11institutetext: Astronomisches Rechen-Institut, Zentrum für Astronomie der
Universität Heidelberg,
Mönchhofstr. 12–14, 69120 Heidelberg, Germany 22institutetext: Institute for
Computational Cosmology, Durham University, Science Site, South Road, Durham,
DH1 3LE, UK 33institutetext: School of Astronomy, Institute for Research in
Fundamental Sciences (IPM), Tehran, 19395-5531, Iran 44institutetext:
Astronomisches Institut der Ruhr-Universität Bochum, Universitätsstr. 150,
D-44780 Bochum, Germany

# Systematic search for tidal features around nearby galaxies

I. Enhanced SDSS imaging of the Local Volume

Gustavo Morales 11 David Martínez-Delgado 11 Eva K. Grebel 11
Andrew P. Cooper 22 Behnam Javanmardi 33 Arpad Miskolczi 44

###### Abstract

Context. In hierarchical models of galaxy formation, stellar tidal streams are
expected around most, if not all, galaxies. Although these features may
provide useful diagnostics of the $\Lambda$CDM model, their observational
properties remain poorly constrained because they are challenging to detect
and interpret and have been studied in detail for only a sparse sampling of
galaxy population. More quantitative, systematic approaches are required. We
advocate statistical analysis of the counts and properties of such features in
archival wide-field imaging surveys for a direct comparison against results
from numerical simulations.

Aims. We aim to study systematically the frequency of occurrence and other
observational properties of tidal features around nearby galaxies. The sample
we construct will act as a foundational dataset for statistical comparison
with cosmological models of galaxy formation.

Methods. Our approach is based on a visual classification of diffuse features
around a volume-limited sample of nearby galaxies, using a post-processing of
Sloan Digital Sky Survey (SDSS) imaging optimized for the detection of stellar
structure with low surface brightness.

Results. At a limiting surface brightness of $28\
\mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$, 14% of the galaxies in our
sample exhibit evidence of diffuse features likely to have arisen from minor
merging events. Our technique recovers all previously known streams in our
sample and yields a number of new candidates. Consistent with previous
studies, coherent arc-like features and shells are the most common type of
tidal structures found in this study. We conclude that although some
detections are ambiguous and could be corroborated or refuted with deeper
imaging, our technique provides a reliable foundation for the statistical
analysis of diffuse circumgalactic features in wide-area imaging surveys, and
for the identification of targets for follow-up studies.

###### Key Words.:

Methods: observational – Techniques: image processing – Galaxies: formation –
Galaxies: structure – Galaxies: halo

##  1 Introduction

In the $\Lambda$ cold dark matter ($\Lambda$CDM) cosmogony, structures grow
hierarchically under the influence of gravity through numerous mergers of
smaller structures consisting mainly of dark matter (DM) (e.g., Press &
Schechter, 1974; White & Rees, 1978; Blumenthal et al., 1984; Davis et al.,
1985; Lacey & Cole, 1993). Baryonic matter collects in the potential wells of
DM halos, then (in sufficiently massive halos) cools and condenses, eventually
leading to star formation. State-of-the-art cosmological simulations seek to
model the assembly of dark and baryonic mass, star formation, stellar
evolution, and so-called ‘feedback’ processes such as supernovae ab initio in
order to demonstrate how complex interactions between these processes give
rise to the observed diversity of the cosmic galaxy population (e.g.,
Kauffmann et al., 1993; Cole et al., 2000; Croton et al., 2006; Vogelsberger
et al., 2014; Schaye et al., 2015).

In such models, the stellar content of galaxies forms partly in situ through
the condensation of gas in the galaxies themselves, and partly through the
accretion of stars tidally stripped from other galaxies that they encounter
over cosmic time, which may be partially disrupted or have merged completely
by the present day (e.g., Searle & Zinn, 1978; Abadi et al., 2006; Purcell et
al., 2007). The assembly histories of galaxies with a stellar mass comparable
to the mass of the Milky Way vary widely in these models (Guo & White, 2008).
This is supported by observational results from the detailed study of nearby
galaxies. Our Milky Way, for instance, appears to have experienced a
relatively quiescent merger history (Hammer et al., 2007), while its neighbor
M31 shows a much more extended stellar structure, including a variety of
bright stellar streams with different morphologies (e.g., Zucker et al., 2004;
McConnachie et al., 2009; Ibata et al., 2014; Thomas et al., 2017).

A well-established prediction is that most of the mass in stellar halos of
present-day Milky Way-mass galaxies was contributed more than $9$ Gyr ago by a
few satellites in the mass range of $10^{8}$ to $10^{9}$ M⊙ (e.g., Bullock &
Johnston, 2005; De Lucia & Helmi, 2008; Cooper et al., 2010; Pillepich et al.,
2015; Amorisco, 2017b). While stars that formed in situ are expected to
dominate the stellar mass profiles of galaxies at small galactocentric radii,
accreted stars have a much wider range of binding energies and can give rise
to stellar halos extending as far as the virial radius of the host DM halo
(e.g., Bullock et al., 2001; Font et al., 2006; Cooper et al., 2013;
Rodriguez-Gomez et al., 2016). Long dynamical times in the outer regions of DM
halos allow coherent structures formed by tidal stripping, such as streams and
shells, to persist for many gigayears (Johnston et al., 2001). Dynamical
friction causes the few most massive satellites to deposit their stars at
small galactocentric radii, while the outer regions of stellar halos are more
likely to consist of material contributed by a number of less massive
satellites (e.g., Bullock & Johnston, 2005; Amorisco, 2017a). Owing to their
low stellar densities and intrinsically low luminosities, it is hard to
determine both the full extent of stellar halos and their contributions to the
innermost regions of galaxies. Together with other difficulties, this makes it
challenging to constrain stellar fractions observationally ex situ (e.g.,
Cooper et al., 2013; D’Souza et al., 2014; Merritt et al., 2016; Harmsen et
al., 2017).

It is more straightforward to detect recent and ongoing accretion events
involving satellites that are sufficiently luminous to give rise to bright
tidal streams in the outskirts of massive galaxies. A growing number of such
features have been detected beyond the Local Group in recent years, and
further extragalactic surveys reaching sufficiently low surface brightness
have recently been completed or are currently ongoing (e.g., Schweizer &
Seitzer, 1990; Martínez-Delgado et al., 2007, 2008; Mouhcine & Ibata, 2009;
Miskolczi et al., 2011; Ludwig et al., 2012; Duc et al., 2015; Okamoto et al.,
2015; Merritt et al., 2016; Crnojević et al., 2016; Spavone et al., 2017;
Harmsen et al., 2017).

Mergers between galaxies with very different stellar masses (typically mass
ratios of around 1:10 or higher) are often called minor mergers. These
generally involve long-period orbits, little orbital decay or angular momentum
loss for the less massive galaxy (which we refer to hereafter as the
‘satellite’), and little disturbance of the central structure of the more
massive galaxy. Consequently, thin, coherent stellar tidal streams are a
distinctive observable signature of such mergers, more so for less massive,
more recently accreted, and kinematically ‘colder’ satellites (Johnston et
al., 2008). Gaseous tidal streams are commonly observed around interacting
galaxies and can be easily traced through $21$ cm observations. They usually
overlap with the stellar features unless, for instance, ram pressure separates
them. Gaseous streams may also be detectable in optical data, for example,
through their H$\alpha$ emission or dust content. Pure gaseous streams (such
as the trailing Magellanic Stream) are rare, whereas pure stellar streams are
more common around massive galaxies following the dispersal of any previously
associated gas, or when gas-deficient early-type satellites are disrupted. For
a review, see Duc & Renaud (2013). In the case of MW-like hosts, we expect
minor merger events to be less frequent in the present-day Universe and the
coherent structures they generate (such as tidal tails) to persist only for a
few billion years before they become undetectable (Wang et al., 2017).
Observationally, however, the frequency with which such streams occur around
MW-like hosts and their distribution of morphologies are poorly constrained.

Over the past decade, the Stellar Tidal Stream Survey (STSS) has carried out
an ultra-deep, wide-field imaging exploration of several nearby spiral
galaxies, based on data taken with amateur robotic telescopes (Martínez-
Delgado et al., 2008, 2009, 2010, 2012, 2015). This survey has revealed
striking stellar tidal streams of different morphologies with unprecedented
depth and detail. Subsequently, Miskolczi et al. (2011) developed a search
strategy for low-surface brightness tidal structures around a sample of 474
galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 7 archive
(Abazajian et al., 2009). The authors calibrated images taken from the SDSS
archive and processed them in an automated manner. Searching for possible
tidal streams by visual inspection, they found that at least 6% of their
sample showed distinct stream-like features (with a total of 19% presenting
faint features of any kind). This study demonstrated that detecting a
meaningful sample of tidal features close to the detection limit of the SDSS
images is feasible.

Although considerable progress has been made by Miskolczi et al. and other
works, studies of structure with low surface brightness in the outskirts of
galaxies remain predominantly discovery-driven and qualitative. To enable a
meaningful statistical comparison between data with low surface brightness and
cosmological models of galaxy formation, two further advances are urgently
required: samples with both a well-defined selection function and uniform
imaging data, and the development of automated methods to detect and quantify
features with low surface brightness.

The majority of existing deep-imaging studies have been targeted at galaxies
that are either very nearby or have known features detected in shallower
imaging. It is clearly impossible to draw any conclusions about how frequent
such features are from these data alone. Furthermore, prior work has focused
on structures associated with Milky Way-type galaxies. This definition is
subjective; it typically includes galaxies that are sufficiently bright,
morphologically regular, and have late Hubble type. Not only does a subjective
selection make it harder to compare one observational sample to another, but
it is almost impossible to apply a comparable qualitative selection to models.
Currently, even the most sophisticated hydrodynamical simulations do not
reliably reproduce the full range of morphological details that such judgments
are based on. Moreover, selection of Milky Way analogues by qualitative
criteria will almost certainly result in a wide sampling of the distribution
of fundamental quantities such as stellar mass, and a highly incomplete sample
at a given stellar mass. It is much more straightforward, and statistically
sound, to carry out comparisons in terms of observable quantities that can be
robustly constrained in models, stellar mass being the most obvious choice.

Therefore, to make a meaningful comparison between data and models, deep
imaging surveys with simple, quantitative selection functions based on
fundamental quantities are necessary. Ideally, these would exploit the
statistics of brighter circumgalactic features that can be detected in large
samples drawn from shallow wide-area surveys, since the expense of targeted
deep imaging is often hard to justify for surveys in which substantial numbers
of (statistically important) non-detections are to be expected. Low-surface-
brightness features are often said to be ubiquitous, but such statements must
take into account the brightness of the features and the depth of the
observations. A known (and for a given sample, uniform) limit on depth is
crucial to make meaningful statements about counts of structures. Finally,
since the role of accretion in the galaxy formation process can be
investigated through correlations between structure with low surface
brightness and other galaxy properties, it will be necessary to examine large
numbers of host galaxies of similar mass without restriction to specific
morphologies.

In this work, we take a step toward this more systematic approach by making a
statistical assessment of the number of features detected in a survey of a
volume-, magnitude-, and size-limited sample of nearby Milky Way-mass (as
opposed to Milky Way-type) host galaxies. To keep the study consistent, we
select our sample on the basis of mass and recessional velocity. We apply a
custom image reduction process uniformly to images of each galaxy in our
sample from Data Release 10 of the SDSS (Ahn et al., 2014), reaching a
detection limit in surface brightness of approximately $28\
\mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$.

This paper presents our observational results. In subsequent work, they will
form the basis of further investigations into the properties and recent
evolution of stellar halos and comparisons with theoretical predictions from
$\Lambda$CDM models. Stellar halos are believed to have formed through a
series of accretion events occurring over the lifetime of their host galaxies.
Debris associated with the most ancient mergers and those with intrinsically
faint progenitors is likely to have extremely low surface brightness at the
present day (below $30\ \mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$). The
technique we describe here is therefore well suited to studying evidence for
more recent ($t_{\mathrm{lookback}}\sim 4-5\ \mathrm{Gyr}$) interactions and
mergers with more massive satellite galaxies, rather than ancient, well-mixed
halo components or the contribution of fainter satellites.

Several previous surveys of tidal features have been published, albeit with
some key differences in sample selection. Kaviraj (2010) focused on early-type
galaxies (ETGs) and found that $\sim 18\%$ of their sample exhibited signs of
disturbed morphologies (e.g., shells). This sample was also based on SDSS
multiband photometry, but combined with the significantly ($\sim
2\mathrm{mag}$) deeper monochromatic images from the SDSS Stripe 82. Atkinson
et al. (2013) studied faint tidal features in galaxies with a wide range of
morphologies using the wide-field component of the Canada–France–Hawaii
Telescope Legacy Survey. Their sample consisted of 1781 luminous galaxies in
the magnitude range $15.5<r<17.0$. A classification of tidal features
according to their morphology (e.g., streams, shells, and tails) was
performed, with no major interpretation in terms of their physical origin,
especially when distinguishing between major and minor mergers. They found
that about 12% of the galaxies in their sample showed clear tidal features at
their highest confidence level. This fraction increased to about 18% when they
included systems with weaker tidal features. The colors and stellar masses of
central galaxies were found to influence these numbers significantly: linear
features, shells, and fans were more likely in galaxies with stellar masses
$>10^{10.5}\ \mathrm{M_{\odot}}$, and red galaxies were found to be twice more
likely to show tidal features than blue galaxies. Table 1 from Atkinson et al.
(2013) summarizes an overview of faint substructures studies from earlier work
in the literature. We note that no publication attempted a less restricted but
still controlled sample, especially focused on a future comparison with state-
of-the-art simulations.

Throughout the text, we use the term ‘overdensity’ to refer to any kind of
diffuse feature in the processed image that is not obviously the outward
continuation of the brighter isophotes of the host galaxy, without making
claims regarding their origin or nature (including whether they are real
stellar features or are physically associated with the host galaxy). Minor
merger signatures, and more specifically, stellar tidal streams, are
understood as a particular class of overdensities, arising from stars
distributed around the orbit of a current or former satellite, or else a tidal
distortion of the host galaxy. In cases where a host galaxy interacts with a
companion of comparable mass (typically referred to as a major merger), both
may be severely distorted. Our sample contains very few of these non-
equilibrium systems, which we exclude from further consideration.

In Section 2 we describe our sample selection and image post-processing
technique. Section 3 presents our results, including the discovery of several
new streams and a list of tidal feature candidates for follow-up observations.
Section 4 discusses these results and directions for future work. The tables
referenced throughout the paper are presented in Appendix A.

##  2 Data

The aim of this work is to compile a catalog of diffuse overdensities to a
known, uniform limiting depth around an approximately volume- and mass-limited
sample of host galaxies. This will allow us to constrain the rate of
occurrence of tidal debris at the present day and hence (in future work) to
test predictions for the frequency and effects of low-redshift minor mergers
in galaxy formation models. This section describes how we used the Spitzer
Survey of Stellar Structure in Galaxies (S4G, Sheth et al., 2010; Querejeta et
al., 2015) to select such a sample of host galaxies, and how we processed the
SDSS imaging data for these galaxies in order to search for diffuse
overdensities.

###  2.1 Sample

The S4G is a volume-, magnitude-, and size-limited ($d<40$ Mpc,
$|b|>30^{\circ}$, $m_{\mathrm{B_{corr}}}<15.5$, and $D_{25}>1^{\prime}$)
survey of 2352 galaxies using the Infrared Array Camera (IRAC, Fazio et al.,
2004) of the Spitzer Space Telescope (Werner et al., 2004) at 3.6 and 4.5 $\mu
m$. The azimuthally averaged surface brightness profiles obtained by S4G are
typically robust to isophotes at $\mu_{3.6\ \mu m}(AB)\sim 27\
\mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$, equivalent to a stellar mass
surface density of about 1 $\mathrm{M_{\odot}\leavevmode\nobreak\ pc^{-2}}$
(Muñoz-Mateos et al., 2015). S4G thus provides an appropriate data set for the
study of the distribution of stellar mass and structure in the local Universe,
and it is complete for galaxies within the volume relevant to our work and for
masses greater than $10^{9.2}\ \mathrm{M_{\odot}}$, allowing us to select a
statistically representative sample of galaxies whose stellar masses have been
measured in a uniform manner.

Our work focuses on the frequency of tidal features around galaxies at and
above the stellar mass of the Milky Way, because contemporary cosmological
volume simulations can readily resolve these galaxies and their brighter
satellites, which give rise to the most conspicuous features. We therefore
selected elliptical, spiral, and S0 galaxies (according to the morphological
type code $T$ given by S4G) with a lower stellar mass limit of
$10^{10}\mathrm{M_{\odot}}$ in the S4G catalog. Constraining the sample in
stellar mass limits bias when comparing with simulations, because samples can
be selected using equivalent criteria in both. We excluded any galaxies in the
region of the Virgo cluster from our parent sample, as defined by the Next
Generation Virgo Cluster Survey (NGVS) footprint (Muñoz et al., 2014), in both
projected position and line-of-sight distance ($15<d_{\mathrm{L.O.S.}}\
(\mathrm{Mpc})<18$). The study of diffuse circumgalactic structure in dense
environments such as Virgo is complicated by additional tidal forces of the
cluster potential acting on the host and its satellites. Virgo is a ‘rare’
system in the context of the volume we study here, and excluding it allowed us
to better represent the statistics of lower-mass groups and isolated galaxies.
Clusters of mass comparable to Virgo ($\sim 10^{14}\ \mathrm{M_{\odot}}$) can
easily be identified in simulations, so this does not compromise a
straightforward model-data comparison. Moreover, $17$ known major mergers were
removed from the final sample111Targets removed as major mergers are NGC 2798,
NGC 3166, NGC 3169, NGC 3190, NGC 3227, NGC 3998, NGC 5953, NGC 5954, NGC
4550, NGC 5774, NGC 5775, NGC 3395, NGC 5194, NGC 5195, NGC 4302, NGC 5566,
and NGC 5574.. We note that S4G already excludes targets at low Galactic
latitudes ($|b|<30^{\circ}$), which is appropriate for our purposes because
the detection of features with low surface brightness is severely limited by
the presence of extended Galactic cirrus, high extinction, and stellar
crowding. Finally, since we used SDSS imaging, we also excluded S4G galaxies
outside the SDSS footprint.

We processed the SDSS images of the targets selected from S4G in two
individually volume-complete chunks to obtain samples that were feasible for
the observing time constraints on follow-up observations of the robotic
telescope network used in the STSS, which prioritizes more nearby galaxies. In
this first paper we present the results for a Local Volume sub-sample
(galaxies selected with a recession velocity lower than 2000 km/s), comprising
a total of 297 galaxies. Figure 1 shows the distribution of the parent sample
across the sky in celestial coordinates. As shown later, the distance
distribution peaks around $20\ \mathrm{Mpc}$, roughly at the boundary of the
Local Volume (Karachentsev & Kashibadze, 2006). The stellar mass distribution
of the sample is limited to the mass range $10^{10-11}\mathrm{M_{\odot}}$,
which follows directly from our selection function. Both mass and distance
measurements were taken directly from the S4G catalog. Later figures (Section
3) show the sample distribution morphologically and in inclination angle as
well.

###  2.2 SDSS data handling and imaging processing

We used SDSS imaging of the target galaxies selected from S4G in order to
search for faint features in their surroundings. The SDSS imaging camera
worked in drift-scan mode, opening its shutter for extended periods and
imaging a continuous strip of the sky (Gunn et al., 1998). This means that,
while not very deep, the SDSS imaging survey was able to deliver data with
consistently low systematic variations from field to field and excellent flat-
fielding. These conditions are critical when searching for extended, diffuse-
light features close to the detection limit. The SDSS imaging data also lie in
the optical range and have better angular resolution than those of S4G, which
is why the latter was used to select the sample, but not for the discovery of
stellar substructures. See Laine et al. (2014) for a comprehensive survey of
faint structures in the S4G images.

For each of the 297 target galaxies selected from S4G, we downloaded and
reprocessed the available SDSS DR10 imaging archive data. We followed the
procedure described by Miskolczi et al. (2011). This consists of four steps:
(1) mosaicing of the SDSS images in each bandpass; (2) stacking images in
multiple bands to improve the signal-to-noise ratio (S/N), with no weighting
applied; (3) two-stage source extraction, including removal of point sources;
and (4) Gaussian filtering to enhance features on the scale of interest.

Figure 1: Aitoff projection of the full S4G catalog (empty and filled red
circles). The filled red circles mark our selected parent galaxy sample. The
dashed lines enclose the Galactic plane area, the solid gray line encompasses
the SDSS DR10 footprint, and the solid gray region encompasses the Virgo
Cluster area as defined by the NGVS.

Square mosaics of $30$ arcmin ($4595$ pixels) per side were created in three
filters, $g$, $r,$ and $i$, using the automatic script in the SDSS Science
Archive Server that can be found online222dr10.sdss.org/mosaics (at $20\
\mathrm{Mpc}$, $30$ arcmin corresponds to approximately $176\ \mathrm{kpc}$).
We used these three filters because they have the highest reported
sensitivity, and because their combined transmission curve closely resembles
the luminance filters used by other observational works, such as Martínez-
Delgado et al. (2010). The mosaics of each filter were then stacked using the
IRAF task `imcombine` with the default parameters, in order to improve the S/N
of the image. We call this stacked image $I_{\mathrm{gri}}$.

Our analysis relies heavily on visual inspection of extended, diffuse features
in moderately crowded stellar fields. We therefore processed the stacked
images with SExtractor (Bertin & Arnouts, 1996) using a two-stage procedure
(known as “hot and cold run”, Caldwell et al. 2008) in order to remove the
majority of unsaturated point sources while preserving regions of diffuse
emission. In Step 1, we extracted all sources covering an area of at least 5
pixels at a signficance of $1.5\sigma$ and saved a FITS file, $I_{5}$,
containing these detections (including the central galaxy, which covers a
significant fraction of the image). In the second run, the minimum source area
was set to 800 pixels ($\approx 30\ \mathrm{kpc^{2}}$ at $20\ \mathrm{Mpc}$),
so that only the central galaxy and any other large objects were detected. We
call the corresponding FITS file $I_{800}$. A final image was then created by
subtracting $I_{800}$ from $I_{5}$, that is, the large-scale source(s) from
the total detections. The image resulting from this operation contains only
compact sources (mainly stars). We call this image file $I_{s}=I_{5}-I_{800}$.
Using the IRAF task `imarith`, the sources previously extracted were
subtracted from the original stacked image, that is,
$I_{*}=I_{\mathrm{gri}}-I_{s}$. Thus, $I_{*}$ is a stacked image with most of
the stars in the field masked out, replaced by the average flux of the
neighboring pixels.

To enhance the visibility of faint, extended features, we then applied a
circularly symmetric Gaussian filter to $I_{*}$. Miskolczi et al. (2011)
reported that other possible filter types are available in IRAF, including
`adaptive` and `hfilter`, which are both based on the Haar-Transform (Fritze
et al., 1977). By testing these filters with different settings, they reported
that while both are able to enhance faint features, neither is clearly an
improvement over Gaussian filtering. A Gaussian filter is then preferred
because it is computationally more efficient than other filters. By
experimenting with the parameters of the Gaussian filter, they also reported
that the best enhancement of faint extended features is achieved with a kernel
scale of $\sigma=7$. We have carried out our own tests and reached similar
conclusions, finding that the best compromise between enhancing diffuse
structures and preserving image resolution can be found at a $\sigma$ of $5$
to $7$ pixels, which at a distance of $20\ \mathrm{Mpc}$ corresponds to
roughly $2$ to $3$ kpc. This works because the diffuse features of interest in
this study have scales of a few kiloparsecs, therefore removing fluctuations
on smaller scales makes them easier to detect by visual inspection.
Convolutions with broader kernels take longer to compute without achieving
higher detectability. Figure (2) shows an example of the use of this
enhancement technique to reveal the giant shell around NGC 4414. Whenever
possible, we have added color insets of the central galaxies to the stretched
images in order to visualize the relative extent of each galaxy and its low
surface brightness halo.

|  |
---|---|---
Figure 2: Example of the enhancement technique described in Sec.2.2 for NGC
4414. The field of view for each panel is $\sim$ 30 $\times$ 30 arcminutes
(north is up, east to the left). Left panel: Original SDSS color-composite
image from the public archive. Middle panel: Final result of our image
processing with an inverted, stretched grayscale showing the extent of a
conspicuous shell of debris southwest of the central galaxy. For illustrative
purposes, we have added a color inset of the disk of the galaxy and any stars
or other objects that are masked in our analysis. Right panel: Same field
taken from the STSS (Martinez-Delgado et al. in preparation), showing the same
overall morphology of this substructure. Credit right panel image: Adam Block.

###  2.3 Photometric calibration and distribution of the surface brightness
limit

An important issue for this work is to quantify the depth to which SDSS data
allow us to explore faint stellar halo structures. In addition, the mean
surface brightness limits of our images must have a narrow distribution to
avoid image-to-image variance biasing any statistics we derive from visual
inspection. Since the SDSS data were taken over a period of several years, we
have to verify that the surface brightness limits of the images of different
galaxies do not reflect variations in the quality of flat-fielding and the sky
conditions during the observations, such as transparency and lunar phase (we
note that SDSS generally observed in dark sky conditions; Eisenstein et al.
2011, e.g.,; York et al. 2000, e.g.,; Gunn et al. 2006, e.g.,). Scattered
light due to bright stars in the vicinity of a galaxy will also contribute to
fluctuations in depth. Large differences in seeing, depth, and the variance of
depth across the image can lead to an important bias in the statistics of
faint overdensities in our galaxy sample, since in some cases, non-detections
of streams could be due to observational effects.

To quantify this, we measured the surface brightness limit of each image in
our sample as follows. First, we performed a photometric calibration to the
SDSS $r$ band for the coadded images, using the same approach as our previous
studies of stellar tidal streams (Chonis et al., 2011) and dwarf satellite
galaxy populations (Javanmardi et al., 2016). We chose the SDSS $r$ band to be
consistent with other optical studies. All 297 processed images were
calibrated using the semi-automatic pipeline developed (and successfully
demonstrated) by the DGSAT333Dwarf Galaxy Survey with Amateur Telescopes
project (Javanmardi et al., 2016).

Given the similarity between the effective bandpass of the stacked SDSS images
and the wide-band luminance filter (used in the DGSAT), the calibration of our
stacked images to the $r$ band requires a color correction, taking the form

$r_{cal}=c_{0}\ell_{\rm{stacked}}+c_{1}(g-r)+c_{2},$ (1)

where $r_{cal}$ is the calibrated $r$ magnitude, $\ell_{\rm{stacked}}$ is the
magnitude measured in the ‘pseudo-luminance’ band of the stacked image,
$c_{0}$ fixes the linear relation between these two magnitudes, $c_{1}$
corrects for a color dependence, and $c_{2}$ is the magnitude zero-point
correction. The constants $c_{i}$ are obtained using a set of calibrating
stars in each image. These stars are selected using an automated statistical
approach (rather than by hand), using the SDSS $g$ and $r$ band as standard
magnitudes.

First, SExtractor (Bertin & Arnouts, 1996) was used to detect all the objects
in each image. The detected objects were then cross-matched with the most
recent SDSS photometric catalog, and only stars with $r\geq 15$,
$0.08<(r-i)<0.5$ and $0.2<(g-r)<1.4$ passed on to the next step (see Chonis &
Gaskell, 2008). At this point, very many stars are available for calibration
of each image. The SDSS r-band magnitudes of the stars were compared
iteratively to $r_{cal}$ calculated from each image and the $c_{i}$ for each
stacked image obtained by a $\chi^{2}$ minimization.

Figure 3: Distribution of the surface brightness limit in our sample with a
Gaussian fit, using the $232$ images in the sample with $N_{\mathrm{star}}>50$
stars after the $\sigma$ clipping as described in Sec. 2.3. We obtained an
average value of $28.11$, with a standard deviation of $0.26$.

Next, any star with $\Delta r\equiv r_{SDSS}-r_{cal}$ deviating by more than
twice the standard deviation $\sigma$ from the best-fit relation was discarded
and the calibration relation was fit again to obtain new $c_{i}$. This
clipping was repeated until no $2\sigma$ outlier remained, which gave us the
final $c_{i}$ for each image. The standard deviation of $\Delta r$ provides an
estimate of the uncertainty in the calibration and is added in quadrature when
we report the uncertainty in magnitudes for each image. See Javanmardi et al.
(2016) for further details of this approach to photometric calibration.

After calibrating the data set to the SDSS $r$ band, the limiting surface
brightnesses of our images were determined following the approach described in
Martínez-Delgado et al. (2010). In short, to estimate the (residual) sky
background, we measured the standard deviation in random sky apertures of $3$
arcseconds in diameter and computed the surface brightness corresponding to
five times the standard deviation. Figure 3 displays the distribution of the
surface brightness limit of all images in our sample due to the mean sky
background, showing that the data used in this work are sufficiently
homogeneous in terms of quality and depth. We conclude that the mean sky
surface brightness limit of our sample in the $r$ band is SB${}_{r,lim}\approx
28.1\ \pm 0.3\ \mathrm{mag/arcsec}^{2}$. This means that for the purposes of
the following analysis, we can neglect variations in depth as a significant
source of bias in the statistics of low surface brightness features recovered
by our visual inspection.

###  2.4 Deeper follow-up of tidal feature candidates

Although our processed SDSS images reach a surface brightness limit in the $r$
band (SBr,lim) that would conventionally be considered ‘deep’, they are still
only deep enough to reveal the brightest structures (if any) in the halos of
our target galaxies. In some cases, the low S/N detection of a particular
feature and artifacts in the image significantly reduce our confidence in the
nature of the detection and/or its interpretation as a signature of tidal
disruption. Better (i.e., deeper) data are necessary to improve confidence in
these detections.

Figure 4 shows some examples of different types of overdensities found in our
search. These illustrate cases in which it is ambiguous whether well-detected
overdensities are the result of minor mergers or perturbations of the central
galaxy, such as extended stellar warps (e.g., NGC 5506), rings (e.g., NGC
2859) or other tidal distortions (e.g., Trujillo et al., 2009). Significant
sky background fluctuations or extended Galactic cirrus (e.g., NGC 7497) are
also a well-known problem for the detection of tidal streams (e.g., Duc et
al., 2015). Finally, NGC 3489 is a clear example of a typical artifact in the
SDSS images, a reflection from a bright star that resembles a diffuse
satellite interacting with the central galaxy.

\begin{overpic}[width=216.81pt]{ngc5506_cutout.png} \put(60.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 5506}}} \end{overpic} | \begin{overpic}[width=216.81pt]{ngc2859_cutout.png} \put(60.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 2859}}} \end{overpic}
---|---
\begin{overpic}[width=216.81pt]{ngc3489_cutout.png} \put(60.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3489}}} \end{overpic} | \begin{overpic}[width=216.81pt]{ngc7497_cutout.png} \put(60.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 7497}}} \end{overpic}
Figure 4: Examples of very faint diffuse overdensities of different types
found during our analysis: i) giant stellar warps of a galactic disk (NGC
5506); ii) a stellar ring with two seemingly interacting, partially disrupted
cores embedded in it (NGC 2859); iii) an image artifact resembling a giant
satellite (NGC 3489); and iv) extensive Galactic cirrus around NGC 7497. All
these images have been processed with our technique, adapted from Miskolczi et
al. (2011), using stacked SDSS $g$, $r,$ an $i$ band images, with a field of
view of 30 arcminutes. North is up, east to the left.

We have explored the availability of deep images for our stream candidates in
two separate sources of additional optical data described below.
Unfortunately, these additional surveys currently cover a smaller sky area and
have fewer bandpasses than the SDSS, and hence are not suitable for the
statistical analysis we attempt with SDSS data in this paper.

####  2.4.1 Stellar Tidal Stream Survey

Figure 5 shows a comparison of our results to the ultra-deep observations of
the STSS (Martínez-Delgado et al., 2010) for a set of well-known diffuse
features. As found by Miskolczi et al. (2011), the filtering technique we used
renders visible in SDSS images the majority of features reported so far by the
robotic amateur telescope observations in the STSS pilot survey, although with
a lower S/N because of the brighter surface brightness limit of the SDSS. The
lower quality of our SDSS data compared to those of Martínez-Delgado et al.
(2010) is mainly explained by the short effective exposure times of the
individual broadband SDSS observations. This complicates the classification of
very faint overdensities, since the lower S/N makes it harder to distinguish
actual tidal features from overdensities related to Galactic cirrus or image
artifacts. Deeper follow-up observations are necessary to classify these
ambiguous detections.

Figure 5: Comparison between our processed SDSS images and the deep images
from the STSS (see Sec. 2.4.1) for the spiral galaxies (from left to right)
NGC 5055, NGC 4651, NGC 1055, and NGC 1084. Top row: Images taken from
Martínez-Delgado et al. (2010). Bottom row: This work, using SDSS data, after
processing as described in Miskolczi et al. (2011), stacking $g-$, $r-,$ and
$i$ -band images. Even at the shallower depth reached by the SDSS, high-
confidence detections can be made with our technique. North is up, east to the
left.

Figure 6 illustrates the benefits of deeper follow-up with observations like
those of the STSS for three galaxies in our sample. The first column presents
NGC 7743, a galaxy with an apparently clear stellar tidal stream candidate in
its outskirts; however, with STSS observations this feature is shown to be (at
least predominantly) Galactic cirrus. The second column presents NGC 5750,
which shows a remarkable irregular substructure apparently emerging from its
disk; deeper STSS observations reveal an additional overdensity on the other
side of the galaxy, which is only barely visible at the detection limit of our
SDSS images. Finally, the third column presents NGC 3041, in which an arc-like
feature is apparent to the north of the galaxy. The amateur telescope data
strongly support the interpretation of this feture as a great-circle stream.

\begin{overpic}[width=433.62pt]{misk_vs_stss2.jpg}
\put(12.0,30.0){\hbox{\pagecolor{white}NGC7743}}
\put(46.0,30.0){\hbox{\pagecolor{white}NGC5750}}
\put(79.0,30.0){\hbox{\pagecolor{white}NGC3041}} \end{overpic} Figure 6:
Examples of some follow-up images used to confirm stellar tidal stream
candidates in our sample. The top row shows the SDSS $g$-$r$-$i$ stacked
images for NGC 7743, NGC 5750, and NGC 3041 (see Sec. 3) processed as
described in Sec. 2, and kindly provided by A. Miskolczi. The bottom row shows
the deep images obtained by the STSS (Martínez-Delgado et al., in prep.) for
the same objects, but with a luminance filter. In all cases, the deeper images
detect additional features or reveal a more detailed morphology of the
features detected in the SDSS images.

####  2.4.2 Dark Energy Camera Legacy Survey

We have also searched for images of galaxies with visible low surface
brightness features (Table LABEL:tab:main_table) in the optical images from
the third data release (DR3) of the Dark Energy Camera Legacy Survey (DECaLS,
Blum et al., 2016). This survey uses the Dark Energy Camera (DECam), a wide-
field CCD imager at the CTIO Blanco 4 m telescope, to obtain optical imaging
covering 14,000 deg2 in three optical bands ($g$,$r$,$z$). Since the footprint
is mostly in the equatorial and southern sky and only a fraction of the DECaLS
data have been publicly released, only a few targets have been imaged with
sufficient quality and depth to aid in the interpretation of our SDSS images.
In the publicly available DECaLS data, we found that three of our targets were
imaged in the $g$, $r$, and $z$ bands, confirming the detected streams or
diffuse-light substructure in the halo from our analysis. Although some sky
regions have been imaged in just one DECaLS band so far, we are able to
improve our confidence in some low surface brightness features with even these
data (see Sec. 3.3). Regarding background subtraction around large objects, it
must also be noted that the DECaLS data reduction for large sources has not
yet been optimized to the same extent as in the SDSS (Blanton et al., 2011).
This explains the rectangular patches in DECaLS images with poor subtraction
around large galaxies, which sometimes mimic diffuse galactic structure.

##  3 Results

###  3.1 Confidence of detections and morphologies

For all of the galaxies listed in Table LABEL:tab:main_table, we estimated our
confidence in the detection of faint tidal features on a five-point scale,
similar to the scheme used by Atkinson et al. (2013). We refer to it as the
detection confidence level (DCL), reflecting our certainty that a tidal
feature with low surface brightness that is associated with the target galaxy
was detected in an image, as follows:

0:

No detection of any sort, or high confidence that any candidates are
perturbations of the central object (spiral arms, cirrus, etc.).

1:

Very uncertain detection of a feature at a S/N too low to judge either the
quality of the detection or its tidal nature.

2:

Possible detection of a low surface brightness feature, but with low
confidence in a tidal origin ($\sim 50\%$ certain).

3:

Strong detection judged highly likely to be of tidal origin, but without
support from any data other than our own.

4:

Strong detection where a tidal origin is supported by other data.

In the same table, we also provide an approximate visual classification system
for the morphology of the most common features we detect using the following
categories, which are not mutually exclusive:

S

for classic shells. Disconnected, coherent arcs of material usually concentric
with the central galaxy.

C

for any coherent, curvilinear features seen in the image (that are not
shells). This includes arcs, plumes of debris, and looped structures of gas or
stars surrounding their host.

Sph

for spheroids and diffuse satellites in the process of disruption, suggestive
of very low surface brightness galaxies.

E

for extensions of the central galaxy, including but not limited to warps and
spiral arms, and some unclassifiable overdensities clearly connected to the
disk.

O

for any other less common type of features not included above, but suggestive
of tidal interactions: fuzzy clouds, spikes, wedges, irregular filaments, etc.

These categories are intended as an simple indication of the appearance of the
features we detect. Stronger conclusions about the true physical nature of
these features are beyond the scope of this work, and in most cases would
require support from techniques other than photometry.

###  3.2 Sample statistics

By visual inspection of the processed images, we determine that $51$ of the
$297$ galaxies in our sample show either clear or potential signatures of
diffuse overdensities in their outskirts above our surface brightness limit
($28.1\ \mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$). Table
LABEL:tab:main_table describe these galaxies and their associated low-surface-
brightness features. Of these $51$ targets, $28$ show overdensities that we
judge to be either stellar or gaseous tidal features on the basis of other,
deeper observations. A further $23$ objects for which we currently lack deeper
observations show overdensities that are likely tidal feature candidates
(listed in Table LABEL:tab:main_table as features with DCL 1 and 2; see Sec.
3.1). Hence a conservative estimate for the frequency with which such features
occur in our volume- and mass-limited sample of the local Universe is $\approx
9\%$. This would rise to $\approx 17\%$ if all candidates were confirmed by
deeper follow-up observations. Considering only previously published features
together with the new discoveries reported in this paper, we estimate that
$\approx 14\%$ of galaxies in the local Universe exhibit diffuse tidal
features brighter than $28.1\ \mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$ in
the SDSS $r$ band. As a reference, all galaxies in our sample that do not show
any evidence of diffuse-light structures are listed in Table 3.

Figure 7 shows histograms of our galaxy samples, including the parent sample
and subsets of targets that show evidence of tidal streams444Instead of using
the mean redshift-independent distances from NED, we here used the Hubble flow
distances, $cz/H_{0}$, where $cz$ is the recessional velocity, and $H_{0}=75\
\mathrm{km/s/Mpc}$.. Furthermore, it shows that above the surface brightness
limit of our sample there are no significant selection effects arising from
either morphology or inclination angle, consistent with a roughly isotropic
distribution of features. There are some hints of an excess of low surface
brightness features at short distance and high stellar mass. The latter is
compatible with the expectation of $\Lambda$CDM, where more massive galaxies
are hosted by more massive DM haloes and are therefore more likely to accrete
brighter satellites. Any selection effect with distance is likely to reflect
the balance between this effect (large volumes include more bright galaxies)
and the increasing difficulty of detecting low surface brightness
substructures at larger distances.

We also computed a two-sample Kolmogorov-Smirnov (KS) test to provide a
quantitative comparison between the distance, mass, morphology, and
inclination angle distributions of the $297$ galaxies in our parent sample and
those of the hosts of high-confidence tidal feature candidates from Table
LABEL:tab:main_table (this means a DCL equal to 3 or 4, i.e., a comparison of
the black and solid green histograms in Fig. 7). The $p$-values obtained are
shown in Table 1. At a significance of $p=0.05$, on the basis of any one of
these four distributions, we cannot reject the null hypothesis that our sample
of galaxies with overdensities is drawn from the same underlying population as
the parent sample we selected from S4G. In other words, random sampling from
our parent sample has a high probability of yielding distributions similar to
those of our sample of galaxies with overdensities.

Variable |  $p$-value
---|---
Distance | 0.113
Stellar Mass | 0.067
Hubble Stage | 0.241
Inclination | 0.654
Table 1: $p$-values obtained from a two-sample KS test applied to the
histograms depicted in Fig. 7; specifically, the distribution of confirmed
tidal streams plus Class I candidates versus the whole sample of $297$
galaxies. We cannot reject the hypothesis that the distributions of the two
samples are the same. Figure 7: Histograms of the diffuse-light features found
in our whole sample, with or without overdensities, as a function of target
distance, stellar mass, morphology and inclination angle. The distribution of
all 297 galaxies in our sample is shown in black, while histograms in color
correspond to the galaxies listed in Table LABEL:tab:main_table, our main
results. The red distributions represent 28 confirmed features, previously
known and new (with a DCL of 4; see Sec. 3.1). Unconfirmed feature candidates
(with a DCL of 1 and 2) are represented by blue dotted histograms. Confirmed
streams and strong candidates (i.e., every feature with a DLC of 3 or 4) are
grouped together in the solid green histogram ($41$ targets). For our limiting
sky surface brightness of $28.1\ \pm 0.3\ \mathrm{mag\leavevmode\nobreak\
arcsec^{-2}}$, this implies that $\approx 14\%$ of the galaxies in the mass
and volume limits our parent sample have detectable stellar overdensities in
their outskirts. No significant biases are apparent in our sample of galaxies
with diffuse overdensities (with respect to the S4G parent sample, black solid
line) except for a somewhat flatter distribution of stellar mass and the lack
of overdensities for galaxies more distant than $35$ Mpc.

###  3.3 Confirmed stellar structures with low surface brightness

Table LABEL:tab:main_table lists, among others, the $28$ tidal streams that we
have confirmed. This list contains $12$ unpublished detections, including
those found recently in the STSS (Martinez-Delgado et al., in preparation).
Figure 8 shows the corresponding images for each of their $12$ host galaxies.
In these images, the disks of galaxies tend to dominate the field of view
because the images have been significantly contrast-stretched to render the
low surface brightness structures visible. These new streams are briefly
described below. The estimated physical extent of these substructures has been
calculated assuming the distance to the target taken from the NASA/IPAC
Extragalactic Database (NED). It must be noted that the NED uses the mean
value of redshift-independent distances. When no mean distance is reported,
the Hubble flow distance is used instead.

\begin{overpic}[width=130.08731pt]{ngc0681_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 681}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc2775_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 2775}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc3041_paperins.jpg} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3041}}} \end{overpic}
---|---|---
\begin{overpic}[width=130.08731pt]{ngc3049_paperins.jpg} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3049}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc3611_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3611}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc3631_paperins.jpg} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3631}}} \end{overpic}
\begin{overpic}[width=130.08731pt]{ngc3682_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3682}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc4203_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 4203}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc4643_paperins.jpg} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 4643}}} \end{overpic}
\begin{overpic}[width=130.08731pt]{ngc5750_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 5750}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc7742_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 7742}}} \end{overpic} | \begin{overpic}[width=130.08731pt]{ngc7743_paperins.png} \put(68.0,2.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 7743}}} \end{overpic}
Figure 8: Confirmed tidal streams from Table LABEL:tab:main_table detected by
stacking $g-r-i$ SDSS bands as described in this work. Streams already
reported in previous publications are not included. The red lines indicate a
scale of 3 arcminutes. In some cases, blue arrows indicate structures of
interest described in Section 3.3. North is up and east to the left.

NGC 681

is an edge-on disk galaxy with a prominent spheroid surrounded by two clear
shells along the major axis, extending to $R=25\ \mathrm{kpc}$ southwest and
$R=39\ \mathrm{kpc}$ northeast. Other possible arc-like features (concentric
around the galaxy $R=10\ \mathrm{kpc}$ to the south and extending northeast
from the south edge of image) are not apparent in DECaLS images (see Fig. 10).

NGC 2775

is an unbarred spiral galaxy showing a prominent $\sim 29\ \mathrm{kpc}$
cloudy structure in its halo, reminiscent of a classical shell from Martínez-
Delgado et al. (2010).

NGC 3041

shows an arc-like stream with an extent along its longest dimension of $\sim
4\ \mathrm{kpc}$, northeast of the central galaxy. STSS and DECaLS data (Fig.
6) show this feature clearly, but they do not reveal any further detail. This
may be the brighter part of a great circle structure similar to the Milky Way
Sagittarius stream, but no surviving progenitor is apparent.

NGC 3049

shows an arc-like feature east of the central galaxy, with a size of $\sim 3\
\mathrm{kpc}$. Another very diffuse substructure can be identified to the
west, suggestive of a shell formed by tidal disruption. More definitive
statements require deeper observations.

NGC 3611

is well known for the peculiar $\sim 30\ \mathrm{kpc}$ bright off-center ring-
like structure previously noted by Schweizer & Seitzer (1990). These authors
favored merging as the origin of this feature, excluding the possibility of a
disturbed polar ring. DECaLS data (Fig. 10) show two distinct features: a
clear umbrella-like stream with shells on both sides of the galaxy (the most
prominent to the east), and an incomplete blue ring or arc encircling the
disk. The colors of both structures are clearly different, and it is unclear
whether they have a common origin (e.g., the tidal disruption of a Magellanic-
type dwarf galaxy).

NGC 3631

shows a giant cloud at a galactocentric distance of $\sim 19\ \mathrm{kpc}$.
This is very similar to the M83 stream (Malin & Hadley, 1997). It is not clear
whether the structure is part of a very faint outer disk or a tidal structure
in the galactic halo. This overdensity has also been observed by the STSS
(Martinez-Delgado et al., in preparation), indicating that it is not an
artifact in the SDSS image.

NGC 3682

shows two classical shells on both sides of the central galaxy, with diameters
of $\sim 2\ \mathrm{kpc}$.

NGC 4203

shows a bright, partially disrupted and nucleated satellite southwest of the
galaxy, with both a leading and a trailing tail of total length $\sim 13\
\mathrm{kpc}$.

NGC 4569

is a spiral galaxy with a dIrr satellite (IC 3583) to the north, with an
apparent interaction between the two555Although gravitational interaction has
been ruled out by some authors (e.g., Boselli et al., 2016).. There is
evidence of a shell-like overdensity on the northern side of the galaxy,
although we cannot reject the possibility that this is an extended warp of the
stellar disk.

NGC 4643

shows a clear stellar tidal stream apparently perpendicular to the plane of
the galaxy. DECaLS data show evidence for a progenitor in the northern tail.
Assuming that both structures apparent in the image are part of the same
feature (for example, an arc viewed edge-on), this feature has an extent of
$\sim 73\ \mathrm{kpc}$. Whitmore et al. (1990) reported an inner, edge-on arc
structure in the main body of the galaxy that is also visible in our images,
but not related to the giant tidal structure we report here.

NGC 5750

Both images from our analysis and the STSS deeper images (see Fig. 6) show a
truncated overdensity west of the central galaxy, which resembles a faint,
distorted satellite galaxy. In addition, an elongated, irregular feature east
of the disk (clearly visible in the STSS image) could be part of a tidal
stream associated with that satellite.

NGC 7742

is a face-on unbarred Seyfert spiral galaxy, which shows three very distinct
stellar arcs, possibly sections of a shell (or shells), each $16-17\
\mathrm{kpc}$ in diameter.

NGC 7743

is a barred Seyfert spiral galaxy showing a giant, $18\ \mathrm{kpc}$ loop
structure to the northeast. Galactic dust clouds dominate the field of view in
longer exposures, as shown in the first column of Fig. 6.

###  3.4 Tidal stream candidates for follow-up studies

Table LABEL:tab:main_table lists the galaxies of our sample with detected
structures for which a tidal origin cannot be confirmed in this work because
we lack deeper data; $23$ in total, with a DCL equal to 1 or 2. Follow-up
observations of these galaxies are currently being carried out by the STSS and
will be published in a forthcoming companion contribution (Martínez-Delgado et
al., in preparation). These signatures define those that are very probably
stellar tidal streams, that is, tracing orbits of satellites in the tidal
field of the host galaxy, and features that are probably linked to disk
warping, polar rings, and other types of signatures. In general, any features
more likely related to galactic perturbations of the central galaxy disk due
to dynamical interaction with other massive galaxies were tagged accordingly.
Some examples of these structures of different types are displayed in Fig. 9.
Figure 10 shows the images used to confirm the faint tidal debris detected
around six of the galaxies listed in Table LABEL:tab:main_table.

\begin{overpic}[width=173.44534pt]{ngc0718_cutoutins.png} \put(75.0,1.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 718}}} \end{overpic} | \begin{overpic}[width=173.44534pt]{ngc0936_cutoutins.png} \put(75.0,1.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 936}}} \end{overpic}
---|---
\begin{overpic}[width=173.44534pt]{ngc3034_cutoutins.png} \put(75.0,1.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 3034}}} \end{overpic} | \begin{overpic}[width=173.44534pt]{ngc4519_cutoutins.png} \put(75.0,1.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 4519}}} \end{overpic}
\begin{overpic}[width=173.44534pt]{ngc4691_paperins.png} \put(75.0,1.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 4691}}} \end{overpic} | \begin{overpic}[width=173.44534pt]{ngc4762_cutoutins.png} \put(75.0,1.0){\hbox{\pagecolor{white}\parbox{173.44534pt}{NGC 4762}}} \end{overpic}
Figure 9: Selection of the diffuse-light features detected around some of the galaxies listed in Table LABEL:tab:main_table. Deeper data are needed to confirm their origin (tidal streams, galactic perturbations, extended spiral arms, etc). The red lines indicate a scale of 3 arcminutes. North is up and east to the left. \begin{overpic}[width=216.81pt]{NGC681ins.png} \put(0.0,2.0){\hbox{\pagecolor{white}\parbox{65.04034pt}{NGC 681}}} \end{overpic} | \begin{overpic}[width=216.81pt]{NGC3041ins.png} \put(0.0,2.0){\hbox{\pagecolor{white}\parbox{73.7146pt}{NGC 3041}}} \end{overpic}
---|---
\begin{overpic}[width=216.81pt]{NGC4772ins.png} \put(0.0,2.0){\hbox{\pagecolor{white}\parbox{73.7146pt}{NGC 4772}}} \end{overpic} | \begin{overpic}[width=216.81pt]{NGC3611ins.png} \put(0.0,2.0){\hbox{\pagecolor{white}\parbox{73.7146pt}{NGC 3611}}} \end{overpic}
\begin{overpic}[width=216.81pt]{NGC4753ins.png} \put(0.0,2.0){\hbox{\pagecolor{white}\parbox{73.7146pt}{NGC 4753}}} \end{overpic} | \begin{overpic}[width=216.81pt]{NGC4643ins.png} \put(0.0,2.0){\hbox{\pagecolor{white}\parbox{73.7146pt}{NGC 4643}}} \end{overpic}
Figure 10: Images taken from DECaLS public survey, confirming some of our
findings. See Figure 8 for more information. A color inset of the disk of each
galaxy taken from this survey has been included as reference.

##  4 Conclusions

We have estimated the frequency of stellar tidal streams in the halos of
massive galaxies in the local Universe by processing SDSS images to reveal low
surface brigthness features, using a technique similar to that of Miskolczi et
al. (2011). Our results are summarized in Table LABEL:tab:main_table. To
facilitate statistical comparisons with cosmological simulations of galaxy
formation, we have defined a volume-, mass-, and size-limited parent sample of
galaxies with stellar masses similar to that of the Milky Way based on the S4G
catalog. From the $2331$ galaxies listed by S4G, our sample selects $297$
targets from the SDSS footprint (excluding low Galactic latitudes, major
mergers, and the Virgo cluster). We estimate that the typical surface
brightness limit of the SDSS images for these galaxies (after stacking their
$g$, $r,$ and $i$ band images) is $28.1\ \pm 0.3\
\mathrm{mag\leavevmode\nobreak\ arcsec^{-2}}$.

By visual inspection, we detected a total of $28$ confirmed tidal streams,
including new features discovered in this study and some previously known
tidal streams. Therefore, our most conservative estimate is that $9\%$ of the
galaxies in our sample show evidence of diffuse features that may be linked to
minor merging events (either stellar or gaseous streams, or a mixture of
both). This fraction of galaxies displaying tidal features does not include
the possible new, but unconfirmed detections listed in Table
LABEL:tab:main_table. When we also count the systems with high-confidence
detections (i.e., with a DCL of 3 or 4), the frequency of tidal features in
our sample rises to $14\%$. It is important to remark that some of these
diffuse-light features may not be the signature of dwarf satellite remnants,
but instead Galactic cirrus, imaging artifacts, or distorted spiral arms. This
underscores the importance of deeper observations to confirm the nature of
these features (see Fig. 4).

These results are broadly consistent with comparable studies cited in Section
1, in particular those listed in Table 1 from Atkinson et al. (2013). Although
the surface brightness limits of the observations used in these earlier
studies are more or less compatible, the wide variety of sample selections
limits a more detailed comparison of the final results. Bright tidal features
are expected to be relatively more likely in ETGs, while the only analogous
study for disk galaxies (Miskolczi et al., 2011) was also less statistically
representative of the galaxy population because it was focused on testing the
image processing method. Comparisons with simulations are still needed, and
will be reported elsewhere.

Last, because our procedure for enhancing images to detect low surface
brightness features relies on stacking images in multiple filters and because
those features have an intrinsically low S/N, we cannot measure their colours.
To do so, deeper multi-band imaging is needed, and will be valuable to
constrain stellar populations and masses of the merging systems. Discussion of
the physical properties of the features we detected and their comparison to
the newest simulations is beyond the scope of this article. These topics will
be addressed in a forthcoming paper.

###### Acknowledgements.

GM thanks Arpad Miskolczi for the image processing training and the SDSS
images showed in Fig. 6, and the Astronomisches Institut der Ruhr-Universitat
Bochum for their hospitality during his visit. GM also thanks Gabriel
Torrealba for his help in mapping the SDSS DR10 footprint, and Néstor Espinoza
for his comments on the statistics of the sample. DMD thanks the team of
astrophotographers from the STSS: Mark Hanson, Adam Block and Ken Crawford for
their images shown in this work; Giuseppe Donatiello for his help with the
presentation of some figures; and Seppo Laine for his help with the target
selection and comments. APC acknowledges the support of STFC Grant
ST/P000541/1. We also thank the anonymous referee for their constructive
comments in the revision stage. The authors acknowledge the use of the Spitzer
Survey of Stellar Structure in Galaxies and the Dark Energy Camera Legacy
Survey as a core part of this work. The authors also acknowledge the use of
IRAF, the Image Reduction and Analysis Facility, a general purpose software
system for the reduction and analysis of astronomical data. IRAF is written
and supported by the National Optical Astronomy Observatories (NOAO) in
Tucson, Arizona. NOAO is operated by the Association of Universities for
Research in Astronomy (AURA), Inc. under cooperative agreement with the
National Science Foundation. Funding for SDSS-III has been provided by the
Alfred P. Sloan Foundation, the Participating Institutions, the National
Science Foundation, and the U.S. Department of Energy Office of Science. This
work made use of the following Python 3 libraries: Matplotlib (Hunter, 2007),
SciPy (Jones et al., 2001–), NumPy. This research also made use of Astropy, a
community-developed core Python package for Astronomy (Astropy Collaboration
et al., 2013).

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##  Appendix A Supplementary tables.

Table 2: Tidal streams found in this work, including previously known features and new discoveries (28 host galaxies), with detection confidence levels (DCL) 3 and 4. Diffuse-light overdensities, with their physical nature yet to be confirmed (23 host galaxies) are also included, with DCL 1 and 2. This implies a total of 51 galaxies with any type of tidal features related to them. Distances and stellar masses were taken from S4G, while their morphology was extracted from NED database. Additionally, substructures we found have been tagged: S for shells; C for curved, arcuated features, including anything coherent and stream like; Sph for spheroidal satellites and partially disrupted cores; E for extensions of the central galaxy (e.g. warps and spiral arms); and O for any other type of less common features (wedges, radial spikes, fuzzy clouds of debris, etc.). For known substructures, references of previous studies have been supplied. MD+ refers to Martínez-Delgado et al. (in prep.), a forthcoming paper. ID |  | Galaxy
---
morphology
| Distance
---
(Mpc)
| log(Stellar Mass)
---
$\mathrm{(M_{\odot})}$
DCL | Tags | Comments
NGC 681 | SAB | 33.600 | 10.752 | 4 | S C | This work
NGC 718 | SAB | 21.400 | 10.283 | 3 | C E |  | Very faint arc-like feature to the north
---
plus possible overdensity to the south
NGC 936 | SB0 | 20.683 | 10.926 | 3 | C E |  | Double arc-like feature;
---
hints of warped disk
NGC 1055 | SBb | 16.630 | 10.739 | 4 | O | Martínez-Delgado et al. (2010)
NGC 1084 | SAc | 21.225 | 10.619 | 4 | C | Martínez-Delgado et al. (2010)
NGC 2775 | SAab | 17.000 | 10.870 | 4 | S | This work; MD+
NGC 2859 | (R)SB0 | 27.333 | 10.882 | 3 | C Sph |  | Two possible partially disrupted satellites
---
within a ring, with leading and trailing tails
NGC 3034 | I0 | 3.777 | 10.449 | 2 | E O | Possible spike features
NGC 3041 | SAB | 26.350 | 10.437 | 4 | C | This work
NGC 3049 | SBab | 30.775 | 10.132 | 4 | S C E | This work; MD+
NGC 3185 | (R)SBa | 24.725 | 10.215 | 3 | C E O |  | Very faint loop connected to the disk,
---
with a compact object embedded on it
NGC 3277 | SA | 25.000 | 10.375 | 1 | S | Possible shells very close to the halo
NGC 3521 | SABbc | 12.078 | 11.030 | 4 | S C E O | Martínez-Delgado et al. (2010)
NGC 3611 | SAa | 33.300 | 10.462 | 4 | C |  |  Schweizer & Seitzer (1990);
---
This work
NGC 3628 | Sb | 11.300 | 10.805 | 4 | Sph | Martínez-Delgado et al. (2010)
NGC 3631 | SAc | 13.102 | 10.163 | 4 | E O | This work; MD+
NGC 3675 | SA | 17.200 | 10.919 | 1 | E |  | Candidate tidal overdensities, not
---
clearly distinguishable from disk warping
NGC 3682 | SA0 | ND | 10.230 | 4 | S | This work
NGC 3729 | SB | 20.183 | 10.233 | 3 | Sph E | Possible satellite being disrupted
NGC 3877 | SA | 15.612 | 10.445 | 1 | E O |  | Asymmetrical and coplanar spike
---
extending from the disk
NGC 3949 | SA | 18.341 | 10.246 | 3 | S E | Possible shell very close to the outer disk
NGC 4013 | Sb | 18.600 | 10.630 | 4 | E O | Martínez-Delgado et al. (2010)
NGC 4051 | SAB | 14.575 | 10.359 | 3 | Sph E O |  | Possible compact object with halo and tail,
---
plus an overdensity south of the galaxy
NGC 4111 | SA0 | 15.550 | 10.452 | 4 | Sph O | Brodie et al. (2014)
NGC 4203 | SAB0 | 14.940 | 10.528 | 4 | Sph | This work
NGC 4262 | SB0 | 20.510 | 10.377 | 2 | E |  | Two overdensities not clearly related to
---
tidal features, perhaps part of the disk
NGC 4293 | (R)SB0 | 14.320 | 10.418 | 3 | E O |  | Clear substructure in the inner halo,
---
very close to the disk
NGC 4394 | (R)SB | 16.800 | 10.440 | 3 | E |  | Possible extended disk features,
---
or tidal arcs surrounding the galaxy
NGC 4414 | SAc | 18.312 | 10.883 | 4 | S | de Blok et al. (2014)
NGC 4494 | E | 13.841 | 10.542 | 2 | O |  | Possible diffuse substructure, resembling
---
symmetric spikes in an elliptical galaxy
NGC 4519 | SB | 28.411 | 10.191 | 3 | C E |  | Filamentary feature with two components,
---
likely related to either the halo or the disk
NGC 4569 | SABab | 12.352 | 10.638 | 4 | E O | Martínez-Delgado et al. (2010)
NGC 4594 | SAa | 10.390 | 11.253 | 4 | C | Malin & Hadley (1997)
NGC 4631 | SBd | 6.050 | 10.127 | 4 | E O | Martínez-Delgado et al. (2015)
NGC 4643 | SB0 | 25.700 | 11.028 | 4 | C Sph | This work
NGC 4651 | SAc | 26.708 | 10.844 | 4 | S C E O | Martínez-Delgado et al. (2010)
NGC 4691 | (R)SB0 | 22.500 | 10.479 | 2 | E O |  | Possible outer halo overdensity with
---
the appearance of a dense stellar cloud
NGC 4753 | I0 | 16.869 | 10.930 | 4 | E | Steiman-Cameron et al. (1992)
NGC 4762 | SB0 | 22.460 | 10.848 | 2 | E O |  | An interesting case of disk warping
---
with mixed tidal features
NGC 4772 | SAa | 30.475 | 10.747 | 4 | E | Haynes et al. (2000)
NGC 4866 | SA0 | 23.800 | 10.689 | 1 | E O |  | Unclassifiable disk feature to the right
---
of the galaxy, possibly with tidal origin
NGC 5055 | SAbc | 8.333 | 10.778 | 4 | C O | Martínez-Delgado et al. (2010)
NGC 5364 | SA | 19.513 | 10.614 | 3 | E O | Giant tidal structure west of the galaxy
NGC 5506 | S pec | 23.833 | 10.122 | 3 | C O |  | Distorted, asymmetric tidal features
---
connected to each side of the disk
NGC 5576 | E | 23.930 | 10.770 | 1 | S | Possible diffuse shells
NGC 5750 | SB0 | 33.633 | 10.741 | 4 | E O | This work
NGC 5806 | SAB | 25.541 | 10.585 | 3 | C S E |  | Diffuse extended overdensity, with a shell
---
or arc-like feature very close to the disk
NGC 5907 | SAc | 16.636 | 10.871 | 4 | C | Martínez-Delgado et al. (2010)
NGC 7241 | SB | ND | 10.263 | 4 | E O | Leaman et al. (2015)
NGC 7742 | SAb | 22.200 | 10.343 | 4 | S C | This work
NGC 7743 | (R)SB0 | 21.433 | 10.447 | 4 | C E | This work; MD+

NGC 7814 | NGC 2967 | NGC 3495 | NGC 3992 | NGC 4343 | NGC 4904 | NGC 5792
---|---|---|---|---|---|---
NGC 157 | NGC 2964 | NGC 3501 | IC 749 | NGC 4356 | NGC 5005 | NGC 5821
NGC 337 | UGC 5228 | NGC 3507 | IC 750 | NGC 4369 | NGC 5033 | NGC 5854
NGC 584 | NGC 3003 | NGC 3512 | NGC 4030 | NGC 4380 | NGC 5112 | NGC 5864
NGC 615 | NGC 3021 | NGC 3556 | NGC 4045 | IC 3322A | NGC 5145 | NGC 5879
NGC 628 | NGC 3044 | NGC 3596 | NGC 4062 | UGC 7522 | NGC 5205 | NGC 5921
NGC 660 | NGC 3055 | NGC 3623 | NGC 4085 | NGC 4405 | IC 902 | NGC 5963
NGC 676 | NGC 3031 | NGC 3626 | NGC 4088 | NGC 4448 | UGC 8614 | NGC 5956
NGC 693 | NGC 3067 | NGC 3629 | NGC 4096 | NGC 4451 | NGC 5248 | NGC 5957
NGC 701 | NGC 3098 | NGC 3637 | NGC 4100 | NGC 4461 | NGC 5301 | NGC 5962
NGC 779 | NGC 3162 | NGC 3642 | NGC 4102 | NGC 4503 | NGC 5300 | NGC 5964
IC 210 | NGC 3177 | NGC 3655 | NGC 4123 | NGC 4437 | NGC 5334 | NGC 5970
NGC 864 | NGC 3185 | NGC 3666 | NGC 4138 | NGC 4527 | NGC 5356 | NGC 6015
NGC 955 | NGC 3184 | NGC 3669 | NGC 4145 | NGC 4536 | NGC 5422 | NGC 6012
NGC 1022 | NGC 3198 | NGC 3681 | NGC 4157 | NGC 4559 | NGC 5443 | IC 1158
NGC 1035 | IC 610 | NGC 3684 | UGC 7267 | NGC 4565 | NGC 5457 | NGC 6106
UGC 4551 | NGC 3254 | NGC 3683 | NGC 4212 | NGC 4580 | NGC 5473 | NGC 6217
NGC 2654 | NGC 3259 | NGC 3686 | NGC 4217 | NGC 4599 | NGC 5480 | NGC 7280
NGC 2683 | NGC 3279 | NGC 3692 | NGC 4220 | NGC 4632 | NGC 5520 | NGC 7497
NGC 2712 | NGC 3294 | NGC 3755 | NGC 4237 | NGC 4639 | NGC 5507 | NGC 7625
NGC 2742 | NGC 3346 | NGC 3756 | NGC 4260 | NGC 4666 | NGC 5584 | NGC 1052
NGC 2770 | NGC 3351 | IC 719 | NGC 4274 | NGC 4710 | NGC 5668 | NGC 2768
NGC 2780 | NGC 3359 | NGC 3810 | UGC 7387 | NGC 4746 | NGC 5690 | NGC 3193
NGC 2805 | NGC 3370 | NGC 3900 | NGC 4303 | NGC 4771 | NGC 5713 | NGC 3608
NGC 2820 | NGC 3389 | NGC 3898 | NGC 4307 | NGC 4800 | IC 1048 | NGC 4278
NGC 2844 | NGC 3430 | NGC 3938 | NGC 4314 | NGC 4808 | NGC 5746 | NGC 5173
NGC 2841 | NGC 3437 | NGC 3953 | NGC 4316 | NGC 4826 | NGC 5768 | NGC 5216
NGC 2903 | NGC 3486 | NGC 3982 | NGC 4324 | NGC 4845 | NGC 5798 | NGC 5846

Table 3: Galaxies with no evidence of observable diffuse overdensities in our
sample of 297 galaxies.