# Catching Tidal Dwarf Galaxies at a Later Evolutionary Stage with ALFALFA

Laurin M. Gray Indiana University, 727 East Third Street, Bloomington, IN
47405, USA<EMAIL_ADDRESS>Katherine L. Rhode Indiana University, 727 East
Third Street, Bloomington, IN 47405, USA  Lukas Leisman Department of
Astronomy, University of Illinois, 1002 W. Green Street, Urbana, IL 61801, USA
Pavel E. Mancera Piña Leiden Observatory, Leiden University, P.O. Box 9513,
2300 RA Leiden, The Netherlands  John M. Cannon Department of Physics &
Astronomy, Macalester College, 1600 Grand Avenue, Saint Paul, MN 55105, USA
John J. Salzer Indiana University, 727 East Third Street, Bloomington, IN
47405, USA  Lexi Gault Indiana University, 727 East Third Street, Bloomington,
IN 47405, USA  Jackson Fuson Department of Physics & Astronomy, Macalester
College, 1600 Grand Avenue, Saint Paul, MN 55105, USA  Gyula I. G. Józsa Max-
Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
Department of Physics and Electronics, Rhodes University, PO Box 94, Makhanda,
6140, South Africa  Elizabeth A. K. Adams ASTRON, Netherlands Institute for
Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
Kapteyn Astronomical Institute, Landleven 12, 9747 AD Groningen, The
Netherlands  Nicholas J. Smith Indiana University, 727 East Third Street,
Bloomington, IN 47405, USA  Martha P. Haynes Cornell Center for Astrophysics
and Planetary Science, Space Sciences Building, Cornell University, Ithaca, NY
14853, USA  Steven Janowiecki University of Texas, Hobby-Eberly Telescope,
McDonald Observatory, TX 79734, USA  Hannah J. Pagel  Indiana University, 727
East Third Street, Bloomington, IN 47405, USA

###### Abstract

We present deep optical imaging and photometry of four objects classified as
“Almost-Dark” galaxies in the ALFALFA survey because of their gas-rich nature
and extremely faint or missing optical emission in existing catalogs. They
have HI masses of $10^{7}$-$10^{9}$ $M_{\odot}$ and distances of $\sim$9-100
Mpc. Observations with the WIYN 3.5m telescope and One Degree Imager reveal
faint stellar components with central surface brightnesses of $\sim$24-25
$\mathrm{mag}\,\mathrm{arcsec}^{-2}$ in the $g$-band. We also present the
results of HI synthesis observations with the Westerbork Synthesis Radio
Telescope. These Almost-Dark galaxies have been identified as possible tidal
dwarf galaxies (TDGs) based on their proximity to one or more massive
galaxies. We demonstrate that AGC 229398 and AGC 333576 likely have the low
dark matter content and large effective radii representative of TDGs. They are
located much farther from their progenitors than previously studied TDGs,
suggesting they are older and more evolved. AGC 219369 is likely dark matter
dominated, while AGC 123216 has a dark matter content that is unusually high
for a TDG, but low for a normal dwarf galaxy. We consider possible mechanisms
for the formation of the TDG candidates such as a traditional major merger
scenario and gas ejection from a high velocity fly-by. Blind HI surveys like
ALFALFA enable the detection of gas-rich, optically faint TDGs that can be
overlooked in other surveys, thereby providing a more complete census of the
low-mass galaxy population and an opportunity to study TDGs at a more advanced
stage of their life cycle.

Galaxy evolution - Dwarf galaxies - Galaxy interaction - Tidal dwarf galaxies

††facilities: Arecibo, WIYN(pODI and ODI), WSRT

##  1 Introduction

The Arecibo Legacy Fast ALFA (ALFALFA) blind extragalactic HI survey
(Giovanelli et al., 2005; Haynes et al., 2018) was designed primarily to probe
the low-mass end of the HI mass function, and has identified over 31,000
sources out to a redshift z $\sim$ 0.06. ALFALFA covered nearly 7000 square
degrees of sky and detected HI sources without regard to their optical
properties, which makes it a powerful tool to search for tidal remnants such
as tidal dwarf galaxies (TDGs) on a larger scope than previously attempted
(Giovanelli et al., 2005).

TDGs are generally composed of material removed from a parent galaxy through
tidal interactions, which means they are usually very gas-rich (Duc, 2012).
They have masses and sizes comparable to dwarf galaxies, and over time will
become dynamically stable systems independent of their parent galaxy (Duc,
2012). TDGs contain clues to the interaction histories of their parent
galaxies, potentially constraining the interaction type and properties of the
merging systems (Lee-Waddell et al., 2014). They are also vital for
determining cosmological constraints in group environments (Lee-Waddell et
al., 2014).

TDGs usually have higher metallicities than normal dwarf galaxies because they
are created out of pre-enriched material stripped from the outer disks of
larger galaxies (Duc & Mirabel, 1999; Duc et al., 2000; Weilbacher et al.,
2000; Duc, 2012). However, Hunter et al. (2000) point out that very old tidal
dwarfs which were formed before spirals could become more enriched could have
metallicities similar to modern metal-poor dwarfs. TDGs have a very low dark
matter content, because tidal forces create gas-rich streams that contain a
small fraction of pre-existing stars and almost no dark matter, and the
potential gravitational well of the dwarf is too shallow to capture dark
matter (Bournaud, 2010). The turbulence of the tidal interaction also
frequently triggers star formation, leading to a population of young blue
stars (Duc et al., 2000).

Kaviraj et al. (2012) conducted a statistical survey of the properties of 405
optically identified TDG candidates and their parent systems and found that
the vast majority of TDGs are within 20 kpc of their progenitors. However, the
most easily identified TDG candidates still have a visible tidal tail
connecting them to their parents. As a result, the sample of known TDGs is
biased towards objects that are near their parent galaxies and still in the
early stages of their evolution, as the tail takes time to dissolve.
Simulations suggest that to become a bona fide TDG, a tidal knot must have
enough mass ($\geq$ $10^{8}$ $M_{\odot}$) and distance from the gravitational
well of the parent to become self-gravitating and avoid falling back into the
parent system (Bournaud & Duc, 2006). Therefore, the overall sample of objects
that have been studied consists mainly of TDG candidates, with some
uncertainty as to whether they will become long-lived ($>$1 Gyr; Kaviraj et
al. 2012; Bournaud & Duc 2006). It is also uncertain how long TDGs are able to
remain stable without a massive dark matter halo, as simulations indicate that
dark-matter-deficient, rotationally supported galaxy disks are prone to
axisymmetric and non-axisymmetric instabilities on dynamical timescales
(Sellwood & Sanders, 2022). As TDGs evolve, they become optically indistinct
from other satellite dwarf galaxies (Duc, 2012). Identification relies on
metallicity measurements and age estimations, usually from time-intensive
spectroscopy. Additionally, the initial burst of star formation will
eventually end, the young stellar population will age, and the higher
metallicity will contribute to a faster rate of dimming, making older TDGs
even more difficult to detect through optical methods (Román et al., 2021).
However, they will remain gas-rich, so HI observations are useful for locating
objects of interest when searching for TDGs because they will be able to catch
sources with extremely low optical surface brightnesses.

Around 99% of the objects observed in ALFALFA could be matched to objects in
previously published optical catalogs such as the Sloan Digital Sky Survey
(SDSS; Eisenstein et al. 2011), though many had never been observed in HI
before. The remaining 1% is a set of gas-rich objects that are missing a clear
counterpart in optical catalogs. A subset of these are classified as Ultra-
Compact High-Velocity Clouds (UCHVCs; Giovanelli et al., 2010; Adams et al.,
2013), which are compact HI clouds with velocities consistent with a location
in the vicinity of the Local Group. Follow-up optical imaging of the UCHVCs
has in some cases revealed a dwarf galaxy or other possible stellar
counterpart (see Rhode et al., 2013; Sand et al., 2015; Janesh et al., 2019).
The remaining objects without clear optical counterparts are classified as
“Almost-Dark” galaxies (ADs); these objects have velocities that place them
outside of the Local Group and HI masses ranging from $10^{7}$ \- $10^{9}$
$M_{\odot}$. Deep optical imaging of several ADs has revealed low surface
brightness stellar components that were below the sensitivity limits of
previous surveys (Cannon et al., 2015; Leisman et al., 2021). As explained in
Cannon et al. (2015), while the majority were either OH megamasers or tidal
debris from a nearby galaxy interaction, a small subset appeared to be more
isolated. Some of the ADs have properties that make them comparable to ultra-
diffuse galaxies (UDGs; van Dokkum et al. 2015; Leisman et al. 2017; Gault et
al. 2021). Other ADs have been identified as likely TDGs that have moved
farther away from their parent sources than the majority of previously studied
TDGs (Lee-Waddell et al., 2016). As we will discuss in this paper, TDGs
(particularly evolved TDGs) have low central surface brightnesses and large
effective radii, which means that some TDGs may fit the criteria used to
define UDGs, so there may be overlap between the two categories.

In this paper, we present HI and optical data of four objects that have been
classified as potential Almost-Dark Tidal Dwarf Galaxies (AD-TDGs). The four
objects, AGC 123216, AGC 219369, AGC 229398, and AGC 333576, were selected
from the AD sample and identified as potential TDGs because of the presence of
at least one HI-rich source that could be classified as a potential parent
galaxy based on that galaxy’s proximity and velocity relative to the AD.
Specifically, the potential parent galaxies for each AD-TDG candidate are
located within 500 kpc on the sky at the reported distance for the AD and have
a measured heliocentric velocity that is within $\pm$500
$\mathrm{km}\,\mathrm{s}^{-1}$ of the AD as measured by Haynes et al. (2011).
The four AD-TDG candidates we analyzed each have between one and three
potential parent galaxies meeting these criteria.

The paper is organized as follows. Section 2 covers the HI and optical
observations and data processing. Section 3 describes the procedures used to
carry out our measurements of quantities such as optical surface brightness,
and stellar, baryonic, and dynamical masses. A discussion of the properties
and environment of each AD is given in Section 4. Section 5 discusses the ADs
in the context of our current understanding of TDGs, including comments on
their possible origins. The last section includes a brief summary of our main
conclusions.

##  2 Observations and Data Processing

###  2.1 HI Data

The AD ALFALFA observations and data reduction processes are described in
detail in other papers (Giovanelli et al., 2005; Saintonge, 2007; Haynes et
al., 2011), and the relevant ALFALFA catalog (Haynes et al., 2018)
measurements for these objects and their possible parents are reproduced in
Table 1, along with photometric data from SDSS for the possible parents for
reference (Ahumada et al., 2020). Generally, the distance for objects with
$v_{helio}>6000$ $\mathrm{km}\,\mathrm{s}^{-1}$ was estimated with the Hubble
Law (with $H_{0}$ = 70 $\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$), and
the local peculiar velocity model of Masters (2005) was used for distances of
objects with $v_{helio}<6000$ $\mathrm{km}\,\mathrm{s}^{-1}$.

In addition to the original ALFALFA observations, the ADs presented in this
paper and their prospective progenitors were also observed with the Westerbork
Synthesis Radio Telescope (WSRT) in an exploratory observational program of a
larger subset of Almost-Dark galaxies (program R13B/001; PI Adams).
Observations consisted of two 12 hour pointings centered on the central HI
velocity from ALFALFA, using a 10 MHz bandpass with 1024 channels and 2
polarizations. Data reduction is detailed in Janowiecki et al. (2015) and
Leisman et al. (2016). The reduction used an automated pipeline based on the
MIRIAD (Sault et al., 1995) data software (see Serra et al., 2012; Wang et
al., 2013). The pipeline automates radio frequency interference flagging and
implements primary bandpass calibration, and iterative deconvolution of the
data with the CLEAN algorithm to apply a self-calibration. We used a
robustness weighting r=0.4 and a velocity resolution binning of 6.0
$\mathrm{km}\,\mathrm{s}^{-1}$ after Hanning smoothing. The resulting images
had synthesized beams with major (north-south) axes ranging from
32-38$\arcsec$ and minor axes from 13-17$\arcsec$. We also performed a primary
beam correction to our measured column densities; note that the FWHM of the
WSRT primary beam is $\sim$35$\arcmin$ at 1.4 GHz, so the column density
sensitivity for potential parent sources near the edges of our images is low.
Total intensity and velocity field maps were created as detailed in Gault et
al. (2021). We were able to retrieve the peak HI column density from the total
intensity maps, under the assumption that the flux is spread out over the
beam, so this measurement is dependent on the resolution of the beam. The peak
HI column density is reported in the Results section for each source.

=30mm

Table 1:  HI Measurements and Other Properties of Candidate AD-TDGs and
Potential Parent Galaxies

ID | Classification | RA | Dec | $v_{helio}$ | W20 | Distance | Angular | log($M_{HI}$) | g | g-r
---|---|---|---|---|---|---|---|---|---|---
|  | [deg] | [deg] | [$\mathrm{km}\,\mathrm{s}^{-1}$] | [$\mathrm{km}\,\mathrm{s}^{-1}$] | [Mpc] | Separation [kpc] |  | [mag] | [mag]
AGC 123216 | Almost-Dark | 31.17792 | 28.80583 | 5111 $\pm$ 14 | 51 $\pm$ 7 | 70.5 $\pm$ 2.3 | – | 8.65 $\pm$ 0.08 | – | –
MRK 365aaMRK 365 is not included in the ALFALFA catalog, so the distance listed here is the NED Hubble flow distance for the heliocentric velocity measured by Thuan et al. (1999), corrected for a 3K CMB according to Fixsen et al. (1996). | Spiral | 31.07729 | 28.65592 | 5151 $\pm$ 5 | – | 72.2 $\pm$ 5.1 | 214 $\pm$ 7 | – | 14.33 | 0.67
NGC 807 | EllipticalbbSee discussion of classification for NGC 807 in Section 4.1 | 31.22917 | 28.98889 | 4750 $\pm$ 218 | 492 $\pm$ 12 | 67.7 $\pm$ 4.4 | 231 $\pm$ 8 | 9.79 $\pm$ 0.07 | 14.20 | 0.87
MCG 05-06-003 | Spiral | 31.38208 | 28.61083 | 5312 $\pm$ 92 | 202 $\pm$ 5 | 73.4 $\pm$ 2.3 | 331 $\pm$ 11 | 9.7 $\pm$ 0.05 | 14.47 | 0.39
AGC 219369ccThe HI mass and angular separation in kpc were calculated using the Haynes et al. (2018) distance of 9.2 Mpc, see Section 4.2 for a discussion on the ambiguity in this measurement. | Almost-Dark | 165.96333 | 28.68583 | 667 $\pm$ 11 | 45 $\pm$ 7 | 9.2 $\pm$ 2.2 | – | 7.25 $\pm$ 0.21 | – | –
NGC 3510 | Spiral | 165.93668 | 28.88806 | 704 $\pm$ 92 | 199 $\pm$ 2 | 16.7 $\pm$ 3.3 | 33 $\pm$ 8 | 9.45 $\pm$ 0.18 | 13.33 | 0.28
AGC 229398 | Almost-Dark | 180.16251 | 21.41556 | 6965 $\pm$ 14 | 49 $\pm$ 3 | 104 $\pm$ 2.3 | – | 9.28 $\pm$ 0.05 | – | –
KUG 1158+216 | Spiral | 180.16458 | 21.3525 | 7388 $\pm$ 125 | 268 $\pm$ 42 | 110.1 $\pm$ 2.3 | 102 $\pm$ 2 | 9.47 $\pm$ 0.06 | 16.36 | 0.59
UGC 6989 | Spiral | 180.02415 | 21.64528 | 6404 $\pm$ 99 | 220 $\pm$ 3 | 96 $\pm$ 2.4 | 482 $\pm$ 11 | 9.87 $\pm$ 0.05 | 15.80 | 0.38
AGC 333576 | Almost-Dark | 358.185 | 28.74667 | 7031 $\pm$ 13 | 37 $\pm$ 3 | 93.9 $\pm$ 4.3 | – | 9.1 $\pm$ 0.07 | – | –
NGC 7775 | Spiral | 358.09833 | 28.77083 | 6760 $\pm$ 65 | 182 $\pm$ 8 | 93.9 $\pm$ 4.3 | 127 $\pm$ 6 | 9.88 $\pm$ 0.06 | 13.74 | 0.54

Note. — Data are taken from Haynes et al. (2018) except when otherwise noted.
Almost-Dark galaxies are listed at the top of each subsection and followed by
their potential progenitors. Classification for the potential parent galaxies
is the galaxy type listed on the NASA/IPAC Extragalactic Database (NED; NED).
RA and Dec are the coordinates for the center of the HI source from ALFALFA,
which is not necessarily the center of the optical component. Angular
separation in kpc is calculated at the ALFALFA distance of the relevant AD.
Listed magnitudes are the CModelMags from SDSS DR16 (Ahumada et al., 2020),
corrected for extinction using the Schlegel et al. (1998) extinction maps.

###  2.2 Optical Data

Optical observations of the ADs and their surrounding areas were carried out
with the WIYN 3.5-m telescope. One object (AGC 229398) was observed in March
2014 with the One Degree Imager with a partially-populated focal plane (pODI).
Before a larger detector array was installed in 2015, pODI had a 3$\times$3
grid of orthogonal transfer arrays (OTAs), with a field of view of
24$\arcmin\times$24$\arcmin$. There were also four more OTAs in the outer
corners that were used to image guide stars. Each OTA is an 8$\times$8
arrangement of 480$\times$496 pixel CCDs, where each pixel has a pixel scale
of 0.11$\arcsec$/pixel. The other three objects were observed on multiple
occasions between 2017 and 2019 with the One Degree Imager (ODI; Harbeck et
al. 2014). The ODI camera has 17 additional OTAs compared to pODI, arranged in
a 5$\times$6 grid for a field of view of 40$\arcmin\times$48$\arcmin$. During
each observing run, each source was observed in the $g^{\prime}$ and
$r^{\prime}$ bands, using a 9-point dither pattern of 300 seconds per exposure
to avoid gaps in the final image resulting from gaps in the CCD array.

We reduced our observations using the One Degree Imager Pipeline, Portal, and
Archive (ODI-PPA; Gopu et al. 2014) QuickReduce (Kotulla, 2014) data reduction
pipeline. The pipeline consists of the following: saturated pixel masking;
corrections for crosstalk, persistence, and nonlinearity; overscan
subtraction; bias, dark, and flat-field corrections; pupil ghost corrections;
and cosmic ray removal. We then stacked our images using the SWarp program
(Bertin et al., 2002) integrated with ODI-PPA’s Stack interface. Due to the
faintness of these objects, we created the deepest combined images possible
without sacrificing image quality by using the best exposure at each dither
point and then including any additional exposures with good focus and seeing
below 1.5$\arcsec$. The total integration times of the images vary from 45 to
90 minutes based on the number of exposures included in the stack. The
background of each image was mapped and subtracted, and then the images were
resampled, combined with a weighted average, and reprojected to a pixel scale
of 0.125 $\arcsec$/pixel. An average background value was then added back to
each image. The average FWHM values of the point spread function (PSF) in the
stacked images ranges from 0.8$\arcsec$ to 1.1$\arcsec$ in $g^{\prime}$, and
0.6$\arcsec$ to 1.0$\arcsec$ in $r^{\prime}$.

##  3 Data Analysis and Measurement Procedures

###  3.1 Gas Mass

In this paper, we make use of two measurements of the HI mass, which are
derived independently from the ALFALFA observations and the WSRT observations.
Measurements derived from the ALFALFA HI measurements are denoted with a prime
(′). The ALFALFA HI mass was taken from Haynes et al. (2018), which calculated
it as a function of the flux $S_{21}^{\prime}$ and the distance $D^{\prime}$
in Mpc using

$M_{HI}^{\prime}[M_{\odot}]=2.356\times 10^{5}D^{\prime 2}S_{21}^{\prime},$
(1)

with an uncertainty calculated with

$\sigma_{logM_{HI}^{\prime}}=\frac{\sqrt{(\frac{\sigma_{S_{21}^{\prime}}}{S_{21}^{\prime}})^{2}+(\frac{2\sigma_{D}^{\prime}}{D^{\prime}})^{2}+0.1^{2}}}{ln(10)}.$
(2)

The WSRT HI mass $M_{HI}$ and its associated uncertainty were calculated using
the WSRT data with the same equations. In three of four cases, the masses
yielded by both measurements were in agreement within uncertainties, but for
AGC 229398, WSRT appears to have only recovered about 40% of the mass measured
by ALFALFA.

The mass of atomic gas in an AD was estimated by multiplying the HI mass by
1.33 in order to account for the presence of helium. Molecular gas is not
expected to be a significant contributor to mass in ADs; Wang et al. (2020)
suggest that the main contributor to the low star formation rate of ADs is a
low efficiency of conversion of atomic gas to molecular gas. Measurements of
atomic and molecular gas in TDGs in Lelli et al. (2015) indicate that
molecular gas mass can range from a few percent up to about a third of the
atomic gas mass, though these estimates are for young objects which presumably
have a larger reservoir of $H_{2}$ gas to support their higher current star
formation rate compared to the AD-TDG candidates. Since we were not sure which
(if any) of these objects are TDGs, we didn’t want to overestimate the gas or
baryonic content; therefore, the baryonic mass calculation did not consider
molecular gas as a significant contributor, and so
$M_{atomic}^{\prime}=1.33\times M_{HI}^{\prime}=M_{gas}^{\prime}$ for data
originating from ALFALFA and $M_{atomic}=1.33\times M_{HI}=M_{gas}$ for WSRT
data.

###  3.2 HI Kinematics

The HI observations of our galaxies allow us to explore their kinematics and
investigate whether the systems show signs of rotational support or if their
ISM is more dominated by turbulence. TDGs are expected to be primarily
supported by rotation (e.g. Duc et al. 2007; Duc 2012; Lelli et al. 2015), but
measuring rotation in TDGs is challenging, especially for lower mass objects
(Hibbard et al., 2001; Lee-Waddell et al., 2012; Duc et al., 2014; Lee-Waddell
et al., 2014). Figure 1 shows the WSRT moment one maps for each AD and its
potential parent galaxies, as well as a close-up of the velocity field for
each AD, with WSRT HI column density contours overlaid. The distortions in the
HI maps themselves will be discussed in the results sections for each object.
In the early stages of a TDG’s evolution, we would expect a continuity in the
velocity gradient between a parent and the TDG along the tidal tail connecting
them. However, this link will diminish over time as the tail fades, the parent
system restabilizes, and the TDG moves away. Because of this, while the
presence of such a connection would support identification of a TDG, the
absence of one does not disqualify it. From the left panels of Fig. 1, there
do not appear to be any HI tails connecting an AD to a potential parent
galaxy. AGC 219369 appears to be close to the velocity at the southern end of
NGC 3510 and the velocity of AGC 333576 follows the direction of the gradient
that is across NGC 7775, but otherwise there are no obvious relationships in
velocity-space between the AD-TDG candidates and any of their potential
parents. The velocity fields of the ADs themselves appear to be messy and
disordered, with the exception of AGC 123216 which appears to show some
ordered rotation.

Figure 1: Moment one velocity maps from WSRT imaging, with WSRT HI column
density contours superimposed in dark gray, for (from top to bottom) AGC
123216, AGC 219369, AGC 229398, and AGC 333576, and their nearby potential
parent galaxies. The left panels show the full field around each AD, and the
right panels show a close-up of the AD. Beam size is shown as a shaded gray
ellipse. The figures for AGC 123216, AGC 219369, and AGC 333576 have column
density contours at $N_{HI}$ = (0.1, 0.5, 1.2, 2.4, 4.5) $\times$ $10^{20}$
$\mathrm{cm}^{-2}$, while the figures for AGC 229398 have contours at $N_{HI}$
= (0.1, 0.2, 0.4, 0.8, 1.6) $\times$ $10^{20}$ $\mathrm{cm}^{-2}$, where the
lowest contours are the first listed. Note that KUG 1158+216 is not included
in the full-field map for AGC 229398 because we did not have WSRT HI maps for
it.

Given the low spatial resolution of the WSRT observations, extracting
kinematic information is not straightforward as the observations are heavily
affected by beam smearing, which tends to erase velocity gradients and to
increase the apparent gas velocity dispersion (Swaters, 1999; Józsa et al.,
2007; Di Teodoro & Fraternali, 2015). In order to account for this when
extracting kinematic information from our data, we use the software 3DBarolo
(Di Teodoro & Fraternali, 2015), which incorporates a forward modeling
approach that considers the beam shape of our observations, and therefore is
largely unaffected by beam smearing (Józsa et al., 2007; Di Teodoro &
Fraternali, 2015; Iorio et al., 2017; Mancera Piña et al., 2020).

Prior to running 3DBarolo, we obtain independent constraints on the
geometrical parameters (center, kinematic position angle, and inclination).
The inclination, $i$, is a particularly crucial parameter given that
$V_{rot}=V_{l.o.s}/sin(i)$. While 3DBarolo can constrain the inclination angle
at high spatial resolution, this becomes challenging for low-resolution
observations (and for slowly-rising rotation curves in general), and therefore
we estimate the geometric parameters based only on the HI morphology of the
galaxies and independently from the kinematics. The approach we follow has
already been introduced in Mancera Piña et al. (2020), Fraternali et al.
(2021) and Mancera Piña et al. (2022b), and consists of generating a set of
beam-convolved, azimuthally-averaged models of our galaxies with different
geometrical parameters drawn from flat prior distributions using a MCMC
Bayesian framework.111The software to do this is called Cannubi, and it is
available at https://www.filippofraternali.com/cannubi. Each model is compared
against the real total intensity map, and residuals are minimized using a
$\chi^{2}$ routine. Given that the inclination can have a degeneracy with the
thickness of the disks, which we do not know precisely for our galaxies, we
performed different tests assuming razor-thin and thick disks up to about 500
pc motivated by observations (Bacchini et al., 2020; Mancera Piña et al.,
2022a), finding a very good agreement between both methods. We use our MCMC
method to estimate the center, position angle, and inclination of our galaxies
based on their HI morphology, and we fix those parameters when modeling the
data with 3DBarolo.

We show our kinematic models in Fig. 2, where we display the major-axis PV
slices of the data and best-fitting model. For these models, we have used a
ring separation of length $\sqrt{b_{maj}\times b_{min}}$. AGC 123216, AGC
219369, and AGC 333576 show clear gradients in velocity, although the gas
velocity dispersion is of comparable magnitude. The results of the modeling
indicate that the velocity gradients can be attributed to a disk with
differential rotation for these three galaxies. For AGC 229398, we did not
manage to obtain a fully satisfactory model, but our preliminary results
indicate that the system may be pressure supported. More definitive models
would require data with a much higher angular resolution.

For completeness, we include the emission-line channel maps of each of our
galaxies and their best-fitting models in Appendix A. With each channel
showing the line-of-sight velocities around the systemic velocity, the maps
show evidence for rotation in AGC 123216, AGC 219369, and AGC 333576.

Figure 2: Position-velocity slices of 1-pixel width along the major-axis from
the best-fitting model of each AD-TDG candidate, from WSRT data. The data is
shown in gray, with white contours at 2, 4, 8, and 16 times the signal to
noise (S/N) of the data. Dashed dark gray contours represent -2 $\times$ S/N.
The red contours represent the best-fit model, and the yellow points mark the
line-of-sight rotation velocities from the model.

###  3.3 Dynamical Mass

For a self-gravitating object, the dynamical mass of the HI region within the
radius $r_{HI}$ can be estimated as

$M_{dyn}[M_{\odot}]=6.78\times
10^{4}r_{HI}D^{\prime}(\frac{W_{20}^{\prime}}{2sin(i)})^{2},$ (3)

where $r_{HI}$ is the radius of the HI in arcminutes derived from the
kinematic modeling, $D^{\prime}$ and $W_{20}^{\prime}$ are the distance to the
source in Mpc and the width of the velocity profile at 20% of the peak flux
density in $\mathrm{km}\,\mathrm{s}^{-1}$, respectively (Haynes et al., 2018).
The inclination $i$ is derived from the MCMC fitting of geometric parameters
described in Section 3.2.

TDGs are distinguished by their low dark matter content, which we evaluate
using the dynamical-to-gas mass ratio, so we want to ensure that we are not
underestimating the dynamical mass. Due to the relatively narrow line widths
of the HI for these objects, we used $W_{20}^{\prime}$ rather than the more
commonly used width at 50% of the velocity profile peak $W_{50}^{\prime}$,
which will provide a more stringent upper limit on the dynamical mass.
Additionally, using the emission line width as a proxy for the rotation
velocity overestimates the dynamical mass due to artificial line broadening
from beam-smearing effects (Lelli et al., 2015). This effect is more
pronounced in systems where the velocity dispersion is of comparable magnitude
to the rotational velocity (Lelli et al., 2015), which is the case for these
objects. However, it is also important to consider that if the ADs are more
pressure-supported than rotation-supported, these dynamical mass values may be
comparatively underestimated. These measurements do not account for turbulence
and asymmetric drift, which may also increase the dynamical mass estimate. We
estimated a rough correction for turbulence and asymmetric drift using

$M_{dyn}[M_{\odot}]=6.78\times
10^{4}r_{HI}D^{\prime}((\frac{\sqrt{W_{20}^{\prime
2}-\sigma^{2}}}{2sin(i)})^{2}+3\sigma^{2}),$ (4)

and a velocity dispersion ($\sigma$) of 11 $\mathrm{km}\,\mathrm{s}^{-1}$ to
evaluate how it may affect the results. We found that it increased the
dynamical mass calculated by 23% for AGC 123216, 40% for AGC 219369, 45% for
AGC 229398, and 66% for AGC 333576. However, this did not change the
conclusions about the nature of each object (see Section 5.6), and so the
reported values do not reflect this correction as it was mostly exploratory.
As stated previously, a robust estimation of the correction through kinematic
modeling would require data with a much higher spatial resolution (Iorio et
al., 2017).

This calculation assumes that the sources are in dynamical equilibrium, which
is a reasonable assumption given the distances of the objects from any nearby
perturbers. The apparent rounded shapes of the HI distributions may be an
additional indicator of dynamical equilibrium, but this may also be an effect
of the elongated beam of WSRT, which could be artificially extending the
emission along that axis. Both the MCMC routine and 3DBarolo take this beam
smearing into account for the geometric fitting and kinematic modeling.

###  3.4 Photometry and Surface Brightness

We measured surface brightness profiles for the AD-TDG candidates using a
procedure similar to those described in Mancera Piña et al. (2019) and Marasco
et al. (2019). Briefly, a concentric set of ellipses were placed, centered on
the optical component of the object. The mean pixel brightness and standard
deviation within each band (meaning the space between adjacent ellipses) was
calculated and pixels with values more than a certain number of standard
deviations above the mean were masked and excluded from further calculations.
For AGC 123216, AGC 229398, and AGC 333576, the threshold was five standard
deviations, while for AGC 219369 it was four standard deviations. Pixels
within three pixels of the one above the threshold were also masked, in order
to reduce contamination from an unassociated bright source that may have bled
into the surrounding region. A new mean brightness and associated standard
deviation were then calculated. The final threshold and mask growth parameters
were determined by evaluating the results of various combinations for a
setting that was as conservative as possible while still removing objects that
were clearly not part of the AD (usually objects that were much brighter,
redder, and/or significantly more concentrated). In a few cases, a region was
manually masked in order to remain consistent between images (e.g. a very red
object that did not have enough emission in $g$-band to exceed the threshold,
but which should still not be included). Due to the faint and irregular nature
of the objects, fitting apertures to the objects was done manually. The
visible portions of AGC 219369 and AGC 333576 are fairly round, so circular
apertures were centered on the optical portion. The optical counterparts of
AGC 123216 and AGC 229398 appear to be quite elongated (in spite of their more
circular HI gas distributions), so we measured the major and minor axis of the
visible components to estimate a center and ellipticity, as well as a position
angle. For each of the four sources, ellipses were separated by two times the
larger FWHM of the two filters for that source. This separation allowed us to
achieve a consistent and precise measurement of surface brightness across
filters without the space between ellipses being smaller than the resolution
scale of the image. Ellipses were extended until the last ellipse before the
signal to noise ratio fell below one in order to be sure we were capturing all
of the light. The apparent magnitude was calculated using the total amount of
light contained within the outermost ellipse.

We obtained a central surface brightness and effective radius by fitting a
Sérsic profile to the observed surface brightness profile using the equation

$\mu(r)=\mu_{0}+1.0857*b_{n}*(r/r_{e})^{1/n},$ (5)

where $\mu(r)$ is the observed surface brightness at radius $r$, $\mu_{0}$ is
the central surface brightness ($r$ = 0), $r_{e}$ is the effective radius, $n$
is the Sérsic index, and $b_{n}$ is approximated as
$2n-\frac{1}{3}+\frac{4}{405n}+\frac{46}{25515n^{2}}+\frac{131}{1148175n^{3}}-\frac{2194697}{30690717750n^{4}}$
for $n$ $>$ 0.36 (Ciotti & Bertin, 1999). The scale radius $r_{d}$ was
obtained with the relation $r_{d}=r_{e}/(b_{n})^{n}$. All of the fits were
near-exponential, with $n$ ranging from 0.45 to 1.85. The masking and
resulting surface brightness profiles for each AD in $g^{\prime}$ and
$r^{\prime}$ are shown in Figs. 3 – 6.

We measured the magnitudes and colors of SDSS stars in each field and used
them to calculate zero-points and color terms for converting our measured
instrumental magnitudes and colors to calibrated values. We also corrected our
photometry for extinction using the Schlegel et al. (1998) dust maps and the
coefficients from Schlafly & Finkbeiner (2011). Though we report results in
both $g$ and $r$ bands, we generally focus on the $g$-band results, as these
objects are quite blue and thus slightly better defined in $g$. This is made
clear by the difference between the leftmost panels of the surface brightness
figures for each object, shown in Figs. 3 – 6. Therefore, the effective radius
and scale radius reported for each object are those calculated using the
$g$-band image.

Figure 3: Masking, surface brightness profiles, and profile fit parameters for
AGC 123216 in $g^{\prime}$ (top row of each panel) and $r^{\prime}$ (bottom
row of each panel), with optical images from the WIYN 3.5m telescope. For each
object, the left images show the original image with a small red x marking the
optical center; the center images show the ellipses that were placed in red
and pixels that were masked in green, based on the masking procedure described
in Section 3.4; and the right images show the best fitting surface brightness
profile, along with the uncertainty shaded in light gray and the parameters
for that fit listed below. For AGC 123216, there were no pixels flagged for
masking in either filter. Figure 4: Masking, surface brightness profiles, and
profile fit parameters for AGC 219369 in $g^{\prime}$ (top row of each panel)
and $r^{\prime}$ (bottom row of each panel), with optical images from the WIYN
3.5m telescope. Figure description is the same as Fig. 3. The physical scale
bar for AGC 219369 is calculated for a distance of 9.2 Mpc. Figure 5: Masking,
surface brightness profiles, and profile fit parameters for AGC 229398 in
$g^{\prime}$ (top row of each panel) and $r^{\prime}$ (bottom row of each
panel), with optical images from the WIYN 3.5m telescope. Figure description
is the same as Fig. 3. Figure 6: Masking, surface brightness profiles, and
profile fit parameters for AGC 333576 in $g^{\prime}$ (top row of each panel)
and $r^{\prime}$ (bottom row of each panel), with optical images from the WIYN
3.5m telescope. Figure description is the same as Fig. 3.

###  3.5 Stellar Mass and Baryonic Mass

We can photometrically estimate the stellar mass ratios and therefore stellar
mass of a galaxy using color-stellar mass-to-light ratio relations (CMLRs)
that relate the optical color and absolute magnitude to the stellar mass. The
CMLRs have been calibrated with model data and observational samples, but the
extreme nature of the galaxies in this study means that it is unclear which
fits are most appropriate. Using the measured $g-r$ color and total magnitudes
from the largest ellipse, we explored the stellar mass-to-light ratio and
resulting stellar mass estimates of two CMLRs: Du et al. (2020), which is
calibrated for low surface brightness galaxies, and Herrmann et al. (2016),
which is calibrated for dwarf irregular galaxies. The Herrmann et al. (2016)
relation consistently gave the highest stellar masses, and the Du et al.
(2020) values are closer in agreement between the two optical bands than the
Herrmann et al. (2016) ones. In this paper, we report the average of the
values derived in both optical bands between the two relations for the stellar
masses of the optical counterparts because it is unclear which is a better fit
for this unusual group of objects. The stellar mass uncertainty is heavily
dependent on the uncertainty in the color measurement, and was estimated by
varying the color by adding or subtracting the associated error and
calculating the resulting stellar mass.

We also evaluated the stellar luminosity by using AB solar magnitudes from
Willmer (2018) to convert the absolute magnitudes in $g$ and $r$ to luminosity
in $g$ and $r$ ($L_{g}$ and $L_{r}$). This allowed us to calculate the HI-
mass-to-stellar-luminosity ratios $M_{HI}^{\prime}/L_{g}$ and
$M_{HI}^{\prime}/L_{r}$.

ALFALFA has a larger beam than WSRT, so it is more sensitive to diffuse, low
surface brightness HI emission and therefore yields a more accurate
measurement of the total HI content, so we estimate the baryonic mass as
$M_{bary}^{\prime}$ = $M_{gas}^{\prime}$ $+$ $M_{*}$.

##  4 Results

###  4.1 AGC 123216

Figure 7: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image showing the
full-field view of AGC 123216 (center) with potential parents NGC 807 (top),
MRK 365 (bottom right), and MCG 05-06-003 (bottom left). There are WSRT HI
column density contours at $N_{HI}$ = (0.1, 0.5, 1.2, 2.4, 4.5) $\times$
$10^{20}$ $\mathrm{cm}^{-2}$ superimposed in white.

There are three potential parent galaxies within 500 kpc in projected distance
and with $v_{helio}$ within 500 $\mathrm{km}\,\mathrm{s}^{-1}$ of AGC 123216,
all of which show distortions in their HI emission (Fig. 7). We discuss them
here in order of increasing angular separation from AGC 123216.

Figure 8: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image of MRK 365
with WSRT HI column density contours at $N_{HI}$ = (0.1, 0.5, 1.2, 2.4)
$\times$ $10^{20}$ $\mathrm{cm}^{-2}$ in white. The HI contours are slightly
offset from the stellar disk, and the image is scaled to show a faint loop of
stellar emission on the right side, between the first and second innermost
contours.

Figure 9: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite images of NGC 807.
Left: Color image revealing low surface brightness, dusty spiral arms
surrounding a large and bright bulge. The image has been scaled to show the
full extent of the faint disk, which overemphasizes the bulge at the center.
Right: Composite $g^{\prime}+r^{\prime}$-band summed image in inverted
grayscale showing arms of stellar emission extending in several directions,
primarily out of the northern edge of the disk. The image has been binned 3x3
to make the arms easier to see. Note that this image is a different scale than
the left panel, as the region of the disk in that image is the entire black
area here.

MRK 365 is a spiral galaxy to the southwest of AGC 123216. MRK 365 is the
potential parent that is closest to AGC 123216, with a minimum projected
separation of 214 $\pm$ 7 kpc and a heliocentric velocity difference of 40
$\pm$ 15 $\mathrm{km}\,\mathrm{s}^{-1}$. The HI gas in MRK 365 appears to be
offset from the optical center (Fig. 8), and high-sensitivity images reveal a
low surface brightness string of stellar emission wrapping around the outside
of the galaxy. It has been listed in the literature as having a double
nucleus, which would suggest a previous or ongoing merger, though there is
discussion about whether this is true (Gimeno et al., 2004). Mezcua et al.
(2014) constructed a luminosity profile and found that it was consistent with
the presence of a single exponential disk; this is a sign that if there is a
merger, it is in a late stage.

NGC 807 is the next closest potential parent to AGC 123216, with a minimum
projected separation of 231 $\pm$ 8 kpc and a heliocentric velocity difference
of 361 $\pm$ 218 $\mathrm{km}\,\mathrm{s}^{-1}$. It has been classified as an
elliptical galaxy in multiple catalogs (Vorontsov-Vel’Yaminov & Arkhipova,
1964; Nilson, 1973; de Vaucouleurs et al., 1991). Since the vast majority of
TDGs originate from interactions between gas-rich galaxies, an elliptical
galaxy would not normally be considered as a likely progenitor (especially
with two other potential spiral parents nearby). However, the extended amount
of HI surrounding NGC 807 is unusual for an elliptical galaxy, and it has
clearly been disturbed (Fig. 7). Fig. 1(a) shows two small clumps of HI to the
left and right of NGC 807 which appear to have similar heliocentric velocities
to that galaxy. The WSRT data is most sensitive towards the center of the
image, so due to their location towards the edge of the image, these may not
be statistically significant measurements of gas. Additionally, they do not
appear as sources in the ALFALFA catalog, which indicates that there is
unlikely to be a deposit of low surface density gas at these locations that
the smaller beam of WSRT is resolving out. Dressel (1987) found that the
neutral hydrogen in NGC 807 has the double-horned line profile characteristic
of a rotating disk of gas. Further studies with deeper optical imaging have
even revealed faint tidal arms (Lucero & Young, 2013). Young (2002) mapped the
CO emission of NGC 807 and found that it was strongly asymmetric, with 70% of
the CO mass being located in the southeast half of the galaxy; Lucero & Young
(2013) also estimated that the southeastern tail comprised 70% of the HI gas
mass within the tails. Young (2002) mentions that the asymmetry of the CO gas
would not be expected to persist for more than 1 Gyr due to shearing by
differential rotation. Inspection of Fig. 9 reveals that the bright bulge is
in the center of a low surface brightness spiral disk with dust lanes (left
panel), and there are several low surface brightness features (tidal arms)
extending outwards in several directions (right panel). In this way, NGC 807
may have some similarities to UGC 1382, a galaxy believed to be a normal
elliptical until deep UV and optical imaging revealed a set of low surface
brightness spiral arms (Hagen et al., 2016).

At a projected separation of 331 $\pm$ 11 kpc, MCG 05-06-003 is the farthest
potential parent from AGC 123216. Not much is known about MCG 05-06-003, which
appears to be an edge-on spiral galaxy with a significant bar. The HI map
shows a slight extension of HI to the northeast, perpendicular to the
direction of AGC 123216. Given the closer proximity (see Table 1) along with
extensive HI distortion or apparent recent interaction history of the other
two potential parent galaxies, we consider MCG 05-06-003 to be the least
likely of the three galaxies to be the progenitor of AGC 123216.

Figure 10: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image of AGC
123216, with WSRT HI column density contours at $N_{HI}$ = (0.1, 0.5, 1.2,
2.4) $\times$ $10^{20}$ $\mathrm{cm}^{-2}$. The stellar component at the
center is extremely blue and elongated in the east-west direction, while the
HI distribution is rounder.

AGC 123216 itself has an interesting appearance, with an optical component
that is elongated in the east-west direction but surrounded by a relatively
rounded concentration of HI gas, although this appearance is somewhat
dependent on the elongated beam (Fig. 10). The measured properties of AGC
123216 can be found in Table 2, and the surface brightness profiles are shown
in Fig. 3. It has a central surface brightness in $g$ of 24.86 $\pm$ 0.03
$\mathrm{mag}\,\mathrm{arcsec}^{-2}$ and an absolute total magnitude in $g$ of
-13.44 $\pm$ 0.08 mag. The $g-r$ color of -0.11 $\pm$ 0.12 makes it
exceptionally blue. The effective radius from the Sersic profile fit is 1.83
$\pm$ 0.04 kpc, which combined with the central surface brightness, places it
in the regime of UDGs as defined by van Dokkum et al. (2015). The stellar mass
of AGC 123216 is estimated at $(3.86\pm 1.24)\times 10^{6}$ $M_{\odot}$, and
its HI-to-stellar mass ratio is 115.28 $\pm$ 42.20. While it is extremely gas-
rich, it has apparently formed relatively few stars for its gas mass. It has a
dynamical mass of $(2.33\pm 0.82)\times 10^{9}$ $M_{\odot}$, which yields a
dynamical-to-gas mass ratio of 4.40 $\pm$ 1.70.

Table 2: Measured and derived properties of AGC 123216

Property [Units] | Value | Property [Units] | Value
---|---|---|---
RA [h m s, J2000] | 02 04 44.6 | Dec [∘ ’ ”, J2000] | +28 48 11.28
$V_{h}^{\prime}$ [$\mathrm{km}\,\mathrm{s}^{-1}$] | 5111 $\pm$ 14 |  $N_{HI,peak}$ [$10^{20}$ $\mathrm{cm}^{-2}$] | 5.02
$S_{21}^{\prime}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.38 $\pm$ 0.05 |  $S_{21}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.34 $\pm$ 0.03
$M_{HI}^{\prime}$ [$10^{8}$ $M_{\odot}$] | 4.45 $\pm$ 0.79 |  $M_{HI}$ [$10^{8}$ $M_{\odot}$] | 3.98 $\pm$ 0.62
$M_{gas}^{\prime}$ [$10^{8}$ $M_{\odot}$] | 5.91 $\pm$ 1.05 |  $M_{gas}$ [$10^{8}$ $M_{\odot}$] | 5.30 $\pm$ 0.83
$R_{HI}$ [kpc] | 7.69 $\pm$ 1.06 | Inclination [∘] | 45 $\pm$ 5
$R_{e}$ [kpc] | 1.83 $\pm$ 0.04 |  $R_{d}$ [kpc] | 2.32 $\pm$ 0.05
$\mu_{g,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 24.86 $\pm$ 0.03 |  $\mu_{r,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 25.05 $\pm$ 0.08
$m_{g}$ [mag] | 20.80 $\pm$ 0.04 |  $m_{r}$ [mag] | 20.91 $\pm$ 0.11
$M_{g}$ [mag] | -13.44 $\pm$ 0.08 |  $M_{r}$ [mag] | -13.33 $\pm$ 0.13
(g-r) [mag] | -0.11 $\pm$ 0.12 |  $M_{*}$ [$10^{6}$ $M_{\odot}$] | 3.86 $\pm$ 1.24
$M_{bary}^{\prime}$ [$10^{8}$ $M_{\odot}$] | 5.96 $\pm$ 1.05 |  $M_{dyn}$ [$10^{9}$ $M_{\odot}$] | 2.33 $\pm$ 0.82
$M_{HI}^{\prime}/L_{g}$ | 17.04 $\pm$ 3.39 | $M_{HI}^{\prime}/L_{r}$ | 28.80 $\pm$ 6.32
$M_{HI}^{\prime}/M_{*}$ | 115.28 $\pm$ 42.20 | $M_{dyn}/M_{gas}$ | 4.40 $\pm$ 1.70

Note. — RA and Dec are listed for the optical component of AGC 123216.
Properties marked with a ′ are derived from ALFALFA measurements. Inclination
is measured from the HI gas distribution, not the optical component. $M_{dyn}$
is calculated using $W_{20}^{\prime}$ and $D^{\prime}$ from ALFALFA data and
$R_{HI}$ and inclination from WSRT data, as described in Sections 3.2 and 3.3.

###  4.2 AGC 219369

Figure 11: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image showing the
full-field view of AGC 219369 (bottom), including potential parent NGC 3510
(top). There are WSRT HI column density contours at $N_{HI}$ = (0.1, 0.5, 1.2,
2.4, 4.5) $\times$ $10^{20}$ $\mathrm{cm}^{-2}$ superimposed in white. The
physical scale bar is calculated for a distance of 9.2 Mpc.

Figure 12: NGC 3510 moment one map from WSRT imaging, with WSRT HI column
density contours superimposed in dark gray. Contour levels are the same as in
Fig. 12.

Figure 13: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image of AGC
219369, with WSRT HI column density contours at $N_{HI}$ = (0.1, 0.5, 1.2,
2.4) $\times$ $10^{20}$ $\mathrm{cm}^{-2}$ superimposed in white. The physical
scale bar is calculated for a distance of 9.2 Mpc.

AGC 219369 has a heliocentric velocity of 667 $\pm$ 11
$\mathrm{km}\,\mathrm{s}^{-1}$, which implies a distance of 9.2 $\pm$ 2.2 Mpc
according to the Masters (2005) flow model that was used to construct the
ALFALFA catalog. However, AGC 219369 is located in the “triple-value region”
of the sky, where proximity to the Virgo Cluster affects the radial velocities
of nearby objects such that objects at three different distances can have the
same radial velocity (Marinoni et al., 1998; Shaya et al., 2017). This makes
measuring the distance to AGC 219369 with only the heliocentric velocity
difficult. Redshift-independent Tully-Fisher distance measurements for the
nearby spiral galaxy NGC 3510 (which has a similar heliocentric velocity to
AGC 219369) place it at 16.8 $\pm$ 2.5 Mpc (Tully et al., 2016), and this is
in agreement with the Haynes et al. (2018) distance of 16.7 $\pm$ 3.3 Mpc from
the Masters (2005) flow model. NGC 3510 has clearly undergone an interaction
that stretched its stellar arms and distorted its HI (Fig. 12), and AGC 219369
is the nearest object to it (angular separation of 12.2 arcminutes, which
corresponds to only 59 $\pm$ 12 kpc at a distance of 16.7 Mpc), so given the
ambiguity on the distance it is reasonable to consider that AGC 219369 may
have a distance of 16.7 Mpc as well.

The HI tail is significantly more substantial on the north side of NGC 3510,
but tidal interactions usually produce two tidal tails which may or may not be
similar sizes based on the parameters of the interaction (Duc & Bournaud,
2008). We can consider whether the HI that formed the southern tail may have
concentrated into a more massive object at its end and separated from it,
producing AGC 219369, or whether AGC 219369 originally came from the larger
tail and the southern tail was always short. In spite of the motion that the
curvature of the HI tails suggests, NGC 3510 is very edge on, and Fig. 12
confirms that the rotation axis is roughly perpendicular to the line of sight.
This makes it particularly difficult to evaluate the state of the stellar
disk, which otherwise may have provided clues about the interaction. Although
they are not pictured in Fig. 12, there are three other galaxies with similar
heliocentric velocities nearby: UGC 6102 ($V_{h}$ = 697 $\pm$ 35
$\mathrm{km}\,\mathrm{s}^{-1}$ from Haynes et al. 2018), UGCA 225 ($V_{h}$ =
647 $\pm$ 22 $\mathrm{km}\,\mathrm{s}^{-1}$ from Haynes et al. 2018), and NGC
3486 ($V_{h}$ = 678 $\pm$ 1 $\mathrm{km}\,\mathrm{s}^{-1}$ from Springob et
al. 2005). UGC 6102 is a dwarf irregular galaxy with an angular separation of
about 27 arcmin directly west from AGC 219369. UGCA 225 is a Blue Compact
Dwarf located about 31 arcmin to the northeast of AGC 219369, and is actively
forming stars (Cairós et al., 2001). NGC 3486 is a spiral galaxy located 49
arcmin to the northwest of AGC 219369, and is of comparable HI mass to NGC
3510 (Haynes et al., 2018).

Table 3:  Distance-Independent Measured Properties of AGC 219369

Property [Units] | Value | Property [Units] | Value
---|---|---|---
RA [h m s, J2000] | 11 03 51.8 | Dec [∘ ’ ”, J2000] | +28 41 17.8
$V_{h}^{\prime}$ [$\mathrm{km}\,\mathrm{s}^{-1}$] | 667 $\pm$ 4 |  $N_{HI,peak}$ [$10^{20}$ $\mathrm{cm}^{-2}$] | 4.40
$S_{21}^{\prime}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.90 $\pm$ 0.04 |  $S_{21}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.60 $\pm$ 0.03
$R_{HI}$ [arcsec] | 32 $\pm$ 3 | Inclination [∘] | 53 $\pm$ 2
$R_{e}$ [arcsec] | 17.43 $\pm$ 5.36 |  $R_{d}$ [arcsec] | 10.35 $\pm$ 3.18
$\mu_{g,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 25.00 $\pm$ 0.03 |  $\mu_{r,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 25.16 $\pm$ 0.02
$m_{g}$ [mag] | 18.12 $\pm$ 0.02 |  $m_{r}$ [mag] | 18.04 $\pm$ 0.02
(g-r) [mag] | 0.08 $\pm$ 0.03 | $M_{HI}^{\prime}/M_{*}$ | 12.42 $\pm$ 5.23
$M_{HI}^{\prime}/L_{g}$ | 3.38 $\pm$ 1.93 | $M_{HI}^{\prime}/L_{r}$ | 4.78 $\pm$ 2.73

Note. — RA and Dec are listed for the optical component of AGC 219369.
Properties marked with a ′ are derived from ALFALFA measurements. Inclination
is measured from the HI gas distribution, not the optical component.

Table 4:  Distance-Dependent Measured Properties of AGC 219369

Distance [Mpc] | 9.2 $\pm$ 2.2 | 16.7 $\pm$ 3.3
---|---|---
$M_{HI}^{\prime}$ [$10^{7}$ $M_{\odot}$] | 1.79 $\pm$ 0.88 | 5.91 $\pm$ 2.43
$M_{gas}^{\prime}$ [$10^{7}$ $M_{\odot}$] | 2.39 $\pm$ 1.17 | 7.87 $\pm$ 3.23
$M_{HI}$ [$10^{7}$ $M_{\odot}$] | 1.20 $\pm$ 0.59 | 3.94 $\pm$ 1.62
$M_{gas}$ [$10^{7}$ $M_{\odot}$] | 1.59 $\pm$ 0.78 | 5.24 $\pm$ 2.15
$R_{HI}$ [kpc] | 1.40 $\pm$ 0.36 | 2.55 $\pm$ 0.56
$R_{e}$ [kpc] | 0.78 $\pm$ 0.24 | 1.41 $\pm$ 0.52
$R_{d}$ [kpc] | 0.46 $\pm$ 0.14 | 0.84 $\pm$ 0.31
$M_{g}$ [mag] | -11.70 $\pm$ 0.52 | -12.99 $\pm$ 0.43
$M_{r}$ [mag] | -11.78 $\pm$ 0.52 | -13.08 $\pm$ 0.43
$M_{*}$ [$10^{6}$ $M_{\odot}$] | 1.44 $\pm$ 0.14 | 4.76 $\pm$ 0.44
$M_{bary}^{\prime}$ [$10^{7}$ $M_{\odot}$] | 2.53 $\pm$ 1.17 | 8.34 $\pm$ 3.23
$M_{dyn}$ [$10^{8}$ $M_{\odot}$] | 2.60 $\pm$ 1.06 | 4.72 $\pm$ 1.81
$M_{dyn}/M_{gas}$ | 16.34 $\pm$ 10.42 | 9.00 $\pm$ 5.06

Note. — Properties marked with a ′ are derived from ALFALFA measurements.
$M_{dyn}$ is calculated using $W_{20}^{\prime}$ ALFALFA data and $R_{HI}$ and
inclination from WSRT data, as described in Sections 3.2 and 3.3.

In Fig. 13, we can see that the HI distribution of AGC 219369 appears to be
round, as is the optical component, which would suggest dynamical stability.
The surface brightness profiles of AGC 219369 are plotted in Fig. 4, with
scale bars for physical units corresponding to the reported ALFALFA distance
of 9.2 Mpc (Haynes et al., 2018). The surface brightness profile in $g$
follows an exponential law very closely, and results in a central surface
brightness in $g$ of 25.00 $\pm$ 0.03 $\mathrm{mag}\,\mathrm{arcsec}^{-2}$.
The $(g-r)$ color of 0.08 $\pm$ 0.03 indicates it is quite blue. Due to the
uncertainty in the distance to AGC 219369, properties that do not depend on
distance are listed in Table 3, and properties which are distance-dependent
have been calculated for both 9.2 Mpc and 16.7 Mpc (the distance of NGC 3510)
and are listed in Table 4. While both sets of values are listed for
completeness, AGC 219369 is assumed to be at the distance of NGC 3510 for the
rest of this work. Under this assumption, the effective radius of AGC 219369,
17.43 $\pm$ 5.36$\arcsec$, would correspond to 1.41 $\pm$ 0.52 kpc. AGC 219369
is the smallest AD-TDG candidate in this study, with an ALFALFA HI mass of
only (5.91 $\pm$ 2.43) $\times$ $10^{7}$ $M_{\odot}$ and an estimated stellar
mass of (4.76 $\pm$ 0.44) $\times$ $10^{6}$ $M_{\odot}$. This gives an HI-to-
stellar mass ratio of 12.42 $\pm$ 5.28. A dynamical mass of (4.72 $\pm$ 1.81)
$\times$ $10^{8}$ $M_{\odot}$ leads to a dynamical-to-gas mass ratio of 9.00
$\pm$ 5.06.

###  4.3 AGC 229398

Figure 14: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image showing the
full-field view of AGC 229398 (lower left) with potential parents UGC 6989
(upper right) and KUG 1158+216 (below label). There are WSRT HI column density
contours at $N_{HI}$ = (0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4) $\times$ $10^{20}$
$\mathrm{cm}^{-2}$ superimposed in white. Note that the prominent spiral
galaxy near the center of the image is CGCG 127-132, which has a heliocentric
velocity of 14,457 $\pm$ 4 $\mathrm{km}\,\mathrm{s}^{-1}$ and is not
associated with the objects of interest in this paper (Albareti et al., 2017).
Figure 15: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image of AGC
229398, with WSRT HI column density contours at $N_{HI}$ = (0.1, 0.2, 0.4,
0.8, 1.6) $\times$ $10^{20}$ $\mathrm{cm}^{-2}$ in white.

Figure 16: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite imaging for the
potential parents of AGC 229398. Left: KUG 1158+216, scaled to show the faint
extension of stellar emission on the left. Right: UGC 6989, with WSRT HI
column density contours at $N_{HI}$ = (0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4)
$\times$ $10^{20}$ $\mathrm{cm}^{-2}$ in white. Due to the large angular
separation from AGC 229398 and the smaller field of view of pODI, UGC 6989 was
located at the edge of the CCD, which resulted in several detector artifacts
in the image.

AGC 229398 is the farthest and most massive AD of the set, with a distance of
104.0 $\pm$ 2.3 Mpc and an HI mass of (1.91 $\pm$ 0.22) $\times$ $10^{9}$
$M_{\odot}$ (Haynes et al., 2018). It has two potential parent galaxies, of
which UGC 6989 is the most distant potential parent in the sample (Fig. 14).
While the HI distribution is round, the optical component of AGC 229398 itself
is elongated in the east-west direction (Fig. 15). There also appears to be a
small knot of stellar emission to the north-east.

The spiral galaxy KUG 1158+216, which is located to the south of AGC 229398,
is the closest potential parent galaxy in distance, heliocentric velocity, and
angular separation. The distance given by the ALFALFA survey is 110.1 $\pm$
2.3 Mpc, the heliocentric velocity difference is 423 $\pm$ 126
$\mathrm{km}\,\mathrm{s}^{-1}$, and the projected separation on the sky is 102
$\pm$ 2 kpc (Haynes et al., 2018). There is a faint stellar tail extending
from the eastern side that may be the remains of a tidal interaction (left
panel of Fig. 16). We do not have maps of the HI emission for KUG 1158+216, so
we are unable to examine the neutral gas distribution for signs of tidal
distortion in the direction of AGC 229398.

UGC 6989 is a spiral galaxy some distance away from AGC 229398, with a
projected separation of 482 $\pm$ 11 kpc. The ALFALFA survey lists the
distance of UGC 6989 as 96.0 $\pm$ 2.4 Mpc, but there are some discrepancies
between other measurement methods. The redshift-independent Tully-Fisher
measurement from the Cosmicflows-4 survey, which uses the relationship between
HI linewidths (i.e. rotation rates) and galaxy luminosities to measure the
distances to almost 10,000 spiral galaxies, is 79.8 $\pm$ 8.9 Mpc (Kourkchi et
al., 2020), which would remove it from consideration as a possible parent. The
HI distribution and spiral disk of UGC 6989 do not show much sign of
disturbance (right panel of Fig. 16), though AGC 229398 is far enough away
that if it had come from UGC 6989, enough time may have passed for it to
restabilize.

Table 5:  Measured and Derived Properties of AGC 229398

Property [Units] | Value | Property [Units] | Value
---|---|---|---
RA [h m s, J2000] | 12 00 39.8 | Dec [∘ ’ ”, J2000] | +21 24 47.6
$v_{h}^{\prime}$ [$\mathrm{km}\,\mathrm{s}^{-1}$] | 6965 $\pm$ 14 |  $N_{HI,peak}$ [$10^{20}$ $\mathrm{cm}^{-2}$] | 3.95
$S_{21}^{\prime}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.75 $\pm$ 0.04 |  $S_{21}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.32 $\pm$ 0.03
$M_{HI}^{\prime}$ [$10^{9}$ $M_{\odot}$] | 1.91 $\pm$ 0.23 |  $M_{HI}$ [$10^{8}$ $M_{\odot}$] | 8.15 $\pm$ 1.11
$M_{gas}^{\prime}$ [$10^{9}$ $M_{\odot}$] | 2.54 $\pm$ 0.31 |  $M_{gas}$ [$10^{9}$ $M_{\odot}$] | 1.09 $\pm$ 0.15
$R_{HI}$ [kpc] | 9.83 $\pm$ 1.53 | Inclination [∘] | 66 $\pm$ 8
$R_{e}$ [kpc] | 9.05 $\pm$ 1.10 |  $R_{d}$ [kpc] | 0.95 $\pm$ 0.12
$\mu_{g,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 23.84 $\pm$ 0.13 |  $\mu_{r,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 24.48 $\pm$ 0.10
$m_{g}$ [mag] | 19.74 $\pm$ 0.11 |  $m_{r}$ [mag] | 19.39 $\pm$ 0.10
$M_{g}$ [mag] | -15.35 $\pm$ 0.12 |  $M_{r}$ [mag] | -15.69 $\pm$ 0.11
(g-r) [mag] | 0.35 $\pm$ 0.15 |  $M_{*}$ [$10^{7}$ $M_{\odot}$] | 9.78 $\pm$ 4.82
$M_{bary}^{\prime}$ [$10^{9}$ $M_{\odot}$] | 2.64 $\pm$ 0.31 |  $M_{dyn}$ [$10^{9}$ $M_{\odot}$] | 1.64 $\pm$ 0.39
$M_{HI}^{\prime}/L_{g}$ | 12.51 $\pm$ 1.99 | $M_{HI}^{\prime}/L_{r}$ | 13.88 $\pm$ 2.10
$M_{HI}^{\prime}/M_{*}$ | 19.54 $\pm$ 9.92 | $M_{dyn}/M_{gas}$ | 1.52 $\pm$ 0.41

Note. — RA and Dec are listed for the optical component of AGC 229398.
Properties marked with a ′ are derived from ALFALFA measurements. Inclination
is measured from the HI gas distribution, not the optical component. $M_{dyn}$
is calculated using $W_{20}^{\prime}$ and $D^{\prime}$ from ALFALFA data and
$R_{HI}$ and inclination from WSRT data, as described in Sections 3.2 and 3.3.

The measured properties of AGC 229398 can be found in Table 5, and Fig. 5
shows the surface brightness profiles. It has the largest effective radius,
with $r_{e}$ = 9.05 $\pm$ 1.10 kpc, and a central surface brightness in $g$ of
23.84 $\pm$ 0.13 $\mathrm{mag}\,\mathrm{arcsec}^{-2}$. The $(g-r)$ color of
0.35 $\pm$ 0.15 mag is the reddest of the AD-TDG candidates. The HI mass
measured by WSRT is significantly smaller than the one measured by ALFALFA,
which suggests that ALFALFA may be detecting diffuse gas that is distributed
over a larger area. AGC 229398 also has the second highest stellar mass of
(9.78 $\pm$ 4.82) $\times$ $10^{7}$ $M_{\odot}$, though this is still small
compared to the gas content, giving a fairly high HI-to-stellar mass ratio of
19.54 $\pm$ 9.92. The estimated dynamical mass is (1.64 $\pm$ 0.39) $\times$
$10^{9}$ $M_{\odot}$, and it has a low dynamical-to-gas mass ratio of 1.52
$\pm$ 0.41.

###  4.4 AGC 333576

Figure 17: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image showing the
full-field view of AGC 333576 and potential parent NGC 7775. There are WSRT HI
column density contours at $N_{HI}$ = (0.1, 0.5, 1.2, 2.4, 4.5) $\times$
$10^{20}$ $\mathrm{cm}^{-2}$ superimposed in white. The nearby elliptical
galaxy WISEA J235250.49+284555.2 is also labeled.

Figure 18: Left: WIYN 3.5m composite $g^{\prime}+r^{\prime}$-band summed image
of NGC 7775 in grayscale, inverted to highlight the tidal tail at the top.
Right: WIYN 3.5m $g^{\prime}+r^{\prime}$-band composite image of AGC 333576,
with same HI column density contours as Fig. 17 in white.

AGC 333576 has one obvious potential parent galaxy, NGC 7775. NGC 7775 is a
spiral galaxy with chaotic stellar arms and a bright area in the lower right
corner of the galaxy which may be a massive star formation region (Fig. 17).
NGC 7775’s HI distribution reveals a clear distortion in the direction of AGC
333576 (Fig. 17) and the optical image shows a tidal tail extending from the
north side and curving toward AGC 333576 (Fig. 18, left). According to the HI
heliocentric velocities from Haynes et al. (2018), both objects are 93.9 $\pm$
4.3 Mpc away, and this is in agreement with other redshift-independent
measurements for NGC 7775 (96.50 $\pm$ 19 Mpc from Theureau et al. 2007). The
optical component of AGC 333576 is relatively rounded, though there appear to
be two distinct branches on the left side and there are clear knots of
brighter stars (right panel of Fig. 18). The surrounding HI is slightly
elongated along the northwest/southeast axis. In the course of investigating
this system, we have also found the elliptical galaxy to the upper left of AGC
333576, WISEA J235250.49+284555.2. Not much is known about this galaxy, and it
should be noted that this galaxy has been mistakenly cross-identified with AGC
333576 in the NASA/IPAC Extragalactic Database, so some of the information
listed there is actually data associated with the AD. It has a measured
heliocentric velocity of 7157 $\pm$ 24 $\mathrm{km}\,\mathrm{s}^{-1}$ (Huchra
et al., 2012), which places it at a similar distance to the other two galaxies
in this system, and it is 105 $\pm$ 0.125$\arcsec$ away from AGC 333576 on the
sky, or roughly 48 $\pm$ 2 kpc. Because WISEA J235250.49+284555.2 is an
elliptical, it likely did not have enough HI gas to be included in the ALFALFA
catalog and thus be identified as a potential parent galaxy; however, it may
still be involved in the interactions of this system.

Table 6:  Measured and Derived Properties of AGC 333576

Property [Units] | Value | Property [Units] | Value
---|---|---|---
RA [h m s, J2000] | 23 52 43.6 | Dec [∘ ’ ”, J2000] | +28 44 42.5
$V_{h}^{\prime}$ [$\mathrm{km}\,\mathrm{s}^{-1}$] | 7031 $\pm$ 13 |  $N_{HI,peak}$ [$10^{20}$ $\mathrm{cm}^{-2}$] | 5.89
$S_{21}^{\prime}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.60 $\pm$ 0.04 |  $S_{21}$ [Jy $\mathrm{km}\,\mathrm{s}^{-1}$] | 0.64 $\pm$ 0.05
$M_{HI}^{\prime}$ [$10^{9}$ $M_{\odot}$] | 1.25 $\pm$ 0.19 |  $M_{HI}$ [$10^{9}$ $M_{\odot}$] | 1.33 $\pm$ 0.21
$M_{gas}^{\prime}$ [$10^{9}$ $M_{\odot}$] | 1.66 $\pm$ 0.25 |  $M_{gas}$ [$10^{9}$ $M_{\odot}$] | 1.77 $\pm$ 0.28
$R_{HI}$ [kpc] | 16.73 $\pm$ 1.57 | Inclination [∘] | 57 $\pm$ 2
$R_{e}$ [kpc] | 4.40 $\pm$ 0.05 |  $R_{d}$ [kpc] | 3.94 $\pm$ 0.04
$\mu_{g,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 24.57 $\pm$ 0.02 |  $\mu_{r,0}$ [$\mathrm{mag}\,\mathrm{arcsec}^{-2}$] | 24.45 $\pm$ 0.02
$m_{g}$ [mag] | 18.48 $\pm$ 0.02 |  $m_{r}$ [mag] | 18.27 $\pm$ 0.02
$M_{g}$ [mag] | -16.38 $\pm$ 0.10 |  $M_{r}$ [mag] | -16.60 $\pm$ 0.10
(g-r) [mag] | 0.21 $\pm$ 0.03 |  $M_{*}$ [$10^{8}$ $M_{\odot}$] | 1.64 $\pm$ 0.12
$M_{bary}^{\prime}$ [$10^{9}$ $M_{\odot}$] | 1.82 $\pm$ 0.25 |  $M_{dyn}$ [$10^{9}$ $M_{\odot}$] | 1.90 $\pm$ 0.37
$M_{HI}^{\prime}/L_{g}$ | 3.18 $\pm$ 0.59 | $M_{HI}^{\prime}/L_{r}$ | 4.00 $\pm$ 0.75
$M_{HI}^{\prime}/M_{*}$ | 7.60 $\pm$ 1.28 | $M_{dyn}/M_{gas}$ | 1.07 $\pm$ 0.27

Note. — RA and Dec are listed for the optical component of AGC 333576.
Properties marked with a ′ are derived from ALFALFA measurements. Inclination
is measured from the HI gas distribution, not the optical component. $M_{dyn}$
is calculated using $W_{20}^{\prime}$ and $D^{\prime}$ from ALFALFA data and
$R_{HI}$ and inclination from WSRT data, as described in Sections 3.2 and 3.3.

The measured properties of AGC 333576 are listed in Table 6, and Fig. 6
displays the surface brightness profiles. It has a central surface brightness
in $g$ of 24.57 $\pm$ 0.02 $\mathrm{mag}\,\mathrm{arcsec}^{-2}$, an effective
radius of 4.40 $\pm$ 0.05 kpc, and a $g-r$ color of 0.21 $\pm$ 0.03 mag. AGC
333576 is estimated as having a stellar mass of (1.64 $\pm$ 0.12) $\times$
$10^{8}$ $M_{\odot}$, the largest in the set, which gives it a HI-to-stellar
mass ratio of 7.60 $\pm$ 1.28. The dynamical mass of (1.90 $\pm$ 0.37)
$\times$ $10^{9}$ $M_{\odot}$ gives a very low dynamical-to-gas mass ratio of
1.07 $\pm$ 0.27.

##  5 Discussion

###  5.1 Basic TDG Properties

Kaviraj et al. (2012) report several general characteristics of TDGs based on
their statistical study of candidate TDGs. This study selects objects that
appear in SDSS images of galaxy mergers and have been identified as separate
photometric objects by the SDSS processing software and have a tidal stellar
tail that connects the object to the parent. These criteria mean that younger
objects are favored. Some of these objects likely will not become independent
self-gravitating objects, so they are only TDG candidates. It is important to
consider which characteristics may change as a TDG ages. The clearest example
of this is that Kaviraj et al. (2012) report that 95% of TDG candidates were
located within a projected distance of $\sim$20 kpc from their progenitors. It
is likely that they have simply not had enough time to move much farther, as
tidal tails are only present for a few hundred million years after the first
pericentric encounter of the interacting galaxies (Bournaud & Duc, 2006).

TDGs tend to be bluer than their parents (with a median offset of 0.3 mag) due
to the star formation triggered by the turbulence of the tidal interaction
(Kaviraj et al., 2012). It may be the case that as TDGs age, this color
differential becomes less pronounced, though they may also remain quite blue.
All of the ADs in this sample are markedly blue, and bluer than their
potential parents, which may indicate that the stellar populations present
were recently formed. However, low-surface-brightness galaxies as a population
tend to be blue for reasons independent of hosting a primarily young stellar
population (McGaugh, 1992; de Blok et al., 1995).

The systems in the Kaviraj et al. (2012) sample primarily involve galaxies
that are clearly in the process of interacting — there are at least two
galaxies fairly close to each other on the sky, showing some sort of stellar
distortion (see merger classification details in Darg et al. 2010). Bournaud &
Duc (2006) conducted a set of numerical simulations of galaxy interactions
with a variety of interaction parameters, in order to examine the merger
scenarios in which TDGs are most likely to form and to survive long-term
(which they defined as $>$1 Gyr). Based on the Bournaud & Duc (2006)
simulations, the interactions most likely to produce long-lived TDGs are those
between spiral galaxies with prograde orbits, where the mass of the companion
galaxy is large enough to drive matter out of the main progenitor galaxy (at
least one-fourth the mass of the progenitor), but not so massive that the
material falls back onto the companion (less than eight times more massive
than the progenitor). In cases where a clearly merging system is present, we
might be able to use these expected properties to evaluate whether an
interaction is likely to have produced a long-lived TDG. However, most of the
proposed parents in this study appear to be single galaxies, well-separated
from the other potential parents and with generally undisturbed stellar
distributions. In some cases the interactions could have progressed enough
that the parent systems have merged completely; learning about the interaction
would then require further analysis of stellar populations, star formation
histories, and gas dynamics.

Simulations indicate that the masses of TDGs are usually a few percent of the
baryonic mass of their parents, and rarely exceed 10% of that mass (Bournaud &
Duc, 2006). We can estimate the baryonic mass of the parent galaxies as
follows: $M_{atomic}$ is estimated to account for the presence of helium and
other elements, so $M_{atomic}^{\prime}$ = 1.33 $\times$ $M_{HI}^{\prime}$,
where $M_{HI}^{\prime}$ is from the ALFALFA survey (Haynes et al., 2018) as
calculated by Eq. 1. The stellar masses were estimated by Durbala et al.
(2020). They calculated stellar masses using CMLRs between photometry and mass
for SDSS optical and unWISE infrared photometry, and checked the agreement
with stellar masses derived from SED fitting in the GALEX-SDSS-WISE Legacy
Catalog 2 (GSWLC-2; Salim et al. 2016, 2018). We used their estimates from the
Taylor relationship, noting that they are generally more conservative than
those from other calibrations, which means that the mass ratios calculated are
on the higher end. As most of the potential parent galaxies are spiral
galaxies, molecular gas mass must be taken into account when estimating the
baryonic mass. Young & Scoville (1991) report median $H_{2}$-to-HI mass ratios
for different types of spiral galaxies, which we used to estimate
$M_{molecular}^{\prime}$ for each potential parent based on the type listed on
NED (NED). For galaxies that did not have a specific type listed, a mass ratio
of one was used. Young & Scoville (1991) note that early-type galaxies have
higher $H_{2}$-to-HI mass ratios than late-types, so we used a ratio of 2.5
for NGC 807. Then, $M_{bary}^{\prime}$ = $M_{atomic}^{\prime}$ \+ $M_{*}$ \+
$M_{molecular}^{\prime}$. This calculation was not done for MRK 365, as we do
not have mass estimates for it. Most of the AD-TDG candidates do not exceed 5%
of the baryonic mass of any individual potential parent. However, AGC 229398
has high mass ratios with respect to its potential parents (15.3% with UGC
6989 and 23.9% with KUG 1158+216), which seems to make it less likely that
either galaxy is the parent; such an enormous removal of mass would cause
major disruption to the parent, but these spirals appear to be relatively
intact.

###  5.2 Context of Other TDGs

The sample of candidate TDGs to compare these candidates to is small, and the
sample of confidently identified TDGs that have completely separated from
their parent systems is even smaller. We have selected a comparison sample of
likely TDGs identified in other studies that have similar measurements to
those we have conducted for the AD-TDG candidates. These are AGC 749170, AGC
208457, NGC 5557-E1, NGC 5557-E2, NGC 5291N, NGC 5291S, NGC 5291SW, NGC 7252E,
NGC 7252NW, VCC 2062, and HCG 16-LSB1.

  * •

In Lee-Waddell et al. (2012, 2014, 2016), two ADs have been identified as
TDGs, and so are included in the discussion of AD-TDGs as a group. The
analyses in those papers were carried out with measurements from the Giant
Metrewave Radio Telescope (GMRT), which has a higher spatial resolution than
the Arecibo telescope. A higher resolution beam does a better job of mapping
the fine gas structure, but does not capture the more diffuse surrounding gas.
Lee-Waddell et al. (2012) note that the GMRT maps capture less than 40% of the
flux density of the ALFALFA measurements and therefore the ALFALFA gas mass.
In the interest of comparing these sources to the work done here, we use the
ALFALFA survey data from Haynes et al. (2018) when discussing the total gas
mass content of the galaxy and the GMRT values reported by Lee-Waddell et al.
(2012, 2014, 2016) for the dynamical-to-gas mass ratio. The estimates reported
for these objects do not include an asymmetric drift correction.

    * –

AGC 749170 has an extremely high gas-mass-to-light ratio ($>$1000; Lee-Waddell
et al. 2014). Lee-Waddell et al. (2014) used stellar population models to
estimate its age at 6.3 - 12 Myr, which is very young for a galaxy’s global
population and suggests that there are very few pre-existing stars in AGC
749170. This stellar population age estimate depends on an estimated $g-i$
range due to a non-detection in the $i$-band. Additionally, in order to reach
its present separation of at least 90 kpc (from the angular distance
projection on the sky, though the true distance is likely greater) in only 12
Myr, AGC 749170 would need to travel at a speed of at least 7300
$\mathrm{km}\,\mathrm{s}^{-1}$, which would be unreasonably fast. The lack of
a gaseous tail stretching from AGC 749170 also seems to imply an older age,
because forming such a large mass of HI would require a significant tail which
would take at least a few hundred million years to fade below the detection
limits. On the other hand, the tail may be present but very diffuse, and
therefore not captured in the higher resolution GMRT images.

    * –

AGC 208457 appears to have the last remnants of an HI tail connecting it to
its potential parent, the spiral galaxy NGC 3169, based on HI maps from Lee-
Waddell et al. (2012). This, in combination with the elongation of the HI in
AGC 208457, suggests that the TDG may not have reached full dynamical
equilibrium yet, so the estimated dynamical mass (and thus the dark matter
content) may not be accurate. AGC 208457 has an estimated age range of 6 -
2600 Myr, based on the age of the stellar component using a Chabrier IMF (Lee-
Waddell et al., 2016). Follow-up spectroscopy of AGC 208457 confirmed that it
has the enriched metallicity indicative of a tidal origin (Lee-Waddell et al.,
2018).

  * •

Duc et al. (2014) identified two objects likely to be TDGs around the
elliptical galaxy NGC 5557: NGC 5557-E1 and NGC 5557-E2. Using
spectrophotometric methods, they analyzed NGC 5557-E1 and came to the
conclusion that its near-solar oxygen abundance was typical of galaxies 10
times more massive, and therefore the material was pre-enriched. Deep optical
imaging from MegaCam on the Canada-France-Hawaii Telescope (CFHT) revealed
that NGC 5557-E1 was located in a large and diffuse stellar stream. They
considered that NGC 5557-E1 could be the remnant of a pre-existing satellite
galaxy that had been tidally disturbed, but the remains of such an interaction
would be redder, and the surrounding tidal tails would likely have an
“S-shape” (Duc et al., 2014). The blue color of NGC 5557-E1 and the
straightness of the tail precluded this as a likely origin scenario, and so
Duc et al. (2014) concluded that it was a TDG formed during a tidal
interaction. NGC 5557-E2 is located farther along this tail and likely
originated in the same interaction. They estimated the age of these objects to
be between 2 and 4 Gyr, which would make them much older than any TDGs
previously identified. Both “older” TDGs have larger effective radii than
other dwarf galaxies of comparable stellar mass, in accordance with other,
younger TDGs that have been identified by their tidal tails (Duc et al.,
2014). Duc et al. (2014) suggested that the larger radii may be used as an
additional tool to aid in distinguishing TDGs from dwarf satellite galaxies
without spectroscopy.

  * •

Lelli et al. (2015) performed new observations and analysis for a sample of
six previously identified candidate TDGs: NGC 5291N, NGC 5291S, NGC 5291SW,
NGC 7252E, NGC 7252NW, and VCC 2062. They also cited additional photometric
properties of the latter three compiled in Duc et al. (2014). Lelli et al.
(2015) found that NGC 7252E and NGC 7252NW are comprised of pre-enriched
material and lack a significant dark matter mass, and are therefore genuine
TDGs, and reference similar results for the three objects around NGC 5291
(Bournaud et al., 2007) and for VCC 2062 (Duc et al., 2007).

  * •

HCG 16-LSB1 is located at the end of an HI tail extending out of the galaxy
HCG 16c, which is part of the complex galaxy interactions occurring in HCG 16.
Román et al. (2021) concluded that HCG 16-LSB1 has a high metallicity that is
compatible with it being a newly-formed TDG. They estimated a dynamical mass
range of (1.2 - 4.1) $\times$ $10^{9}$ $M_{\odot}$, with the further caveat
that HCG 16-LSB1 may be too young to be gravitationally bound (Román et al.,
2021). Even the low end of this range would indicate a higher than expected
amount of dark matter for a TDG, yet the object has clearly formed from
enriched material at the end of a tidal tail. The mass and location of HCG
16-LSB1 at the end of a tidal tail make it very likely to have longevity based
on the results of the simulations of Bournaud & Duc (2006), so it seems
feasible that it will become gravitationally independent as a proper TDG in
the future.

###  5.3 Dark Matter Content

Figure 19: Comparison of dynamical-to-gas mass ratios for objects from this
work (purple, various symbols) to the young TDG candidate HCG 16-LSB1 (Román
et al. 2021; blue pentagon), AD-TDG candidates from Lee-Waddell et al. (2016;
green right-pointing triangles), and TDG candidates from Lelli et al. (2015;
turquoise circles). For the comparison of TDG properties to those of normal
(non-TDG) dwarf galaxies, we have plotted a sample of Local Group dIrrs from
McConnachie (2012; dark gray triangles). $M_{gas}$ for the LG dIrrs is
calculated using 1.33 $\times$ the HI mass reported in McConnachie (2012), and
$M_{dyn}$ uses the dynamical masses from the same paper supplemented by the
total masses reported in Mateo (1998) when necessary. $M_{gas}$ for the TDGs
from Lelli et al. (2015) is the sum of $M_{atomic}$ and $M_{molecular}$
reported in that work. All objects that have been identified as TDGs have
filled symbols, and those that are not TDGs have unfilled symbols.

The ratio of the dynamical (total) mass to the gas mass provides a measure of
the dark matter content in a galaxy. To calculate the numerator in this ratio,
we use the dynamical mass described in Sec. 3.3, which is calculated with Eq.
3 and uses the ALFALFA velocity width and distance ($W_{20}^{\prime}$ and
$D^{\prime}$ and the inclination and radius ($R_{HI}$) derived from the WSRT
data. Because the spatial values used to calculate dynamical mass (inclination
and radius) are derived from spatial measurements from the WSRT data, we use
the WSRT gas mass as the denominator in the dynamical-to-gas mass ratio. For
our ADs, the stellar contribution to the mass is minimal, so we consider only
the gas mass for the current discussion. TDGs are primarily composed of gas
from the disk material of their progenitors, and so should contain very little
dark matter and therefore are expected to have $M_{dyn}/M_{gas}$ near 1. Fig.
19 shows the dynamical-to-gas mass ratios of the four candidate AD-TDGs in
this sample in comparison to the values for the TDGs in Román et al. (2021),
Lelli et al. (2015), and Lee-Waddell et al. (2016). To provide a comparison
sample of non-TDG dwarf galaxies we have also plotted values for the dwarf
irregular galaxies in the Local Group compiled by McConnachie (2012).

AGC 229398 and AGC 333576 have ratios that clearly place them in the regime of
previously identified TDGs in the lower right corner of the plot, while AGC
219369 appears to be dark matter dominated (Fig. 19). This suggests that AGC
219369 is unlikely to be a TDG. Instead, it may simply be a small dwarf galaxy
that happens to be near a tidally disturbed spiral in the sky, or may have
even interacted with it previously. AGC 123216’s dynamical mass to gas mass
ratio indicates a higher dark matter content than expected for an object of
tidal origin, though it still has a lower amount of dark matter than most of
the Local Group dwarf irregular galaxies. It is worth noting that while HCG
16-LSB1, which is a clearly tidal object, is located in the dark matter
dominated portion of the plot, it is such a young object that it may not be
dynamically stable yet. This means the currently estimated dynamical mass may
be larger than the actual total dynamical mass.

###  5.4 Stellar Content

Figure 20: Comparison of HI-to-stellar mass vs. baryonic mass for objects from
this work (purple, various symbols) to the young TDG candidate HCG 16-LSB1
(Román et al. 2021; blue pentagon), AD-TDG candidates from Lee-Waddell et al.
(2016; green right-pointing triangles), TDG candidates from Lelli et al.
(2015; turquoise circles), and likely older TDGs identified in Duc et al.
(2014; red left-pointing triangles). $M_{HI}^{\prime}$ and $M_{bary}^{\prime}$
for the objects from this work and from Lee-Waddell et al. (2016) are
calculated with the ALFALFA measurements (Haynes et al., 2018). The HI masses
for the Duc et al. (2014) TDGs used in the baryonic mass calculation are from
Duc et al. (2011). For the comparison of TDG properties to those of normal
(non-TDG) dwarf galaxies, we have plotted Local Group dIrrs from McConnachie
(2012; dark gray triangles). As with Fig. 19, filled symbols correspond to
objects that have been identified as TDGs.

The four AD-TDG candidates studied in this work were selected from the larger
ALFALFA AD sample in part because of their large HI-to-optical-light ratios.
As previously mentioned, it is likely that ADs may not efficiently convert
neutral HI to cold molecular gas (Wang et al., 2020), impacting their star
formation rate. According to simulations, the critical column density
threshold of HI for star formation is thought to range from (3-10) $\times$
$10^{20}$ $\mathrm{cm}^{-2}$ (Schaye, 2004), depending on the local
conditions. The critical surface density corresponds to a critical minimum
pressure to trigger a transition to a cold phase, where the temperature of the
gas drops and the $H_{2}$ formation rate increases in order to maintain the
pressure, thereby increasing the fraction of molecular gas (Schaye, 2004). The
phase transition also causes gravitational instability in the gas cloud, which
results in fragmentation and, eventually, star formation (Schaye, 2004). If
there is not a high enough column density (and therefore pressure) of neutral
gas to cause the phase transition and increase the molecular gas fraction, the
gas cloud does not become unstable and collapse to form stars. The peak column
densities for the four objects in this work are on the low-to-mid end of the
range (3.95 $\times$ $10^{20}$ $\mathrm{cm}^{-2}$ for AGC 229398 at the least,
5.89 $\times$ $10^{20}$ $\mathrm{cm}^{-2}$ for AGC 333576 at the most), so one
could suggest that they did not have a high enough gas density for efficient
star formation as an explanation for their high HI-to-optical-light ratios.

On the other hand, TDGs are expected to have a burst of star formation during
their formation, due to the instability of the gas from turbulence, and then
fade over time, which would also result in a higher HI-to-optical-light ratio
as they age. For example, Román et al. (2021) predicted the evolution of the
surface brightness for HCG 16-LSB1 based on its metallicity and the aging of
its stellar population. They expect that the dimming of HCG 16-LSB1 will be
rather extreme; in 400 Myr, the effective surface brightness will decrease by
more than 1 $\mathrm{mag}\,\mathrm{arcsec}^{-2}$, making it fall below the
optical threshold of the survey used in their work (DECaLS). Stellar
populations with higher metallicities will experience more dimming, which
means that TDGs will be particularly affected, though they are assumed to
continue forming stars at a lower rate (Duc et al., 2014). This means that an
evolved TDG could have a stellar population mainly formed in an initial burst
followed by a lower rate of formation, but a high HI-to-optical-light ratio
due to dimming.

While this idea does not easily distinguish TDGs from dIrr galaxies that have
produced stars normally, objects that are faint due to a lack of stars
proportional to their HI contents may be considered less likely to be TDGs
because they likely didn’t have this initial burst of star formation. Fig. 20,
which plots the HI-to-stellar mass ratio against the baryonic mass of each
object, demonstrates how this appears to be true for AGC 123216, which has an
extreme $M_{HI}^{\prime}/M_{*}$ of 115.28 $\pm$ 42.20. This could mean that
AGC 123216 lacked the star formation burst at its formation that would be
expected for a TDG. HCG 16-LSB1 and AGC 208457 also fall higher than the
distribution of the rest of the TDGs, even though they are confirmed tidal
objects. Considering the young age of HCG 16-LSB1 ($57.9^{+21.7}_{-9.4}$ Myr
according to Román et al. 2021) and the possible still-extant tidal tail and
estimated age range of 6-2600 Myr for AGC 208457 (Lee-Waddell et al., 2016),
they might have a high HI-to-stellar mass ratio because they are so young that
they have not had sufficient time to convert gas into stars. The two older
TDGs from Duc et al. (2014) have relatively average HI-to-stellar mass ratios
compared to the TDGs from Lelli et al. (2015). Fig. 20 also shows that the
other three AD-TDG candidates appear to have $M_{HI}^{\prime}/M_{*}$ that is
comparable to these TDGs and about an order of magnitude higher than dwarf
irregulars. This suggests that their high HI-to-optical-light ratios may be
the result of dimming rather than a deficit of stars in proportion to their HI
content.

Figure 21: Comparison of central surface brightness vs. stellar mass for
objects from this work (purple, various symbols) to the young TDG candidate
HCG 16-LSB1 (Román et al. 2021; blue pentagon), TDG candidates discussed in
Lelli et al. (2015; turquoise circles), and likely older TDGs identified in
Duc et al. (2014; red left-pointing triangles). The non-TDG dwarf galaxy
comparison samples plotted are Local Group dwarf irregulars from McConnachie
(2012; dark gray triangles) and Hydra I cluster dwarf ellipticals whose
properties were compiled by Misgeld et al. (2008) and Misgeld & Hilker (2011;
light gray squares). Conversions from surface brightness in $g$ to V were made
with the Jester et al. (2005) transformation equations and the central color
of the object where possible. If the central color was not known, the total
$g-r$ color of the object was used, and if no color information was given, an
average estimate of 0.4 $\pm$ 0.1 for dwarf galaxies based on the colors of
Honey et al. (2018) was used. As with Fig. 19, filled symbols correspond to
objects that have been identified as TDGs.

Due to this dimming, we can also expect TDGs to increasingly be found on the
lower end of the central surface brightness versus stellar mass relationship
as they age. Fig. 21 shows that this is the case for the older TDGs from Duc
et al. (2014), while younger TDGs (HCG 16-LSB1, the sample from Lelli et al.
2015), though still low, are more scattered along the relation shown by the
comparative non-TDG sample, which is comprised of dwarf irregulars in the
Local Group and dwarf ellipticals from the Hydra I cluster (Misgeld et al.,
2008; Misgeld & Hilker, 2011; McConnachie, 2012). AGC 229398 and AGC 333576
also have low central surface brightnesses for their stellar masses, appearing
quite similar to NGC 5557-E1. AGC 123216 and AGC 219369 are located within the
distribution of dwarf ellipticals, so their central surface brightnesses are
low compared to dwarf irregular galaxies of similar stellar mass. HCG 16-LSB1
is similarly placed, though it is unknown whether this is because it is so
young that it simply may not have had enough time to form a larger stellar
population yet. Over time, it is expected to eventually move farther right and
lower in the plot as it forms stars and dims. It is important to note that
though UDGs are not shown here, because they are defined as having
$\mu_{g,0}>$ 24 $\mathrm{mag}\,\mathrm{arcsec}^{-2}$ (van Dokkum et al., 2015)
they will also occupy the lower portion of the plot and may overlap with the
evolved TDGs.

Duc et al. (2014) considered a comparison of the effective radius to the
stellar mass as a tool for the optical identification of TDG candidates. TDGs
tend to have effective radii larger than those of dwarf irregulars or dwarf
ellipticals of a comparable stellar mass. In this sense, they resemble UDGs
because their stellar mass is more spread out than usual. In the comparison of
effective radius to stellar mass in Fig. 22, it is clear that other identified
TDGs occupy the top part of the distribution. AGC 229398 and AGC 333576 are
located well above the distribution, along with the TDGs from Lee-Waddell et
al. (2016). AGC 123216 and AGC 219369 appear to be on the upper end of the
distribution as well (though not as dramatically as the other two objects).

Figure 22: Comparison of effective radius vs. stellar mass for objects from
this work (purple, various symbols) to the young TDG candidate HCG 16-LSB1
(Román et al. 2021; blue pentagon), AD-TDG candidates from Lee-Waddell et al.
(2016; green right-pointing triangles), TDG candidates from Lelli et al.
(2015; turquoise circles), and likely older TDGs identified in Duc et al.
(2014; red left-pointing triangles). We have also plotted the sample of UDGs
from Mancera Piña et al. (2020; dark gray circles). For the comparison of TDG
properties to those of normal (non-TDG) dwarf galaxies, we have plotted Local
Group dIrrs from McConnachie (2012; dark gray triangles), and Hydra I cluster
dwarf ellipticals compiled by Misgeld & Hilker (2011; light gray squares). As
with Fig. 19, filled symbols correspond to objects that have been identified
as TDGs.

###  5.5 Estimation of Travel Time

It is common to use the combination of stellar population models and
photometry in multiple bands to estimate the age and metallicity of a galaxy
(Bruzual & Charlot, 2003). Our photometry in $g$ and $r$ bands for our TDG
candidates is not sufficient to break the age-metallicity degeneracy
associated with some broadband filter combinations, and a third filter (e.g.
$i$-band) would be required. Therefore, we must turn to other methods to
evaluate the evolutionary histories of the sample galaxies.

The simulations from Bournaud & Duc (2006) give us a few markers to estimate
the evolutionary progress of the TDG systems. They show that tidal tails fade
within 300-500 Myr, so based on the absence of tidal tails, our TDG candidates
would be at least a few hundred million years old if they are genuine TDGs.
This alone would make them older than the majority of previously studied TDGs.
TDGs face many obstacles to their survival: a significant number simply fall
back onto their parent galaxy, or are torn apart by tidal disruption from the
progenitor galaxy or by feedback from star formation. Bournaud & Duc (2006)
found that only 25% of tidal knots more massive than $10^{8}$ $M_{\odot}$
survive longer than 800 Myr, and that 45% of knots surviving at least 1 Gyr
have masses exceeding $10^{9}$ $M_{\odot}$. Note that “surviving” in this
simulation meant remaining above the detection threshold of $10^{8}$
$M_{\odot}$ within a diameter of 3 kpc or $3\times 10^{8}$ $M_{\odot}$ within
a diameter of 6 kpc, due to computational constraints. The tidal knots may
undergo mass loss that puts them below this threshold while still appearing as
distinct, intact knots that would continue to be classified as candidate TDGs
in a higher resolution simulation than that from Bournaud & Duc (2006).

If the ADs in this study are indeed TDGs, they are located much farther from
their parents than the majority of previously proposed candidate TDGs, so it
is necessary to show that it is possible for them to travel the observed
distance in a reasonable time scale. The logic is similar to the logic we used
to evaluate whether AGC 749170 could have reasonably reached its present
location in 12 Myr, though now we consider rotational velocities and
orientations of the potential parents. For each TDG-parent pair, we estimate a
travel time as follows: TDGs are expected to have velocities with respect to
their parent galaxies comparable to the rotational velocities of those parent
galaxies (Bournaud & Duc, 2006). We approximate the rotational velocity using

$V_{rot}^{\prime}=\frac{W_{20}^{\prime}}{2sin(i)}$ (6)

with the $W_{20}^{\prime}$ value measured by the ALFALFA survey. Inclination
$i$ here is estimated from reported optical semimajor and semiminor axis
measurements of the galaxy, using

$cos^{2}(i)=\frac{(b/a)^{2}-q_{0}^{2}}{1-q_{0}^{2}},$ (7)

with $q_{0}$ = 0.13 as is appropriate for spirals (all of the potential parent
galaxies are classified as spirals with the exception of NGC 807, which
nevertheless shows evidence of a disk). The resulting rotational velocities
(and thus TDG candidate travel velocities) are on the order of 100-300
$\mathrm{km}\,\mathrm{s}^{-1}$, which is typical for spiral galaxies and
consistent with the velocities of the TDGs simulated by Bournaud & Duc (2006),
so this is a reasonable estimate. TDGs in simulations tend to have low orbital
inclination ($<$40∘) with respect to the rotational plane of their progenitor
(Bournaud & Duc, 2006), so for simplicity we assume that the TDG candidate
remained in the rotation plane of the parent. Therefore, we can use the
inclination axis of the parent to deproject the angular separation on the sky
and estimate a total travel distance for the TDG candidate. For this
calculation, we consider the TDG candidates to be at the distance of the
parent galaxy, give or take a negligible distance from any component of the
velocity along the line-of-sight, which is consistent with the observations
within uncertainties for all sources (given the previous assumption that AGC
219369 is at the distance of NGC 3510). With these approximations for velocity
and travel distance, we can estimate the time it would take for a newly-formed
TDG to travel to its current position from each potential parent. Ranges for
the travel velocities, travel distance, and travel time estimates for each
TDG-parent pair are included in Table 7. In most cases, it is reasonable for
the candidate TDGs to travel the observed distance in several hundred
megayears to a few gigayears. This timescale is also consistent with the
absence of a tidal tail. The older TDGs identified in Duc et al. (2014) are
estimated to be 2-4 Gyr, so our rough travel time estimates suggest that it is
reasonable to think that our AD galaxies may indeed be older TDGs. Another way
to evaluate whether these systems are in dynamical equilibrium would be to
obtain resolved kinematics and compare the dynamical timescales with these
travel times — if a dynamical time is much less than the estimated travel
time, it becomes more likely that that system is dynamically stable.

Table 7:  Estimated Travel Time for TDG-Parent Candidate Pairs Source | Parent | Estimated Travel Velocity [$\mathrm{km}\,\mathrm{s}^{-1}$] | Estimated Travel Distance [kpc] | Estimated Travel Time [Gyr]
---|---|---|---|---
AGC 123216 | MRK 365 |  $\sim$210 | 260-310 | 1.2-1.4
| NGC 807 | 310-360 | 300-350 | 0.8-1.1
| MCG 05-06-003 | 100-110 | 900-1050 | 8.1-9.6
AGC 219369 | NGC 3510 | 100-110 | 170-790 | 1.5-7.7
AGC 229398 | KUG 1158+216 | 150-160 | 210-270 | 1.3-1.8
| UGC 6989 | 120-170 | 570-1020 | 3.2-8.2
AGC 333576 | NGC 7775 | 140-220 | 150-170 | 0.7-1.2

###  5.6 The Origins of the Almost-Dark Galaxies in This Work

Much of the previous work on TDGs has been carried out with objects formed in
merging galaxy systems, since ongoing interactions are easier to spot than
past ones and the TDGs in these cases are readily identifiable as tidal
debris. According to the simulations of Bournaud & Duc (2006), the
interactions most likely to form long-lived TDGs are those that involve two
gas-rich spiral galaxies with mass ratios of at least 1:8. Following the first
pericenter passage of a gas-rich merging system, two opposing tidal tails of
gas stretch out, and denser knots form along the tails relatively quickly.
Knots located within the tails suffer significant mass loss and are more
likely to fall back into the parent galaxies or disperse in under 1 Gyr, while
those formed at the end (which also tend to be the most massive) have a better
chance at long-term survival, becoming fully-fledged TDGs (Bournaud & Duc,
2006).

Another proposed formation mechanism for TDGs is a high velocity encounter.
Duc & Bournaud (2008) suggest that high velocity encounters can produce
independent HI clouds with minimal stellar content, resulting in tidal debris
that is gas-rich but extremely optically faint. This scenario would explain
the lack of a disrupting companion and the apparent minimal perturbation of
the stellar disk for many of the proposed parents. Duc & Bournaud (2008)
simulated the results of various encounters at $\sim$300-1000
$\mathrm{km}\,\mathrm{s}^{-1}$ and showed that fly-bys of 1000
$\mathrm{km}\,\mathrm{s}^{-1}$ or more are capable of producing primary tidal
tails that are just as long as those in merger scenarios. Rather than the two
large tails produced in a standard major merger, the tidal tails formed in the
high velocity fly-by consist of a long tail and a fainter, shorter countertail
that quickly falls back onto the parent’s disk. The tails have a lower stellar
content than tails produced in a lower velocity interaction (i.e. a galaxy
merger) because most stars remain in the disk. While the total mass of gas
removed from the parent in a high velocity fly-by is much lower than in a more
traditional merger scenario, this is due to the shortness of the countertail;
the gas mass of the primary tidal tail is comparable to the mass of an
individual tail in a slower encounter. According to Duc & Bournaud (2008), the
velocity of the tail is determined by the mass of the progenitor galaxy, not
the speed of the interloper, and is on the same order of magnitude as the
rotational velocity of the parent, so the reasoning behind the travel times as
calculated in Section 5.5 should still be valid for TDGs formed in this way.
With this understanding of how TDGs can form, we now move on to examining the
potential origins of each system presented here.

AGC 123216 is the most ambiguous and complex case in the sample. AGC 123216
has three potential parents, two of which show signs of a previous interaction
(the elongation of the HI around NGC 807, and the slight offset of HI from the
optical center of MRK 365). The disturbance around NGC 807 is much more
pronounced, and so it would be considered the primary candidate for providing
most of AGC 123216’s material. The estimated travel time for AGC 123216 from
NGC 807 (assuming its relative travel speed is similar to NGC 807’s rotation
velocity) is around 1 Gyr. This is also approximately the timescale that Young
(2002) estimates for the asymmetry of the CO gas to settle, though they note
that the molecular gas may be farther from the center than it appears, which
would extend this timescale. Young (2002) also mentions that the gas in this
galaxy may have come from a merger between two gas-rich spiral galaxies, an
event which potentially could have produced a TDG. If AGC 123216 is a TDG and
was instead created by a later fly-by interaction, MRK 365 is near the
direction of travel that we would expect for an interloper, and would only
need a velocity of $\sim$600 $\mathrm{km}\,\mathrm{s}^{-1}$ relative to NGC
807 to reach its current position in 1 Gyr. AGC 123216 has a large effective
radius for its stellar mass, which would be expected for a TDG. However, the
dark matter content of AGC 123216 appears to be rather high for a TDG
candidate. The object is well separated from the surrounding HI sources, so it
is valid to assume that it is dynamically stable. Wang et al. (2020) studied
other ADs with properties similar to AGC 123216 and found that they had low
molecular-to-atomic gas mass ratios, so it seems unlikely that there is a
large deposit of unseen molecular gas. Therefore, the majority of the unseen
mass is likely to be non-baryonic dark matter. It is important to remember
that the results here represent an upper limit for the dynamical mass ratio,
because the kinematic modeling indicated that the velocity dispersion was on
the same order of magnitude as the rotation velocity and so the emission line
width would be artificially broadened (Lelli et al., 2015). This would mean
the dynamical mass ratio (which is already somewhat low compared to most of
the LG dwarf irregular galaxies) is potentially lower than we have estimated
here (Fig. 19). This makes it challenging to definitively say that AGC 123215
is not a TDG based solely on the estimate of the dark matter content. AGC
123216 also has an unusually high HI-to-stellar mass ratio compared to other
TDGs, which could indicate it never experienced the increased rate of star
formation expected to occur for TDGs when they form. AGC 123216 has many
properties in common with the ALFALFA AD sources in the HI1232+20 system
investigated by Janowiecki et al. (2015). That work concluded that AGC 229383,
AGC 229384, and AGC 229385 were too isolated to be likely tidal features, and
all three objects have some of the highest HI-to-stellar mass ratios measured
to date for the AD sample (Janowiecki et al., 2015). If the objects in
Janowiecki et al. (2015) are indeed non-tidal, they could potentially be
genuine “dark” galaxies- otherwise ordinary dwarf galaxies with unusually low
stellar masses for the gaseous matter present. Janowiecki et al. (2015) also
found that these objects appear to rotate slower than their measured baryonic
mass would imply based on the baryonic Tully-Fisher relation (BTFR). The width
of the velocity profile of AGC 123216 is rather small for a rotating disk of
similar baryonic mass, and the velocity gradient map appears to show some
minor ordered rotation (Fig. 1b), which is supported by the kinematic model.
AGC 123216’s BTFR location, effective radius, and low surface brightness are
also similar to those of UDGs (van Dokkum et al., 2015; Mancera Piña et al.,
2019), though the distinction between a UDG and an “almost-dark” galaxy is not
well-defined.

AGC 219369 is possibly located very near to NGC 3510, which clearly has
significant disruption to its HI distribution, so at first glance AGC 219369
is a good candidate to be a TDG. The edge-on orientation of NGC 3510 (Fig. 12
and Fig. 12) makes it difficult to evaluate the state of the stellar disk, but
the stretched stellar limbs suggest that it has been severely disturbed. The
orientation of NGC 3510 also makes it difficult to estimate the travel time
for AGC 219369 (see the wide range in Table 7; additionally, if the angular
separation is used as a minimum travel distance, it could be as low as 0.5
Gyr). The very blue color of NGC 3510 suggests that there has been fairly
recent star formation activity, which may help constrain the length of time
since the interaction. A more face-on orientation of NGC 3510 may have
revealed a second interacting galaxy. NGC 3510 appears to be in a group with
three other nearby galaxies (UGCA 225, UGC 6102, and NGC 3486), so a fly-by
scenario for the disruption of NGC 3510 (potentially resulting in the
formation of AGC 219369) is also possible. However, the high dynamical mass
ratio indicates AGC 219369 is more likely to be a dark matter dominated dwarf
irregular galaxy. It is possible that AGC 219369 was a pre-existing dwarf
irregular galaxy which interacted with NGC 3510 in the past and caused the
disruption of its HI, and not a post-interaction product such as a TDG. The
large effective radius may be explained by the fact that pre-existing dwarf
galaxies may experience a temporary increase in size following tidal
threshing, as shown in Paudel et al. (2013). On the other hand, it seems
unlikely that an object as small as AGC 219369 could have caused such a large
disturbance to the much more massive NGC 3510 and remained intact. We must
also consider that AGC 219369 may be closer than 16.7 Mpc and the disturbed
state of NGC 3510 may be entirely unrelated. If AGC 219369 is at a distance of
9.2 Mpc, the dynamical mass ratio would be even higher and the effective
radius and stellar mass would be smaller. This means the central surface
brightness and effective radius would be closer to those of other dwarf
irregular galaxies of similar stellar mass. For these reasons, we consider AGC
219369 unlikely to be a TDG. While the central surface brightness is fainter
than 24 $\mathrm{mag}\,\mathrm{arcsec}^{-2}$, the effective radius is at most
1.41 $\pm$ 0.52 kpc, which is not large enough to clearly classify it as a UDG
(van Dokkum et al., 2015). Therefore, we will simply identify AGC 219369 as a
low surface brightness dwarf irregular galaxy.

AGC 229398 and AGC 333576 appear to have low dark matter contents (Fig. 19),
and very large effective radii for their stellar masses (Fig. 22), both of
which are indicators that they may be TDGs. They also have fainter central
surface brightnesses compared to dwarf irregular and dwarf elliptical galaxies
of similar stellar mass (Fig. 21), which suggests their stellar populations
may have dimmed over time, as is expected for TDGs. AGC 229398 has two
potential parents identified by the velocity and angular separation selection
criteria: KUG 1158+216 and UGC 6989. Based on mass ratio predictions for TDGs
and their parents, AGC 229398 seems too massive to have come out of KUG
1158+216, so we turn our attention to UGC 6989. The mass ratio is still higher
than that which is predicted by simulations, but more viable than for KUG
1158+216. However, UGC 6989 is 482 kpc away from AGC 229398 on the sky, much
farther than any other TDG-parent system studied. The TDGs simulated in
Bournaud & Duc (2006) could have travel velocities ranging from 50-400
$\mathrm{km}\,\mathrm{s}^{-1}$ relative to a parent with a virial velocity of
220 $\mathrm{km}\,\mathrm{s}^{-1}$, so we could consider the case of a TDG
travel speed of 400 $\mathrm{km}\,\mathrm{s}^{-1}$ and the minimum travel
distance of 445 kpc (using the Haynes et al. 2018 distance of UGC 6989) to
estimate a minimum travel time of 1.09 Gyr between UGC 6989 and the current
location of AGC 229398. This would be an extreme case, so it is likely that
AGC 229398 would be older than this; the travel times estimated in Table 7 are
at least 3.2 Gyr. The $g-r$ color of AGC 229398 is 0.35, making it the reddest
TDG candidate in our sample; this is consistent with it also being the oldest.
UGC 6989’s undisturbed spiral structure suggests that it is unlikely to have
undergone a recent major merger, but a high velocity fly-by could have pulled
off gas without disrupting the interior disk. There is no obvious interloper
candidate in the images, but UGC 6989 was already at the limits of the
selection criteria; whatever speed AGC 229398 is traveling at relative to UGC
6989, the interloper would only need to go a little more than twice that speed
to end up outside of the angular separation selection criteria and be
overlooked. Duc & Bournaud (2008) notes that in 2 Gyr, an interloper traveling
at 1000 $\mathrm{km}\,\mathrm{s}^{-1}$ relative to the parent galaxy could be
a projected distance of 2 Mpc away — at the distance of AGC 229398, this is
over 1 degree of separation, outside the field of view of the pODI images.

AGC 333576 seems to have a more obvious progenitor: the nearby spiral galaxy
NGC 7775. The HI gas surrounding NGC 7775 is distorted in the direction of AGC
333576, and the distorted stellar arms and bright region of star formation in
the southwest imply a recent interaction of some kind. A major merger would
likely have disrupted the structure of the arms even further, but a fly-by
interaction might not have, so we searched the field surrounding AGC 333576
and found the elliptical galaxy WISEA J235250.49+284555.2. As an elliptical
galaxy, WISEA J235250.49+284555.2 would not have possessed very much gas and
so would not have been the main contributor to a tidal dwarf, but it might
have flown by NGC 7775 and pulled out the material from that disk, producing
AGC 333576. The proximity of these galaxies implies that the interaction would
not have happened a very long time ago, with travel time estimates for AGC
333576 from NGC 7775 between 0.7 and 1.2 Gyr; this is enough time for the
majority of the gaseous tidal tail to have disappeared, but the end of a
stellar tail connected to NGC 7775 is still slightly visible on the north side
(Fig. 18, left). Depending on the parameters of the interaction, the
countertail may have been very short, which could explain why there is no
strong evidence of one; the star formation region is located roughly opposite
the stellar tail and might have been triggered by the same tidal forces.

##  6 Summary

We have investigated the HI and optical properties and possible origins of
four Almost-Dark galaxies selected from the ALFALFA survey. After exploring HI
kinematics and analyzing deep optical images, we concluded that AGC 229398 and
AGC 333576 are the likeliest candidates to be TDGs based on their apparent low
dark matter content and large effective radii compared to other dwarf
irregular and elliptical galaxies of similar stellar masses. AGC 123216 is
ambiguous — it is near other galaxies with large HI reservoirs that have
clearly had an interaction of some kind, and it has a large effective radius.
Its central surface brightness is also low compared to dwarf irregular
galaxies of similar stellar mass. However, the upper limit on the dark matter
content is too high to positively confirm it as a TDG, and it has an unusually
high HI-to-stellar mass ratio for a TDG that should have formed stars when it
was created. AGC 123216 also meets the criteria outlined in van Dokkum et al.
(2015) for a UDG. AGC 219369 is most likely to be a low surface brightness
dwarf irregular galaxy. While AGC 219369 appears in the sky near the spiral
galaxy NGC 3510 (which has undergone some kind of interaction that disrupted
its HI and stellar distributions), it appears to be dominated by dark matter
and therefore is unlikely to have formed via the same tidal processes that
create TDGs. All four of the objects would benefit from higher resolution HI
observations to better constrain their kinematics and dynamical masses.

In this study, we distinguished TDG candidates from irregular dwarf galaxies
based on their low dark matter content and larger than expected effective
radius for their stellar content. These candidate TDGs are located farther
from any potential parents than the vast majority of previously studied TDGs,
and the tidal tail from which they would have formed is nowhere to be found.
While nearby surrounding galaxies often have disrupted HI distributions, none
show clear signs of a recent merger that would be the expected source for a
TDG. This suggests that either enough time has passed for the parent galaxy to
mostly restabilize, or that the interaction was one that did not cause obvious
disruption to the stellar disk. The overall picture provided by the HI and
optical measurements of these objects suggests that they are older and more
evolved than most of the TDGs that have previously been identified. Blind HI
surveys with wide-field coverage like ALFALFA provide an opportunity to detect
TDGs that have moved away from their parents and become optically fainter over
their evolution, and which may be missed in more traditional optical surveys
that prioritize stellar emission. Such surveys provide us with a more complete
picture of galaxy formation and evolution at the low-mass end of the HI mass
function.

The authors acknowledge the ALFALFA collaboration’s work in observing,
processing, and extracting sources. The authors would also like to thank the
anonymous referee for their thorough comments, which greatly improved the
quality of the manuscript. LMG acknowledges support from the Indiana Space
Grant Consortium and thanks Laura Hunter for her explanations about the
nuances of radio astronomy. This work was supported in part by NSF grant
AST-1615483 to KLR. L.L. acknowledges support from NSF grant AST-2045369. MPH
acknowledges support from NSF/AST-1714828 and grants from the Brinson
Foundation. EAKA is supported by the WISE research programme, which is
financed by the Dutch Research Council (NWO). JMC and JF are supported by NSF
grant AST-2009894. We thank the Indiana University (IU) College of Arts and
Sciences for funding IU’s share of the WIYN telescope. We thank the staff of
the WIYN Observatory and Kitt Peak National Observatory for their help and
support during our WIYN pODI observing runs. We are grateful to the staff
members at WIYN, NOIRLab, and Indiana University Pervasive Technology
Institute for designing and implementing the ODI-PPA and assisting us with the
pODI data reduction. We owe special thanks to Wilson Liu for helping us to
troubleshoot and optimize the ODI image stacking process. Funding for SDSS-III
and SDSS-IV has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. SDSS acknowledges support and
resources from the Center for High-Performance Computing at the University of
Utah. The SDSS web site is www.sdss.org.

##  Appendix A HI Channel Maps

Here we present the WSRT HI emission-line channel maps and the corresponding
best-fitting kinematic models for AGC 123216 (Figure 23), AGC 219369 (Figure
24), AGC 229398 (Figure 25), and AGC 333576 (Figure 26). AGC 123216 and AGC
333576 show the clearest signs of rotation and have models that most closely
resemble the data, followed by AGC 219369. The data for AGC 229398 do not
demonstrate a clear rotation gradient, and the model is a poor fit for the
data, which indicates it may be more pressure supported than rotation
supported.

Figure 23: HI emission-line channel maps for AGC 123216 from WSRT data. The
white cross marks the center of the galaxy and the velocity for each channel
map is listed in the lower left corner. The emission of the galaxy is
displayed by gray background and blue contour lines. The best-fitting model is
shown by the red contour lines. Solid contours are at 2, 4, and 8 times the
S/N of the data, and dashed contours represent -2 $\times$ S/N. Figure 24: HI
emission-line channel maps for AGC 219369 from WSRT data. The white cross
marks the center of the galaxy and the velocity for each channel map is listed
in the lower left corner. The emission of the galaxy is displayed by gray
background and blue contour lines. The best-fitting model is shown by the red
contour lines. Solid contours are at 2, 4, and 8 times the S/N of the data,
and dashed contours represent -2 $\times$ S/N. Figure 25: HI emission-line
channel maps for AGC 229398 from WSRT data. The white cross marks the center
of the galaxy and the velocity for each channel map is listed in the lower
left corner. The emission of the galaxy is displayed by gray background and
blue contour lines. The best-fitting model is shown by the red contour lines.
Solid contours are at 2, 4, and 8 times the S/N of the data, and dashed
contours represent -2 $\times$ S/N. Figure 26: HI emission-line channel maps
for AGC 333576 from WSRT data. The white cross marks the center of the galaxy
and the velocity for each channel map is listed in the lower left corner. The
emission of the galaxy is displayed by gray background and blue contour lines.
The best-fitting model is shown by the red contour lines. Solid contours are
at 2, 4, and 8 times the S/N of the data, and dashed contours represent -2
$\times$ S/N.

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