# All Puffed Up: Tidal Heating as an Ultra Diffuse Galaxy Formation Pathway

Catherine Fielder Steward Observatory, University of Arizona, 933 North Cherry
Avenue, Rm. N204, Tucson, AZ 85721-0065, USA  Michael G. Jones Steward
Observatory, University of Arizona, 933 North Cherry Avenue, Rm. N204, Tucson,
AZ 85721-0065, USA  David J. Sand Steward Observatory, University of Arizona,
933 North Cherry Avenue, Rm. N204, Tucson, AZ 85721-0065, USA  Paul Bennet
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  Denija Crnojević University of Tampa, 401 West Kennedy Boulevard, Tampa,
FL 33606, USA  Ananthan Karunakaran Department of Astronomy & Astrophysics,
University of Toronto, Toronto, ON M5S 3H4, Canada  Dunlap Institute for
Astronomy and Astrophysics, University of Toronto, Toronto ON, M5S 3H4, Canada
Burçin Mutlu-Pakdil Department of Physics and Astronomy, Dartmouth College,
Hanover, NH 03755, USA  Kristine Spekkens Department of Physics and Space
Science, Royal Military College of Canada P.O. Box 17000, Station Forces
Kingston, ON K7K 7B4, Canada  Department of Physics, Engineering Physics and
Astronomy, Queen’s University, Kingston, ON K7L 3N6, Canada

###### Abstract

We present new follow-up observations of two ultra-diffuse galaxies (UDGs),
part of a total sample of five chosen for their distorted morphologies,
suggestive of tidal influence. Using Hubble Space Telescope Advanced Camera
for Surveys F555W and F814W imaging, we identify $8\pm 2$ globular clusters
(GCs) in KUG 0203-Dw1 and $6\pm 2$ in KDG 013, abundances that are fairly
typical for normal dwarf galaxies of similar stellar mass. Jansky Very Large
Array data reveal a clear H i detection of KUG 0203-Dw1 with a gas mass
estimate of $\log{M_{\rm{H}\,\rm{\textsc{i}}\ }/M_{\odot}}\lesssim 7.4$ and
evidence of active stripping by the host. H i gas is found near the location
of KDG 013 but is likely unrelated to the UDG itself due to the morphology and
the numerous gas tails within the host group. Given that these UDGs have GC
abundances typical for galaxies at their luminosity, these findings suggest
that they likely originated as normal dwarf galaxies that have been subjected
to significant stripping and tidal heating, causing them to become more
diffuse. These two UDGs complete a sample of five exhibiting tidal features in
the Canada-France-Hawaii Telescope Legacy Survey area (CFHTLS; $\sim 150^{2}$
deg), including UDGs with and without UV emission, indicative of recent star
formation. Four UDGs in this sample, consistent with dwarfs ‘puffed-up’ by
tidal interactions, contrast with an outlier, suggesting a dwarf merger
origin. These findings indicate that tidal heating of dwarfs is a viable
formation pathway for UDGs.

††facilities: HST(ACS), VLA, CFHT††software: Astropy (Astropy Collaboration et
al., 2013, 2018, 2022), CASA (McMullin et al., 2007), CGAT-core (Cribbs et
al., 2019), Dolphot (Dolphin, 2000, 2016), Galfit (Peng et al., 2010),
Photutils (Bradley et al., 2022), Reproject (Robitaille et al., 2020), Source
Extractor (Bertin & Arnouts, 1996),

##  1 Introduction

While low-surface-brightness (LSB) galaxies have been studied for decades
(e.g., Sandage & Binggeli, 1984; Impey et al., 1988; Thompson & Gregory, 1993;
Dalcanton et al., 1997), it is only within the past decade that modern deep
imaging has allowed astronomers to recognize a subset of extremely LSB
galaxies with large spatial sizes. These objects, ultra diffuse galaxies
(UDGs) lie at the extreme of galaxy evolution, given their unique combination
of large size (half-light radii $>1.5$ kpc), extreme low surface brightness
(central $g$-band surface brightness $>24$ mag arcsec-2; van Dokkum et al.
2015; Mihos et al. 2015), and prevalence across all types of environments
including clusters (Koda et al., 2015; Mihos et al., 2015; van Dokkum et al.,
2015; Yagi et al., 2016; Venhola et al., 2017; Wittmann et al., 2017; Amorisco
et al., 2018; Lim et al., 2018; Forbes et al., 2020; Lim et al., 2020), groups
(Merritt et al., 2016; Bennet et al., 2017; Román & Trujillo, 2017; van der
Burg et al., 2017; Spekkens & Karunakaran, 2018; Jones et al., 2021), and the
field (Martínez-Delgado et al., 2016; Leisman et al., 2017; Greco et al.,
2018; Janowiecki et al., 2019; Román et al., 2019; Prole et al., 2019, 2021;
Jones et al., 2023a).

The formation mechanisms of UDGs remain enigmatic, with proposed mechanisms
including stellar feedback (Di Cintio et al., 2017; Chan et al., 2018), high-
spin host dark matter (DM) halos (Amorisco & Loeb, 2016; Rong et al., 2017),
early mergers (Wright et al., 2021), failed galaxies (van Dokkum et al.,
2016), tidal heating of normal dwarf galaxies (Conselice, 2018; Bennet et al.,
2018; Carleton et al., 2019; Tremmel et al., 2020; Jones et al., 2021), and
tidal dwarf galaxies (TDGs; Duc & Mirabel 1998; Duc 2012; Román et al. 2021).
The diverse properties within the UDG population (e.g., gas content, UV
emission, GC abundances, stellar masses, etc) suggest multiple formation
pathways, or combinations thereof (e.g., Pandya et al., 2018; Ruiz-Lara et
al., 2019; Trujillo et al., 2019). By focusing on UDGs with specific features
or in particular environments, we can begin to disentangle formation pathways
more clearly. In this study, we concentrate on a sample of five UDGs
exhibiting clear tidal features, expecting them to align with formation
pathways associated with galaxy interactions. However, these tidal features
may also be linked to other formation mechanisms, depending on the observed
properties of the UDGs.

Various galaxy interactions can plausibly lead to the formation of UDGs. Early
mergers of low-mass galaxies in hydrodynamical simulations result in present-
day UDGs due to increased radius and angular momentum, leading to reduced
central surface brightness (Wright et al., 2021). Interactions involving
massive, gas-rich galaxies may produce diffuse TDGs (Duc & Mirabel 1998; Duc
2012; Bennet et al. 2018; Román et al. 2021). Tidal interactions arising from
gravitational interplay between a low mass galaxy and a more massive neighbor
(e.g., tidal heating) or entry into a cluster environment (e.g., ram pressure
stripping and galaxy harassment) can redistribute stars, creating extended and
low surface brightness features (Román & Trujillo, 2017; Conselice, 2018;
Carleton et al., 2019; Tremmel et al., 2020; Jones et al., 2021).

Key observational constraints that serve as discriminators for UDG formation
pathways include their star cluster populations and H i gas mass and
morphology. Globular clusters (GCs) serve as cosmic fossils, tracing early
star formation epochs (Renaud, 2018). By characterizing their abundance and
spatial distribution in a UDG we can infer essential details about its
assembly history. For example, UDGs containing smaller GC populations are
thought to have originated as dwarf galaxies in low mass DM halos, while UDGs
with no GC population may be consistent with TDG formation. In tandem, the H i
in a galaxy is typically one of its most loosely bound baryonic components,
making it a sensitive tracer of tidal interactions (e.g., Duc & Renaud, 2013).
Therefore the morphology of the H i within a UDG or even the absence of such a
neutral gas reservoir can offer valuable insight into the evolutionary history
of the system.

Even with GC and H i constraints, discerning UDG formation pathways in groups
remains challenging. A study by Jones et al. (2021) of two UDGs with tidal
features (a subset of our sample of five) suggested they are likely puffed-up
dwarfs due to the absence of H i and typical GC abundances for dwarfs.
However, Jones et al. (2023a) studied H i bearing field UDGs that revealed a
scarcity of globular clusters, aligning with expectations for similar-mass
dwarfs. This result suggests that certain group UDGs may have been pre-
existing entities accreted from the field rather than being transformed within
the group environment (consistent with hydrodynamical simulation predictions,
e.g., Jiang et al. 2019; Liang et al. 2023). Fielder et al. (2023) studied a
dramatically different UDG (another of our sample of five), with features
pointing to a dwarf merger origin, indicating diverse formation pathways for
UDGs within group environments. Collectively, these findings point to at least
three distinct mechanisms contributing to UDG formation in group settings.

Here we present new data on two UDGs that contain evidence of a tidal
disturbance, clear detections in the UV, and that lie in close proximity to a
plausible group ‘host’ galaxy. These UDGs, KUG 0203-Dw1 and KDG 013, complete
our sample of five identified in a semi-automated search (Bennet et al., 2017)
of the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS). Utilizing Hubble
Space Telescope (HST) and Jansky Very Large Array (VLA) observations, we
investigate GC candidates, H i mass, and morphology to distinguish between UDG
formation scenarios. Our full sample includes UDGs with a variety of
characteristics. In addition to the two new UDGs presented in this work, we
also include two optically redder UDGs observed to lack UV and H i presented
in Bennet et al. (2018, hereafter B18) and Jones et al. (2021, hereafter J21),
and a bluer UDG with both UV and H i presented in Fielder et al. (2023,
hereafter F23). With this sample of five we can assess the variety of
properties exhibited by UDGs displaying tidal features, and determine the most
plausible formation mechanisms of this sub-type of UDGs.

This manuscript is structured in the following way. Section 2 briefly
describes the systems in which these UDGs reside. In Section 3 we describe the
HST and VLA data obtained for this work, along with additional supplementary
observations employed to enhance the constraints on the properties of KUG
0203-Dw1 and KDG 013. In Section 4 we discuss our calculations and provide
measurements of the physical properties of the UDGs studied. Section 5
explores the GC systems of the UDGs. In Section 6 we compare our full sample
of UDGs with tidal features and in Section 7 we discuss the formation
mechanism for KUG 0203-Dw1 and KDG 013. We summarize and conclude in Section
8. In Appendix A we provide tables of the properties of GC candidates
identified in KUG 0203-Dw1 and KDG 013.

##  2 The UDG Host Systems

Table 1: Properties of UDG Hosts

Galaxy | Morphology | $v_{\rm{helio}}$ | D | $M_{V}$
---|---|---|---|---
|  | $\mathrm{km\,s^{-1}}$ | Mpc | mag
KUG 0203-100 | SB(s)m pec | $1885\pm 1$ | $26.8\pm 1.9$ | $\simeq-18.2$
NGC 830 | SB0 | $3856\pm 2$ | $55.5\pm 3.9$ | $\simeq-20.7$
NGC 829 | SB(s)c pec | $4074\pm 2$ | $58.73\pm 4.11$ | $\simeq-15.5$

Columns: 3) Heliocentric velocity. For KUG 0203-100 this value comes from
Filho et al. (2013). For NCG 830 and NGC 829 this value comes from Albareti et
al. (2017). 4) Virgo-infall distance. This value is derived from Karachentsev
et al. (2004) for KUG 0203-100 and from Albareti et al. (2017) for NGC 830 and
NGC 829. 5) $V$-band absolute magnitudes derived using SDSS magnitudes
(Adelman-McCarthy et al., 2008) converted from AB to Vega and then converted
to $V$ with documented SDSS
conversionsaahttp://classic.sdss.org/dr4/algorithms/sdssUBVRITransform.html.

Both of the UDGs that we present new data for in this work, KUG 0203-Dw1 and
KDG 013, have associated galaxies in their respective groups which we briefly
describe below. Further measurements are provided in Table 1.
KUG 0203-100: This galaxy is the primary group member, with KUG 0203-Dw1 as
the closest companion in addition to 3 other small galaxies. KUG 0203-100
(also known as SDSS J0205-0949) is an extremely metal poor galaxy, identified
in Kniazev et al. (2003). Pustilnik & Martin (2007) notes that it exhibits a
warped disk at both edges, a feature attributed to tidal interactions, and is
rather luminous for such a low metallicity galaxy.

Pustilnik & Martin (2007) also suggest that a nearby low surface brightness
companion we now identify as KUG 0203-Dw1 may play a hand in the disturbed
morphology of KUG 0203-100, which we expand upon in Section 7. KUG 0203-Dw1
lies directly to the south-west of KUG 0203-100, with faint stellar material
falling between the two (see Figure 1 left column). We adopt the Virgo in-fall
distance of KUG 0203-100 for KUG 0203-Dw1.
NGC 830: The NGC 830 group contains NGC 829 and approximately 5 additional
members of which these two are the dominant members. Their properties are
summarized in Table 1. The heliocentric velocities of the other group members
range from $3756\pm 3$ $\text{km}\,\text{s}^{-1}$ to $4045\pm 2$
$\text{km}\,\text{s}^{-1}$. In general many of the objects in the system are
marginally disturbed, with a deformed disk present in NGC 829.

KDG 013 was first identified in Karachentseva (1968), and was also identified
in HYPERLEDA (Paturel et al., 2003) and the southern SMUDGes catalog
(Systematically Measuring Ultra-diffuse Galaxies; Zaritsky 2022). It lies in
the south-west part of the NGC 830 group, with faint stellar material
extending predominantly in the northeast southwest directions but not directly
connected to any other galaxy within the group (see Figure 1 right column).
For KDG 013 we adopt the distance of NGC 830 which is the approximate average
distance of the other group members, ranging from $54.1\pm 3.6$ to $58.7\pm
4.1$ Mpc. However, despite it’s morphology, it is unclear which galaxy in the
group the UDG has interacted with.

##  3 Observations

All of the UDGs studied in this work were originally identified in a semi-
automated search for diffuse dwarfs in CFHTLS imaging. The initial findings
are presented in Bennet et al. (2017), with the completed survey covering
$\sim 150\;\rm{deg}^{2}$. From the investigation area, five UDGs were selected
for follow-up due to evidence of tidal disturbance through either possible
associated tidal streams or elongated/amorphous morphology. This sample is
meant to be representative rather than complete, spanning the range of UDGs
with tidal signatures in that data set.

###  3.1 VLA Observations

Table 2: Properties of VLA observations Object | VLA config. | Bandwidth | # channels | Band center | Robust | Beam size |  $\sigma_{\mathrm{rms}}$aaRMS noise in 5 km s-1 channels.
---|---|---|---|---|---|---|---
|  | MHz |  | $\mathrm{km\,s^{-1}}$ |  | ″$\times$″ | mJy/beam
KUG 203-Dw1 | C | 4 | 1024 | 1885 | 0.5 | $19\times 15$ | 0.85
D | 4 | 1024 | 1885 | 2.0 | $72\times 56$ | 0.98
C+D | 4 | 1024 | 1885 | 0.5 | $27\times 22$ | 0.47
KDG 013-Dw1 | D | 8 | 2048 | 4074 | 2.0 | $74\times 60$ | 0.77

KUG 0203-Dw1 and KDG 013 were observed in the VLA D-configuration during July
2022, as a part of project 22A-225 (PI: D. Sand). Each target had a total on-
source integration time of approximately 4 h. Both targets were observed with
a velocity resolution of $\sim$0.8 $\text{km}\,\text{s}^{-1}$ (averaged to 5
$\text{km}\,\text{s}^{-1}$ during imaging). A 4 MHz band (1024 channels) was
used for KUG 0203-Dw1 and an 8 MHz band (2048 channels) for KDG 013. These
bands were centered at 1885 km s-1 and 4074 km s-1for KUG 0203-Dw1 and KDG
013, respectively. KUG 0203-Dw1 was also selected for follow-up under
Director’s Discretionary Time in the VLA C-configuration during winter of 2022
(PI: C. Fielder), with the same spectral configuration and a total on source
integration time of 4 h. The results of these observations are presented in
Figure 1. For KUG 0203-Dw1 we imaged the C and D array data both separately
and together, with the latter used for the contour plots (referred to as VLA
C+D data). The properties of these observations are summarized in Table 2.

The data were reduced with the H i pipeline111https://github.com/AMIGA-
IAA/hcg_hi_pipeline of Jones et al. (2023b). For a full description we refer
the reader to that work. In brief the pipeline performs both manual and
automated flagging before proceeding with gain and phase calibrations, $uv$
continuum subtraction, and imaging using standard CASA tasks (Common Astronomy
Software Applications; McMullin et al. 2007).

The KUG 0203-Dw1 data suffered from moderate interference in C-configuration
where $\sim$19% of visibilities were flagged, while $\sim$42% were flagged in
D-configuration. The higher fraction of flagged data in D-configuration is
mostly the result of four antenna failures. A Briggs robust parameter of 0.5
was used during imaging for the C+D data to offer a compromise between
sensitivity and resolution. The synthesized beam size was determined to be
$27.0\times 22.0$ arcsec2 and the central velocity is 1885 km s-1 (a similar
measurement to the host).

The KDG 013 D-array data had moderate interference with $\sim$22% of
visibilities flagged. Imaging was conducted with automated masking, applying a
Briggs robust parameter of 2.0 (i.e. natural weighting) in order to maximize
sensitivity to the extended features. This resulted in a synthesized beam size
of $74\times 60$ arcsec2.

For the generation of the VLA moment zero maps in Figure 1, we utilized the
SoFiA software (Serra et al., 2015) to create a source mask. Employing the
standard smooth and clip algorithm, we conducted the process both with no
smoothing and with Gaussian smoothing kernels approximately 0.5 and 1.0 times
the beam size. Additionally, we applied boxcar spectral smoothing over 0 and 3
channels. The clip threshold was set at $3.5\sigma$, and to ensure robustness,
we imposed a stringent 95% reliability threshold.

Figure 1: VLA H i contours overlaid on CFHTLS imaging for KUG 0203-Dw1 (left
column) and KDG 013 (right column). The top row is centered on the UDG while
the bottom row shows a wider view of the respective galaxy group. Upper left:
A high-contrast CFHT $g$-band image of KUG 0203-Dw1 with integrated VLA C+D
array H i emission contours overlaid. The minimum contour is $1.3\times
10^{19}\;\mathrm{cm^{-2}}$ ($3\sigma$) in column density (over 10 km s-1).
Each contour is double the previous. The synthesized beam is shown as a
semitransparent ellipse in the lower left corner, which corresponds to a beam
size of $27.0\times 22.0$ arcsec2. Lower left: Same as upper left, but showing
the full system with KUG 0203-100. A small over-density to the north of KUG
0203-100 is highlighted by the small cross-hair, which is a real detection and
not noise. Upper right: Similar to the left panels, for KDG 013. The H i
emission is derived from VLA D-array only. Here the minimum contour is
$8.4\times 10^{18}\;\mathrm{cm^{-2}}$ ($3\sigma$) in column density (over 20
km s-1). The synthesized beam size corresponds to $73.5\times 59.6$ arcsec2.
Lower right: Same as upper right, but showing a majority of the NGC 830 group.

###  3.2 HST Observations

KUG 0203-Dw1 and KDG 013 were observed in July and September of 2022, under
HST program ID 16890 (Sand et al., 2021). Both targets were observed by the
Advanced Camera for Surveys (ACS) with the Wide Field Channel (WFC) in the
F555W and F814W filters. The total integration time for KUG 0203-Dw1 is 2046 s
in F555W and 2098 s in F814W. Integration times for KDG 013 correspond to 2046
s and 2089 s in F555W and F814W respectively. In addition, Wide Field Camera 3
(WFC3) images were taken in parallel to utilize as reference background fields
as needed.

We present RGB color composite images for KUG 0203-Dw1 and KDG 013 in Figure
2, constructed from the combined F555W and F814W exposures. Highlighted
sources are discussed in detail in Section 5. After obtaining the standard
data products from the STScI archive, the individual exposures were aligned
and background subtracted using the Dolphot 2.0 software (Dolphin, 2000, 2016)
with the standard ACS and WFC3 parameters provided in the user manual. Then, a
combined point source catalog for each of the fields was generated. Dolphot
used the HST to Johnson-Cousins magnitude conversion factors presented in
Sirianni et al. (2005) to determine the $V$\- and $I$-band magnitudes from
F555W and F815W magnitudes. The photometry was then corrected for Galactic
extinction using the
NASA/IPAC222https://irsa.ipac.caltech.edu/applications/DUST/ online tool, with
values derived from the Schlafly & Finkbeiner (2011) extinction coefficients.
Unless otherwise indicated, all magnitudes presented in this work are Milky
Way extinction-corrected Vega magnitudes.

Completeness limits are determined via artificial star tests with the tools
provided by Dolphot. We place nearly $100,000$ artificial stars into the ACS
field, which span a large color range from $-$1 to 2 in F555W-F814W (well
beyond the range used to select GCs). We then measure the fraction of those
stars that we recover as a function of apparent magnitude. For KUG 0203-Dw1 we
find that we are $90\%$ complete to $m_{F814W}=26.0$ and $50\%$ complete to
$m_{F814W}=26.8$. For KDG 013 we are $90\%$ complete to $m_{F814W}=26.3$ and
$50\%$ complete to $m_{F814W}=27.1$.

Figure 2: HST ACS/WFC F555W/F814W composite color images of KUG 0203-Dw1 (left
column) and KDG 013 (right column). The upper row is centered on the UDG while
the lower row shows the full HST frame. Upper Left: HST ACS/WFC F555W/F814W
composite color image of KUG 0203-Dw1. The inner, white dotted circular
aperture marks $r_{1/2}$ (11.8”), and the dashed circular aperture marks
$2\times r_{1/2}$ (23.6”) which we select as the outer edge of the UDG. Small
cyan apertures enclose all GCCs within the image, with a total of 5 within the
aperture of the UDG. Lower Left: The full HST image of KUG 0203-Dw1, which
includes its host galaxy KUG 0203-100. Upper Right: Same as the left panel,
but for KDG 013. Here the apertures correspond to 12.5” and 25”, with a total
of 4 GCCs. GCCs of either UDG are selected from within the $2\times r_{1/2}$
UDG boundary. Lower right: The full HST image of KDG 013. The edge of Mrk 1019
is visible to the northeast of KDG 013.

###  3.3 Supplementary Observations

####  3.3.1 CFHT

The UDGs were first identified in the CFHTLS. Specifically, our observations
are supplemented with the Wide portion of the survey, conducted between 2003
and 2009 and covering 171 square degrees in the $u$, $g$, $r$, $i$ & $z$
bands. Using the nomenclature of Figure 4 of Gwyn (2012), KUG 0203-Dw1 was
observed in the W$1-3-3$ tile and KDG 013 was observed in the W$1-2-1$ tile.
Exposure times for each stack and filter varies, with 2500 s in $g$, 2180 s in
$r$, and 4305 s in $i$ for the W$1-3-3$ tile. For the W$1-2-1$ tile the
exposure times are 5000 s in $g$, 3180 s in $r$, and 4305 s in $i$. The tiles
were downloaded directly from the Canadian Astronomy Data Centre (CADC) and
have been processed by the Terapix 7 pipeline. The point spread functions
(PSFs) for those image stacks were also downloaded from the CADC, which were
used for measuring dwarf structural parameters. The construction and
calibration of these utilized the MegaPipe data pipeline (Gwyn, 2008) and is
described in detail by Gwyn (2012). The CFHT images are used to derive the
physical properties of the UDGs given the increased surface brightness
sensitivity compared to HST ACS/WFC (see Jones et al. 2021 for further
discussion). High-contrast CFHT $g$-band images are utilized as the background
for our radio contours in Figure 1.

####  3.3.2 GALEX Ultraviolet Observations

Data from GALEX (Martin & GALEX Team, 2005) were used to measure the star
formation rates of KUG 0203-Dw1 and KDG 013. Both targets were observed in NUV
for $\sim$1600 s as part of the guest investigator program (GI5-028, PI:
Balogh), which did not include FUV observations. KUG 0203-Dw1 was also
observed as part of the GALEX all-sky survey at medium depth for $\sim$1600 s
in both NUV and FUV. In Figure 3 we provide the GALEX images of both UDGs.

##  4 Physical Properties

The UDGs considered in this work contain evidence of past or ongoing
interactions, manifest in tidal streams and/or disturbed morphologies. These
objects have large half-light radii ($>1.5$ kpc) and faint central surface
brightnesses (central $g$-band surface brightness $>24$ mag arcsec-2), meaning
that they fit into the standard definition of a UDG (see Section 4.2 for
discussion on how these quantities are derived). The physical properties
discussed in the following sub-sections are summarized in Table 3. Note that
the section to the right of the vertical divide in this table reproduces the
literature values of the respective UDGs presented in F23, J21, and B18. These
quantities were all derived in the same manner as the UDGs presented in this
work.

The morphology of KUG 0203-Dw1 exhibits elongation in the northeast-southwest
direction, perpendicular to the disk of KUG 0203-100 (see the left columns of
Figure 1 and Figure 2). This galaxy displays a somewhat clumpy appearance,
accentuated by a discernible faint tidal plume evident in the high contrast
CFHT image, extending from the southwest. KDG 013 shares a comparable
elongated morphology in the northeast-southwest direction, pointing towards
Mrk 1019. There are more clear clumps in the southwest with additional diffuse
material in the northwest (features more obvious in the high contrast CFHT
image, Figure 1).

###  4.1 HI Properties

####  4.1.1 KUG 0203-Dw1

The H i morphology of KUG 0203-Dw1 is complex, with a bridge connecting to KUG
0203-100 and a spur extending to the southeast. However, there is a clear
concentration of H i at the center of the UDG (left column, Figure 1). In the
zoomed-out lower-left panel of Figure 1 there is a small feature to the north
of KDG 0203-100, highlighted by the smaller cross-hair. This is a real
detection and not noise, as this feature is visible in the separate
C-configuration and D-configuration data cubes as well as the combined C+D
data. It is likely the end of a trailing/leading tail of H i gas, where the
rest is blended with the H i emission of the host.

The total mass of the HI feature that extends to the south of KUG 0203-100 is
approximately $\log{M_{\rm{H}\,\rm{\textsc{i}}\ }/M_{\odot}}=7.6$. The mass
that is gravitationally bound to KUG 0203-Dw1 is certainly less than this
value. To obtain an approximate upper limit we placed an aperture equal in
area to the synthesized beam at the location of the peak of H i emission
centered on KUG 0203-Dw1. This gave a value of
$\log{M_{\rm{H}\,\rm{\textsc{i}}\ }/M_{\odot}}=7.4$. We note that this is not
a strict upper limit as the beam is only slightly smaller than the entire
feature, thus this approach may still include some emission from gas that is
not bound to the UDG. However, this provides a reasonable approximation for
the H i mass of KUG 0203-Dw1.

Figure 3: Left: Composite GALEX FUV and NUV image of KUG 0203-Dw1. Three
background galaxies fall very close to the UDG, so we apply a mask setting
values above the threshold of $0.008$ to $0$. The positions of these objects
are marked by gray circles. Right: GALEX NUV image of KDG 013. Circular
apertures are the same as those shown in Figure 2. No threshold was applied to
this image as it was not necessary. Both images have the same scaling.

####  4.1.2 KDG 013

The H i morphology of the NGC 830 group is large and complex. In the vicinity
of KDG 013, four galaxies show H i detections, with three embedded in a cloud
of extended gas features. This includes a notable intergalactic concentration
of gas and star formation just north of LEDA 1012109 (see the oval orange
contour in the lower right panel of Figure 1) which may be a source like those
discovered in (Jones et al., 2022). A spur of this complex H i distribution
extends towards KDG 013, overlapping with it at the resolution of the VLA
observations. However, there is no evidence of an H i concentration directly
centered on the UDG. As such, it is improbable that KDG 013 harbors a
significant gas reservoir. Similarly, it is unlikely that KDG 013 is related
to the gas disturbance given that the feature does not align with KDG 013
(e.g., see the purple contour in the right column of Figure 1), but a
conclusive determination would require comparing the optical redshift of the
UDG to that of the gas. Given the disorganized nature of the gas in the NGC
830 group, the gas overlapping with KDG 013 could originate from one of the
other galaxies in the group.

Based on the contours in the image and the beam size, if KDG 013 had an H i
mass above $\log{M_{\rm{H}\,\rm{\textsc{i}}\ }/M_{\odot}}=8.6$ then it would
certainly cause a visible concentration in the contours. This places a weak
upper limit on the H i content of KDG 013, which is likely considerably lower.
For instance, if KDG 013 is not close in velocity to the gas cloud it is
projected near, the constraint on its H i content would be the point source
detection limit of our observations, which is
$\log{M_{\rm{H}\,\rm{\textsc{i}}\ }/M_{\odot}}=8.1$ at $3\sigma$.

###  4.2 Optical/UV Properties

The optical/UV properties of both UDGs are determined by GALFIT (Peng et al.,
2002), using the same methodology presented in Bennet et al. (2017, 2018) (see
also Merritt et al., 2016). The optical properties are derived from the CFHT
data, but the HST data has been shown to provide near identical results (see
J21). Both galaxies were modeled using a standard Sérsic profile (Sérsic,
1963), but KUG 0203-Dw1 was more of a challenge for GALFIT to constrain and
ultimately required two different Sérsic profiles to fit. Otherwise all fit
parameters are allowed to vary without restriction. The uncertainties on the
parameters for each UDG are determined by injecting 100 simulated UDGs into
the image, each with the best fitting properties of the given UDG as
determined by GALFIT. Then GALFIT is used to recover the properties of the
simulated UDGs. The scatter on the recovered properties of the simulated UDGs
represents the uncertainty on the best fit properties of the real UDG. We
present our parameter estimates in Table 3. $FUV$, $NUV$, $g$, and $r$-band
magnitudes are presented in the AB system, while $V$ and $I$-band magnitudes
remain in the Vega system. The best-fit GALFIT models both have an
ellipticity, consistent with their elongated morphology, as well as a
circularized radius.

Stellar masses are derived using the relations from table 1 of Zhang et al.
(2017) and our CFHT derived $(V-I)$ and $M_{V}$. We derive a stellar mass-to-
light ratio $\Gamma_{*}=0.5$ for KUG 0203-Dw1 and $\Gamma_{*}=0.9$ for KDG 013
which we then convert to stellar mass. We caution the reader to see this is an
estimate from a model and not a derived quantity.

The UV data of both UDGs originate from GALEX (Martin & GALEX Team, 2005).
Foreground sources are first masked (see the left panel of Figure 3). Then UV
fluxes are determined via aperture photometry, with an aperture radius
equivalent to two half-light radii of the best fit GALFIT model to the optical
data (see the dashed aperture in Figure 3. We derive star formation rates
using the relation from Iglesias-Páramo et al. (2006).

Table 3: Summary of Properties for UDGs with Tidal Features

Property | KUG 0203-Dw1 | KDG 013 | UGC 9050-Dw1 | NGC 2708-Dw1 | NGC 5631-Dw1
---|---|---|---|---|---
RA (J2000) | 02:05:46.5 | 02:08:33.6 | 14:09:13 | 08:56:12.7 | 14:26:13.6
Dec (J2000) |  $-$09:50:30.8 |  $-$07:50:59.2 | +51:13:28 |  $-$03:25:14.8 | +56:31:50.2
$D$ (Mpc) | $26.8\pm 1.9$ | $55.5\pm 3.9$ | $35.2\pm 2.5$ | 40.6 | 28.4
$v_{\rm{helio}}$ (km/s) | $1885\pm 1$ | $3856\pm 2$ | $1952.1\pm 0.3$ |  |
$M_{V}$ | $-13.7\pm 0.2$ | $-15.5\pm 0.3$ | $-14.0\pm 0.2$ | $-14.0\pm 0.4$ | $-12.0\pm 0.5$
$\log{\rm{L_{V}}/\rm{L}_{\odot}}$ | $7.4\pm 0.1$ | $8.1\pm 0.1$ | $7.5\pm 0.1$ | $7.5\pm 0.2$ | $6.7\pm 0.2$
$(V-I)$ | $0.6\pm 0.3$ | $0.8\pm 0.1$ | $0.8\pm 0.3$ | $0.8\pm 0.3$ | $0.6\pm 0.4$
$m_{g}$ | $18.5\pm 0.1$ | $18.4\pm 0.2$ | $18.9\pm 0.2$ | $19.3\pm 0.3$ | $20.5\pm 0.4$
$(g-r)$ | $0.2\pm 0.2$ | $0.4\pm 0.3$ | $0.3\pm 0.3$ | $0.5\pm 0.4$ | $0.4\pm 0.6$
$m_{NUV}$ | $19.1\pm 0.4$ | $21.3\pm 0.4$ | $19.9\pm 0.2$ | – | –
$m_{FUV}$ | $23.4\pm 0.3$ | – | – | – | –
$\mu(0,g)$ (mag arcsec-2) | $25.5\pm 0.3$ | $25.4\pm 0.3$ | $\sim 36.6\pm 6$ | $24.9\pm 0.6$ | $27.3\pm 0.7$
$r_{1/2}$ (arcsec) | $11.8\pm 1.8$ | $12.5\pm 0.9$ | $\sim 36.6\pm 6$ | $13.2\pm 2.9$ | $15.6\pm 3.6$
$r_{1/2}$ (kpc) | $1.5\pm 0.3$ | $3.4\pm 0.3$ | $\sim 6.2\pm 1$ | $2.6\pm 0.6$ | $2.2\pm 0.5$
$b/a$ | $\sim 0.5$ | $0.7\pm 0.1$ | – | $0.8\pm 0.1$ | $0.5\pm 0.1$
$\theta$ (deg) | 14 | 35 | – |  |
Sérsic index |  $<0.52$aaBecause a double fit was required this value is based on the Sérsic fit of the core. | $0.6\pm 0.1$ | – | $1.2\pm 0.2$ | 1.0bbThe Sérsic index was fixed to 1 in this fit.
$\log(M_{*}/M_{\odot})$ | $\sim 7.1$ | $\sim 8.0$ |  $\sim$7.5 | $\sim 7.5$ | $\sim 6.4$
$\log(M_{\rm{H}\,\rm{\textsc{i}}}/M_{\odot})$ | $\lesssim 7.4$ | $\lesssim 8.6$ | $8.4\pm 0.0$ | $\lesssim 7.3$ | $\lesssim 7.2$
Projected distance (kpc) | 10.9 | 128.8 | $68.9\pm 3.5$ | 45.2 | 34.1
SFR (NUV; $\rm{M}_{\odot}$ yr-1 $\times 10^{-3}$) | $6.2\pm 2.2$ | $3.5\pm 1.3$ | $5.1\pm 1.0$ | – | –
SFR (FUV; $\rm{M}_{\odot}$ yr-1 $\times 10^{-6}$) | $78\pm 41$ | – | – | – | –

The left two UDG columns are the new data presented in this work. The right
three UDG columns summarize the results reported in B18, J21, andF23
(specifically the “Total” column for UGC 9050-Dw1). Note that uncertainty
estimates do not include the distance uncertainty.
Rows: 1) RA: Right ascension in sexigesimal hh:mm:ss. 2) Dec: Declination in
dd:mm:ss. 3) D: Assumed distance in Mpc 4) $v_{\rm{helio}}$: Heliocentric
velocity. 5) $M_{V}$: $V$-band absolute Vega magnitude determined from CFHT
data. 6) $\log{\rm{L_{V}}/\rm{L}_{\odot}}$: $V$-band luminosity. 7) $(V-I)$:
$V-I$ color determined from CFHT data in Vega magnitudes. 8) $m_{g}$: $g$-band
apparent AB magnitude, determined from CFHT data. 9) $(g-r)$: $g-r$ color
determined from CFHT data, in AB magnitudes. 10) $m_{NUV}$: $NUV$ apparent
magnitude determined from GALEX data, in AB magnitudes. 11) $m_{FUV}$: $FUV$
apparent magnitude determined from GALEX data, in AB magnitudes. 12)
$\mu(0,g)$: $g$-band surface brightness in AB magnitudes. 13) & 14) $r_{1/2}$:
Circularized half-light radius (except for UGC 9050-Dw1, which is the radius
at which the counts match the background). 15) $b/a$ Ratio of semi-minor to
semi-major axis for the derived Galfit model. 16) $\theta$: Position angle of
derived GALFIT model in degrees counterclockwise from north. 17) Sérsic index
($n$). 18) $\log({M_{*}/M_{\odot}})$: Logarithm of stellar mass using the M/L
derived from Zhang et al. (2017). 19) $\log({M_{\rm{H}\,\rm{\textsc{i}}\
}/M_{\odot}})$: Logarithm of H i mass. 20) Projected distance from presumed
host. 21) SFR: NUV derived star formation rate. 22) SFR: FUV derived star
formation rate.

##  5 The Globular Cluster Systems

###  5.1 Globular Cluster Selection

In this work, the globular cluster candidate (GCC) selection is identical to
that described in J21 and F23. In brief, we perform aperture photometry on the
HST images using the Dolphot v2.0 software. We then perform subsequent cuts on
the Dolphot produced point source catalog such that we limit to sources
classified as ‘stars’ (other source identifiers are ‘elongated object’,
‘object too sharp’, and ‘extended object’), with no photometric flags, and
with S/N $>5$. For both HST filters we further constrain with fit quality
diagnostics. The sharpness is enforced to fall within the bounds of $-$0.3 to
0.3 and roundness is required to be less than 0.3, limiting elongated or
distorted sources and those that are overly compact. We set a maximum limit on
crowding to 0.5 mag in both filters. The Dolphot magnitude uncertainties are
required to be less than 0.3 mag. Next a color cut is used, to limit sources
to those within the color range expected for GCs. We use $0.5<(V-I)<1.5$ from
Brodie & Strader (2006), which should generally eliminate blue star-forming
regions from our source selection.

Then we apply a concentration cut, which is determined by comparing the flux
of the background subtracted $F814W$ image in concentric circular apertures of
4 and 8 pixels in diameter (see similar approaches in e.g., Peng et al. 2011;
Beasley & Trujillo 2016; Saifollahi et al. 2021). We define our concentration
index as $C_{4-8}=-2.5\log_{10}{(\frac{N_{4\rm{pix}}}{N_{8\rm{pix}}})}$ where
$N_{4\rm{pix}}$ represents the sum of flux values in a 4 pixel aperture. To
select GCCs we allow the concentration index parameter to span the range
$0.2-0.8$ mag where we expect GCs to lie, which accounts for the extended
locus of point sources (in magnitude-concentration space) and slightly
extended sources. This is because larger GCs may not be perfect point sources,
particularly at the distance of KUG 0203-Dw1. This selection is designed to
eliminate diffraction spikes, compact background galaxies, and any other high
concentration index sources.

Last, we employ a cut in magnitude in an effort to maximize the number of real
GCs and eliminate contaminants. We do this by assuming the GCs follow the
Gaussian dwarf elliptical GC luminosity function (GCLF) of Miller & Lotz
(2007), similar to the approach of Peng et al. (2011). The Gaussian GCLF peaks
at $M_{I}=-8.12$ with $\sigma_{M_{I}}=1.42$ mag. We use the peak of the GCLF
at the distance of each UDG to serve as a brightness minimum in selecting our
GCCs. This is used in lieu of the completeness limit in order to minimize
stellar contaminants. We also employ a brightness maximum, above which we
expect most point sources to be foreground stars. This value corresponds to
$M_{I}>-12.38$, or $3\sigma$ from the mean of the GCLF. In apparent magnitude,
we select all GCCs in the range of $19.8<m_{I}<24.0$ for KUG 0203-Dw1, and
$21.3<m_{I}<25.6$ for KDG 013. Such a cut means we are only sampling half of
the luminosity function. As a result, our final GC counts will be corrected by
multiplying the initial resultant GC counts by 2.

We provide a color-magnitude diagram in Figure 7 of point sources identified
in Dolphot. All plotted points pass the initial set of signal-to-noise,
sharpness, roundness, crowding, and magnitude uncertainty cuts, and red points
pass the subsequent concentration cut. Point sources that fall within the
color and magnitude selection criteria and lie within $2\times r_{1/2}$
constitute the final GCC sample. These sources are highlighted in the HST
images in Figure 2, encircled by teal apertures. Note that in the KUG 0203-Dw1
frame (Figure 2, lower left) a majority of the GC candidates are centered on
the two galaxies with few additional contaminants in the field, while the KDG
013 frame has substantially more contaminants (Figure 2, lower right).

###  5.2 Globular Cluster Abundances

After the DOLPHOT photometric catalog has been constrained following the
procedure described above, we elect to select GCCs within $2\times$ the best
fit circularized aperture radius (similar to other work in the literature,
e.g., Müller et al. 2021; Danieli et al. 2022; Janssens et al. 2022; Jones et
al. 2023a.) In Section 4.2 note that the best GALFIT models had some
ellipticity. Selecting GCCs within an elliptical aperture yielded similar
counts to those selected within a circularized aperture. Likewise, due to the
tidal features of these UDGs, defining a strict boundary for these galaxies is
non-trivial. We therefore choose to adopt the simpler approach of counting
GCCs within a general circularized radius and subsequently subtracting
contaminants.

Contaminant counts for false GCCs were determined with a parallel WFC3 field
taken in an empty patch of sky close to the host systems. To determine
contaminant rates we employ the same cuts used to identify GCCs in the ACS
field as described in Section 5.1. Note that the WFC3 field-of-view
(160”x160”) is smaller than the ACS field-of-view (202”x202”), so the number
of contaminants identified must be scaled relative to the ACS detector sky
area before scaling to within the area of the actual GC searches.

The raw GCC counts within $2\times$ the effective radii of either UDG are
small ($<10$ per UDG), where number counts are dominated by Poisson
statistics. We thus rely on a Bayesian approach to determine the number of GCs
within the UDG aperture analytically. The procedure for this method is
outlined in Section 4.3 of J21, which we summarize here. The count of
potential false GC candidates within the UDG’s aperture conforms to a Poisson
distribution with an unknown mean, denoted as ‘b,’ representing the background
rate of false positives arising from GCs linked to the host galaxy and other
incidental sources such as Milky Way foreground and compact background
galaxies. The probability of false GCCs within the aperture of the UDG can be
described by a normal Poisson process. Multiplying this probability with the
analytic Bayesian solution with a flat prior to estimate $b$ and $b$
marginalized yields the probability mass function for the number of GCs. This
result is written as:

$p(N_{\rm{GC}}|O)=\frac{\Gamma(N_{\rm{bg}}+N_{\rm{GCC}}-N_{\rm{GC}}+1)}{(A_{\rm{bg}}+1)^{(N_{\rm{bg}}+N_{\rm{GCC}}-N_{\rm{GC}}+1)}(N_{\rm{GCC}}+N_{\rm{GC}})},$
(1)

where $O$ is short for observations, $N_{\rm{GC}}$ is the number of genuine
GCs in the UDG apertures, $N_{\rm{GCC}}$ is the number of GCCs in the UDG
aperture, $N_{\rm{bg}}$ is the number of background sources that pass as false
GCCs, and $A_{\rm{bg}}$ is the area of the background field. $A_{\rm{bg}}$ is
dimensionless as it is expressed in terms of the area of the circular aperture
used to count GCCs around the target. Because we use the WFC3 field to
determine background counts, $A_{\rm{bg}}$ is scaled such that it is in units
of the ACS area.

The search radius of KUG 0203-Dw1 is equivalent to $23.6\pm 3.6$ arcsec or
$3.1\pm 0.6$ kpc at its distance (see Table 3). A total of 5 GCCs were
identified within this aperture (see the outer dashed radiis in Figure 2). We
find a total contaminant abundance in the parallel field of 13, which when
scaled to the ACS area covered by the UDG yields a raw abundance of 1
contaminant. With our probabilistic approach for determining GC abundance and
multiplying our result by $2$ to account for only sampling the bright half of
the GCLF, our final most probable GC abundance for KUG 0203-Dw1 is
$N_{\rm{GC}}=8\pm 2$.

The search radius of KDG 013 is $25.0\pm$1.8 arcsec or $6.7\pm 0.5$ kpc .
Within this aperture we identify a total of 4 GCCs, with a raw contaminant
abundance of 2 in the UDG area. After performing our probabilistic analysis we
find our most probable GC abundance for KDG 013 is $N_{\rm{GC}}=6\pm 2$.

We can extend the $I$-band magnitude cut in Section 5.1 from $M_{I}<-8.12$
down to our $90\%$ completeness limit, which corresponds to $M_{I}<-6.14$ for
KUG 0203-Dw1 (sampling about 2/3 of the faint-end GCLF) and $M_{I}<-7.42$ for
KDG 013 (sampling nearly the full GCLF). While a looser cut such as this may
allow for an increase in contaminants, we find the same predicted abundance
for both systems (within error) that we do when determining the GC abundance
from the bright half of the GCLF alone. At this extended magnitude limit we
find $9^{+1}_{-2}$ GCs for KUG 0203-Dw1 and $4\pm 1$ for KDG 013.

Figure 4: Counts of GCs ($N_{\rm{GC}}$) plotted against the $V$-band absolute
magnitude ($M_{V}$). To provide context, we compare our findings to several
data sets found in the literature, including a general galaxy data set,
cluster UDGs, group UDGs, and other distinct GC-rich UDGs from various
environments. The solid, dashed, and dotted black lines represent specific
frequency ($S_{N}$) values of 1, 10, and 100, respectively. Our full sample of
five UDGs with tidal features is shown by orange points: KUG 0203-Dw1 (star),
KDG 013 (half filled star), UGC 9050-Dw1 (diamond), NGC 2708-Dw1 (square), and
NGC 5631-Dw1 (half filled square). KUG 0203-Dw1 and KDG 013 are slightly more
GC rich than the two UV-bereft UDGs in our sample (NGC 2708-Dw1 and NGC
5631-Dw1; J21).

The GC abundances for these systems are plotted in Figure 4 (orange stars)
alongside the rest of our sample of UDGs with tidal features (other orange
points). The nearby galaxy sample of Harris et al. (2013) is plotted for
comparison, which includes elliptical, spiral, lenticular, and irregular
galaxies and extends to brighter galaxies. We also include a number of UDG
samples from both clusters (blue points) and groups (pink points) for
comparison: Coma cluster UDGs (Forbes et al., 2020), Virgo cluster UDGs (Lim
et al., 2020), Hydra I cluster UDGs (Iodice et al., 2020; La Marca et al.,
2022), and group UDGs compiled in Somalwar et al. (2020). There are also a
number of individual UDGs in the literature that we include, a majority of
which are considered to be GC-rich: Dragonfly 2 (DF2) and Dragonfly 4 (DF4)
(NGC 1052 UDGs; van Dokkum et al. 2022), Dragonfly 44 (DF44, a Coma UDG;
Saifollahi et al. 2021), Dragonfly 17 (DF17, a Coma UDG; Beasley & Trujillo
2016), VCC1287 (a Virgo UDG; Beasley et al. 2016), NGC 5846-UDG1/MATLAS19 (NGC
5846 group UDG; Müller et al. 2021; Danieli et al. 2022), DGSAT 1 (in a low
density region of the Pisces-Perseus supercluster; Janssens et al. 2022). For
a full discussion on the GC abundance refer to Section 6.2.

###  5.3 Specific Frequency

A convenient way to describe GC richness relative to the galaxy’s luminosity
is to calculate specific frequency. While this quantity is common to calculate
even at dwarf galaxy masses, the relation between GC abundance and luminosity
does not hold as well as it does at higher masses. This is speculated to be
due to the stellar-to-halo mass relation becoming less linear at low mass, as
GCs are found to trace total DM halo mass and luminosity traces stellar mass
(hence why at higher masses a specific frequency of 1 is more common). The
definition of specific frequency presented in Harris & van den Bergh (1981) is
$S_{N}=N_{\rm{GC}}10^{0.4(M_{V}+15)}$. Using our derived galaxy $M_{V}$ from
the CFHT data and the GC abundances this yields a specific frequency of
$S_{N}=26.9_{-8.8}^{+8.2}$ for KUG 0203-Dw1 and $S_{N}=3.3_{-0.6}^{+0.8}$ for
KDG 013.

In Figure 4 we include diagonal lines of constant specific frequency. KUG
0203-Dw1 and KDG 013 both have specific frequencies consistent with other UDGs
and dwarf galaxies (generally between 1 and 50).

##  6 Comparative Analysis of the UDG Sample

In addition to the two UDGs presented here, we also have previously reported
an additional 3 UDGs that were identified and observed in an identical manner,
constituting a full sample of 5 UDGs. These UDGs were selected such that they
are a) in group-like environments within proximity to a more massive ‘host’
galaxy and b) have telltale signs of tidal disturbances through elongated or
amorphous morphology. Of this set of five, two of the UDGs - NGC 2708-Dw1 and
NGC 5631-Dw1 - contain little evidence of recent star formation or neutral gas
and exhibit optically red colors. The other three - UGC 9050-Dw1, KUG
0203-Dw1, and KDG 013 - in contrast have GALEX UV detections which is
suggestive of recent star formation ($<100$ Myr) and also exhibit bluer
optical colors. We briefly summarize the previously reported results of the
first three UDGs within our sample below before discussing the full sample.
The properties of these UDGs are also presented in Table 3.

###  6.1 Targets Previously Reported

NGC 2708-Dw1 is an elongated UDG companion to NGC 2708 (of the NGC 2698
group), with a faint linear stellar stream connecting the two. J21 identified
$N_{\rm{GC}}=3^{+1}_{-2}$ and $S_{N}=3.3^{+5.6}_{-1.0}$ for NGC 2708-Dw1.
Additionally there is no trace of H i in the UDG itself or of a H i tidal
connection to the host NGC 2708, indicating that the stellar stream originated
from a gas poor object (likely the UDG itself) and not the disk of NGC 2708.

NGC 5631-Dw1 is more notably elongated, connected to NGC 5631 with a faint
curved stellar stream. J21 finds a slightly higher GC abundance, with
$N_{\rm{GC}}=5^{+1}_{-2}$ and a much higher specific frequency of
$S_{N}=54^{+49}_{-33}$. There is a plausible H i detection coincident with the
UDG and connected to the disturbed H i content of NGC 5631. But because the H
i tails are significantly larger than the stellar tails, they may not be
physically connected nor associated with the UDG.

UGC 9050-Dw1 is a highly amorphous UDG with a distinct tidal plume, in the
proximity of UGC 9050, but with no clear stellar or H i streams between the
two. It contains a brighter “core” region with overlapping UV emission while
the remainder of the galaxy consists of very low surface brightness and redder
stellar material. F23 reports an extraordinary GC population of
$N_{\rm{GC}}=52\pm 12$ and $S_{N}=122\pm 38$. The colors of the GCs are also
uniquely monochromatic, indicating that all of them likely formed at the same
time. This UDG has a clear H i detection, with an estimated mass of
$\log{M_{\rm{H}\,\rm{\textsc{i}}\ }/M_{\odot}}=8.44\pm 0.04$.

###  6.2 Comparisons Between UDGs With Tidal Features

We have completed the first comprehensive look at UDGs displaying tidal
features or amorphous morphology indicative of an interaction within 150 deg2
of sky of the CFHT legacy survey. Here we discuss the similarities and
differences between the observed properties of the sample.

Physical Properties In terms of size, NGC 2708-Dw1, NGC 5631-Dw1, KUG
0203-Dw1, and KDG 013 have comparable dimensions, with half-light radii
ranging from 1.5 to 3.4 kpc. UGC 9050-Dw1 is larger, with an approximated
radius of $\sim 6$ kpc (though this is not the half-light radius because of
the complex morphology of the UDG). In terms of luminosity or stellar mass
these UDGs exhibit a variety of measurements but with no strong outlier. NGC
5631-Dw1 has a much fainter surface brightness than the other UDGs, as does
UGC 9050-Dw1 outside of the “core” region. We plot these properties in Figure
5 in comparison to a Coma cluster UDG sample from van Dokkum et al. (2015), a
group UDG sample from Somalwar et al. (2020), and a H i bearing UDG sample
from Leisman et al. (2017). UGC 9050-Dw1 is a clear outlier in the size-
luminosity relation, with the remaining four UDGs consistent with the Coma
cluster and group UDGs. In terms of central surface brightness-half light
radius parameter space, UGC 9050-Dw1 is somewhat consistent with the H i UDG
population (although still rather large) while NGC 5631-Dw1 is an outlier due
to its central surface brightness. However, previous studies limited by
surface brightness may not have thoroughly explored this parameter space,
rather than NGC 5631-Dw1 being a significant outlier. We also note that these
other samples tend to assume $n=1$ for the Sérsic index, which complicates
this comparison. Additionally, the radius of UGC 9050-Dw1 is not a half light
radius derived from GALFIT like our other UDGs, rather the radius at which the
counts are comparable to the background (the complex morphology and extreme
LSB nature of this UDG inhibited determining such a quantity).

Figure 5: Left: Size-luminosity relation for the sample of 5 UDGs with tidal
features compared to Coma cluster UDGs (van Dokkum et al. 2015; blue
triquetra), group UDGs (Somalwar et al. 2020; pink pentagons), and H i-rich
UDGs (Leisman et al. 2017; purple points). All of our UDGs are consistent with
the Coma sample, aside from UGC 9050-Dw1 which is unusually large for its
brightness. The dashed vertical line marks the defined UDG lower limit on size
used in this work. Right: Central surface brightness as a function of half
light radius for the same sample. Here UGC 9050-Dw1 is more consistent with
the H i sample while NGC 5631-Dw1 has a very faint central surface brightness.
We note that the comparative samples are surface brightness limited so there
may be other sources currently undetected at lower central surface brightness.
The dashed horizontal line is analogous to that in the left panel. The dashed
vertical line indicates the maximum central surface brightness for a UDG as
defined in this work (please note that the H i UDGs adhere to a distinct
definition hence why some are brighter).

Optical Morphology Our sample exhibits a variety in its optical morphology.
NGC 2708-Dw1, NGC 5631-Dw1, and KUG 0203-Dw1 have associated stellar streams
connecting to a massive host. All of the UDGs are elongated with some
ellipticity, although it is unclear exactly how much for the case of UGC
9050-Dw1 since the more complex morphological features have extremely low
surface brightnesses. UGC 9050-Dw1 has a very clear tail feature extending to
the north of the UDG and KUG 0203-Dw1 has a plume extended in the southwest.
It is less clear if KDG 013 has a plume in the southwest or if it is just
excess clumpy material (see Figure 1).

Stellar Populations While we cannot make detailed assessments of the stellar
populations within the UDGs, we can comment on the overall color. NGC 2708-Dw1
is the reddest ($g-r=0.5$; B18), followed by NGC 5631-Dw1 and KDG 013
($g-r=0.4$), UGC 9050-Dw1 ($g-r=0.3$; F23), and KUG 0203-Dw1 ($g-r=0.2$).
Therefore we expect that the stellar populations are generally older in the
reddest of the UDGs. UGC 9050-Dw1 is a special case where the color in the
“core” region is very blue ($g-r=-0.2$) which has likely been the site of more
recent star formation. These conclusions are further supported by the GALEX UV
luminosity observed in KDG 013, UGC 9050-Dw1, and KUG 0203-Dw1. All of the UV
emission in UGC 9050-Dw1 comes from the core which is likely dominated by
young stars. KUG 0203-Dw1 has the highest UV luminosity and UV derived star
formation rate, consistent with a bluer and younger stellar population
throughout the UDG.

Gas Content Only two of the UDGs have clear neutral gas detections: KUG
0203-Dw1 ($\sim 10^{7}~{}\rm{M}_{\odot}$) and UGC 9050-Dw1 ($2.75\times
10^{8}~{}\rm{M}_{\odot}$). There are detections coincident with NGC 5631-Dw1
and KDG 013 but because there is no statistically significant concentrations
of H i at the location of the galaxies, it is not clear that the H i belongs
to them.

The morphology of the H i of KUG 0203-Dw1 shows both a connection between the
UDG and the host, in addition to a spur to the southeast and a
trailing/leading tail detection to the northeast of the host. This suggests
that the system initially contained gas, which is currently undergoing tidal
stripping by the host galaxy, rather than the UDG stripping gas from the host.
The latter would not lead to a pronounced concentration of H i centered on the
UDG. In contrast, while the H i in UGC 9050-Dw1 is also distorted, it is not
as obvious if this is due to its neighbor UGC 9050. UGC 9050 does have an H i
spur extended in the direction of UGC 9050-Dw1, possibly indicative of a prior
interaction.

GC Populations In comparison to the two UV bereft UDGs included in our sample
(NGC 2708-Dw1 and NGC 5631-Dw1 from J21), KUG 0203-Dw1 and KDG 013 contain
similar but slightly more abundant GC populations (see Figure 4). Thus while
the bluer UDGs with UV detections have slightly more GCs than the red UDGs
(not including UGC 9050-Dw1), all four have abundances comparable to normal
galaxies at their luminosity (see Section 5.2). In general, cluster UDGs lie
above group UDGs in parameter space (not unexpected based on theoretical work,
e.g., Carleton et al. 2021) with more elevated GC abundances. However, group
UDGs seem to display a rather wide variety in GC abundances overall given that
of UGC 9050-Dw1 and the more GC abundance UDGs identified in Somalwar et al.
(2020) and the NGC 1052 group (van Dokkum et al., 2022).

In terms of colors of the GC candidates themselves, results in F23 show that a
vast majority of those identified in UGC 9050-Dw1 are strikingly monochromatic
and blue. We plot the colors of the GCs of the full sample in Figure 6. Note
that the histograms have been normalized to have an integrated area of 1 due
to the high GC abundance of UGC 9050-Dw1. The other UDGs within our sample
generally fill the full parameter space of allowed $(V-I)$ color (see Section
5.1). Interestingly KUG 0203-Dw1 also appears to have a GC population with a
uniform and blue color, with mean $(V-I)=0.83$ mag, median $(V-I)=0.85$ mag,
and standard deviation $0.08$ mag. These measurements are very similar to UGC
9050-Dw1 and other monochromatic GC UDG populations in the literature,
although KUG 0203-Dw1 has the smallest GC population of them (NGC 1052-DF2 and
NGC1052-DF4 have the second fewest with 12 GCs each; van Dokkum et al. 2022).
Given that the field KUG 0203-Dw1 resides in has a small number of
contaminants it is not likely that any of these are foreground stars or
background galaxies.

Figure 6: $(V-I)$ color distribution of the 5 UDGs with associated tidal
features. The sample is split for readability. The left histograms shows the
UDGs with monochromatic GCs and the right histogram shows the other 3 UDGs.
The histogram for each UDG is normalized such that it has an integrated area
of 1 such that the histograms can be compared on similar axes (hence non
integer GC abundances). The vertical dashed lines correspond to the color cut
employed for GC selection; $0.5<(V-I)<1.5$. KUG 0203-Dw1 exhibits a blue
monochromatic GC population, similar to UGC 9050-Dw1. The GC candidates of NGC
2708-Dw1, NGC 5631-Dw, and KDG 013 generally span the full color space.

Environment All of the UDGs studied in this work reside in group environments.
Each of the groups have a confirmed membership of $n\gtrsim 4$ except for UGC
9050-Dw1, which currently has only two known members (note that the UGC 9050
pair lies at the fringe of a larger group, although association is unclear).
This is also the only group where the host galaxy has a rather similar mass
(both stellar and H i) to the UDG. This environment may be connected to the
more unusual properties exhibited by the UDG. KUG 0203-Dw1 and KDG 013, though
smaller, exhibit sizes comparable to the other members of their respective
systems. In contrast, NGC 2708-Dw1 and NGC 5631-Dw1 are significantly dwarfed
by their companions. Possibly, the stronger influence of the host on these
smaller systems led to an earlier period of gas stripping. This, in turn,
resulted in a smaller GC abundance and a lack of UV emission. However, outside
of the stellar populations, the physical properties of the UDGs of our sample
do not deviate substantially among one another (aside from UGC 9050-Dw1 as
noted above).

In our comparative analysis of the five UDGs in our sample, UGC 9050-Dw1 is a
clear outlier, setting itself apart from the others in several key aspects.
The remaining four generally share common characteristics. However, we do find
that KUG 0203-Dw1 also contains uniform and blue GC candidates just like UGC
9050-Dw1 and the only other UDG in the sample with a clear H i detection. That
said, with only a total of 5 GCCs identified at present in KUG 0203-Dw1, this
monochromatic sample is difficult to interpret.

##  7 The Formation of KUG 0203-Dw1 and KDG 013

In this section we comment on the possible formation scenarios of KUG 0203-Dw1
and KDG 013. As both UDGs exhibit clear tidal features we will be considering
formation mechanisms that are likely to produce such features, such as: 1)
Dwarf mergers, 2) TDGs, 3) Dwarf galaxies “puffed up” by interactions with a
more massive galaxy, and 4) pre-existing UDGs subsequently processed by the
group environment.

###  7.1 Dwarf-Dwarf Interactions

When dwarf galaxies undergo collisions, the result can manifest as an increase
in the effective radius and angular momentum of the system, accompanied by a
decrease in surface brightness and a redistribution of star formation towards
the outer regions of the resulting (merged) galaxy. A hydrodynamical
simulation study (ROMULUS25) conducted by Wright et al. (2021) suggests that
decentralized star formation leads to a steep color gradient. Despite this,
the UV emission is distributed evenly across the surfaces of our two UDGs, KUG
0203-Dw1 and KDG 013, with no discernible color gradient.

There is also increasing evidence that dwarf mergers enhance star formation
rates (e.g., Stierwalt et al., 2015; Gao et al., 2023; Subramanian et al.,
2023), but the star formation rates of KUG 0203-Dw1 and KDG 013 are fairly
typical of UDGs - blue UDGs have star formation rates between $\sim 0.001-0.1$
$\rm{M}_{\odot}$ yr-1 (Kado-Fong et al., 2022). This implies that if either
UDG originated from a merger, the event must have occurred recently, preceding
the development of the observed color gradient.

Dwarf major mergers can also give rise to distinctive tidal features such as
tails, bridges, and shells, expected to last $2-5$ Gyrs (e.g., Johnston et
al., 2001; Pearson et al., 2018), features present in both UDGs. However,
distinguishing effects caused by tidal interactions with a massive companion
from those caused by a dwarf merger is often challenging, aside from when the
dwarfs are not completely merged (Paudel et al., 2018).

The H i and optical morphology of KUG 0203-Dw1 paint a clear picture of a
direct interaction with the host KUG 0203-001. While it is possible a dwarf
merger occurred before the system began interacting with the host, invoking
multiple formation mechanisms for this UDG is unnecessary. Similarly, KDG 013,
which lacks a clear gas detection, would also have had to be gas stripped post
merger. Therefore we find that the dwarf major merger formation mechanisms is
unlikely for either UDG.

###  7.2 Tidal Dwarf Galaxies

Tidal dwarf galaxies (TDGs) form as a result of tidal interactions between two
or more massive galaxies, where the tidal forces generated during close
encounters lead to the ejection of stellar and gaseous material into extended
tidal tails or bridges. These ejected materials can then coalesce and form
new, self-gravitating galaxies known as TDGs (e.g., Elmegreen et al., 1993;
Duc & Mirabel, 1998; Kaviraj et al., 2012). Note that TDGs and UDGs with tidal
features (sometimes called tidal UDGs) refer to different classes of objects,
which in some instances may or may not overlap. In this subsection we explore
whether our UDGs with tidal features are consistent with a TDG origin.

Because TDGs form very differently from typical galaxies, the expectation is
that TDGs do not contain GCs (or DM), and at present studies of low redshift
TDGs do not find GCs (e.g., Fensch et al., 2019). While chances are small, at
most a TDG could strip a GC from the parent. From our Bayesian analysis
discussed in Section 5.2 we can obtain probabilities that either UDG has 0
real GCs. In the case of KUG 0203-Dw1 there is only a $0.75\%$ probability
that none of the GC candidates are real, with a $7.26\%$ probability for KDG
013. Hence, the abundances of GCs provide strong evidence against categorizing
these UDGs as TDGs.

As a result of their formation mechanism, young TDGs are gas rich, inheriting
gas from the tidal material that formed them, with the gas reservoir
contributing to ongoing star formation. H i streams are expected to have a
longer visibility lifetime than stellar streams, and young TDGs have H i
connections to the parent object (which has been observed a number of times in
interacting systems with TDG candidates, Jones et al. 2019; Lee-Waddell et al.
2019; Namumba et al. 2021). The VLA H i observations indicate a clear
connection between KUG 0203-Dw1 and KUG 0203-100 given the over-density
present in KUG 0203-Dw1. This may strengthen a TDG origin for KUG 0203-Dw1,
but TDGs must form from the interactions between multiple massive galaxies.
For a TDG origin we must then either be at a viewing angle where we cannot see
the system KUG 0203-100 interacted with (as there are no other obvious nearby
massive systems), or the interaction must have been substantially old enough
for the two to coalesce (also an unlikely scenario given that KUG 0203-100
does not appear to be a merger remnant). Long-lived TDGs are also expected to
form at the tips of H i tails (Bournaud & Duc, 2006), but KUG 0203-Dw1 is
closer to the center of the H i stream. This stream also has both leading and
trailing tails which are typically more indicative of dwarf stripping.

The VLA H i observations of KDG013 reveal an overlapping H i detection, but it
is unlikely to be associated with the UDG due to its offset from the UDG.
Consequently, this H i detection is improbable as the tail that formed KDG013,
assuming a TDG origin. Overall, we conclude that the TDG origin hypothesis is
very unlikely for either UDG.

###  7.3 Tidally ‘Puffed Up’ Dwarfs

Tidal interactions instigated by strong gravitational effects imparted by a
massive companion can expand a galaxy’s stellar halo with increased orbital
energy and decrease the surface brightness, pushing these dwarf galaxies into
UDG parameter space (Errani et al., 2015; Conselice, 2018; Carleton et al.,
2019; Tremmel et al., 2020). While the majority of studies on UDGs influenced
by companions have predominantly concentrated on cluster environments (e.g.,
Sales et al., 2020; Carleton et al., 2021, and sources mentioned above), there
is mounting evidence indicating that this phenomenon may also occur in lower
density group environments. For example, hydrodynamical simulations by Jiang
et al. (2019) and Liao et al. (2019) both estimate that $\approx 50\%$ of
group UDGs formed from dwarfs on eccentric orbits that suffered from tidal
stripping and heating (with the other half as pre-existing UDGs that were
later processed by the group).

After a pericentric passage the UDG progenitor is stripped of a substantial
portion of its gas and star formation slows (Román & Trujillo, 2017; Benavides
et al., 2021). Jiang et al. (2019) and Liao et al. (2019) find that within 1
to 2 pericentric passages a dwarf is transformed into a UDG. This narrative
fits appropriately with the observed properties of KDG 013. There is no clear
H i detection, meaning NGC 830 or other group members may have pulled its gas
off. The extension of the H i contours near KDG 013 may even be the
gravitational influence of the UDG pulling gas from the intra-group medium,
but it is equally as likely that it could be a trailing or leading tail from a
number of objects in the group. Despite the lack of a clear gas detection, KDG
013 still has traces of recent star formation (at least within the past $\sim
100$ Myr) indicating it has not been without cold gas for a substantial period
of time.

The situation is a little different for KUG 0203-Dw1 which still contains an
over density of H i and is in close proximity in projection to the host (only
10.9 kpc in projection). Thus the UDG interaction with the host is likely in
an early phase, where the UDG is being tidally puffed but has not yet been
fully stripped of its gas. This is further motivated by the rather small
circularized radius of the UDG, which just barely passes the UDG criteria
($1.53\pm 0.3$ kpc compared to the limit of $>1.5$ kpc). Because KUG 0203-Dw1
has a bluer stellar population and high specific star formation rate than KDG
013 one can envision them at different stages in the tidal processing in the
group with KUG 0203-Dw1 just forming into a UDG and KDG 013 already having
been processed.

We have demonstrated both KUG 0203-Dw1 and KDG 013 display GC abundances
rather typical of galaxies given their $V$-band brightness (Figure 4),
indicating an origin as a dwarf galaxy. A study of local volume dwarfs
performed by Carlsten et al. (2022) finds that in the stellar mass range of
$7<\log{M_{*}/M_{\odot}}<8$ (the approximate mass range of these UDGs) the
typical GC abundance ranges from approximately $1-7$. Specifically, the Fornax
dwarf ($\log{M_{*}/M_{\odot}}\sim 8$) hosts $6$ bright GCs (de Boer & Fraser,
2016; Pace et al., 2021) at $\sim 1.5$ magnitudes below the peak of the GCLF.
These results for local dwarfs are very comparable to the values we derive for
these UDGs ($8\pm 2$ for KUG 0203-Dw1 and $6\pm 2$ for KDG 013 accounting for
the full GCLF). Therefore the observed properties of KUG 0203-Dw1 and KDG 013
are most consistent with a formation scenario where they were tidally heated
and transformed into UDGs by their group.

###  7.4 Pre-existing UDGs Processed By the Group

While half of the group UDGs in the simulations of Jiang et al. (2019) and
Liao et al. (2019) originate as dwarf galaxies where subsequent tidal effects
transformed them into UDGs, the other half originate as pre-existing UDGs in
the field or group periphery that then experience environmental tidal effects.
This would mean tidal features are coincidental and unrelated to the diffuse
nature of the UDGs. However, the resultant UDG is not significantly different,
as these pre-existing simulated UDGs are also stripped of gas and their star
formation has halted.

Jones et al. (2023a) discovered that gas-rich field UDGs exhibit GC abundances
similar to regular dwarf galaxies, ranging from $0-2$. While this is roughly
consistent with the UDGs in our study, the lack of specific predictions for GC
abundances in hydrodynamical simulations complicates distinguishing between
UDG formation via tidal heating and pre-existing UDGs undergoing tidal
heating. We contend that the stellar populations in both KUG 0203-Dw1 and KDG
013 are distinctly influenced by their group environments. The observation
that KUG 0203-Dw1 narrowly meets the UDG criteria suggests that it might not
have originally qualified as a UDG before interacting with its host. However,
presently, origins as pre-existing UDGs cannot be conclusively dismissed.

We also note a study by Kong et al. (2022) whereby gas rich field UDGs are
compared to hydrodynamical simulations concluded that the simulations were not
able to realistically produce observed features. This suggests that galaxy
formation models may be inaccurate for gas-rich UDGs at present. Thus a more
comprehensive understanding of group UDGs is warranted before arguments for
the processing of pre-existing UDGs can be made.

###  7.5 Formation Mechanisms for UDGs with Tidal Features

KUG 0203-Dw1 and KDG 013 are most consistent with formation via tidal heating
in their groups. But what of the other 3 UDGs that complete our sample, as
discussed in Section 6? J21 concludes that NGC 2708-Dw1 and NGC 5631-Dw1 are
most consistent with the same formation mechanisms of tidally heated dwarfs.
In contrast, due to the unique properties of UGC 9050-Dw1, F23 finds that the
UDG is most consistent with formation via a dwarf major merger.

##  8 Conclusion

We present HST imaging and VLA H i mapping to follow-up two UDGs with
elongated morphologies indicative of a tidal disturbance. We find the GC
counts of both KUG 0203-Dw1 and KDG 013 to be consistent with normal dwarf
galaxies of similar luminosities. There is a clear H i detection in KUG
0203-Dw1, with morphology highly suggestive that the host galaxy KUG 0203-100
is actively stripping gas off of the dwarf. There is also a faint, curved
stellar stream between the two. KDG 013 has a coincident H i detection at its
location, but the morphology of the gas indicated that it is unlikely to be
associated with the UDG. While we consider that these UDGs may have formed
from dwarf mergers, TDGs, or were preexisting UDGs, the most likely formation
origin is in typical dwarf galaxies that then suffered from tidal effect of
their group, transforming them to UDGs.

These two UDGs complete a sample of five that were identified in the CFHTLS
area. All of the UDGs were identified as having morphology suggestive of tidal
interactions and in group environments of 2 or more. This sample can be
further broken up into UDGs that do contain GALEX UV detections and those that
do not. This sample has one dramatic outlier - UGC 9050-Dw1 - while the
remaining four are fairly self consistent. The two UDGs of the four (KUG
0203-Dw1 and KDG 013) that have UV detections have slightly elevated GC
populations compared to the two that do not have UV detections (NGC 2708-Dw1
and NGC 5631-Dw1), but all four have GC abundance expected for galaxies at
their luminosity. Three of these UDGs have no clear neutral gas and one is
having its gas stripped. Thus all four of these UDGs are consistent with
tidally heated dwarfs, but at different evolutionary stages. NGC 2708-Dw1 and
NGC 5631-Dw1 were likely stripped the earliest (particularly NGC 5631-Dw1 with
its anomalously low central surface brightness), given the lack of UV
detections and older/red stellar populations. This is followed by KDG 013,
which was able to form a few more GCs, and lastly KUG 0203-Dw1 which has not
been entirely stripped yet.

Therefore we conclude that the UDG population in group environments,
specifically those exhibiting indications of tidal disturbance, appears to be
dominated by tidally heated dwarf galaxies. Both N-body (Ogiya, 2018;
Benavides et al., 2021) and hydrodynamical simulations (Jiang et al., 2019;
Liao et al., 2019) have previously indicated that tidal stripping in groups is
an important processing method for UDG formation. However, these simulations
do not have predictions for GC abundances. On top of that our sample only
consists of 5 UDGs, with one a very unusual outlier in UDG parameter space,
with properties best described as a resultant of a dwarf major merger. Thus a
larger sample of objects is needed before a more robust conclusion can be made
about UDG formation in groups. This will be contingent on more robust
identification of UDGs in surveys.

There are several avenues that may prove fruitful, such as a manual inspection
through the SMUDges catalog (Systematically Measuring Ultra-diffuse Galaxies;
Zaritsky et al. 2019) for objects with tidal features or even re-training the
CNN (convolutional neural net) used for identifying objects in SMUDges to
identify tidal features. Applying the source detection algorithm used to
detect the UDGs studied here (see Bennet et al. 2017) to other surveys (e.g.,
DECaLS; Dey et al. 2019) may also yield additional sources. In the long term,
such approaches could be extended to large-scale surveys like LSST. Future
studies will allow for a more complete census of UDG formation in group
environments (particularly those with tidal features) and allow us to more
thoroughly assess the rarity of outlier UGC 9050-Dw1 and dwarf major mergers
as a UDG formation mechanism.

This work is based on observations made with the NASA/ESA Hubble Space
Telescope, obtained at the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS5-26555. These observations are associated with program
# 16890. DJS acknowledges support from NSF grants AST-1821967, 1813708 and
AST-2205863. The work used data observed with the Karl G. Jansky Very Large
Array. The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc. This work is based on observations obtained with
MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-France-
Hawaii Telescope (CFHT) which is operated by the National Research Council
(NRC) of Canada, the Institut National des Science de l’Univers of the Centre
National de la Recherche Scientifique (CNRS) of France, and the University of
Hawaii. This work is based in part on data products produced at Terapix
available at the Canadian Astronomy Data Centre as part of the Canada-France-
Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. AK
acknowledges financial support from the grant CEX2021-001131-S funded by
MCIN/AEI/ 10.13039/501100011033 and from the grant POSTDOC_21_00845 funded by
the Economic Transformation, Industry, Knowledge and Universities Council of
the Regional Government of Andalusia. KS acknowledges support for the Natural
Sciences and Engineering Research Council of Canada (NSERC).

##  Appendix A Supplementary Tables

Here we include figures of the color-magnitude diagrams of sources identified
by DOLPHOT in each UDG. We also provide data of the individual GC candidates
identified in KUG 0203-Dw1 (Table 4) and KDG 013 (Table 5).

Figure 7: Left: Color-Magnitude Diagrams (CMDs) of sources within the KUG
0203-Dw1 HST/ACS frame, presented in two panels: sources within the GC search
radius of the UDG ($r<2\times r_{1/2}$) at left and sources outside of the
search radius at right. Note that in the right panel we have excluded GC
candidates that fall inside of the host galaxy KUG 0203-100 as they are
unlikely contaminants. Dolphot identified sources classified as “stars” that
meet the criteria for Signal-to-Noise (S/N), sharpness, roundness, and
uncertainty described in Section 5.1 are represented by blue circles. Orange
squares depict sources that successfully pass the subsequent concentration cut
used to select GC candidates. The CMD space includes a gray outlined box
representing the color and magnitude cuts for GCCs. A horizontal black dashed
line indicates the 90% completeness limit. Right: Same as left, but for KDG
013. Table 4: Globular cluster candidates in KUG 0203-Dw1

No. | R.A. | Dec | F555W | F814W | $m_{V}$ | $m_{I}$ | $M_{I}$ | $(V-I)$ | $c_{4-8}$ | $\rm{R}_{\rm{proj}}$
---|---|---|---|---|---|---|---|---|---|---
| deg | deg | mag | mag | mag | mag | mag | mag | mag | kpc
1 | 31.440109 | -9.836753 | $23.82\pm 0.02$ | $22.88\pm 0.01$ | 23.77 | 22.88 | -8.37 | 0.89 | 0.50 | 3.59
2 | 31.438186 | -9.843140 | $24.44\pm 0.03$ | $23.56\pm 0.02$ | 24.39 | 23.56 | -7.75 | 0.83 | 0.41 | 3.57
3 | 31.443381 | -9.836248 | $24.32\pm 0.02$ | $23.60\pm 0.02$ | 24.28 | 23.60 | -7.86 | 0.68 | 0.75 | 2.89
4 | 31.438003 | -9.846574 | $24.55\pm 0.02$ | $23.58\pm 0.01$ | 24.50 | 23.58 | -7.65 | 0.91 | 0.36 | 4.21
5 | 31.442585 | -9.842759 | $24.86\pm 0.03$ | $23.96\pm 0.02$ | 24.81 | 23.96 | -7.33 | 0.85 | 0.50 | 1.54

Columns: 1) Number. 2) Right ascension in decimal degrees. 3) Declination in
decimal degrees. 4) F555W apparent magnitude and errors determined from
Dolphot. 5) F814W apparent magnitude and errors determined from Dolphot. 6)
Extinction corrected $V$-band apparent magnitude using conversions presented
in Sirianni et al. (2005). 7) Extinction corrected $I$-band apparent
magnitude. 8) Extinction corrected $I$-band absolute magnitude. 9) $(V-I)$
color. 10) Concentration index determined from the GCC magnitudes in 4 and 8
pixel diameter apertures. 11) Projected distance from the center of KUG
0203-Dw1.

Table 5: Globular cluster candidates in KDG 013

No. | R.A. | Dec | F555W | F814W | $m_{V}$ | $m_{I}$ | $M_{I}$ | $(V-I)$ | $c_{4-8}$ | $\rm{R}_{\rm{proj}}$
---|---|---|---|---|---|---|---|---|---|---
| deg | deg | mag | mag | mag | mag | mag | mag | mag | kpc
1 | 32.140328 | -7.847680 | $24.77\pm 0.03$ | $23.89\pm 0.02$ | 24.72 | 23.89 | -9.00 | 0.83 | 0.58 | 2.10
2 | 32.138603 | -7.853665 | $25.28\pm 0.04$ | $24.26\pm 0.02$ | 25.23 | 24.26 | -8.49 | 0.97 | 0.49 | 3.93
3 | 32.143510 | -7.845069 | $25.88\pm 0.06$ | $25.16\pm 0.04$ | 25.84 | 25.16 | -7.88 | 0.68 | 0.53 | 5.88
4 | 32.143052 | -7.844414 | $26.88\pm 0.13$ | $25.48\pm 0.06$ | 26.81 | 25.48 | -6.92 | 1.33 | 0.76 | 6.12

Same as Table 4 but for KDG 013.

## References

  * Adelman-McCarthy et al. (2008) Adelman-McCarthy, J. K., Agüeros, M. A., Allam, S. S., et al. 2008, ApJS, 175, 297, doi: 10.1086/524984
  * Albareti et al. (2017) Albareti, F. D., Allende Prieto, C., Almeida, A., et al. 2017, ApJS, 233, 25, doi: 10.3847/1538-4365/aa8992
  * Amorisco & Loeb (2016) Amorisco, N. C., & Loeb, A. 2016, MNRAS, 459, L51, doi: 10.1093/mnrasl/slw055
  * Amorisco et al. (2018) Amorisco, N. C., Monachesi, A., Agnello, A., & White, S. D. M. 2018, MNRAS, 475, 4235, doi: 10.1093/mnras/sty116
  * 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
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, apj, 935, 167, doi: 10.3847/1538-4357/ac7c74
  * Beasley et al. (2016) Beasley, M. A., Romanowsky, A. J., Pota, V., et al. 2016, ApJ, 819, L20, doi: 10.3847/2041-8205/819/2/L20
  * Beasley & Trujillo (2016) Beasley, M. A., & Trujillo, I. 2016, ApJ, 830, 23, doi: 10.3847/0004-637X/830/1/23
  * Benavides et al. (2021) Benavides, J. A., Sales, L. V., Abadi, M. G., et al. 2021, Nature Astronomy, 5, 1255, doi: 10.1038/s41550-021-01458-1
  * Bennet et al. (2017) Bennet, P., Sand, D. J., Crnojević, D., et al. 2017, ApJ, 850, 109, doi: 10.3847/1538-4357/aa9180
  * Bennet et al. (2018) Bennet, P., Sand, D. J., Zaritsky, D., et al. 2018, ApJ, 866, L11, doi: 10.3847/2041-8213/aadedf
  * Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164
  * Bournaud & Duc (2006) Bournaud, F., & Duc, P. A. 2006, A&A, 456, 481, doi: 10.1051/0004-6361:20065248
  * Bradley et al. (2022) Bradley, L., Sipőcz, B., Robitaille, T., et al. 2022, astropy/photutils: 1.5.0, 1.5.0, Zenodo, doi: 10.5281/zenodo.6825092
  * Brodie & Strader (2006) Brodie, J. P., & Strader, J. 2006, ARA&A, 44, 193, doi: 10.1146/annurev.astro.44.051905.092441
  * Carleton et al. (2019) Carleton, T., Errani, R., Cooper, M., et al. 2019, MNRAS, 485, 382, doi: 10.1093/mnras/stz383
  * Carleton et al. (2021) Carleton, T., Guo, Y., Munshi, F., Tremmel, M., & Wright, A. 2021, MNRAS, 502, 398, doi: 10.1093/mnras/stab031
  * Carlsten et al. (2022) Carlsten, S. G., Greene, J. E., Beaton, R. L., & Greco, J. P. 2022, ApJ, 927, 44, doi: 10.3847/1538-4357/ac457e
  * Chan et al. (2018) Chan, T. K., Kereš, D., Wetzel, A., et al. 2018, MNRAS, 478, 906, doi: 10.1093/mnras/sty1153
  * Conselice (2018) Conselice, C. J. 2018, Research Notes of the American Astronomical Society, 2, 43, doi: 10.3847/2515-5172/aab7f6
  * Cribbs et al. (2019) Cribbs, A., Luna-Valero, S., George, C., et al. 2019, F1000Research, 8, doi: 10.12688/f1000research.18674.1
  * Dalcanton et al. (1997) Dalcanton, J. J., Spergel, D. N., Gunn, J. E., Schmidt, M., & Schneider, D. P. 1997, AJ, 114, 635, doi: 10.1086/118499
  * Danieli et al. (2022) Danieli, S., van Dokkum, P., Trujillo-Gomez, S., et al. 2022, ApJ, 927, L28, doi: 10.3847/2041-8213/ac590a
  * de Boer & Fraser (2016) de Boer, T. J. L., & Fraser, M. 2016, A&A, 590, A35, doi: 10.1051/0004-6361/201527580
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168, doi: 10.3847/1538-3881/ab089d
  * Di Cintio et al. (2017) Di Cintio, A., Brook, C. B., Dutton, A. A., et al. 2017, MNRAS, 466, L1, doi: 10.1093/mnrasl/slw210
  * Dolphin (2016) Dolphin, A. 2016, DOLPHOT: Stellar photometry, Astrophysics Source Code Library, record ascl:1608.013.  http://ascl.net/1608.013
  * Dolphin (2000) Dolphin, A. E. 2000, PASP, 112, 1383, doi: 10.1086/316630
  * Duc (2012) Duc, P.-A. 2012, in Astrophysics and Space Science Proceedings, Vol. 28, Dwarf Galaxies: Keys to Galaxy Formation and Evolution, 305, doi: 10.1007/978-3-642-22018-0_37
  * Duc & Mirabel (1998) Duc, P. A., & Mirabel, I. F. 1998, A&A, 333, 813
  * Duc & Renaud (2013) Duc, P.-A., & Renaud, F. 2013, in Lecture Notes in Physics, Berlin Springer Verlag, ed. J. Souchay, S. Mathis, & T. Tokieda, Vol. 861, 327, doi: 10.1007/978-3-642-32961-6_9
  * Elmegreen et al. (1993) Elmegreen, B. G., Kaufman, M., & Thomasson, M. 1993, ApJ, 412, 90, doi: 10.1086/172903
  * Errani et al. (2015) Errani, R., Penarrubia, J., & Tormen, G. 2015, MNRAS, 449, L46, doi: 10.1093/mnrasl/slv012
  * Fensch et al. (2019) Fensch, J., Duc, P.-A., Boquien, M., et al. 2019, A&A, 628, A60, doi: 10.1051/0004-6361/201834403
  * Fielder et al. (2023) Fielder, C. E., Jones, M. G., Sand, D. J., et al. 2023, arXiv e-prints, arXiv:2306.06164, doi: 10.48550/arXiv.2306.06164
  * Filho et al. (2013) Filho, M. E., Winkel, B., Sánchez Almeida, J., et al. 2013, A&A, 558, A18, doi: 10.1051/0004-6361/201322098
  * Forbes et al. (2020) Forbes, D. A., Alabi, A., Romanowsky, A. J., Brodie, J. P., & Arimoto, N. 2020, MNRAS, 492, 4874, doi: 10.1093/mnras/staa180
  * Gao et al. (2023) Gao, Y., Gu, Q., Liu, G., et al. 2023, A&A, 677, A179, doi: 10.1051/0004-6361/202346753
  * Greco et al. (2018) Greco, J. P., Goulding, A. D., Greene, J. E., et al. 2018, ApJ, 866, 112, doi: 10.3847/1538-4357/aae0f4
  * Gwyn (2008) Gwyn, S. D. J. 2008, PASP, 120, 212, doi: 10.1086/526794
  * Gwyn (2012) —. 2012, AJ, 143, 38, doi: 10.1088/0004-6256/143/2/38
  * Harris et al. (2013) Harris, W. E., Harris, G. L. H., & Alessi, M. 2013, ApJ, 772, 82, doi: 10.1088/0004-637X/772/2/82
  * Harris & van den Bergh (1981) Harris, W. E., & van den Bergh, S. 1981, AJ, 86, 1627, doi: 10.1086/113047
  * Iglesias-Páramo et al. (2006) Iglesias-Páramo, J., Buat, V., Takeuchi, T. T., et al. 2006, ApJS, 164, 38, doi: 10.1086/502628
  * Impey et al. (1988) Impey, C., Bothun, G., & Malin, D. 1988, ApJ, 330, 634, doi: 10.1086/166500
  * Iodice et al. (2020) Iodice, E., Cantiello, M., Hilker, M., et al. 2020, A&A, 642, A48, doi: 10.1051/0004-6361/202038523
  * Janowiecki et al. (2019) Janowiecki, S., Jones, M. G., Leisman, L., & Webb, A. 2019, MNRAS, 490, 566, doi: 10.1093/mnras/stz1868
  * Janssens et al. (2022) Janssens, S. R., Romanowsky, A. J., Abraham, R., et al. 2022, MNRAS, 517, 858, doi: 10.1093/mnras/stac2717
  * Jiang et al. (2019) Jiang, F., Dekel, A., Freundlich, J., et al. 2019, MNRAS, 487, 5272, doi: 10.1093/mnras/stz1499
  * Johnston et al. (2001) Johnston, K. V., Sackett, P. D., & Bullock, J. S. 2001, ApJ, 557, 137, doi: 10.1086/321644
  * Jones et al. (2021) Jones, M. G., Bennet, P., Mutlu-Pakdil, B., et al. 2021, ApJ, 919, 72, doi: 10.3847/1538-4357/ac0975
  * Jones et al. (2019) Jones, M. G., Verdes-Montenegro, L., Damas-Segovia, A., et al. 2019, A&A, 632, A78, doi: 10.1051/0004-6361/201936349
  * Jones et al. (2022) Jones, M. G., Sand, D. J., Bellazzini, M., et al. 2022, ApJ, 935, 51, doi: 10.3847/1538-4357/ac7c6c
  * Jones et al. (2023a) Jones, M. G., Karunakaran, A., Bennet, P., et al. 2023a, ApJ, 942, L5, doi: 10.3847/2041-8213/acaaab
  * Jones et al. (2023b) Jones, M. G., Verdes-Montenegro, L., Moldon, J., et al. 2023b, A&A, 670, A21, doi: 10.1051/0004-6361/202244622
  * Kado-Fong et al. (2022) Kado-Fong, E., Greene, J. E., Huang, S., & Goulding, A. 2022, ApJ, 941, 11, doi: 10.3847/1538-4357/ac9964
  * Karachentsev et al. (2004) Karachentsev, I. D., Karachentseva, V. E., Huchtmeier, W. K., & Makarov, D. I. 2004, AJ, 127, 2031, doi: 10.1086/382905
  * Karachentseva (1968) Karachentseva, V. E. 1968, Communications of the Byurakan Astrophysical Observatory, 39, 61
  * Kaviraj et al. (2012) Kaviraj, S., Darg, D., Lintott, C., Schawinski, K., & Silk, J. 2012, MNRAS, 419, 70, doi: 10.1111/j.1365-2966.2011.19673.x
  * Kniazev et al. (2003) Kniazev, A. Y., Grebel, E. K., Hao, L., et al. 2003, ApJ, 593, L73, doi: 10.1086/378259
  * Koda et al. (2015) Koda, J., Yagi, M., Yamanoi, H., & Komiyama, Y. 2015, ApJ, 807, L2, doi: 10.1088/2041-8205/807/1/L2
  * Kong et al. (2022) Kong, D., Kaplinghat, M., Yu, H.-B., Fraternali, F., & Mancera Piña, P. E. 2022, ApJ, 936, 166, doi: 10.3847/1538-4357/ac8875
  * La Marca et al. (2022) La Marca, A., Iodice, E., Cantiello, M., et al. 2022, A&A, 665, A105, doi: 10.1051/0004-6361/202142367
  * Lee-Waddell et al. (2019) Lee-Waddell, K., Koribalski, B. S., Westmeier, T., et al. 2019, MNRAS, 487, 5248, doi: 10.1093/mnras/stz017
  * Leisman et al. (2017) Leisman, L., Haynes, M. P., Janowiecki, S., et al. 2017, ApJ, 842, 133, doi: 10.3847/1538-4357/aa7575
  * Liang et al. (2023) Liang, J., Jiang, F., Danieli, S., Benson, A., & Hopkins, P. 2023, arXiv e-prints, arXiv:2304.14431, doi: 10.48550/arXiv.2304.14431
  * Liao et al. (2019) Liao, S., Gao, L., Frenk, C. S., et al. 2019, MNRAS, 490, 5182, doi: 10.1093/mnras/stz2969
  * Lim et al. (2018) Lim, S., Peng, E. W., Côté, P., et al. 2018, ApJ, 862, 82, doi: 10.3847/1538-4357/aacb81
  * Lim et al. (2020) Lim, S., Côté, P., Peng, E. W., et al. 2020, ApJ, 899, 69, doi: 10.3847/1538-4357/aba433
  * Martin & GALEX Team (2005) Martin, C., & GALEX Team. 2005, in Maps of the Cosmos, ed. M. Colless, L. Staveley-Smith, & R. A. Stathakis, Vol. 216, 221, doi: 10.1017/S0074180900196664
  * Martínez-Delgado et al. (2016) Martínez-Delgado, D., Läsker, R., Sharina, M., et al. 2016, AJ, 151, 96, doi: 10.3847/0004-6256/151/4/96
  * McMullin et al. (2007) McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 376, Astronomical Data Analysis Software and Systems XVI, ed. R. A. Shaw, F. Hill, & D. J. Bell, 127
  * Merritt et al. (2016) Merritt, A., van Dokkum, P., Danieli, S., et al. 2016, ApJ, 833, 168, doi: 10.3847/1538-4357/833/2/168
  * 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
  * Miller & Lotz (2007) Miller, B. W., & Lotz, J. M. 2007, ApJ, 670, 1074, doi: 10.1086/522323
  * Müller et al. (2021) Müller, O., Durrell, P. R., Marleau, F. R., et al. 2021, ApJ, 923, 9, doi: 10.3847/1538-4357/ac2831
  * Namumba et al. (2021) Namumba, B., Koribalski, B. S., Józsa, G. I. G., et al. 2021, MNRAS, 505, 3795, doi: 10.1093/mnras/stab1524
  * Ogiya (2018) Ogiya, G. 2018, MNRAS, 480, L106, doi: 10.1093/mnrasl/sly138
  * Pace et al. (2021) Pace, A. B., Walker, M. G., Koposov, S. E., et al. 2021, ApJ, 923, 77, doi: 10.3847/1538-4357/ac2cd2
  * Pandya et al. (2018) Pandya, V., Romanowsky, A. J., Laine, S., et al. 2018, ApJ, 858, 29, doi: 10.3847/1538-4357/aab498
  * Paturel et al. (2003) Paturel, G., Petit, C., Prugniel, P., et al. 2003, A&A, 412, 45, doi: 10.1051/0004-6361:20031411
  * Paudel et al. (2018) Paudel, S., Smith, R., Yoon, S. J., Calderón-Castillo, P., & Duc, P.-A. 2018, ApJS, 237, 36, doi: 10.3847/1538-4365/aad555
  * Pearson et al. (2018) Pearson, S., Privon, G. C., Besla, G., et al. 2018, MNRAS, 480, 3069, doi: 10.1093/mnras/sty2052
  * Peng et al. (2002) Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2002, AJ, 124, 266, doi: 10.1086/340952
  * Peng et al. (2010) —. 2010, AJ, 139, 2097, doi: 10.1088/0004-6256/139/6/2097
  * Peng et al. (2011) Peng, E. W., Ferguson, H. C., Goudfrooij, P., et al. 2011, ApJ, 730, 23, doi: 10.1088/0004-637X/730/1/23
  * Prole et al. (2019) Prole, D. J., van der Burg, R. F. J., Hilker, M., & Davies, J. I. 2019, MNRAS, 488, 2143, doi: 10.1093/mnras/stz1843
  * Prole et al. (2021) Prole, D. J., van der Burg, R. F. J., Hilker, M., & Spitler, L. R. 2021, MNRAS, 500, 2049, doi: 10.1093/mnras/staa3296
  * Pustilnik & Martin (2007) Pustilnik, S. A., & Martin, J. M. 2007, A&A, 464, 859, doi: 10.1051/0004-6361:20066137
  * Renaud (2018) Renaud, F. 2018, New A Rev., 81, 1, doi: 10.1016/j.newar.2018.03.001
  * Robitaille et al. (2020) Robitaille, T., Deil, C., & Ginsburg, A. 2020, reproject: Python-based astronomical image reprojection, Astrophysics Source Code Library, record ascl:2011.023.  http://ascl.net/2011.023
  * Román et al. (2019) Román, J., Beasley, M. A., Ruiz-Lara, T., & Valls-Gabaud, D. 2019, MNRAS, 486, 823, doi: 10.1093/mnras/stz835
  * Román et al. (2021) Román, J., Jones, M. G., Montes, M., et al. 2021, A&A, 649, L14, doi: 10.1051/0004-6361/202141001
  * Román & Trujillo (2017) Román, J., & Trujillo, I. 2017, MNRAS, 468, 4039, doi: 10.1093/mnras/stx694
  * Rong et al. (2017) Rong, Y., Guo, Q., Gao, L., et al. 2017, MNRAS, 470, 4231, doi: 10.1093/mnras/stx1440
  * Ruiz-Lara et al. (2019) Ruiz-Lara, T., Trujillo, I., Beasley, M. A., et al. 2019, MNRAS, 486, 5670, doi: 10.1093/mnras/stz1237
  * Saifollahi et al. (2021) Saifollahi, T., Trujillo, I., Beasley, M. A., Peletier, R. F., & Knapen, J. H. 2021, MNRAS, 502, 5921, doi: 10.1093/mnras/staa3016
  * Sales et al. (2020) Sales, L. V., Navarro, J. F., Peñafiel, L., et al. 2020, MNRAS, 494, 1848, doi: 10.1093/mnras/staa854
  * Sand et al. (2021) Sand, D. J., Bennet, P., Crnojevic, D., et al. 2021, Ultra-Diffuse Galaxy Formation in Groups - Tidal or Born That Way?, HST Proposal. Cycle 29, ID. #16890
  * Sandage & Binggeli (1984) Sandage, A., & Binggeli, B. 1984, AJ, 89, 919, doi: 10.1086/113588
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103, doi: 10.1088/0004-637X/737/2/103
  * Serra et al. (2015) Serra, P., Westmeier, T., Giese, N., et al. 2015, MNRAS, 448, 1922, doi: 10.1093/mnras/stv079
  * Sérsic (1963) Sérsic, J. L. 1963, Boletin de la Asociacion Argentina de Astronomia La Plata Argentina, 6, 41
  * Sirianni et al. (2005) Sirianni, M., Jee, M. J., Benítez, N., et al. 2005, PASP, 117, 1049, doi: 10.1086/444553
  * Somalwar et al. (2020) Somalwar, J. J., Greene, J. E., Greco, J. P., et al. 2020, ApJ, 902, 45, doi: 10.3847/1538-4357/abb1b2
  * Spekkens & Karunakaran (2018) Spekkens, K., & Karunakaran, A. 2018, ApJ, 855, 28, doi: 10.3847/1538-4357/aa94be
  * Stierwalt et al. (2015) Stierwalt, S., Besla, G., Patton, D., et al. 2015, ApJ, 805, 2, doi: 10.1088/0004-637X/805/1/2
  * Subramanian et al. (2023) Subramanian, S., Mondal, C., & Kalari, V. 2023, arXiv e-prints, arXiv:2310.02595, doi: 10.48550/arXiv.2310.02595
  * Thompson & Gregory (1993) Thompson, L. A., & Gregory, S. A. 1993, AJ, 106, 2197, doi: 10.1086/116793
  * Tremmel et al. (2020) Tremmel, M., Wright, A. C., Brooks, A. M., et al. 2020, MNRAS, 497, 2786, doi: 10.1093/mnras/staa2015
  * Trujillo et al. (2019) Trujillo, I., Beasley, M. A., Borlaff, A., et al. 2019, MNRAS, 486, 1192, doi: 10.1093/mnras/stz771
  * van der Burg et al. (2017) van der Burg, R. F. J., Hoekstra, H., Muzzin, A., et al. 2017, A&A, 607, A79, doi: 10.1051/0004-6361/201731335
  * van Dokkum et al. (2016) van Dokkum, P., Abraham, R., Brodie, J., et al. 2016, ApJ, 828, L6, doi: 10.3847/2041-8205/828/1/L6
  * van Dokkum et al. (2022) van Dokkum, P., Shen, Z., Romanowsky, A. J., et al. 2022, ApJ, 940, L9, doi: 10.3847/2041-8213/ac94d6
  * van Dokkum et al. (2015) van Dokkum, P. G., Abraham, R., Merritt, A., et al. 2015, ApJ, 798, L45, doi: 10.1088/2041-8205/798/2/L45
  * Venhola et al. (2017) Venhola, A., Peletier, R., Laurikainen, E., et al. 2017, A&A, 608, A142, doi: 10.1051/0004-6361/201730696
  * Wittmann et al. (2017) Wittmann, C., Lisker, T., Ambachew Tilahun, L., et al. 2017, MNRAS, 470, 1512, doi: 10.1093/mnras/stx1229
  * Wright et al. (2021) Wright, A. C., Tremmel, M., Brooks, A. M., et al. 2021, MNRAS, 502, 5370, doi: 10.1093/mnras/stab081
  * Yagi et al. (2016) Yagi, M., Koda, J., Komiyama, Y., & Yamanoi, H. 2016, ApJS, 225, 11, doi: 10.3847/0067-0049/225/1/11
  * Zaritsky (2022) Zaritsky, D. 2022, MNRAS, 513, 2609, doi: 10.1093/mnras/stac1072
  * Zaritsky et al. (2019) Zaritsky, D., Donnerstein, R., Dey, A., et al. 2019, ApJS, 240, 1, doi: 10.3847/1538-4365/aaefe9
  * Zhang et al. (2017) Zhang, H.-X., Puzia, T. H., & Weisz, D. R. 2017, ApJS, 233, 13, doi: 10.3847/1538-4365/aa937b