s-1] | [log ${\rm L}_{\odot}$] |  | [hours] | [mag arcsec-2 ] | degrees2 |
CIG 11 | UGC 139 | 3906 | 10.03 | VST | 4.8 | 29.7 | 4.936 |
CIG 33 | NGC 237 | 4090 | 9.95 | VST | 4.8 | 29.7 | 4.987 |
CIG 59 | UGC 1167 | 4193 | 9.56 | VST | 4.8 | 29.7 | 6.040 |
CIG 94 | UGC 1706 | 4694 | 9.74 | INT | 4.8 | 29.8 | 0.451 |
CIG 96 | NGC 864 | 1562 | 9.57 | VST | 5.9 | 29.7 | 6.041 |
CIG 100 | UGC 1863 | 6546 | 9.86 | HSC-SSP | - | 29.5 | 0.155 |
CIG 154 | UGC 3171 | 4530 | 10.06 | VST | 4.8 | 29.5 | 6.006 |
CIG 279 | NGC 2644 | 2196 | 9.03 | VST | 4.8 | 29.5 | 6.046 |
CIG 329 | NGC 2862 | 4473 | 9.27 | INT | 3.5 | 29.8 | 0.318 |
CIG 335 | NGC 2870 | 3568 | 10.17 | INT | 6.2 | 30.0 | 0.340 |
CIG 340 | IC 2487 | 4710 | 9.61 | INT | 5.7 | 30.3 | 0.418 |
CIG 512 | UGC 6903 | 2234 | 8.65 | HSC-SSP | - | 29.6 | 0.155 |
CIG 568 | UGC 8170 | 11094 | 10.02 | VST | 6.8 | 30.4 | 0.598 |
CIG 613 | UGC 9048 | 11121 | 10.72 | INT | 4.1 | 30.0 | 0.307 |
CIG 616 | UGC 9088 | 6668 | 9.65 | INT | 3.8 | 30.0 | 0.308 |
CIG 626 | NGC 5584 | 1934 | 9.43 | HSC-SSP | - | 29.8 | 0.155 |
CIG 744 | UGC 10437 | 3088 | 9.16 | HSC-SSP | - | 29.6 | 0.155 |
CIG 772 | IC 1231 | 5643 | 10.34 | INT | 4.7 | 30.1 | 0.309 |
CIG 800 | NGC 6347 | 6636 | 10.08 | INT | 4.2 | 29.9 | 0.307 |
CIG 838 | IC 1269 | 6558 | 10.74 | INT | 3.6 | 29.6 | 0.315 |
CIG 947 | NGC 7217 | 952 | 10.52 | JRT | 10.3 | 29.0 | 0.142 |
CIG 971 | UGC 12082 | 802 | 8.48 | JRT | 3.0 | 28.5 | 0.118 |
CIG 1002 | NGC 7451 | 6638 | 9.96 | VST | 10.0 | 29.9 | 7.297 |
CIG 1004 | NGC 7479 | 2443 | 9.70 | JRT | 3.7 | 28.5 | 0.127 |
CIG 1047 | UGC 12857 | 2465 | 9.45 | VST | 6.2 | 29.6 | 6.456 |

111The first two columns show the CIG name and the main ID of each galaxy. The
third and fourth columns show the radial velocity and the absolute luminosity
in the B band of the galaxy, obtained from the last revision of the AMIGA
parameters Jones et al. (2018). The fifth column shows the telescope used to
acquire the images (see Section 2.1). The sixth and seventh columns show the
total integration time in hours and the surface brightness limits
[$3\sigma,\,10^{\prime\prime}\times 10^{\prime\prime}$] of the image in
$\textrm{mag\,arcsec}^{-2}$ computed as explained in Román et al. (2020),
respectively. The eighth column shows the field of view (FOV) of the whole
image in degrees2.

###  2.1 Sample selection and observations

We use the AMIGA sample (Verdes-Montenegro et al., 2005), based on the
original CIG catalogue by Karachentseva (1973). The latest revision of the
isolation parameters of the AMIGA catalogue was carried out by Argudo-
Fernández et al. (2013), a work on which we base the selection of our sample.

Our selection criteria are as follows. The targets belong to the AMIGA
catalogue. We require that the galaxies have a reliable determination of the
distance (latest revision for AMIGA sample in Jones et al., 2018) as well as a
detection in H i, in order to also further explore possible correlations
between the fainter optical morphology and their gas content. The photometric
isolation parameters measured by Verley et al. (2007b) are the local number
density of neighbours galaxies, $\eta_{k,\textrm{p}}$ and the tidal strength,
$Q_{\textrm{Kar,p}}$. We require galaxies to have a local number density of
neighbouring galaxies $\eta_{k,\textrm{p}}<2.7$.

We observed 25 galaxies meeting these criteria with different telescopes.
These galaxies have morphologies that range from Hubble types of
$3\leq\rm{T}\leq 5$, which is a similar sample of the complete AMIGA catalogue
(see Sulentic et al., 2006). Here we briefly describe the instrumentation
used: 1) The Isaac Newton Telescope (INT), located in the Observatorio del
Roque de los Muchachos in La Palma, Spain, has a 2.5 m diameter primary
mirror. We used the Wide Field Camera (WFC), a four-CCD mosaic covering 33
arcmin on a side with a pixel scale of 0$\aas@@fstack{\prime\prime}$333\. 2)
The VLT Survey Telescope (VST), located in Cerro Paranal, Chile. The VST has a
2.65 m primary mirror. We used OmegaCAM which has 32 CCDs covering a field-of-
view of approximately 1 degree2, with a pixel scale of
0$\aas@@fstack{\prime\prime}$21\. 3) The 0.7 m Jeanne-Rich Telescope (JRT) is
located at the Polaris Observatory Association site, Pine Mountain,
California. The camera covers approximately 40 arcmin on a side with a pixel
scale of 1$\aas@@fstack{\prime\prime}$114.

Due to the high observational cost of ultra-deep optical imaging, and to
optimise the detection of faint features we only obtained r band data.
Observations were carried out mostly in dark time, although grey nights with
little Moon were also used. In the worst cases, the Moon was far enough with a
low phase to not produce any gradient in the image. Dithering patterns of tens
of arcseconds were used in order to improve the flat field. The exposure time
was set between one and five minutes for each individual frame.

The imposed surface brightness limits rule out the use of most general-purpose
optical surveys. Only the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP)
(Aihara et al., 2018) is able to fulfil our surface brightness requirements.
HSC-SSP is a survey produced with the Subaru 8.2 m aperture telescope and the
Hyper Suprime-Cam. We found four galaxies within the HSC-SSP footprint meeting
our selection criteria, that are included in our sample. We used the second
data release of the survey (Aihara et al., 2019). Although there are
additional filters, for the purposes of our work we only use the r band data.

We set a requirement of $\mu_{r,\textrm{lim}}>29.5\,\textrm{mag\,arcsec}^{-2}$
for the surface brightness measured as 3$\sigma$ in $10^{\prime\prime}\times
10^{\prime\prime}$ boxes following the nominal depth description by Román et
al. (2020). This limit is set to have a compromise between deep images to
detect faint structures and observational costs. We add an exception to this
limit to data from the JRT. This telescope has a small aperture but is built
to be extremely efficient in the low surface brightness regime. Therefore,
although the Poissonian noise with which the surface brightness limits are
measured will tend to be higher for this telescope, the detectability of
extremely low surface brightness features is comparable to data of higher
nominal depth, as we will show in the results section. Additionally, on this
telescope, we use a broad luminance band, in order to maximise detection. This
type of band has been proven to be similar to r-band Martínez-Delgado et al.
(2015). We therefore set a limit of
$\mu_{L,\textrm{lim}}>28.5\,\textrm{mag\,arcsec}^{-2}$ for data from the JRT.

Figure 1: Comparison between the Sloan Digital Sky Survey (left), the Legacy
Survey (middle) and our data for the galaxy CIG 340 (IC2487). The upper-right
value indicates the surface brightness limit [$3\sigma,10^{\prime\prime}\times
10^{\prime\prime}$] of each image computed as explained in Section 2. The
arrow in the left pannel indicates the low surface brightness feature only
visible in our data.

###  2.2 Data Reduction

The observations were reduced following a procedure aimed at preserving the
low surface brightness features. First, a bias subtraction (and dark if
necessary) is performed, following an ordinary procedure of combining bias
images (and dark). For the flat-fielding, we use the science images
themselves. This procedure consists of using heavily masked science images,
masked with specialised software such as SExtractor (Bertin & Arnouts, 1996,
version 2.25.0) and Noisechisel (Akhlaghi & Ichikawa, 2015, version 0.18),
which are normalised in flux and subsequently combined using a resistant mean
algorithm to produce a flat that is representative of the sky background
during the observations. This procedure, building the flat from the science
images, has significant advantages over the usual dome or twilight flats. The
main one is a considerable decrease in the strength of gradients present in
the images, allowing, as we will detail later, a less aggressive subtraction
of the sky background, and therefore, higher reliability of the
characterisation of the faintest sources. An additional advantage is that the
fringing structures contained in the science images are perfectly corrected,
allowing to improve the quality of the final images. Given that the
sensitivity of the CCD cameras can vary over time, and that the time range
between different observations is very wide (of the order of years), the flats
are built and applied to data sets taken close in time, typically during the
few days of each observation campaign.

Once the images are reduced, we proceed with their combination. First, the
images are astrometrically calibrated, using the Astrometry.net software
package (Lang et al., 2010) to obtain an approximate solution, and SCAMP
(Bertin, 2006) to obtain the final astrometry. The next step is the coaddition
of the individual frames, which is the most crucial step in the process. We
perform an iterative loop converging on what we consider the final coadd. The
procedure is as follows. First, we obtain a seed coadd, which is the starting
point of the iteration. This coadd is produced by subtracting a constant sky
value for each of the individual frames to be combined. The consequence of
this is that we preserve the lowest surface brightness structures that were
not removed by the sky subtraction. However, the frequent gradients in the
individual frames produce considerable fluctuations in the sky background
which remain in the coadd. This coadd is heavily masked with Noisechisel,
choosing parameters that maximised the masking of the real sources, trying to
leave the smooth gradients of the sky background unmasked. This mask produced
with the coadd is applied to the individual frames and we perform a smooth
polynomial sky fitting to the individual masked frames. We use as sky-fitting
surfaces Zernike polynomials (see Zernike, 1934), always with values equal to
or less than n $\leq$ 4, using for each n order all the azimutal components.
This Zernike polynomials fitting produce smooth surfaces that do not impact in
the oversubstraction around galaxies. Once all the gradients of the individual
frames are fitted and subtracted, they are combined to produce a new coadd
that is used again as a seed to get a new mask. This process is iterated a
number of times. Depending on how strong the gradients are, the number of
iterations and the degree of the polynomial are varied to obtain an optimal
result. Most cases, given the high quality of flat-fielding, the polynomials
have a low degree (n$=2,3$). In extreme cases, and mainly due to the presence
of the Moon in the observations, we increase the degree of the polynomial
(n$=4$) in order to obtain an optimal final coadd. In general, the reliability
of our sky background subtraction allows us to preserve the lower surface
brightness structures within our depth limits. We do not find signs of
oversubtraction in the images and profiles, such as high-contrast regions
close to the end of the galaxies, or systematically truncated profiles (see
Sect.3.3). The combination process is performed by photometrically calibrating
the individual frames, measuring their signal to noise, and combining them by
means of a weighted mean, thus optimising the signal-to-noise ratio of the
final coadd.

In Table 1 we show the final sample. The depth of the images was calculated
following the method of Román et al. (2020), appendix A, according to a
standard metric of 3 sigmas in $10^{\prime\prime}\times 10^{\prime\prime}$
boxes. We can see that all galaxies have a nominal limiting surface brightness
above 29.5 $\textrm{mag \,arcsec}^{-2}$, except those observed with the JRT,
which, as already mentioned, have a slightly lower nominal depth which is
compensated by having flatter fields on large angular scales. The total
integration time of our campaign, excluding data from the HSC-SSP survey, is
110 hours.

In Fig. 1 we show the galaxy CIG 340 together with a comparison with SDSS
(Abazajian et al., 2009) and Legacy Survey data (Dark Energy Survey
Collaboration et al., 2016). The difference in depth is significant between
that obtained in our work (30.3 $\textrm{mag\,arcsec}^{-2}$), SDSS (27.6
$\textrm{mag\,arcsec}^{-2}$) and the Legacy Survey (28.8
$\textrm{mag\,arcsec}^{-2}$), all measured at [3$\sigma$;
$10^{\prime\prime}\times 10^{\prime\prime}$]. While the morphology of CIG 340
appears similar in the SDSS and the Legacy Survey, in our data we detect new
structure, with a clear tidal stream to the south of CIG 340 and diffuse light
appearing in the direction transverse to the disc, showing a halo-like
structure. This highlights the considerable jump in detection power from
previously existing data, and the capacity of our observations to reveal the
presence of past minor interactions.

##  3 Analysis

Figure 2: Left panel: r-band image of CIG 340 (IC 2487). The scale of the
colours represents the surface brightness of the image and the scale is shown
in the profile panel (right) following the y-axis scale. Middle panel: Same
image with the mask applied and the elliptical apertures of the dynamic
position angle and ellipticity profile. Right panels: Surface brightness
profile (top), position angle (middle), and ellipticity (bottom) with respect
to the radial distance in arcseconds (bottom) and kpc (top). The red and green
curves show the fit with dynamic and fixed elliptical apertures, respectively.
The blue curve represents the fit with rectangular apertures. The position of
the disc break (if any) is shown with the dashed elliptical aperture and the
vertical dashed line in the middle and right panels, respectively. The figures
for the whole sample of galaxies are in Appendix B.

###  3.1 Masking procedure

The masking of light coming from sources other than the target galaxy is one
of the most delicate processes needed to obtain the cleanest and deepest
possible surface brightness profiles. This task not only requires extracting
the signal of astronomical sources from the emission of the background but
also requires the attribution (segmentation and deblending) of the signal to
one particular source when there is an overlap.

We combine two of the most popular software tools used in astronomical
detection, SExtractor (Bertin & Arnouts, 1996, , version 2.25.0) and
NoiseChisel and Segment (Akhlaghi, 2019, , version 0.18) part of the GNUastro
package. First, we run NoiseChisel & Segment in hot and cold configuration
modes for the whole set of images. This allows us to select a region occupied
by the galaxy of interest. Since this algorithm can detect very low signal-to-
noise ratios (lower than $\lesssim 1$) this region extends to very low surface
brightness ($\lesssim 27\,\textrm{mag\,arcsec}^{-2}$), including the outskirts
of the galaxy. We execute SExtractor with the parameters set to optimise the
detection of point-like sources (the configuration file can be found in
Appendix A). All the sources detected outside the galaxy region are then
masked.

To improve the detection of the faintest parts of the sources we first smooth
the image with the Fully Adaptive Bayesian Algorithm for Data Analysis, FABADA
(Sánchez-Alarcón & Ascasibar, 2023, version 0.1). We used an overestimation of
the variance of the image in FABADA to obtain a slightly smoother result and
thus larger masks. This allows the detection of even fainter point sources in
the proximity of the outskirts of galaxy.

Since we did not mask smaller sources inside the large region occupied by the
galaxy we run an extra step to mask these objects. We mask all the sources
detected by SExtractor outside a smaller region, occupied by the galaxy, that
corresponds to a level of five times the standard deviation of the image.
NoiseChisel is then run again on the image with the mask applied. This last
step allowed the detection of faint extended regions in the image. Given the
depth of our data, a considerable amount of faint extended regions (e.g.,
stellar haloes of background sources, Galactic cirrus, reflections from bright
stars, and residual light) appear in the images. All regions that are not
spatially connected with the galaxy region and that remain unmasked by the
automatic procedure described above are then masked. Finally we visually
inspect all masks to improve the masking of sources blended with the target
galaxy.

###  3.2 Radial profiles

Photometric profiles of galaxies allow regions of approximately equal
isophotal magnitude to be averaged to obtain a higher combined signal-to-noise
ratio. This allows to reach lower limiting surface brightnesses than with two-
dimensional imaging. However, although most galaxies have a simple morphology
that allows the different isophotal radii to be fitted by a single elliptical
aperture with a given position angle and ellipticity, prominent features in
galaxies, such as bars, rings, spiral arms, warps, produce radial variations
in the position angle and ellipticity. Additionally, the lower the surface
brightness limits of the image, the more galaxies tend to vary their
morphology in their outskirts, as other structures such as outer discs or
stellar haloes appear. Thus, the isophotes of galaxies can no longer be
modelled by fixed ellipses. We fit elliptical apertures to the image leaving
the parameters of the ellipses free in each radial bin (e.g. Knapen et al.,
2000; Pohlen & Trujillo, 2006; Muñoz-Mateos et al., 2015; Pranger et al.,
2017; Watkins et al., 2019), thus describing the different structures of the
galaxy without any prior assumptions for the whole galactic structure.

We use the implementation in Astropy (Astropy Collaboration et al., 2013,
2018) of the iterative ellipse-fitting method described by Jedrzejewski
(1987). This implementation needs the parameters of a first ellipse to
initialise the iterative fitting. We measure the initial parameters using the
image moments from a cropped binary image created from the mask image; we
select the values above four times the standard deviation of the masked image
described in the previous section. This step allows the definition of the
morphology in an efficient way.

We then initialise the elliptical isophote analysis. The elliptical isophote
fitting algorithm adjusts ellipses to isophotes of equal intensity pixel
values in the images and then computes corrections for the geometrical
parameters of the current ellipse by essentially “projecting” the fitted
harmonic amplitudes onto the image plane. With this method, we can measure the
radial surface brightness profile of the galaxy with a robust mean of the
pixels inside the fitted isophotes.

We redefine the morphology of the galaxy using the geometrical parameters of
the ellipses as fitted by the algorithm. As a verification step, we produce
two other profiles, one using fixed ellipses at the morphology parameters of
the galaxy and the other with rectangular apertures separated by a width of
five arcseconds along the major axis. These profiles allow us to verify the
correct fitting of the previous method by highlighting significant differences
in the profiles.

To further improve the reliability of the profiles, we perform additional
local sky background corrections. First, we create a preliminary profile with
the elliptical apertures parameters fixed. We then select an annular aperture
5 arcsec wide around the galaxy where we reach the level of the local
background (often a plateau or an infinite drop). We calculate the sky
background value as the mode of the distribution of pixels inside the annular
region fitting a Gaussian distribution. This provides a robust sky background
reference associated with the galaxy location. In some cases, the surroundings
of the galaxy are contaminated by diffuse emission from some other regions, in
which case the sky apertures are measured at a larger distance.

Figure 2 shows as example the image of the galaxy CIG 11 (UGC 139). In the
left panel we show the surface brightness distribution of the image. In the
middle panel we show the same image with a grey layer showing the masked
regions. We also show the apertures used for the profiles and the radius where
the break is detected (if present). In the right panel we show the surface
brightness profile in its three versions: from fixed ellipticity and position
angle, with elliptical and rectangular apertures and from elliptical apertures
with adaptive ellipticity and position angle. The position of the break (if
present) is denoted with a dashed line. In the lower panels we show the
variation of ellipticity and position angle as a function of radius. In
Appendix B we show the figures for the rest of the galaxies in our sample.

###  3.3 Reliability of the profiles

In order to obtain reliable measurements in the extreme low surface brightness
regime, numerous factors have to be taken into account. Most are related to
the processing of the data and the instrumentation, such as data reduction and
processing, scattered light as described by the point spread function (PSF),
or the presence of reflections and artefacts in the images related to
instrumentation. Additionally, the presence of Galactic cirrus is ubiquitous
and may produce confusion depending on the degree of contamination of the
target.

As discussed in Sect. 2.2, the data processing was carried out using
techniques designed to be respectful with the extremely low surface brightness
features. This is noticeable in the absence of oversubtraction of the profiles
(see Fig. 2) in the fainter regions, and allows us to achieve in most cases
surface brightness profiles reliable below 30 $\textrm{mag\,arcsec}^{2}$.
However, as noted by Sandin (2014); Karabal et al. (2017); Martínez-Lombilla &
Knapen (2019), and Gilhuly et al. (2022), the light scattered by the bright
part of the galaxy itself through the PSF has a decisive impact on the
photometric profiles in this extremely low surface brightness regime. In order
to obtain better reliability, a proper PSF deconvolution of the galaxy has to
be performed. However, given that our data originates from several instruments
over a very wide range in time (of the order of years), and that no specific
observations of bright stars were carried out we lack a PSF model for each
epoch and telescope with which to do the proper PSF deconvolution. Following
Trujillo & Fliri (2016) we estimate that the photometric profiles will be
unaffected to a surface brightness of around 28 $\textrm{mag\,arcsec}^{-2}$.
Since disc breaks are found to take place at surfaces brightness levels no
lower than 26 mag arcsec-2 (Gutiérrez et al., 2011; Pranger et al., 2017;
Watkins et al., 2019) our reliability limit is more than sufficient to explore
them. However, the lack of adequate PSF models rules out a potential
quantitative study of truncations or stellar halos in the outermost regions of
the galaxies in our sample.

The presence of Galactic cirrus in our images is also problematic due to the
extremely low brightness reached (cirrus indeed appears clearly in some of our
images). The maximum possible surface brightness of these cirrus features is
26 $\textrm{mag\,arcsec}^{2}$ (see Román et al., 2020). Considering that this
problem affects mostly surface brightnesses below a value of approximately 26
$\textrm{mag\,arcsec}^{-2}$ we can again conclude that this does not have an
impact on the study of disc breaks. It will, however, have a decisive impact
on contaminating the outer regions of galaxies hiding possible interaction
features. The presence of cirrus should therefore be taken into account in the
study of the potential presence of minor interactions, as we will describe
later on (Sect. 3.5).

###  3.4 Break identification and classification

Figure 3: Radii found via an automatic procedure as explained in Watkins et
al. (2019) compared to those found via visual inspection of the profiles. Gray
dotted line represents the 1:1 line, while the orange dashed line represents a
linear fit to the data. Error bars were estimated using the distance to the
next radial bins in the surface brightness profile at the distance in which
the break was measured.

We define a disc break as an abrupt change in the slope of the exponential
disc of a galaxy. Following Erwin et al. (2005) and Pohlen & Trujillo (2006)
we define three different types of profiles for our classification: Type I
$\equiv$ single exponential profile with no change in the slope; Type II
$\equiv$ down-bending break, with a steeper outer region; and Type III
$\equiv$ up-bending break, with a steeper inner region. We only search for the
most prominent breaks, that are the consequence of a change in the global
structure and not due to a local change (such as irregular morphology due to
prominent H ii regions). To characterise the breaks we use two different
approaches. First, given the small sample, we classify the break radii and
type through a visual inspection of the surface brightness profiles. Second,
we use the statistical approach of Watkins et al. (2019) where a change point
analysis is applied to identify the break radius. This method looks for
significant changes in the smooth derivative of the profile. We measure the
slope of the surface brightness profile (as done in Pohlen & Trujillo, 2006)
using the four nearest points for each radial distance and we smooth the
resulting slope with a median filter. We follow a classification similar to
that of previous works (Pranger et al., 2017; Watkins et al., 2019) for the
consistency of the comparison. Fig. 3 shows the break radii found by the two
different methods. We estimate the errors as the resolution of the profiles in
the region of the break (distance between each point). In most cases, both
approaches converge to the same solution although the automatic method finds
the break $2.06\,\textrm{kpc}$ closer to the galactic centre than visual
inspection. We expect an offset, as explained in Watkins et al. (2019), due to
the smoothing of the derivative of the profile and the cumulative sum, which
can induce small offsets in the radius thus we decide to adopt the value of
the radii found by the visual inspection. In Table 2 we indicate the
classification of the different types of profiles in our sample, together with
the values of the break radii, found visually, and the surface brightness
levels where the breaks occur.

Table 2: Results of the break identification.

Galaxy | Break | Break | Break | $Q_{\textrm{Kar,p}}$ | $\eta_{k,\textrm{p}}$ | Class
---|---|---|---|---|---|---
| Type | Radius | $\mu$ |  |  |
CIG 11 | II | $19\pm 3$ | $24.8\pm 0.7$ | -1.23 | 2.03 | -
CIG 33 | III | $12\pm 2$ | $23.6\pm 0.4$ | -3.11 | 2.09 | H
CIG 59 | I | - | - | -3.10 | 1.89 | -
CIG 94 | II | $10\pm 2$ | $22.5\pm 0.4$ | - | - | -
CIG 96 | III | $17\pm 3$ | $25.5\pm 0.2$ | - | - | H
CIG 100 | II | $5\pm 1$ | $21.9\pm 0.2$ | -3.01 | 2.16 | -
CIG 154 | I | - | - | - | - | C
CIG 279 | I | - | - | -3.04 | 2.16 | -
CIG 329 | II | $16\pm 3$ | $22.0\pm 0.3$ | -3.57 | 1.31 | T
CIG 335 | II | $15\pm 3$ | $23.5\pm 0.5$ | -3.48 | 1.42 | H
CIG 340 | II | $14\pm 3$ | $22.4\pm 0.4$ | -3.85 | 1.04 | H+T
CIG 512 | II | $9\pm 2$ | $24.2\pm 0.5$ | -3.40 | 1.38 | -
CIG 568 | II | $22\pm 5$ | $23.3\pm 0.5$ | -2.80 | 2.44 | -
CIG 613 | II | $39\pm 7$ | $24.9\pm 0.9$ | -3.33 | 1.78 | T
CIG 616 | I | - | - | -3.02 | 2.55 | H
CIG 626 | I | - | - | -3.93 | 1.05 | -
CIG 744 | I | - | - | -2.20 | 2.47 | -
CIG 772 | II | $17\pm 3$ | $23.1\pm 0.4$ | - | - | -
CIG 800 | II | $17\pm 3$ | $23.6\pm 0.5$ | - | - | C
CIG 838 | I | - | - | - | - | -
CIG 947 | I | - | - | - | - | C
CIG 971 | I | - | - | - | - | C
CIG 1002 | II | $14\pm 3$ | $22.8\pm 0.5$ | -2.42 | 2.69 | -
CIG 1004 | II | $15\pm 3$ | $22.3\pm 0.4$ | -2.25 | 1.49 | C
CIG 1047 | II | $7\pm 2$ | $22.6\pm 0.9$ | -2.62 | 2.25 | H

222The first column shows the galaxy CIG name. The second, third and fourth
show the type of break found, the break radii in kpc if any, and the surface
brightness level in mag arcsec-2 of the break, respectively. The fifth and
sixth columns show the interaction parameters $Q_{\textrm{Kar,p}}$ and
$\eta_{k,\textrm{p}}$ from the AMIGA catalogue (Argudo-Fernández et al.
(2013)). The seventh column indicates the presence of interaction features
found in this work. We define three different categories, Halo-perturbed (H),
Tidal streams (T) and Cirrus contamination (C). More information about the
classification can be found in Sect. 3.5.

###  3.5 Identification of interactions

We visually inspect our sample in search of signatures of perturbations
following the definitions of Martínez-Delgado et al. (2023), and references
therein. The large field of view of our images corresponds to at least 100
kpc, enough to explore the presence of interactions with confidence. In order
to provide a simple and general classification with which to introduce a
perturbation parameter, we distinguish galaxies according to their morphology
as follows. Tidal Stream (T): The galaxy shows a tidal stream, elongated in
shape consistent with an in-falling satellite in current interaction. Halo-
Perturbed (H): The galaxy has asymmetries or debris in the outermost part of
the disc. Cirrus (C): In the case of strong Galactic cirrus contamination, a
correct interpretation of the degree of galaxy perturbation or interaction is
not possible. In this case, we discard the galaxy as non-tractable, excluding
it from the statistics that imply using the presence of interactions. When a
galaxy appears fairly symmetrical in morphology with no signs of disturbance,
no classification is given. We describe the presence of interactions as
effects from mergers in the outer regions of galaxies. These are
distinguishable from lopsidedness potentially produced by gas (Bosma, 2017),
since our surface brightness limits allow us to explore the outer or halo
regions of galaxies, beyond simply tracing the central morphology where star
formation is dominant.

The result of this classification for each galaxy is shown in Table 2, and in
Fig. 4 we show representative examples of the interaction classification
scheme. In the top-row panels, we show a symmetric non-classified (left),
halo-perturbed (middle), and tidal stream (right) examples. In the bottom
panels we show three different examples of galaxies with strong Galactic
cirrus contamination that do not allow us to assure the presence or absence of
potential interaction features in the galaxies.

Figure 4: Different examples of the interaction classification scheme. In the
top panel, we show an unperturbed, symmetric example (top-left panel), CIG 100
(UGC 1863). The top middle and right panels show examples of perturbed
galaxies. CIG 335 (NGC 2870) shows an overdensity in the halo region, while
CIG 340 (IC 2487) shows a tidal stream in the southern region. All
perturbations features are indicated with a black arrow. The bottom panels
represent galaxies classified as cirrus-contaminated. CIG 1004 (NGC 7479), CIG
947 (NGC 7217), and CIG 154 (UGC 1706) are shown in the bottom left, middle
and right panels, respectively. These examples show considerable amounts of
diffuse emission associated with Galactic cirrus only seen in our images. All
of the images, except the one of CIG 100, were smoothed with FABADA to enhance
the structure.

##  4 Results

We present below individual comments on each of the galaxies with a short
discussion of the decisions made in the different classifications. In Table 2
we show the results of the classification of profiles for each galaxy,
together with the radius at which a break has been found (if any) and its
surface brightness level.

  * *

CIG 11 [UGC 139]: Although this galaxy could have been classified as Type
III+II at $10+20\,\textrm{kpc}$ (see discussion by Watkins et al., 2019), we
classify as a Type II. The reason is that extra flux originates by H ii
regions seen in the inner disc region. This extra flux could be misinterpreted
as Type III, although according to Pranger et al. (2017) Type III breaks occur
further away. Thus, for the sake of a fair comparison, we classify this as a
Type II break at $19\,\textrm{kpc}$. We also consider this galaxy as
unperturbed due to its symmetric structure. Diffuse cirrus emission is
present, but that does not prevent the detection of interactions.

  * *

CIG 33 [NGC 237]: We consider this a clear Type III with a break radius of
$\sim$12 kpc and a perturbed halo. The diffuse emission around the galaxy is
asymmetric with a bump in the North-East region of the outskirts.

  * *

CIG 59 [UGC 1167]: Exponential disc without break, with symmetric structure.
Presence of instrumental reflection of a nearby star that when correctly
masked does not contaminate the rest of the galaxy.

  * *

CIG 94 [UGC 1706]: Type II break at $\sim 10\,\textrm{kpc}$, with absence of
interaction signatures.

  * *

CIG 96 [NGC 864]: Type III break at $\sim 16\,\textrm{kpc}$ with perturbed
halo. Extra flux at the North-East region of the disc outskirts.

  * *

CIG 100 [UGC 1863]: Type II break at 5 kpc, symmetric structure. Possible Type
III break around 18.5 kpc at 28 mag arcsec${}^{-}2$. However, at this depth,
we cannot distinguish between instrumental effects such as extended PSF
contribution as explained in Sect. 3.3.

  * *

CIG 154 [UGC 3171]: Exponential disc with symmetric structure. Hints of a
larger spiral arm, at around $\sim$ 17 kpc, of the southern region. The
presence of filamentary cirrus prevents us from determining the presence of
any faint interaction feature in the outer regions of the galaxy.

  * *

CIG 279 [NGC 2644]: Exponential disc with symmetric structure. The presence of
diffuse cirrus emission would not prevent the detection of interaction
features if present. Possible Type III at $\sim 13\,\textrm{kpc}$, however,
the depth and presence of cirrus do not allow us to distinguish between the
possible origins.

  * *

CIG 329 [NGC 2862]: Type II break at $\sim 16\,\textrm{kpc}$, clear tidal
stream at the end of the disc in the South-East region. Presence of
instrumental reflection of a nearby star that correctly masked does not
contaminate the rest of the galaxy.

  * *

CIG 335 [NGC 2870]: Type II break at $\sim 15\,\textrm{kpc}$. Signatures of
overdensities and perturbations in the halo region so we classify this as a
perturbed halo. Fig. 4 shows an enhanced image of the galaxy for greater
clarity.

  * *

CIG 340 [IC 2487]: Type II at $\sim 14\,\textrm{kpc}$, clear tidal stream in
the south region.

  * *

CIG 512 [UGC 6903]: Symmetric galaxy with a Type II break at $\sim
9\,\textrm{kpc}$. Oversubstractions effects could cause the significant drop
in brightness seen at 20 kpc, which can be a result of the Subaru pipeline.

  * *

CIG 568 [UGC 8170]: Symmetric galaxy with a Type II break at $\sim
21\,\textrm{kpc}$.

  * *

CIG 613 [UGC 9048]: Type II break at $\sim 40\,\textrm{kpc}$. Galaxy also
exhibits signatures of a very faint and warped tidal stream. Appendix B shows
an enhanced image with an arrow showing this stream.

  * *

CIG 616 [UGC 9088]: Type I exponential disc, with an elliptical-like shape in
the halo region with extra flux perpendicular to the major axis. Extra flux in
clumps in the outermost regions indicating past interaction. Classified as
perturbed halo.

  * *

CIG 626 [NGC 5584]: Symmetric galaxy with a featureless disc profile, Type I.

  * *

CIG 744 [UGC 10437]: Although this galaxy seems to have some fluctuations
between $7\,\textrm{kpc}$ and $15\,\textrm{kpc}$ that could be classified as
breaks, the constant global decrease in average surface brightness in the disc
makes us to classify it as an exponential disc (Type I). We identify the local
fluctuations coming from clumpy H ii regions of the arms. The absence of
features indicating interactions makes us classify this galaxy as symmetric.

  * *

CIG 772 [IC 1231]: Symmetric galaxy with Type II break at $17\,\textrm{kpc}$.

  * *

CIG 800 [NGC 6347]: Type II break at $\sim 19\,\textrm{kpc}$. The galaxy is
fully embedded in a region heavily contaminated by cirrus, making the
classification of possible interaction features unfeasible. Furthermore,
several stars lay in the line of sight, in the North-West region, and faint
contamination due to the extended PSF can cause extra light at the end of the
profile (see Sect. 3.3).

  * *

CIG 838 [IC 1269]: Galaxy with an exponential Type I disc. From our optical
imaging or the derived profile we do not detect any signs of interaction, even
though the northern spiral arm shows asymmetries with respect to the other
one. Some diffuse cirrus emission is present, but not enough to prevent the
detection of faint interaction features.

  * *

CIG 947 [NGC 7217]: Although this object can be misinterpreted as an early-
type galaxy, high-resolution colour images, show spiral structures with two
blue rings in the inner and outer regions. The radial profile exhibits a clear
exponential disc. We see clear signatures of cirrus contamination (Fig. 4)
preventing any detection of possible interaction features.

  * *

CIG 971 [UGC 12082]: Exponential disc, Type I. The galaxy is fully embedded in
a region heavily contaminated by cirrus, making the classification of possible
interaction features unfeasible. Furthermore, the field is crowded with stars.
This contamination can be also be seen in the rectangular radial profile as a
plateau at $\sim 28\,\textrm{mag\,arcsec}^{-2}$ (as explained in Sect. 3.3).

  * *

CIG 1002 [NGC 7451]: Type II break at $14\,\textrm{kpc}$. We detect a possible
companion in the South-West region of the galaxy. However, there is no
available spectra to confirm the association of the two galaxies. We do not
see any interaction signature between them.

  * *

CIG 1004 [NGC 7479]: Type II with a break radius of $15\,\textrm{kpc}$. The
difference between the fixed and free ellipticity surface brightness profiles
comes from the presence of the extended stellar bar. We are also able to see
the same break with the rectangular aperture. The galaxy is fully embedded in
a region heavily contaminated by cirrus (see Fig.4), making the classification
of possible interaction features unfeasible from deep optical imaging. The
asymmetry of the galaxy disc and spiral arms is well known, however, and may
indicate a minor merger origin (e.g. Laine & Gottesman, 1998).

  * *

CIG 1047 [UGC 12857]: Type II break at $8\,\textrm{kpc}$. We see a warp in the
southern part of the outer disc, so we classify this galaxy as a perturbed
halo. Presence of diffuse cirrus emission that would not prevent the detection
of interaction features if present.

Figure 5: Left: Normalised distribution of the frequency of the types of
breaks found in this work (left-blue) and in Pranger et al. (2017) for their
field (middle-green) and cluster (right-red) samples. Right: Normalised
distribution of the frequency of the types of breaks. Galaxies strongly
contaminated by cirrus are excluded from this figure. We also show the
contribution of unperturbed (blue) and perturbed (green) for galaxies with
each type of break.

In total, among 25 galaxies, we identify 9 Type I single exponential with no
significant break, 14 Type II down-bending breaks, and 2 Type III up-bending
breaks. The overall statistics of the sample are $36\%\pm 10\%$ Type I,
$56\%\pm 10\%$ Type II, and $8\%\pm 5\%$ Type III breaks. We estimate the
uncertainties assuming a binomial distribution,
$\epsilon=\sqrt{f\,(1-f/N)}*(100/N)$ [%] where $f$ is the fraction of galaxies
within each type and $N$ is the total number of galaxies in our sample
($N=25$).

###  4.1 Break type vs. interactions

We find 5 galaxies with strong contamination by Galactic cirrus clouds that do
not allow us to confirm or rule out the presence of interactions thus these 5
galaxies are excluded from this analysis. Among the remaining 20, we find 8
galaxies with signatures of interactions. Of these, 4 show asymmetries in the
halo, 3 have tidal streams, and the remaining one shows both tidal streams and
halo asymmetries. Therefore, 40%$\pm$14% of the isolated galaxies in our
classified sample show the presence of interactions; out of these galaxies,
25%$\pm$10% show an asymmetric halo and 20%$\pm$8% show some tidal streams. We
found 12 galaxies (60%$\pm$17%) with no interaction features.

Given the small sample size, we consider any type of interaction as a single
class named perturbed (8 galaxies) (presence of interactions) while the
remaining galaxies (that lack cirrus contamination) are classified as
unperturbed (12 galaxies). In the right panel of Fig. 5 we show the fraction
of perturbed and unperturbed galaxies for each type of break. We found that
for Type I breaks, 6 ($83\%\pm 37\%$) are unperturbed galaxies and 1 ($17\%\pm
17\%$) is perturbed; for Type II, 8 ($58\%\pm 22\%$) are unperturbed and 5
($42\%\pm 19\%$) are perturbed. Finally, we find that the two galaxies with
Type III are perturbed ($100\%\pm 71\%$). We estimate the errors assuming
Poisson statistics since we have few of galaxies in each type.

The low number of galaxies in our sample is insufficient to allow us to make
strong statements. However, we find certain indications that are undoubtedly
interesting. First, both Type III galaxies (CIG 33 and CIG 96) appear strongly
perturbed. This is noticeable in the images in the Appendix in which we can
appreciate how these two galaxies have an expanded halo with clear signs of
strong disturbance, possibly due to a recent major merger. Second, we find a
significantly higher fraction of perturbed galaxies (42% $\pm$ 19%) among Type
II break hosts than among Type I (17% $\pm$ 17%).

###  4.2 Break type vs. environment

In the left panel of Fig. 5 we show the fraction of surface brightness profile
types in our sample of isolated galaxies in comparison with the previous work
by Pranger et al. (2017) who explored the surface brightness type in a sample
of 700 disc galaxies at low redshift ($z<0.063$) using SDSS data. These
galaxies were classified according to their environment into field (low-
density) and cluster (high-density). The fractions of Type I, II, and III
discs found by Pranger et al. (2017) are 29 ($6\%\pm 1\%$), 343 ($66\%\pm
2\%$), and 149 ($29\%\pm 2\%$) in the field sample and 27 ($15\%\pm 3\%$), 98
($56\%\pm 4\%$), and 50 ($29\%\pm 3\%$) in the cluster sample. For the sake of
a fair comparison, we estimate the Pranger et al. (2017) uncertainties in the
same way as we do for our results. We compare these statistics with the sample
of isolated galaxies from our work. As illustrated in Fig. 5, left panel, we
find a considerably higher fraction of isolated Type I galaxies and a lower
fraction of isolated Type III galaxies than what was found by Pranger et al.
(2017) for field galaxies and clusters. The results for Type II are similar
for different environments.

A Kolmogorov–Smirnov statistical test proves that our results are
significantly different from those of Pranger et al. (2017) ($P$-value ¡
0.01). The highest difference between our results and those of the Pranger et
al. (2017) sample is found for Type I discs. We find six times more single
exponential discs in our isolated sample. This difference holds when compared
to other studies, such as that by Gutiérrez et al. (2011), who found around
$\sim 10-15\%$ of Type I disc in field late-type spirals, around two to three
times less often than us. We also find a much lower fraction, around seven
times lower, of Type III discs than Pranger et al. (2017).

In Fig. 6 we show a correlation test between the degree of isolation and the
disc type of the galaxies in our sample. We plot the local number density of
neighbours galaxies $\eta_{k,\textrm{p}}$ and the tidal strength
$Q_{\textrm{Kar,p}}$ obtained by Argudo-Fernández et al. (2013) for the 18
galaxies in our sample that have these parameters calculated. An increasing
value for $\eta_{k,\textrm{p}}$ or $Q_{\textrm{Kar,p}}$ indicates a higher
environmental density. We show as a comparison these parameters for other
galaxy catalogues, including galaxies located in regions of higher density. In
particular, we show values for isolated pairs of galaxies (KGP; Karachentsev,
1972); galaxy triplets (KTG; Karachentseva et al., 1979); galaxies in compact
groups (HCG; Hickson, 1982); and galaxies in Abell clusters (ACO; Abell, 1958;
Abell et al., 1989) computed by Argudo-Fernández et al. (2013). We find that
the galaxies in our sample tend to be located at low values of
$\eta_{k,\textrm{p}}$ and $Q_{\textrm{Kar,p}}$, confirming their location in
regions of low environmental density, a consequence of the sample selection
criteria. The colour code indicates the type of surface brightness profile,
while the symbols show the two populations according to our classification,
perturbed and unperturbed galaxies. The average values of the
$\eta_{k,\textrm{p}}$ and $Q_{\textrm{Kar,p}}$ parameters for each break type
are indicated by colour bars, while for the unperturbed and perturbed
population, they are shown with symbols. We see that for the galaxies in our
sample, the different disc types tend to be located on average in regions of
similar density, with these regions in any case having a very low density.

Figure 6: Photometric isolation parameter for 18 galaxies of our sample, the
local number density of neighbour galaxies, $\eta_{k,\textrm{p}}$ compared to
the tidal strength, $Q_{\textrm{Kar,p}}$ from Argudo-Fernández et al. (2013).
The colour code represents the type of disc found, blue, green, and red for
Types I, II, and III, respectively. The mean values of each type are
represented by the line close to the axis (bottom and left) with its
corresponding error. Circle and star symbols represent unperturbed and
perturbed galaxies, respectively. The mean values of perturbed and unperturbed
galaxies are represented by the symbols close to the axis (upper and right)
with its corresponding error. The cross symbols correspond to galaxies not
classified due to galactic cirrus. Background grey values represent Galaxies
from different samples (see Sect. 4 for details).

##  5 Discussion

We present deep optical imaging of a sample of 25 isolated galaxies from the
AMIGA project in order to reach low surface brightness limits. The nominal
surface brightness limits achieved are
$\mu_{r,\textrm{lim}}\,>\,29.5\,\textrm{mag\,arcsec}^{-2}$ [3$\sigma$;
$10^{\prime\prime}\times 10^{\prime\prime}$], and
$\mu_{L,\textrm{lim}}\,>\,28.5\,\textrm{mag\,arcsec}^{-2}$ [3$\sigma$;
$10^{\prime\prime}\times 10^{\prime\prime}$] for the three galaxies observed
with the JRT. Because of our careful data processing, our images show an
absence of oversubtracted regions and a high efficiency in the detection of
extreme low surface brightness features.

The depth of our data is more than 1 $\textrm{mag\,arcsec}^{-2}$ (r band)
deeper than that in preceding studies (see e.g., Martínez-Delgado et al.,
2023, using the Legacy Survey). This gives us the possibility to look for the
presence of minor interaction signatures at very low surface brightness. A
representative example of this quantitative leap is shown in Fig. 1 where we
compare images of CIG 340 (IC 2487) with SDSS and Legacy Survey data. This
comparison clearly shows that only in our data is it possible to detect the
clear interaction that CIG 340 is undergoing with a low-mass satellite,
appearing as a tidal stream with surface brightness around
$26.8-27.3\leavevmode\nobreak\ \textrm{mag\,arcsec}^{-2}$ and an extension of
around $\sim 116\,\textrm{arcsec}$ ($35\,\textrm{kpc}$), not detectable in
shallower optical data.

The potential detection of minor interactions has a decisive impact on the
interpretation of galaxy properties, and the isolated galaxy CIG 340 is a
perfect example. Shallow optical images of CIG 340 revealed a fairly symmetric
disc, albeit with a small disc warp. Additionally, the H i-integrated spectra
from single-dish observations showed a very symmetric profile (see Espada et
al., 2011). More recent high-resolution interferometric observations by Scott
et al. (2014) revealed a striking asymmetry of the H i component of CIG 340,
with 6% of the H i mass located in an extension of the disc to the north.
These findings led Scott et al. (2014) to propose two different hypotheses to
explain them. On the one hand, this H i asymmetry could be caused by a minor
interaction with a satellite, not detected in the optical images available at
the time. On the other hand, it could be due to some internal secular process,
for example the result of a long-lived dark matter halo asymmetry. More recent
work by Kipper et al. (2020) proposed that the gravitational interaction of a
background medium of dark matter particles in the surroundings of CIG 340 is
capable of inducing a dynamical friction enough to cause the H i asymmetries
observed by Scott et al. (2014). In light of the results of our work, we can
affirm that the H i asymmetries observed in the isolated galaxy CIG 340 are
most likely caused by a minor interaction, the signatures of which we have
unveiled for the first time.
The galaxy CIG 96 (NGC 864) is another well-studied isolated galaxy. Recent
work detected two H i asymmetries in the North-West and South-East regions of
the galaxy (Ramírez-Moreta et al., 2018), not detected in the optical range.
The main hypotheses to explain the HI features of CIG 96 are possible accreted
companions and cold gas accretion. However, Ramírez-Moreta et al. (2018) ruled
out the possibility of major mergers events due to the isolation criteria
(discarded possible interactions in the last 2.7 Gyr). Despite the high degree
of isolation of this galaxy, with our deep data we are able to detect a bigger
external faint halo in the galaxy, which along with its Type III profile
suggests that this galaxy might have experimented a recent merger event
causing the extended emission of light (e.g. Laurikainen & Salo, 2001; Lotz et
al., 2008; Borlaff et al., 2014; Barrera-Ballesteros et al., 2015; Pfeffer et
al., 2022).
The possibility of achieving surface brightness levels as low as the ones
shown here offers a new decisive parameter to explain some morphological
features in galaxies. This would not only be useful to investigate the main
reasons for H i asymmetries of galaxies, but also in other fields such as the
possible induction of active galactic nuclei (AGN) by minor interactions in
galaxies, among many others. These issues will be investigated in future
works.

The types of discs in the isolated galaxies from our sample show significant
differences with respect to the results of previously studied samples in other
environments. We find a significantly higher fraction of Type I and a
significantly lower fraction of Type III profiles than in works by Pranger et
al. (2017) and Gutiérrez et al. (2011) for denser environments. This is a
striking result which we further discuss now.

Type III profiles can be produced by mergers of galaxies (e.g., Laurikainen &
Salo, 2001; Borlaff et al., 2014; Pfeffer et al., 2022, and references
therein). The low number of Type III profiles in our sample of isolated
galaxies is in agreement with this statement since undoubtedly a lower density
would imply a lower merger ratio. Additionally and importantly, the only two
Type III galaxies found in our sample (CIG 33 and CIG 96) show disturbed
morphology with a puffed-up external halo, compatible with a recent major
merger (Lotz et al., 2008; Barrera-Ballesteros et al., 2015).

Type II galaxies are widely agreed to be the result of discs with breaks
caused by a star formation threshold (e.g., Tang et al., 2020; Pfeffer et al.,
2022). A cessation or decrease in star formation would tend to homogenise
through stellar migration effects (Sánchez-Blázquez et al., 2009) the stellar
populations and produce a Type I profile (e.g., Pfeffer et al., 2022). In our
case this is hardly testable directly due to the absence of star formation
measurements in our sample. However, an indirect hint that could indicate that
this is the case is the considerably higher fraction of perturbed Type II
(42%$\pm$19%) galaxies when compared to Type I (17%$\pm$17%) galaxies. While
the rate of star formation may depend on various circumstances such as the
rate of pristine gas inflow, it is known that satellite interactions are
capable of triggering star formation (Barton et al., 2000; Alonso et al.,
2004; Knapen et al., 2015; Mesa et al., 2021), which would be in accordance
with our findings. The low ratio of perturbations detected in Type I discs
galaxies in our results and the lower specific star formation rate in isolated
galaxies than in higher-density environments (Lisenfeld et al., 2011; Melnyk
et al., 2015; Domínguez-Gómez et al., 2023) suggest that unperturbed galaxies,
evolving slowly with a low star formation rate could explain the high rate, of
Type I discs in isolated galaxies.

##  6 Conclusions

We study a sample of 25 “isolated” galaxies from the AMIGA revised CIG
catalogue, which lack major companions, to identify how internal or external
processes impact the discs of galaxies. We conduct a diverse observational
campaign using the INT, VST, JRT, and archival data from HSC-SSP to obtain
unprecedentedly deep images. We measure the surface brightness profiles and
classify the galaxies according to their disc break (Type I $\equiv$ single
exponential, Type II $\equiv$ down-bending, Type III $\equiv$ up-bending) and
to the presence of interaction signatures (Tidal Stream, Halo perturbation,
and unperturbed). The conclusions of our work are the following:

  * •

Our images have similar depth as those to come from future surveys, like LSST,
through careful data processing and background subtraction. The nominal
surface brightness limit of the images is
$\mu_{r,\textrm{lim}}\,>\,29.5\,\textrm{mag\,arcsec}^{-2}$ [3$\sigma$;
$10^{\prime\prime}\times 10^{\prime\prime}$]. The data processing is optimized
to preserve low surface brightness features.

  * •

As a result of the depth obtained, we can trace interaction signatures in
galaxies classified as isolated (see Figure 1). However, five galaxies are
affected by cirrus and we could not explore the presence of signatures, ruling
them out from this analysis. We find that 25% $\pm$ 10% of the galaxies in our
sample show an asymmetric halo and 20% $\pm$ 10% show a tidal stream (see
Figure 4). In total, 40% $\pm$ 14% show signs of interactions.

  * •

We are able to produce reliable surface brightness profiles down to a critical
surface brightness of $\gtrsim 30\,\textrm{mag\,arcsec}^{-2}$ for all of the
galaxies in our sample (see Appendix B).

  * •

We successfully classified the disc type in all the galaxies in our sample. We
identify nine ($36\%\pm 5\%$) Type I discs with no significant break, fourteen
($56\%\pm 7\%$) Type II down-bending discs, and two ($8\%\pm 3\%$) Type III
up-bending discs.

  * •

The fraction of perturbed galaxies correlates with the type of disc. We
identify $17\%\pm 17\%$, $42\%\pm 19\%$ , and $100\%\pm 71\%$ perturbed
galaxies with Type I, II, and III discs, respectively.

  * •

We find significantly higher Type I and lower Type III frequencies with
respect to other studies (such as Pranger et al., 2017; Gutiérrez et al.,
2011) with more perturbed galaxies in Type II and III than in Type I. This is
in agreement with a proposed formation scenario in which Type III discs are
formed via interactions such as major mergers (see Laine et al., 2014; Watkins
et al., 2019), and Type II discs stem from a star formation threshold. The
increased fraction of Type I discs with respect to that in other samples could
be attributed to the low ratio of disturbance in our sample of isolated
galaxies.

In the near future, the advent of the next generation optical and infrared
surveys (e.g., LSST, Euclid) will increase the number of galaxies observed at
surface brightness limits equivalent to those that we present in this work by
several orders of magnitude. This will allow to further strengthen and refine
our statements, provided the data reduction and analysis allows for the
detection of low surface brightness.

###### Acknowledgements.

We thank Ignacio Trujillo for helpful insights about this work and Aaron
Watkins for providing us with the implementation of the automatic break
detection method. PMSA, JHK, and JR acknowledge financial support from the
State Research Agency (AEI-MCINN) of the Spanish Ministry of Science and
Innovation under the grant ”The structure and evolution of galaxies and their
central regions” with reference PID2019-105602GBI00/10.13039/501100011033,
from the ACIISI, Consejería de Economía, Conocimiento y Empleo del Gobierno de
Canarias and the European Regional Development Fund (ERDF) under grant with
reference PROID2021010044, and from IAC project P/300724, financed by the
Ministry of Science and Innovation, through the State Budget and by the Canary
Islands Department of Economy, Knowledge and Employment, through the Regional
Budget of the Autonomous Community. JR acknowledges funding from University of
La Laguna through the Margarita Salas Program from the Spanish Ministry of
Universities ref. UNI/551/2021-May 26, and under the EU Next Generation. LVM
acknowledges financial support from grants CEX2021-001131-S funded by
MCIN/AEI/ 10.13039/501100011033, RTI2018-096228-B-C31 and PID2021-123930OB-C21
by MCIN/AEI/ 10.13039/501100011033, by “ERDF A way of making Europe” and by
the ”European Union” and from IAA4SKA (R18-RT-3082) funded by the Economic
Transformation, Industry, Knowledge and Universities Council of the Regional
Government of Andalusia and the European Regional Development Fund from the
European Union. SC acknowledges funding from the State Research Agency (AEI-
MCINN) of the Spanish Ministry of Science and Innovation under the grant
“Thick discs, relics of the infancy of galaxies” with reference
PID2020-113213GA-I00. MAF acknowledges support from FONDECYT iniciación
project 11200107 and the Emergia program (EMERGIA20_38888) from Consejería de
Transformación Económica, Industria, Conocimiento y Universidades and
University of Granada. PMSA and LVM acknowledge the Spanish Prototype of an
SRC (SPSRC) service and support funded by the Spanish Ministry of Science,
Innovation and Universities, by the Regional Government of Andalusia, by the
European Regional Development Funds and by the European Union
NextGenerationEU/PRTR. The SPSRC acknowledges financial support from the State
Agency for Research of the Spanish MCIU through the ”Center of Excellence
Severo Ochoa” award to the Instituto de Astrofísica de Andalucía
(SEV-2017-0709) and from the grant CEX2021-001131-S funded by MCIN/AEI/
10.13039/501100011033. Based on observations made with the Isaac Newton
Telescope operated on the island of La Palma by the Isaac Newton Group of
Telescopes in the Spanish Observatorio del Roque de los Muchachos of the
Instituto de Astrofísica de Canarias. The WFC imaging was obtained as part of
the programs C163, C106, and C106/13B. Based on observations collected at the
European Organisation for Astronomical Research in the Southern Hemisphere
under ESO programme(s) 098.B-0775(A), 093.B-0894(A). Based on data collected
at the Subaru Telescope and retrieved from the HSC data archive system, which
is operated by Subaru Telescope and Astronomy Data Center at National
Astronomical Observatory of Japan.

## References

  * Abell (1958) Abell, G. O. 1958, ApJS, 3, 211. doi:10.1086/190036
  * Abell et al. (1989) Abell, G. O., Corwin, H. G., & Olowin, R. P. 1989, ApJS, 70, 1. doi:10.1086/191333
  * Abraham & van Dokkum (2014) Abraham, R. G. & van Dokkum, P. G. 2014, PASP, 126, 55. doi:10.1086/674875
  * Aihara et al. (2018) Aihara, H., Arimoto, N., Armstrong, R., et al. 2018, PASJ, 70, S4. doi:10.1093/pasj/psx066
  * Aihara et al. (2019) Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, PASJ, 71, 114. doi:10.1093/pasj/psz103
  * Akhlaghi & Ichikawa (2015) Akhlaghi, M. & Ichikawa, T. 2015, ApJS, 220, 1. doi:10.1088/0067-0049/220/1/1
  * Akhlaghi (2019) Akhlaghi, M. 2019, arXiv:1909.11230
  * Alonso et al. (2004) Alonso, M. S., Tissera, P. B., Coldwell, G., et al. 2004, MNRAS, 352, 1081. doi:10.1111/j.1365-2966.2004.08002.x
  * Arakelian & Magtesian (1981) Arakelian, M. A. & Magtesian, A. P. 1981, Astrofizika, 17, 53
  * Argudo-Fernández et al. (2013) Argudo-Fernández, M., Verley, S., Bergond, G., et al. 2013, A&A, 560, A9. doi:10.1051/0004-6361/201321326
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33. doi:10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123. doi:10.3847/1538-3881/aabc4f
  * Abazajian et al. (2009) Abazajian, K. N., Adelman-McCarthy, J. K., Agüeros, M. A., et al. 2009, ApJS, 182, 543. doi:10.1088/0067-0049/182/2/543
  * Azzollini et al. (2008) Azzollini, R.; Trujillo, I.; Beckman, J. E. 2008, ApJ, 679L, 69A
  * Bakos et al. (2008) Bakos, Judit; Trujillo, Ignacio; Pohlen, Michael 2008, ApJ, 683L, 103B
  * Bakos & Trujillo (2012) Bakos, Judit; Trujillo, Ignacio 2012, arXiv1204.3082B
  * Baldry et al. (2006) Baldry, I. K., Balogh, M. L., Bower, R. G., et al. 2006, MNRAS, 373, 469. doi:10.1111/j.1365-2966.2006.11081.x
  * Balogh et al. (2004) Balogh, M. L., Baldry, I. K., Nichol, R., et al. 2004, ApJ, 615, L101. doi:10.1086/426079
  * Barton et al. (2000) Barton, E. J., Geller, M. J., & Kenyon, S. J. 2000, ApJ, 530, 660. doi:10.1086/308392
  * Barrera-Ballesteros et al. (2015) Barrera-Ballesteros, J. K., García-Lorenzo, B., Falcón-Barroso, J., et al. 2015, A&A, 582, A21. doi:10.1051/0004-6361/201424935
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393. doi:10.1051/aas:1996164
  * Bertin (2006) Bertin, E. 2006, Astronomical Data Analysis Software and Systems XV, 351, 112
  * Borlaff et al. (2014) Borlaff, A., Eliche-Moral, M. C., Rodríguez-Pérez, C., et al. 2014, A&A, 570, A103. doi:10.1051/0004-6361/201424299
  * Borlaff et al. (2018) Borlaff, A., Eliche-Moral, M. C., Beckman, J. E., et al. 2018, A&A, 615, A26. doi:10.1051/0004-6361/201732090
  * Borlaff et al. (2019) Borlaff, A., Trujillo, I., Román, J., et al. 2019, A&A, 621, A133. doi:10.1051/0004-6361/201834312
  * Bosma (2017) Bosma, A. 2017, Outskirts of Galaxies, 434, 209. doi:10.1007/978-3-319-56570-5_7
  * Dark Energy Survey Collaboration et al. (2016) Dark Energy Survey Collaboration, Abbott, T., Abdalla, F. B., et al. 2016, MNRAS, 460, 1270. doi:10.1093/mnras/stw641
  * Debattista et al. (2006) Debattista, Victor P.; Mayer, Lucio; Carollo, C. Marcella; Moore, Ben; Wadsley, James; Quinn, Thomas 2006, ApJ, 645, 209D
  * Domínguez-Gómez et al. (2023) Domínguez-Gómez, J., Pérez, I., Ruiz-Lara, T., et al. Nature (2023). https://doi.org/10.1038/s41586-023-06109-1
  * Duc et al. (2015) Duc, P.-A., Cuillandre, J.-C., Karabal, E., et al. 2015, MNRAS, 446, 120. doi:10.1093/mnras/stu2019
  * de Vaucouleurs (1958) de Vaucouleurs, G. 1958, ApJ, 128, 465D
  * Eliche-Moral et al. (2015) Eliche-Moral, M. C., Borlaff, A., Beckman, J. E., et al. 2015, A&A, 580, A33. doi:10.1051/0004-6361/201424692
  * Erwin et al. (2005) Erwin, Peter; Beckman, John E.; Pohlen, Michael 2005, ApJ, 626L, 81E
  * Erwin et al. (2012) Erwin, Peter; Gutiérrez, Leonel; Beckman, John E. 2012, ApJ, 744L, 11E
  * Espada et al. (2011) Espada, D., Verdes-Montenegro, L., Huchtmeier, W. K., et al. 2011, A&A, 532, A117. doi:10.1051/0004-6361/201016117
  * Fliri & Trujillo (2016) Fliri, J. & Trujillo, I. 2016, MNRAS, 456, 1359. doi:10.1093/mnras/stv2686
  * Freeman (1970) Freeman, K. C. 1970, ApJ, 160, 811. doi:10.1086/150474
  * Gilhuly et al. (2022) Gilhuly, C., Merritt, A., Abraham, R., et al. 2022, ApJ, 932, 44. doi:10.3847/1538-4357/ac6750
  * Gutiérrez et al. (2011) Gutiérrez, L., Erwin, P., Aladro, R., et al. 2011, AJ, 142, 145. doi:10.1088/0004-6256/142/5/145
  * Haigh et al. (2021) Haigh, C., Chamba, N., Venhola, A., et al. 2021, A&A, 645, A107. doi:10.1051/0004-6361/201936561
  * Herpich et al. (2017) Herpich, J., Stinson, G. S., Rix, H.-W., et al. 2017, MNRAS, 470, 4941. doi:10.1093/mnras/stx1511
  * Hickson (1982) Hickson, P. 1982, ApJ, 255, 382. doi:10.1086/159838
  * Huang & Fan (2022) Huang, Q. & Fan, L. 2022, ApJS, 262, 39. doi:10.3847/1538-4365/ac85b1
  * Huchra & Thuan (1977) Huchra, J. & Thuan, T. X. 1977, ApJ, 216, 694. doi:10.1086/155511
  * Infante-Sainz et al. (2020) Infante-Sainz, R., Trujillo, I., & Román, J. 2020, MNRAS, 491, 5317. doi:10.1093/mnras/stz3111
  * Jablonka et al. (2010) Jablonka, P., Tafelmeyer, M., Courbin, F., et al. 2010, A&A, 513, A78. doi:10.1051/0004-6361/200913320
  * Jedrzejewski (1987) Jedrzejewski, R. I. 1987, MNRAS, 226, 747. doi:10.1093/mnras/226.4.747
  * Jiang et al. (2014) Jiang, L., Fan, X., Bian, F., et al. 2014, ApJS, 213, 12. doi:10.1088/0067-0049/213/1/12
  * Johnston et al. (2001) Johnston, K. V., Sackett, P. D., & Bullock, J. S. 2001, ApJ, 557, 137. doi:10.1086/321644
  * Johnston et al. (2008) Johnston, K. V., Bullock, J. S., Sharma, S., et al. 2008, ApJ, 689, 936. doi:10.1086/592228
  * Jones et al. (2018) Jones, M. G., Espada, D., Verdes-Montenegro, L., et al. 2018, A&A, 609, A17. doi:10.1051/0004-6361/201731448
  * Karabal et al. (2017) Karabal, E., Duc, P.-A., Kuntschner, H., et al. 2017, A&A, 601, A86. doi:10.1051/0004-6361/201629974
  * Karachentsev (1972) Karachentsev, I. D. 1972, Soobshcheniya Spetsial’noj Astrofizicheskoj Observatorii, 7, 1
  * Karachentseva (1973) Karachentseva, V. E. 1973, Soobshcheniya Spetsial’noj Astrofizicheskoj Observatorii, 8, 3
  * Karachentseva et al. (1979) Karachentseva, V. E., Karachentsev, I. D., & Shcherbanovsky, A. L. 1979, Astrofizicheskie Issledovaniia Izvestiya Spetsial’noj Astrofizicheskoj Observatorii, 11, 3
  * Kipper et al. (2020) Kipper, R., Benito, M., Tenjes, P., et al. 2020, MNRAS, 498, 1080. doi:10.1093/mnras/staa2486
  * Knapen et al. (2000) Knapen, J. H., Shlosman, I., & Peletier, R. F. 2000, ApJ, 529, 93. doi:10.1086/308266
  * Knapen et al. (2015) Knapen, J. H., Cisternas, M., & Querejeta, M. 2015, MNRAS, 454, 1742. doi:10.1093/mnras/stv2135
  * Kormendy & Kennicutt (2004) Kormendy, J. & Kennicutt, R. C. 2004, ARA&A, 42, 603. doi:10.1146/annurev.astro.42.053102.134024
  * Laine et al. (2002) Laine, S., Shlosman, I., Knapen, J. H., et al. 2002, ApJ, 567, 97. doi:10.1086/323964
  * Laine & Gottesman (1998) Laine, S. & Gottesman, S. T. 1998, MNRAS, 297, 1041. doi:10.1046/j.1365-8711.1998.01513.x
  * Laine et al. (2014) Laine, S., Knapen, J. H., Muñoz-Mateos, J.-C., et al. 2014, MNRAS, 444, 3015. doi:10.1093/mnras/stu1642
  * Lang et al. (2010) Lang, D., Hogg, D. W., Mierle, K., et al. 2010, AJ, 139, 1782. doi:10.1088/0004-6256/139/5/1782
  * Laurikainen & Salo (2001) Laurikainen, E. & Salo, H. 2001, MNRAS, 324, 685. doi:10.1046/j.1365-8711.2001.04347.x
  * Lisenfeld et al. (2011) Lisenfeld, U., Espada, D., Verdes-Montenegro, L., et al. 2011, A&A, 534, A102. doi:10.1051/0004-6361/201117056
  * Lotz et al. (2008) Lotz, J. M., Jonsson, P., Cox, T. J., et al. 2008, MNRAS, 391, 1137. doi:10.1111/j.1365-2966.2008.14004.x
  * Maltby et al (2012) Maltby, David T.; Gray, Meghan E.; Aragón-Salamanca, Alfonso et al. 2012, MNRAS, 419, 669M
  * Martin et al. (2022) Martin, G., Bazkiaei, A. E., Spavone, M., et al. 2022, MNRAS, 513, 1459. doi:10.1093/mnras/stac1003
  * Martínez-Delgado et al. (2015) Martínez-Delgado, D., D’Onghia, E., Chonis, T. S., et al. 2015, AJ, 150, 116. doi:10.1088/0004-6256/150/4/116
  * Martínez-Delgado (2019) Martínez-Delgado, D. 2019, Highlights on Spanish Astrophysics X, 146
  * Martínez-Delgado et al. (2023) Martínez-Delgado, D., Cooper, A. P., Román, J., et al. 2023, A&A, 671, A141. doi:10.1051/0004-6361/202245011
  * Martínez-Lombilla & Knapen (2019) Martínez-Lombilla, C. & Knapen, J. H. 2019, A&A, 629, A12. doi:10.1051/0004-6361/201935464
  * Martín-Navarro et al (2012) Martín-Navarro, Ignacio; Bakos, Judit; Trujillo, Ignacio et al. 2012, MNRAS, 427, 1102M
  * Martínez-Serrano et al (2009) Martínez-Serrano, F. J.; Serna, A.; Doménech-Moral, M.; Domínguez-Tenreiro, R. 2009, ApJ, 705L, 133M
  * Melnyk et al. (2015) Melnyk, O., Karachentseva, V., & Karachentsev, I. 2015, MNRAS, 451, 1482. doi:10.1093/mnras/stv950
  * Mesa et al. (2021) Mesa, V., Alonso, S., Coldwell, G., et al. 2021, MNRAS, 501, 1046. doi:10.1093/mnras/staa3720
  * Mihos et al. (2015) Mihos, J. C., Durrell, P. R., Ferrarese, L., et al. 2015, ApJ, 809, L21. doi:10.1088/2041-8205/809/2/L21
  * Mihos et al. (2017) Mihos, J. C., Harding, P., Feldmeier, J. J., et al. 2017, ApJ, 834, 16. doi:10.3847/1538-4357/834/1/16
  * Mihos (2019) Mihos, J. C. 2019, arXiv:1909.09456
  * Muñoz-Mateos et al. (2015) Muñoz-Mateos, J. C., Sheth, K., Regan, M., et al. 2015, ApJS, 219, 3. doi:10.1088/0067-0049/219/1/3
  * Patterson (1940) Patterson, F., S. 1940, BHar, O.914, 9P
  * Pfeffer et al. (2022) Pfeffer, J. L., Bekki, K., Forbes, D. A., et al. 2022, MNRAS, 509, 261. doi:10.1093/mnras/stab2934
  * Planck Collaboration et al. (2020) Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6. doi:10.1051/0004-6361/201833910
  * Pranger et al. (2017) Pranger, F., Trujillo, I., Kelvin, L. S., et al. 2017, MNRAS, 467, 2127. doi:10.1093/mnras/stx199
  * Pohlen & Trujillo (2006) Pohlen, M.; Trujillo, I. 2006, A&A, 454, 759P
  * Pohlen et al. (2002) Pohlen, M.; Dettmar, R. -J.; Lütticke, R.; Aronica, G. 2002, A&A, 392, 807P
  * Ramírez-Moreta et al. (2018) Ramírez-Moreta, P., Verdes-Montenegro, L., Blasco-Herrera, J., et al. 2018, A&A, 619, A163. doi:10.1051/0004-6361/201833333
  * Román & Trujillo (2018) Román, J. & Trujillo, I. 2018, Research Notes of the American Astronomical Society, 2, 144. doi:10.3847/2515-5172/aad8b8
  * Román et al. (2020) Román, J., Trujillo, I., & Montes, M. 2020, A&A, 644, A42. doi:10.1051/0004-6361/201936111
  * Román et al. (2021) Román, J., Castilla, A., & Pascual-Granado, J. 2021, A&A, 656, A44. doi:10.1051/0004-6361/202142161
  * Román et al. (2023) Román, J., Rich, R. M., Ahvazi, N., et al. 2023, arXiv:2305.03073. doi:10.48550/arXiv.2305.03073
  * Roškar et al. (2008) Roškar, Rok; Debattista, Victor P.; Stinson, Gregory S.; Quinn, Thomas R. et al. 2008, ApJ, 675L, 65R
  * Ruiz-Lara et al. (2016) Ruiz-Lara, T., Pérez, I., Florido, E., et al. 2016, MNRAS, 456, L35. doi:10.1093/mnrasl/slv174
  * Sánchez-Alarcón & Ascasibar (2023) Pablo M Sánchez-Alarcón, Yago Ascasibar, RAS Techniques and Instruments, Volume 2, Issue 1, January 2023, Pages 129–141, doi.org/10.1093/rasti/rzad006
  * Sánchez-Blázquez et al. (2009) Sánchez-Blázquez, P.; Courty, S.; Gibson, B. K.; Brook, C. B. 2009, MNRAS, 398, 591
  * Sandin (2014) Sandin, C. 2014, A&A, 567, A97. doi:10.1051/0004-6361/201423429
  * Schlafly & Finkbeiner (2011) Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103. doi:10.1088/0004-637X/737/2/103
  * Schwarzkopf & Dettmar (2001) Schwarzkopf, U. & Dettmar, R.-J. 2001, A&A, 373, 402. doi:10.1051/0004-6361:20010548
  * Scott et al. (2014) Scott, T. C., Sengupta, C., Verdes Montenegro, L., et al. 2014, A&A, 567, A56. doi:10.1051/0004-6361/201423701
  * Staudaher et al. (2019) Staudaher, S. M., Dale, D. A., & van Zee, L. 2019, MNRAS, 486, 1995. doi:10.1093/mnras/stz935
  * Slater et al. (2009) Slater, C. T., Harding, P., & Mihos, J. C. 2009, PASP, 121, 1267. doi:10.1086/648457
  * Sulentic et al. (2006) Sulentic, J. W., Verdes-Montenegro, L., Bergond, G., et al. 2006, A&A, 449, 937. doi:10.1051/0004-6361:20054020
  * Tang et al. (2020) Tang, Y., Chen, Q., Zhang, H.-X., et al. 2020, ApJ, 897, 79. doi:10.3847/1538-4357/ab98fd
  * Thomas et al. (2005) Thomas, D., Maraston, C., Bender, R., et al. 2005, ApJ, 621, 673. doi:10.1086/426932
  * Trujillo & Fliri (2016) Trujillo, I. & Fliri, J. 2016, ApJ, 823, 123. doi:10.3847/0004-637X/823/2/123
  * Trujillo et al. (2021) Trujillo, I., D’Onofrio, M., Zaritsky, D., et al. 2021, A&A, 654, A40. doi:10.1051/0004-6361/202141603
  * van der Kruit (1979) van der Kruit, P. C. 1979, A&AS, 38, 15V
  * van der Kruit & Searle (1981) van der Kruit, P. C.; Searle, L. 1981, A&A, 95, 105V
  * van der Kruit & Searle (1981b) van der Kruit, P. C.; Searle, L. 1981, A&A, 95, 116V
  * Varela et al. (2004) Varela, J., Moles, M., Márquez, I., et al. 2004, A&A, 420, 873. doi:10.1051/0004-6361:20035697
  * Verdes-Montenegro et al. (2005) Verdes-Montenegro, L., Sulentic, J., Lisenfeld, U., et al. 2005, A&A, 436, 443. doi:10.1051/0004-6361:20042280
  * Verley et al. (2007a) Verley, S., Odewahn, S. C., Verdes-Montenegro, L., et al.
  * Verley et al. (2007b) Verley, S., Leon, S., Verdes-Montenegro, L., et al. 2007, A&A, 472, 121. doi:10.1051/0004-6361:20077481 2007, A&A, 470, 505. doi:10.1051/0004-6361:20077307
  * Wang et al. (2018) Wang, J., Zheng, Z., D’Souza, R., et al. 2018, MNRAS, 479, 4292. doi:10.1093/mnras/sty1687
  * Watkins et al. (2016) Watkins, A. E., Mihos, J. C., & Harding, P. 2016, ApJ, 826, 59. doi:10.3847/0004-637X/826/1/59
  * Watkins et al. (2019) Watkins, A. E., Laine, J., Comerón, S., et al. 2019, A&A, 625, A36. doi:10.1051/0004-6361/201935130
  * York et al. (2000) York, D. G., Adelman, J., Anderson, J. E., et al. 2000, AJ, 120, 1579. doi:10.1086/301513
  * Zernike (1934) Zernike, . von F. 1934, Physica, 1, 689. doi:10.1016/S0031-8914(34)80259-5
  * Zheng et al. (2015) Zheng, Zheng; Thilker, David A.; Heckman, Timothy M. 2015A, pJ, 800, 120Z

##  Appendix A SExtractor configuration parameters.

The parameters that were not set to their default values are:

CHECKIMAGE_TYPE SEGMENTATION
DEBLEND_MINCONT 0.005
DEBLEND_NTHRESH 32
BACK_SIZE 20
DETECT_THRESH 0.9

##  Appendix B Images, masks, and surface brightness radial profiles.

Figure 7: Left panel: r-band or luminance images for the galaxies in the
sample. The ID of each galaxy is shown above. The scale of the colours
represents the surface brightness of the image and the scale is shown in the
profile panel (right) following the y-axis scale. Middle panel: Same image
with the mask applied and the elliptical apertures of the dynamic positional
angle and ellipticity profile. Right panel: Surface brightness profile (top),
positional angle (middle), and ellipticity (bottom) as a function of the
radius in arcseconds (bottom) and kpc (top). The red and green line the
dynamic and fixed elliptical apertures, respectively. The blue line represents
the profiles obtained from rectangular apertures. The position of the disc
break (if any) is shown with the vertical and elliptical aperture of the
dashed line. We smooth CIG 613 image using the FABADA algorithm (Sánchez-
Alarcón & Ascasibar 2023) to enhance the faint structures and we indicate with
arrows the tidal stream found for this galaxy. More information about the
figure can be found in Section 4.