# Star Clusters in Tidal Debris

Michael Rodruck,1,2 Jane Charlton,1 Sanchayeeta Borthakur,3 Aparna Chitre,4
Patrick R. Durrell,5 Debra Elmegreen,6 Jayanne English,7 Sarah C. Gallagher,8
Caryl Gronwall,1,9Karen Knierman,3 Iraklis Konstantopoulos,10 Yuexing Li,1
Moupiya Maji,11 Brendan Mullan,12Gelys Trancho13 and William Vacca14
1Department of Astronomy and Astrophysics, The Pennsylvania State University,
University Park, PA 16802, USA
2Department of Physics, Engineering, and Astrophysics, Randolph-Macon College,
Ashland, VA 23005, USA
3School of Earth and Space Exploration, Arizona State University, 550 E. Tyler
Mall, Room PSF-686 (PO Box 871404), Tempe, AZ
85287-1404, USA
4Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA
5Department of Physics, Astronomy, Geology and Environmental Sciences,
Youngstown State University, Youngstown, OH 44555, USA
6Department of Physics and Astronomy, Vassar College, Poughkeepsie, NY 12604,
USA
7Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T
2N2, Canada
8Department of Physics and Astronomy and Institute for Earth and Space
Exploration, University of Western Ontario,
London, ON N6A 3K7, Canada
9Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA
10Independent scholar, Wellington, New Zealand
11Inter-University Centre for Astronomy and Astrophysics (IUCAA), Post Bag 4,
Ganeshkhind, Pune 411 007, India
12Department of Natural Sciences and Engineering Technology , Point Park
University 201 Wood St, Pittsburgh, PA 15222, USA
13Thirty Meter Telescope International Observatory, 100 W Walnut St, #300,
Pasadena, CA 91124, USA
14SOFIA-USRA, NASA Ames Research Center, MS N232-12, Moffett Field, CA
94035-1000, USA E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present results of a Hubble Space Telescope (HST) UBVI-band study of star
clusters in tidal tails, using new WFC3 and ACS imaging to complement existing
WFPC2 data. We survey 12 tidal tails across seven merging systems, deriving
ages and masses for 425 star cluster candidates (SCCs). The stacked mass
distribution across all systems follows a power law of the form $dN/dM\propto
M^{\beta}$, with $\beta=-2.02\pm 0.15$, consistent with what is seen in other
star forming environments. GALEX and Swift UV imaging provide star formation
rates (SFRs) for our tidal tails, which when compared with ages and masses of
our SCCs, allows for a determination of the cluster formation efficiency
(CFE). We find the CFE increases with increasing SFR surface density, matching
the theoretical model. We confirm this fit down at SFR densities lower than
previously measured (log
$\Sigma_{\text{SFR}}\>(\text{M}_{\odot}\>\text{yr}^{-1}\>\text{kpc}^{-2})\approx-4.2$),
as related to the CFE. We determine the half-light radii for a refined sample
of 57 SCCs with our HST WFC3 and ACS imaging, and calculate their dynamical
age, finding the majority of them to be gravitationally bound. We also provide
evidence of only low-mass ($<10^{4}$ M⊙) cluster formation in our nearest
galaxy, NGC 1487, consistent with the theory that this system is a dwarf
merger.

###### keywords:

galaxies: interactions – galaxies: star formation – galaxies: star clusters:
general

††pubyear: 2021††pagerange: Star Clusters in Tidal Debris–A.7

##  1 Introduction

The gravitational origin of tidal tails was first realized with the pivotal
work by Toomre & Toomre (1972), who showed that galactic tidal tails and
warped disks could be simulated as gravitational encounters with another
galaxy. In a very forward thinking section of their work, they suggested that
galaxy mergers may be able to produce large amounts of star formation. This
prediction was later borne out with the discovery of luminous infrared
galaxies (LIRGs), made possible with the launch of the IR telescope IRAS. IRAS
found that many galaxies with high ($>10^{11}L_{\odot}$) IR luminosites have
disturbed morphologies, indicative of past merging events (Sanders et al.,
1988). The IR emission of these LIRGs suggested star formation rates (SFRs) on
the order of 100 M⊙/ yr (Schweizer, 1987).

Galaxy mergers can produce collisions between clouds of gas, which can provoke
star formation. The high pressures generated in these collisions will lead to
enhanced star formation efficiency (Jog & Solomon, 1992) and the formation of
massive star clusters (Zubovas et al., 2014; Maji et al., 2017). Additionally,
cloud collisions may provide external pressure to young clusters, keeping
their contents gravitationally bound, preventing their destruction (Elmegreen,
2008). The advent of high-resolution imaging, possible with HST, has found
evidence of such massive clusters within the interiors of merging galaxies in
the form of bright, blue, compact objects (e.g. Zepf et al., 1999; Whitmore &
Schweizer, 1995; Whitmore et al., 1993). These objects, labeled as young
massive clusters (YMCs), show properties similar to what is expected for young
globular clusters, such as mass and radius. Therefore, by studying YMCs, we
may be able to study the formation of today’s globular clusters.

While the interiors of mergers have been well-studied in the past, few surveys
have looked at the tidal debris associated with mergers. However, simulations
are now showing that star formation can occur in the extended regions of a
merger. Simulations with explicit stellar feedback indicate that $\sim
20-50\%$ of a merger’s SFR can occur in extended debris (Hopkins et al.,
2013). Observations of the Tadpole galaxy confirm this prediction, as $\sim
30\%$ of the system’s star formation is occurring in tidal tail star clusters
(Jarrett et al., 2006). Tidal tails also offer a relatively clean and
uncluttered environment as compared to the interiors of galaxies. Their sparse
environments mean clusters will not be subject to shocks and tides found in
the dense nuclear region, and may avoid disruption, surviving to the present
day (Renaud, 2018).

Despite the differences in location and interaction, several common properties
seem to exist between studies of YMCs found in merging and quiescent galaxies.
The slopes of the mass and luminosity functions has been measured to be
between $-1.8$ and $-2.2$ for both types of galaxies. The cluster formation
efficiency, a measure of the percentage of the SFR occurring within star
clusters, tracks the local SFR density in both environments. Additionally,
cluster radii are similar, with half-light radii of $\sim 0.5-10$ pc
(Portegies Zwart et al., 2010). Such similarities suggests common physics
behind star cluster formation.

This paper builds on previous work by Mullan et al. (2011) and Knierman et al.
(2003), who studied clusters in tidal tails using the WFPC2 camera on HST.
Both works found statistically significant populations of clusters in a
variety of tails, with colours suggesting masses comparable to the YMCs found
in the interiors of mergers. Merging systems with young interaction ages and
bright tails produced the most star clusters. However, analysis was limited by
the lack of multiband photometry. Our new observations of 12 tails in seven
interacting systems add F336W and F438W WFC3 and F435W ACS imaging to existing
WFPC2 F606W and F814W observations, to allow for age and mass determination.

We will begin in Section 2 by describing our imaging datasets and our analysis
methods. In Section 3 we show our results. In Section 4 we discuss our
findings, and conclude our chapter with the main points of our research in
Section 5. We add notes for individual tails in Section A.

##  2 Data Analysis

Our analysis consists of two parts: HST imaging to identify tidal tail star
clusters and determine their ages and masses, and UV imaging with GALEX and
Swift to derive the local star formation rates. Both efforts are described
below.

###  2.1 HST

Our optical and near-IR observations consist of WFPC2, ACS, and WFC3 imaging
from HST across multiple cycles; the full sample is shown in Figure 1.
Properties of our sample are highlighted in Table 1, with systems ordered
according to their interaction age. We sample not only major disk mergers, but
minor and dwarf mergers as well.

Table 1: System information. Interaction age gives the most recent interaction, which produced the visible tidal features. System | Interaction Age | Distance | Merger Type | Tidal Features | Tidal Features $\mu_{V}$
---|---|---|---|---|---
| (Myr) | (Mpc) |  |  | (mag arcsec-1)
NGC 1614N/S | 50 | 65.6 | Major | Tidal tails | 22.27/23.00
AM1054-325/ESO 376-28 | 85 | 52.9 | Major | Tidal tails and tidal dwarf | 22.65/22.76
NGC 2992/3 | 100 | 36.6 | Major | Tidal tails and tidal bridge | 23.47/24.78
MCG-03-13-063 | 100 | 46.2 | Minor | Extended spiral arm | 23.91
NGC 6872 | 150 | 62.6 | Minor | Tidal tails | 24.06
NGC 3256E/W | 400 | 42.8 | Major | Tidal tails | 24.04/23.75
NGC 1487E/W | 500 | 10.8 | Dwarf | Tidal tails | 24.02/24.57

WFPC2 F555W and F814W data were taken in Cycle 7 (GO 7466) Knierman et al.
(2003) for NGC 3256. The remaining samples of AM1054-325, MCG-03-068-13, NGC
1487, NGC 2992, NGC 2993, NGC 6872, and NGC 1614 were observed with WFPC2 in
Cycle 16 (GO 11134), in F606W and F814W Mullan et al. (2011). Galaxies from
Mullan et al. (2011) represent an extension of the original sample in Knierman
et al. (2003), designed to sample a variety of ages, mass ratios, and optical
properties. Our survey adds WFC3 F336W and WFC3 F438W/ACS F435W imaging to
galaxies lying in the Southern hemisphere, which have also been observed with
the Gemini-South GMOS detector, and will be the subject of a forthcoming paper
on the diffuse light in the tidal debris. Archival ACS F438W and WFC3 F336W
data for NGC 1614N/S are used from Cycle 14 (GO 10592) and Cycle 23 (GO
14066). A full description of our HST observations is in Table 2. We refer to
our F606W, F814W, F336W, F438W, and F435W observations as V${}_{\text{606}}$,
I${}_{\text{814}}$, U${}_{\text{336}}$, B${}_{\text{438}}$, and
B${}_{\text{435}}$, respectively.

Figure 1: Snapshots of our sample from the Digitized Sky Survey (DSS). Red
outlines indicate WFPC2 pointings from Mullan et al. (2011) and Knierman et
al. (2003). Blue and cyan squares show the WFC3 and ACS footprints,
respectively.

WFPC2 data were reduced in IRAF and corrected for degraded charge transfer
effects (CTE) using Dolphin (2000). We refer the reader to the respective
papers (Mullan et al., 2011; Knierman et al., 2003) for a more in depth
discussion on WFPC2 data reduction. WFPC2 magnitudes were taken from Mullan et
al. (2011) and Knierman et al. (2003). Objects in Knierman et al. (2003) were
transformed from the WFPC2 Vegamag photometric system to the Johnson-Cousins
system using transformations found in Holtzman et al. (1995), going from F555W
and F814W to V and I. Rather than converting back to WFPC2 magnitudes, we keep
them in their transformed system. Data from Mullan et al. (2011) were provided
in WFPC2 Vegamag magnitudes (V${}_{\text{606}}$ and I${}_{\text{814}}$).

ACS and WFC3 images were downloaded from the HST archive, which have been
processed through the standard ACS and WFC3 pipelines. ACS images have a scale
of 0.05” per pixel, while WFC3 observations have a scale of 0.04” per pixel.
This is compared to the WFPC2 WF scale of 0.1” per pixel; objects on the WFPC2
PC were not analyzed due to its larger readnoise.

We perform aperture photometry on all our objects using the DAOPHOT.PHOT
(Stetson, 1987) task in IRAF. We choose to match the aperture settings in
Mullan et al. (2011), which uses radii of 2, 5, and 8 pixels for object, inner
background, and outer background annuli, respectively. When translated to the
WFC3 scale, this results in radii of 5, 12.5, and 20 pixels. For ACS, we use
radii of 4, 10, and 16 pixels. In this manner, we are assured that we are
measuring our clusters to the same physical extent, camera to camera. Aperture
corrections to bright, isolated stars were performed out to a radius of 10
pixels for WFC3 and ACS imaging. Due to the lack of adequate stars in the NGC
1487 field, we take the average aperture corrections from all other fields and
apply them to NGC 1487W and NGC 1487E. 10 pixel zeropoints of 23.392, 24.895,
and 25.762 were used for U${}_{\text{336}}$, B${}_{\text{438}}$, and
B${}_{\text{435}}$, respectively.

Table 2: HST observations.

System | Filter | Exposure time (s) | Date | Program ID | Camera
---|---|---|---|---|---
NGC 1614N/S | F336W | 6510 | 2015 Dec 12 | 14066 | WFC3
| F438W | 1260 | 2006 Aug 14 | 10592 | ACS
| F606W | 1900 | 2007 Nov 15 | 11134 | WFPC2
| F814W | 1900 | 2007 Nov 15 | 11134 | WFPC2
AM 1054-325/ESO 376-28 | F336W | 3440 | 2017 Nov 6 | 14937 | WFC3
| F435W | 1520 | 2017 Nov 7 | 14937 | WFC3
| F606W | 1900 | 2008 Feb 24 | 11134 | WFPC2
| F814W | 1900 | 2008 Feb 24 | 11134 | WFPC2
NGC 2992 | F336W | 2230 | 2018 Nov 27 | 15083 | WFC3
| F438W | 2100 | 2018 Apr 19 | 15083 | ACS
| F606W | 1000 | 2007 Dec 28 | 11134 | WFPC2
| F814W | 900 | 2007 Dec 28 | 11134 | WFPC2
NGC 2993 | F336W | 2230 | 2018 Apr 19 | 15083 | WFC3
| F438W | 2100 | 2018 Nov 27 | 15083 | ACS
| F606W | 1000 | 2007 Dec 3 | 11134 | WFPC2
| F814W | 900 | 2007 Dec 3 | 11134 | WFPC2
MCG-03-13-063 | F336W | 3420 | 2017 Sep 27 | 14937 | WFC3
| F435W | 1520 | 2017 Sep 28 | 14937 | WFC3
| F606W | 1000 | 2007 Nov 24 | 11134 | WFPC2
| F814W | 900 | 2007 Nov 24 | 11134 | WFPC2
NGC 6872a | F336W | 3920 | 2018 Jul 24 | 15083 | WFC3
| F435W | 1760 | 2018 Jul 24 | 15083 | WFC3
| F606W | 2100/1900 | 2008 Feb 23/2008 May 16 | 11134 | WFPC2
| F814W | 2100/1900 | 2008 Feb 23/2008 May 16 | 11134 | WFPC2
NGC 3256E | F336W | 3520 | 2018 Jun 15 | 15083 | WFC3
| F435W | 1600 | 2018 Jun 15 | 15083 | WFC3
| F555W | 1000 | 1999 Oct 11 | 7466 | WFPC2
| F814W | 1000 | 1999 Oct 11 | 7466 | WFPC2
NGC 3256W | F336W | 3520 | 2018 Jan 15 | 15083 | WFC3
| F435W | 1600 | 2018 Jan 15 | 15083 | WFC3
| F555W | 1000 | 1999 Mar 24 | 7466 | WFPC2
| F814W | 1000 | 1999 Mar 24 | 7466 | WFPC2
NGC 1487E | F336W | 3520 | 2017 Nov 25 | 15083 | WFC3
| F435W | 1600 | 2017 Nov 25 | 15083 | WFC3
| F606W | 1000 | 2008 Aug 9 | 11134 | WFPC2
| F814W | 900 | 2008 Aug 9 | 11134 | WFPC2
NGC 1487W | F336W | 3520 | 2019 Mar 24 | 15083 | WFC3
| F435W | 1600 | 2019 Mar 24 | 15083 | WFC3
| F606W | 1000 | 2008 Aug 31 | 11134 | WFPC2
| F814W | 900 | 2008 Aug 31 | 11134 | WFPC2

aNGC 6872 was measured in two pointings with WFPC2.

###  2.2 GALEX

The Galaxy Evolution Explorer (GALEX) operated from 2003 to 2012 as an
orbiting UV telescope. Its 50 cm diameter mirror imaged a 1.25∘ FOV with two
separate microchannel-plate detectors, designated as the near-ultraviolet
(NUV) and far-ultraviolet (FUV) channels. The telescope has a pixel scale of
1.5” per pixel. GALEX conducted several surveys, including the All-Sky Imaging
survey (AIS), Medium Imaging Survey (MIS), Deep Imaging Survey (DIS), and
Nearby Galaxy Survey (NGS), to varying depths. Our targets are drawn from AIS
(AM1054-325, ESO 376-28, MGC-03-13-063, NGC 1487E/W) and NGS (NGC 6872, NGC
2992, NGC 2993). Our GALEX observations are listed in Table 3, along with our
Swift observations (described below).

We use images taken in the FUV ($\lambda_{\text{eff}}=1538.6\AA$) obtained
from the MAST archive. These have been pipeline processed. While background
subtracted images are available via MAST, we do not use these because the
background subtraction can be inaccurate for extended objects. Photometry was
performed on the entire flux enclosed within the tail boundary, as described
in Section 2.4. The sky background was determined by sampling five nearby
regions of 30 x 30 pixels and taking the mean value. For NGC 2992, a bright,
blue star visible in the FUV image was manually masked.

We corrected for Galactic extinction using coefficients from Yuan et al.
(2013) for GALEX FUV.

Table 3: GALEX and Swift observations. System | Observatory | Filter | Exposure time (s) | Observation ID | Observation date
---|---|---|---|---|---
NGC 1614N/S | Swift | UVM2 | 3271.5 | 00046270001; 00046270002 | 2012 May 10; 2012 Jul 6
AM1054-325/ESO 376-28 | GALEX | FUV | 108 | 6386924688810967040 | 2007 Feb 3
NGC 2992/3 | GALEX | FUV | 1045.5 | 2485918962089459712 | 2005 Feb 12
MCG-03-13-063 | GALEX | FUV | 204 | 6381260060739239936 | 2006 Jan 8
NGC 6872 | GALEX | FUV | 3371.3 | 2505622210593423360 | 2006 Jun 29
NGC 3256E/W | Swift | UVM2 | 1867.2 | 00049720003; 00049720012 | 2013 Sep 15; 2014 Sep 18
NGC 1487E/W | GALEX | FUV | 108 | 6385833989382340608 | 2007 Jan 5

###  2.3 Swift

NGC 3256 and NGC 1614 do not have FUV exposures with GALEX; instead, we have
opted to use NUV data from Swift, downloaded from the MAST archive. The Swift
satellite operates the 30 cm UltraViolet-Optical Telescope (UVOT), with a FOV
of 17 x 17 arcmin. Images were taken in 2 $\times$ 2 binned mode, with a pixel
scale of 1” per pixel. The UVOT CCD operates as a photon counter, which is
susceptible to coincidence loss if two or more photons arrive within a single
frame. The effect of this scales with brightness, and past analysis has shown
that coincidence loss becomes greater than 1% when the count rate is greater
than 0.007 counts sec-1 pixel-1; for 2 x 2 binned images, as we use, the count
rate threshold is then 0.028 counts sec-1 pixel-1. The faint tails of these
two systems, NGC 3256 and NGC 1614, fall well below this threshold, and we can
discount effects from coincidence loss.

Swift offers three UV filters, uvw1, uvw2, and uvm2. We use the uvm2 filter
($\lambda_{\text{eff}}=2221\AA$) as the other two filters have extended red
tails which leak optical light into the UV. Images were co-added together
using the HEASOFT software package.

Photometry was performed using the previously mentioned procedure for GALEX
imaging. Extinction coefficients were taken from Roming et al. (2009) for the
uvm2 filter.

###  2.4 Tail definition

Regions defined as tidal debris are taken from Mullan et al. (2011). The “in-
tail” and “out-of-tail” regions were defined using images taken with the WFPC2
V${}_{\text{606}}$ filter. Images were smoothed with a Gaussian kernel at 5 -
7 pixels FWHM, and a contiguous region one count above background was defined
as “in-tail”, using SAO DS9; all other regions were defined as “out-of-tail”.
In the cases of NGC 1487W, AM1054-325, ESO 376-28, and NGC 6872, the centre of
the galaxy is imaged as well. The boundary between the centre and the tail is
found where the radial light profile changes in scale length.

###  2.5 Cluster Detection

Objects were detected using the DAOPHOT.DAOFIND (Stetson, 1987) task in IRAF.
Selection criteria for the initial WFPC2 cluster list required 2 counts per
object in both V${}_{\text{606}}$ and I${}_{\text{814}}$, a signal-to-noise
(S/N) ratio of at least 3, error in F606W less than 0.25 mag, and detections
in at least one dither position. For our ACS/WFC3 imaging, we require an S/N
of at least 3 in both U${}_{\text{336}}$ and
B${}_{\text{438}}$/B${}_{\text{435}}$. Objects had to be detected in all four
filters. We further excluded objects which were fit to our simple stellar
population cluster models (Marigo et al., 2008) with a $\chi^{2}>3$.

Magnitude and colour cuts were applied to our source catalogue to separate
potential clusters from contaminant stars and background galaxies. Objects
which met these requirements are defined as Star Cluster Candidates (SCCs). We
apply a magnitude cut of $M_{V}<-8.5$ ($M_{F606W}<-8.6$) designed to eliminate
individual stars. Magnitude cuts between $-8<M_{V}<-9$ are commonly used in
studies of star clusters (Konstantopoulos et al., 2010). Whitmore et al.
(2010) found that even at fainter magnitudes, down to $M_{V}=-7$, more than
60% of detected objects were clusters as opposed to individual stars, adding
confidence to our selection criteria. In addition to discriminating against
non-clusters, a magnitude cut allows a uniform measurement standard across our
systems, most of which have nearly complete samples of SCCs down to the MV =
-8.5 cutoff, as shown in Section 2.6. A colour cut of $V-I<2.0$
(V${}_{\text{606}}$ \- I${}_{\text{814}}$ < 1.4) is added as well; this will
still allow for old globular clusters which have reddened as they evolve,
while eliminating individual stars.

###  2.6 Completeness

Completeness curves from Mullan et al. (2011) show that our WFPC2 data are on
average 50% complete at $m_{\text{V${}_{\text{606}}$}}\approx 25.5$ and
$m_{\text{I${}_{\text{814}}$}}\approx 24.5$. To measure the completeness of
our WFC3 and ACS imaging, we perform a similiar analysis as in Mullan et al.
(2011); we add 10,000 fake stars to each individual image, 100 at a time, with
DAOPHOT.ADDSTAR (Stetson, 1987), and calculate how many are recovered above a
3$\sigma$ limit. Our completeness curves are shown in Figure 2. For systems
AM1054-325, ESO 376-28, NGC 3256, NGC 1487, MCG-03-13-063, and NGC 6872, we
are complete at 50% at $m_{\text{B${}_{\text{438}}$}}=25.5$ and
$m_{\text{U${}_{\text{336}}$}}=24.8$. NGC 2992 and NGC 2993 are 50% complete
at $m_{\text{B${}_{\text{435}}$}}=26.5$ and
$m_{\text{U${}_{\text{336}}$}}=24.5$. NGC 1614, observed with program GO-14066
and GO-10592 is complete at $m_{\text{B${}_{\text{435}}$}}=26.5$ and
$m_{\text{U${}_{\text{336}}$}}=25.4$.

Figure 2: Completeness data for our WFC3 F336W/F435W and ACS F438W imaging.
Solid curves represent data for F438W, dotted curves represent data for F336W,
and dashed curves represent data for F435W.

##  3 Results

###  3.1 Colour-colour diagrams

In Figures 3-14 we show the U${}_{\text{336}}$ \- B${}_{\text{438}}$ vs
V${}_{\text{606}}$ \- I${}_{\text{814}}$ colour-colour diagrams for all our
observed systems. Systems are ordered in reference to the age of the tidal
debris (see Table 1). The interaction age of the merger is plotted as a yellow
circle. Objects which fulfill our SCC criteria in Section 2.5 are shown as
dark blue circles. For completeness, we show objects which do not meet our
criteria as gray boxes, with arrows indicating upper and lower limits.

Data are plotted against simple stellar population (SSP) models from Marigo et
al. (2008), with logarithmic ages overplotted on the evolutionary track. We
use a Salpeter IMF; however, the choice of IMF is negligible in determining
ages, and the tracks are also consistent expectations for a Chabrier
(Chabrier, 2001) or Kroupa (Kroupa, 2001) IMF. We corrected for foreground
Galactic extinction using an $R_{\lambda}=A_{\lambda}/E(B-V)$ reddening law,
with $R_{V}=3.1$, with data from Schlafly & Finkbeiner (2011). Internal
cluster extinction is not corrected for when plotting our colour-colour
diagrams. However, this is taken into account when SED fitting our clusters
(Section 3.3). We also include a reddening arrow in the lower right hand
corner of our plots for AV = 0.5.

Figure 3: Top left: HST B${}_{\text{435}}$-band image of NGC 1614N, with the
tail region outlined with a black, dashed curve. In-tail SCCs are shown as
blue circles, while out-of-tail SCCs are red circles. Non-SCC detected objects
are shown as crosses. Top middle: Colour-colour diagrams for in-tail and out-
of-tail sources plotted against stellar evolutionary tracks from Marigo et al.
(2008) in solid black; the dashed light blue line is the same track with
nebular continuum and emission lines added. The yellow circle indicates the
age of the merger. Blue/red circles represent SCCs for in-tail/out-of-tail
sources, and gray boxes are non-SCC detected objects. The total area enclosed
in each in-tail or out-of-tail region in kpc2 is indicated on the upper left,
along with median error bars. Top right: Ages and masses for detected objects.
SCCs are shown in blue, non-SCCs in gray. The solid black curve is our
magnitude limit of MV = -8.5, while the red, green, purple, and cyan curves
show 50% completeness limits. The vertical yellow line marks the interaction
age of the system, and the horizontal dashed line marks our mass cut-off of
log Mass = 4.3 for our CFE determinations. Bottom row: age and mass
distributions for our SCCs. A vertical dashed line marks the median distance
from the centre. We find 21 in-tail SCCs, and 11 out-of-tail SCCs for NGC
1614N. The tail curls to the North from the East, with young clusters
scattered throughout the region. Figure 4: Same as 3, but for NGC 1614S. We
find 33 in-tail SCCs, and 11 out-of-tail SCCs. This system has a statistically
significant excess cluster density above $3\sigma$. The tail extends to the
south from the center of the merging system. Young objects are found
throughout the tail, similar to NGC 1614N. Figure 5: Same as 3, but for
AM1054-325. We find 135 in-tail SCCs, and 23 out-of-tail SCCs. This system has
a statistically significant excess cluster density above $3\sigma$. A tidal
dwarf is directly North of the center of the galaxy, while the tidal tail
extends Northward from the Western edge. Many SCCs show signs of emission
lines, indicated by their large B – V values. Its interacting partner can be
seen at the top right of the image. Figure 6: Same as 3, but for ESO 376-28.
We find 1 in-tail SCC, and 23 out-of-tail SCCs. Little structure is seen in
this galaxy. Figure 7: Same as 3, but for NGC 2992. We find 22 in-tail SCCs,
and 4 out-of-tail SCCs. This system has a statistically significant excess
cluster density above $3\sigma$. We have targeted the tidal dwarf, with the
Northern edge of the galaxy NGC 2992 shown on the left. We do not include
sources from the galaxy itself. Figure 8: Same as 3, but for NGC 2993. We find
9 in-tail SCCs, and 0 out-of-tail SCCs. We capture the tidal tail of NGC 2993
(seen at the top of the image). Most of the SCCs in the tail have ages
comparable to the interaction age of the NGC 2992/3 system. Figure 9: Same as
3, but for MCG-03-13-063. We find 10 in-tail SCCs, and 9 out-of-tail SCCs.
This system has a statistically significant excess cluster density above
$3\sigma$. An extended, thin tail is seen, produced from an unseen companion.
All the SCCs in the tail are < 10 Myr. Figure 10: Same as 3, but for NGC 6872.
We find 158 in-tail SCCs, and 19 out-of-tail SCCs. This system has a
statistically significant excess cluster density above $3\sigma$. This is
Eastern tidal tail of NGC 6872, which stretches out to 70 kpc; the center of
the galaxy lies to the West. A range of ages are seen, with young SCCs spread
out along the length of the tail. Figure 11: Same as 3, but for NGC 3256E. We
find 11 in-tail SCCs, and 5 out-of-tail SCCs. Emission line clusters do not
clearly stand out, as the NGC 3256 system was imaged with the F555W filter,
which weakly covers the H$\alpha$ line. Despite the old age of the
interaction, we see a few SCCs with young ages. Figure 12: Same as 3, but for
NGC 3256W. We find 24 in-tail SCCs, and 9 out-of-tail SCCs. This system has a
statistically significant excess cluster density above $3\sigma$. Many of the
SCCs are clustered around the interaction age of the merger, suggesting they
formed from the interaction. Figure 13: Same as 3, but for NGC 1487E. We find
0 in-tail SCCs, and 0 out-of-tail SCCs. Note that as NGC 1487E has no detected
SCCs, age and mass distribution figures are not included. Although no SCCs are
found in this system, a large number of non-SCC objects are detected, which do
not make the $M_{V}<-8.6$ cutoff. This suggests the presence of low-
luminosity, low-mass objects. Figure 14: Same as 3, but for NGC 1487W. We find
1 in-tail SCC, and 0 out-of-tail SCCs. Like NGC 1487E, we again find a number
of non-SCC objects in the tail, suggesting low-mass objects present in the
tail.

The area inside and outside the tail was calculated using SAO DS9 regions of
the tail, as defined in Section 2.4. We subtract the cluster density outside
the tail ($N^{\textrm{SCC}}_{\textrm{out}}/A_{\textrm{out}}$) from inside the
tail ($N^{\textrm{SCC}}_{\textrm{in}}/A_{\textrm{in}}$) to determine the
excess cluster density, $\Sigma_{\textrm{SCC}}$. Errors are determined from
Poisson statistics. Half of our tails show excesses above the $3\sigma$ level,
indicating significant amounts of SCCs. It is important to note that while
some systems may not contain significant numbers of SCCs, some individual
objects in tails may still be real star clusters. The data are shown in Table
4.

Table 4: Cluster excesses.

System | $N^{\text{SCC}}_{\text{in}}$ | $N^{\text{SCC}}_{\text{out}}$ | A${}_{\text{in}}$ | A${}_{\text{out}}$ | Density${}_{\text{in}}$ | Density${}_{\text{out}}$ | $\Sigma_{SCC}$
---|---|---|---|---|---|---|---
|  |  | (kpc2) | (kpc2) | (kpc-2) | (kpc-2) | (kpc-2)
NGC 1614N | 21 | 11 | 304.6 | 483.6 | 0.069 | 0.023 | $0.046\pm 0.017$
NGC 1614S | 33 | 11 | 327.8 | 483.6 | 0.101 | 0.023 | $0.078\pm 0.019^{*}$
AM1054-325 | 135 | 23 | 129.5 | 869.5 | 1.042 | 0.026 | $1.016\pm 0.090^{*}$
ESO 376-28 | 1 | 23 | 88.9 | 869.5 | 0.011 | 0.026 | $-0.015\pm 0.013$
NGC 2992 | 22 | 4 | 242.4 | 193.9 | 0.091 | 0.021 | $0.070\pm 0.022^{*}$
NGC 2993 | 9 | 0 | 179.1 | 90.0 | 0.050 | 0 | $0.050\pm 0.017$
MCG-03-13-063 | 10 | 9 | 12.8 | 400.0 | 0.781 | 0.023 | $0.76\pm 0.25^{*}$
NGC 6872 | 158 | 19 | 890.3 | 662.7 | 0.179 | 0.029 | $0.150\pm 0.016^{*}$
NGC 3256E | 11 | 5 | 246.0 | 473.2 | 0.045 | 0.011 | $0.034\pm 0.014$
NGC 3256W | 24 | 9 | 199.9 | 519.9 | 0.120 | 0.017 | $0.103\pm 0.025^{*}$
NGC 1487E | 0 | 0 | 12.4 | 28.5 | 0 | 0 | 0
NGC 1487W | 1 | 0 | 13.7 | 33.3 | 0.073 | 0 | $0.073\pm 0.073$

∗Signifies excess at 3$\sigma$ or above.

We perform Kolmogorov–Smirnov (KS) tests on the distributions of
U${}_{\text{336}}$ \- B${}_{\text{438}}$, B${}_{\text{438}}$ \-
V${}_{\text{606}}$, and V${}_{\text{606}}$ \- I${}_{\text{814}}$ colours
between in-tail and out-of-tail objects for all detected objects and for SCCs
only. This is another way to determine the likelihood that objects within the
tail are unique and independent from those outside the tail region, in
addition to measuring cluster excess. Recorded p-values are shown in Table 5.
Our V${}_{\text{606}}$ \- I${}_{\text{814}}$ colour is most useful in
discriminating between tail and non-tail objects. Of the eight systems which
contain enough SCCs for a KS test, five of them show p-values less than 0.04,
indicating the data are drawn from independent distributions.

Table 5: KS test results for our photometric data. We include results for all of our sources on the left, and SCC objects only on the right. | All | SCC only
---|---|---
System | Nin | Nout | KSU-B | KSB-V | KSV-I | Nin | Nout | KSU-B | KSB-V | KSV-I
NGC 1614N | 26 | 14 | 0.025 | 0.020 | 6.6 $\times 10^{-3}$ | 21 | 11 | 0.17 | 0.19 | 7.2 $\times 10^{-3}$
NGC 1614S | 40 | 14 | 0.068 | 2.0 $\times 10^{-3}$ | 5.852 $\times 10^{-5}$ | 33 | 11 | 0.65 | 0.045 | 1.2$\times 10^{-4}$
AM1054-325 | 172 | 51 | 0.40 | 6.9 $\times 10^{-6}$ | 6.6 $\times 10^{-18}$ | 135 | 23 | 0.166 | 4.5 $\times 10^{-3}$ | $2.0\times 10^{-8}$
ESO 376-28 | 3 | 51 | N/A | N/A | N/A | 1 | 23 | N/A | N/A | N/A
NGC 2992 | 61 | 15 | 0.058 | 0.42 | 0.75 | 22 | 4 | 0.73 | 0.87 | 0.50
NGC 2993 | 23 | 5 | 0.19 | 0.018 | 0.34 | 9 | 0 | N/A | N/A | N/A
MCG-03-13-063 | 19 | 24 | 2.3 $\times 10^{-3}$ | 0.73 | 1.8 $\times 10^{-3}$ | 10 | 9 | 2.1 $\times 10^{-3}$ | 0.35 | 1.7 $\times 10^{-3}$
NGC 6872 | 205 | 29 | 1.6 $\times 10^{-3}$ | 0.031 | 0.012 | 158 | 19 | 0.026 | 0.049 | 0.025
NGC 3256E | 71 | 53 | 0.74 | 0.021 | 0.061 | 11 | 5 | 0.92 | 0.17 | 0.23
NGC 3256W | 92 | 74 | 0.055 | 8.1 $\times 10^{-3}$ | 6.7 $\times 10^{-4}$ | 24 | 9 | 0.97 | 0.33 | 0.18
NGC 1487E | 83 | 33 | 0.75 | 0.083 | 4.5 $\times 10^{-3}$ | 0 | 0 | N/A | N/A | N/A
NGC 1487W | 92 | 44 | 0.39 | 0.36 | 0.46 | 1 | 0 | N/A | N/A | N/A

###  3.2 Addition of nebular flux

Clusters less than 10 Myr old can show strong emission lines, as the
surrounding hydrogen gas from cluster formation is ionized and undergoes
recombination. An example of these systems is shown in Figure 15 for NGC 1614.
As clusters will expel their hydrogen gas via stellar feedback on timescales
of several million years (Pang et al., 2020), the presence of recombination
lines indicates recent star formation.

Figure 15: Colour image of NGC 1614S. The data through filters F435W (ACS),
F606W (WFPC2), F814 (ACS), and F665N (ACS) were stretched with a logarithm and
bias/contrast adjustment in CARTAa. Subsequently in GIMPb they were assigned
the colours blue, yellow-green, red and pink respectively and using a layering
schema blended with the screen algorithm (English, 2017). Several regions
containing SCCs with emission lines are highlighted in yellow, showing that
star cluster formation is ongoing in this tidal tail.

aCARTA: Cube Analysis and Rendering Tool for Astronomy. https://cartavis.org
bGnu Image Manipulation Program. https://www.gimp.org

Our SSP model (black solid line in Figures 14 \- 3) does not contain nebular
continuum emission, nor flux from emission lines; we use Starburst99
(Leitherer et al., 1999) to calculate contributions from the nebular
continuum, as well as the H$\alpha$ and H$\beta$ emission lines. We include
the H$\gamma$ line, with the flux ratio of H$\gamma$ / H$\beta$ = 0.47
(Osterbrock, 1989), and the O[III] and O[II] lines as well. The oxygen lines
are determined from the KPNO International Spectroscopic Survey (KISS) sample
of nearby, low-mass star forming galaxies (Salzer et al., 2005); we take the
median log ratio of these lines to the H$\beta$ line, O[III]/H$\beta$ = 0.08
and O[II]/H$\beta$ = 0.56.

The effect of the emission lines depends on the filter. The H$\alpha$,
H$\beta$, and O[III] lines are covered by the F606W filter, while the
H$\gamma$ line falls in the middle of the B${}_{\text{438}}$ and
B${}_{\text{435}}$ filters. The O[II] line is at the edge of the F435W and
F336W filters. The result is that the V${}_{\text{606}}$ filter is most
strongly affected by the presence of emission lines, due to the strong
H$\alpha$ and H$\beta$ lines, while the effect in the other filters is
relatively inconsequential. This shifts the V${}_{\text{606}}$ \-
I${}_{\text{814}}$ colour towards bluer colours in our colour-colour plots.
The resulting evolutionary track is degenerate with extinction for ages $<10$
Myr for our U${}_{\text{336}}$ \- B${}_{\text{438}}$ vs V${}_{\text{606}}$ \-
I${}_{\text{814}}$ diagrams. The effect is more apparent when we plot
B${}_{\text{438}}$ \- V${}_{\text{606}}$ vs V${}_{\text{606}}$ \-
I${}_{\text{814}}$; the evolutionary track dramatically swings upward in our
plots as the B${}_{\text{438}}$ \- V${}_{\text{606}}$ colour trends towards
redder values. This effect is seen for similar young clusters in interacting
systems as well, using the V${}_{\text{606}}$ filter (Fedotov et al., 2015,
2011; Gallagher et al., 2010).

Data for NGC 3256 were taken from Knierman et al. (2003). For NGC 3256W/E, we
determined the magnitudes in the F555W and F814 filters, and then transformed
these to the Johnsons-Cousins system, as in Knierman et al. (2003), using
transformations from Holtzman et al. (1995). The shape and wavelength
boundaries of the F555W filter transmission are noticeably different from the
V${}_{\text{606}}$ filter in that the H$\alpha$ line falls at the edge of the
filter, thus it has a much less of an effect on our model magnitudes.
Therefore, on the colour-colour diagrams for NGC 3256W/E, there is less of a
difference between the nebular emission evolutionary tracks and the SSP models
than for our other systems.

###  3.3 Ages and Masses

Ages and masses of clusters were determined using the 3DEF spectral energy
distribution (SED) fitting code, as described in Bik et al. (2003). This code
compares a set of input magnitudes to a grid of SSP models with ages between
106 and 1010.12 yr. It will apply an extinction to our observed magnitudes
through a range of $E(B-V)$ values, compare the set of model magnitudes and
extincted, observed magnitudes, and minimize the resulting $\chi^{2}$ value to
determine the best fit ages and masses. We use an evolutionary track from
Marigo et al. (2008) with solar metallicity and a Salpeter IMF (Salpeter,
1955), with nebular flux added to it (see Section 3.2). Our models do not
account for binary star evolution. Spectroscopic observations of clusters and
merging systems have found metallicities in the range of $\sim$ 1.0 - 1.5 Z⊙
(Rosa et al., 2014; Trancho et al., 2012; Bastian et al., 2009b; Trancho et
al., 2007b, a). For comparison, we run our 3DEF algorithm for NGC 6872, with
158 SCCs, using a tracks at 0.5 Z⊙ and 2 Z⊙. We find the median ratio of ages
and masses determined using solar and half solar metallicity to be 1 and 1.1,
respectively. The ratio of ages and masses between Z⊙ and 2 Z⊙ is 1.02 and
0.98, respectively. A comparison of the different metallicities and their
effects on our U${}_{\text{336}}$\- B${}_{\text{438}}$, B${}_{\text{438}}$\-
V${}_{\text{606}}$, and V${}_{\text{606}}$\- I${}_{\text{814}}$colours is
shown in Figure 16. Here, we plot data for NGC 6872 against SSP models and SSP
models with nebular emission added, for metallicities of Z⊙, 0.5 Z⊙, and 2 Z⊙.
The similarity between all three metallicities shows that our age and mass
estimates will not be sensitive to our chosen metallicity.

Figure 16: Comparison of SSP tracks at different metallicities, plotted
against data for NGC 6872. Data points are objects that fall within the tail,
as in Figure 10. Black lines correspond to Z = Z⊙, red corresponds to Z = 0.5
Z⊙, and gold corresponds to Z = 2 Z⊙. On the left, we plot tracks from Marigo
et al., 2008. On the right, we include nebular emission (see Section 3.2) from
Starburst99 models (Leitherer et al., 1999); the inclusion of line emission
affects only ages < 10 Myr. In both cases, for a pure SSP and one with nebular
emission added to it, the tracks are similar to one another; consequently, the
ages and masses derived using either metallicity will be similar.

The choice of IMF will influence the masses of our clusters, but generally has
little effect on the derived ages. A Chabrier or Kroupa IMF will decrease the
masses by a factor of $\sim 2$ relative to our assumed Salpeter IMF.

Ages and masses for all our systems are plotted ndividually in Figures 3 \-
14, and collectively in Figure 17. We see a gap in age from log Age = 7.0 to
7.5 yr in many of our systems; this is an artifact of the fitting process and
is seen in similar studies of star clusters (e.g. Randriamanakoto et al.,
2019; de Grijs et al., 2013; Bastian et al., 2005b). The true ages are likely
spread over neighboring ages. It is worth noting, however, that every system,
with the exception of NGC 1487, contains SCCs with ages $<$ 10 Myr. This shows
us that tidal debris are capable of supporting cluster formation.

Figure 17: Ages and masses from Figures 3 \- 14, compiled together. All
systems except for NGC 1487 have at least one SCC with an age $<$ 10 Myr,
indicating recent cluster formation. Both NGC 3256W and NGC 3256E show a
number of non-SCC objects at the interaction age, with large masses. Their
high masses, indicating bright absolute magnitudes, along with poor fits to
our SSP model ($\chi^{2}>3$, Section 2.5) suggest these objects are foreground
stars in the Milky Way. It is notable that these only appear in NGC 3256,
which has the lowest Galactic latitude of our systems. They are not included
in our SCC analysis.

###  3.4 Cluster radii

The radii of our SCCs were found using the program ISHAPE (Larsen, 1999).
ISHAPE requires that sources are isolated to prevent PSF blending and at a
high S/N. We perform an additional cut on our SCCs by visually selecting
objects which are not in crowded regions and do not have highly elliptical
shapes, which could indicate we are looking at blended clusters. We choose
objects with a S/N $>$ 25 as determined by ISHAPE, as the program also
requires bright objects to perform accurate measurements.

ISHAPE will deconvolve selected sources with a user supplied PSF and a
selected analytic model. Both an EFF (Elson et al., 1987) and King (King,
1962) model have been used in the past to study star clusters. We use a King
model as it has been used to describe extragalactic and Galactic globular
clusters (Correnti et al., 2021; Larsen et al., 2021; Chandar et al., 2016;
Bastian et al., 2012). ISHAPE will fit the model to an ellipse and produce the
FWHM of the major axis, and the ratio between the minor and major axes (q),
for each selected source. We take the FWHM as the average between the major
and minor axes of the fit. We require that q > 0.3 to eliminate
unrealistically elliptical sources, as in Brown & Gnedin (2021). ISHAPE is
able to reliably determine a FWHM for sources at 10% of the size of the PSF,
which for our WFC3 and ACS images, corresponds to $\approx 0.2$ pix (the pixel
scale for WFC3 is 0.04” per pixel, and 0.05” per pixel for ACS). We remove
objects smaller than this size. The result of our selection criteria reduces
the number of SCCs for analysis from 425 to 57, largely as a result of
selecting isolated clusters. Our furthest systems, NGC 6872 in particular, are
susceptible to crowding as the angular separation for nearby objects
decreases, and this is borne out in our reduced number of sources. As a
result, we emphasize that our radii sample is biased towards isolated,
physically large SCCs.

This FWHM value is converted to a half-light radius rh (also referred to as
the effective radius Reff) by multiplying the FWHM by 1.48, as noted in the
ISHAPE manual. We note that while an EFF and King model will produce unique
FWHM values, the resulting half-light radii are similar to one another
(Larsen, 1999). The minimum value of rh we are able to detect, when combining
our FWHM and axis ratio limits and converting FWHM to rh, is 0.19 pix,
corresponding to 0.0076” for WFC3 and .0095” for ACS. We use our
B${}_{\text{438}}$\- and B${}_{\text{435}}$-band images to derive radii as
they offer a better S/N than our U${}_{\text{336}}$-band images.

Our cluster radii are shown in Figure 18, with interacting pairs grouped
together. The minimum detectable radius for each system is shown as a vertical
dashed line. The combined distribution for all our sources is shown as the
bottom left plot. The distribution shows a peak at $\approx 5.6$ pc, with an
extended tail up to $>100$ pc. Objects at the tail end of the distribution are
likely blended together, but are included for completeness. While our objects
peak at a larger value than typical of Milky Way globular clusters ($\sim 3.2$
pc, Baumgardt & Hilker, 2018), objects of this size are seen in both the Milky
Way and in extragalactic systems (Baumgardt & Hilker, 2018; Ryon et al., 2017;
Chandar et al., 2016).

Note that ESO 376-28 is not included as it only contained one SCC, which was
eliminated due to a low S/N in ISHAPE, and NGC 1487W’s single SCC did not have
a good fit. We address NGC 1487 in Section 4.6.

Figure 18: Half-light radii for our sources. Gray boxes indicate counts per
bin for each system as a whole, while coloured lines represent individual
tails (where applicable). The vertical dashed line represents the minimum size
of an object able to be detected by ISHAPE (0.2 pix) in an image.

##  4 Results and Discussion

###  4.1 Mass Function

A global mass function for all our systems is presented in Figure 19. We stack
our measured masses together for all our SCCs and plot them with bins of
constant number, at 20 per bin, with 235 SCCs total. The mass bins are modeled
as a power law with the form $dN/dM\propto M^{\beta}$. The slope, $\beta$, is
found with a linear fit to log $(dN/dM)$ with $\beta=-2.02\pm 0.15$. The lower
mass cutoff for our fit is at log $M$ = 4.6 M⊙, where the mass function begins
to turnover. This turnover is caused by incompleteness at the lower mass
limit. While some studies have suggested the mass function follows the form of
a Schecter function (Messa et al., 2018; Adamo et al., 2015; Bastian et al.,
2012), we see no turnover at high masses, leading us to conclude a power law
is a good fit for our data.

The value of $\beta$ has been measured for many other systems as well, with
values ranging from $\approx$ -2.15 – -1.85. Our result of $\beta=$ -2.02 $\pm
0.15$ for our stacked distribution is consistent with these previous results.
Varying the number of objects per bin finds values of $\beta$ consistent with
our stated value, with $\beta=2.14\pm 0.11$ and $\beta=2.08\pm 0.19$ for 10
and 30 objects per bin, respectively.

The low numbers of SCCs in each system means we cannot generate a useful mass
function for each system. It is, however, useful to look at our two systems
with the largest numbers of SCCs, AM1054-325 and NGC 6872. These contain 89
and 87 SCCs below 10 Myr, respectively. As these constitute more than half of
the objects in our stacked mass function, it is possible that they have a
heavy influence on the derived slope and form of the distribution. To ensure
we are not affected by this, we also look at the mass function while excluding
objects from AM1054-325 and NGC 6872. In Figure 19 we include these three
cases to compare to our full, stacked function.

The peak of the function at log Mass = 4.6 M⊙ is normalized to the stacked
function, and vertically offset in steps of 0.75 dex to plot all functions on
the same plot. We again plot data using bins of constant number, 10 for
AM1054-325 and NGC 6872, and 7 for the excluded function. All cases are
consistent with one another, and the stacked mass function as well, suggesting
our more populous systems are not over-influencing the stacked mass function.

Figure 19: Mass functions for all, stacked objects (blue), AM1054-325
(purple), NGC 6872 (green), and stacked (orange), but excluding AM1054-325 and
NGC 6872. Data are normalized to the stacked mass function and vertically
offset to include all curves on the same plot. The corresponding fit slopes
are shown on the right. While there is some scatter in $\beta$, all values are
consistent with each other, within their uncertainties. Vertical dashed line
indicates our cut-off mass at log Mass = 4.6.

As a separate check, we fit our data to a power law using the the IDL program
mspecfit.pro, developed by Rosolowsky (2005). This uses a maximum-likelihood
fitting technique to the cumulative distribution to find the slope of a power
law distribution, and factors in the individual errors in mass for each data
point. It will perform a fit to a regular power law $N(M^{\prime}>M)\propto
M^{\beta}$ as well as determine the possibility of the cumulative distribution
having the form of a truncated power law, given as $N(M^{\prime}>M)\propto
N_{0}[(M/M_{0})^{\beta}-1]$, where $M_{0}$ is the cutoff mass and $N_{0}$ is
the number of objects more massive than $2^{1/\beta}M_{0}$. If $N_{0}\lesssim
1$, then the distribution is best fit to a single power law. We fit the four
datasets shown in Figure 19 and find that $N_{0}=0.0\pm 1.8,1.0\pm
2.0$,$0.0\pm 0.8$, and $0.0\pm 1.3$ for our stacked mass function, AM1054-325,
NGC 6872, and our excluded function, respectively. This suggests our data is
best fit with a power law distribution. We thus plot our cumulative
distribution functions of our data in Figure 20, along with the best fit
values of $\beta$, using a standard power law function. We find our results
are consistent with that of our binned data within a standard deviation.

Figure 20: Cumulative mass distribution for stacked objects (blue), AM1054-325
(purple), NGC 6872 (green), and stacked (orange), but excluding AM1054-325 and
NGC 6872. Data are vertically offset to include all curves on the same plot.
The corresponding fit slopes are shown on the right. Values of $\beta$ shown
here are consistent with those from Figure 19 to within a standard deviation.
Horizontal gray bars indicate 1$\sigma$ error bars for the individual mass
points. Vertical dashed line indicates our cut-off mass at log Mass = 4.6.

###  4.2 Cluster formation efficiency

Stars form in clustered fashion, as seen in the Milky Way and in galaxies
beyond (Bressert et al., 2010; Whitmore et al., 2010; Lada & Lada, 2003;
Clarke et al., 2000; Zepf et al., 1999). Observational studies have attempted
to determine how many stars are born in bound clusters by measuring the amount
of star formation occurring in clusters, compared to the local region (e.g.
Adamo et al., 2015; Ryon et al., 2014; Goddard et al., 2010). The cluster
formation efficiency (CFE) is defined as the ratio of the cluster formation
rate and the star formation rate (both in units of M⊙/ yr), so that CFE = CFR
/ SFR. Difficulty arises in the definition of “bound” clusters, as internal
and environmental processes are capable of disrupting and unbinding clusters
(Krumholz et al., 2019; Portegies Zwart et al., 2010), requiring age limits
for cluster analysis.

To match previous observations, we limit our SCC ages to 1 - 10 Myr. The SFR
is measured from the UV flux of our GALEX and Swift images and converted to
SFR using the following relation from Kennicutt & Evans (2012):

$\text{log SFR}\>(\text{M}_{\odot}\>\text{yr}^{-1})=\log L_{x}-\log C_{x},$
(1)

where $L_{x}$ is luminosity (ergs/s), and $C_{x}$ is a calibration constant
dependent on the observed wavelength (43.35 for GALEX FUV and 43.17 for Swift
uvm2).

The CFR was found by summing the mass of all clusters with an age between 1 -
10 Myr, and dividing by the time interval of 9 Myr. Completeness will affect
the total mass of clusters which can be detected; low-mass clusters will not
be observed in our images. We find the approximate mass of a 10 Myr old
cluster with MV = -8.5 (from our detection cutoff in Section 2.5) to be
$\approx$ 104.3 M⊙. We assume we are complete above this mass limit, and
calculate the missing, or undetected mass, assuming the cluster mass function
follows a power law with slope $\beta$ = -2.0, extending from 100 M⊙to 107 M⊙.
We perform the same calculation with slopes of $\beta$ = -2.15 and -1.85 for
our upper and lower error bounds. For $\beta$ = -2.0, -2.15, and -1.85, we
find the total percentage of mass in clusters with masses greater than 104.3
M⊙ to be 54%, 33%, and 74%, respectively. Note that a shallower slope implies
we measure a more complete sample of our clusters.

Our results are shown in Table 6. As NGC 1487W/E both do not contain clusters
which fit our criterion, they do not have a corresponding CFE. The general
trend is that systems with a higher SFR density ($\Sigma_{\text{SFR}}$) show
more efficient cluster formation. Data are plotted in Figure 21. We plot our
data against a theoretical CFE from Kruijssen (2012) for comparison, with
dotted lines indicating a variation factor of 2. This model predicts cluster
formation to follow the surface gas density ($\Sigma_{\text{gas}}$), and
therefore $\Sigma_{\text{SFR}}$ via the Kennicutt-Schmidt law (Kennicutt,
1998). The CFE tails off at high $\Sigma_{\text{SFR}}$. At the high gas
densities implied by the high $\Sigma_{\text{SFR}}$ tidal interactions between
neighboring GMCs can impede cluster formation.

While the Kennicutt-Schmidt law assumes the relation between
$\Sigma_{\text{gas}}$ and $\Sigma_{\text{SFR}}$ remains the same at all
scales, this may not be the case. When studying star formation at sub-kpc
scales, Bigiel et al. (2008) found a decrease in $\Sigma_{\text{SFR}}$ at low
values of $\Sigma_{\text{gas}}$. This decrease is correlated with saturation
of Hi in the total gas content of the region (Hi $+$ H2). This effect has been
parameterized by Johnson et al. (2016), using a broken power law, to predict
$\Sigma_{\text{SFR}}$ based on $\Sigma_{\text{gas}}$. We include the CFE as a
function of $\Sigma_{\text{SFR}}$ based on this relation, again using the
formulation from Kruijssen (2012), in Figure 21 as a dashed line. The broken
power law formula manifests as a flattening of the curve at -2.3 in log
$\Sigma_{\text{SFR}}$, corresponding to the gas environment being dominated by
Hi over H2. Upper and lower limits provided by Johnson et al. (2016), derived
from the Bigiel et al. (2008) data, are plotted as dot-dash lines.

We find a good agreement with the Bigiel et al. (2008) curve, with only NGC
3256W and NGC 1614N falling more than 1$\sigma$ below the lower limit.
Notably, our data fall on the flattened part of the CFE curve, corresponding
to an Hi dominated environment, suggesting the star forming regions in our
tails are primarily composed of Hi over H2.

We note that relation between the CFE and $\Sigma_{\text{SFR}}$ was designed
for a “typical” spiral galaxy, and should used as a rough estimate (Kruijssen,
2012). In Figure 21, we include data from previous surveys (Adamo et al.,
2015; Lim & Lee, 2015; Ryon et al., 2014; Adamo et al., 2011; Annibali et al.,
2011; Silva-Villa & Larsen, 2011; Goddard et al., 2010) as compiled by Adamo
et al. (2015). Our data extend to smaller $\Sigma_{\text{SFR}}$ values than
previously measured.

The dependence of the CFE on $\Sigma_{\text{SFR}}$ has been questioned by
Chandar et al. (2017), who studied several systems and found an average CFE of
24%, independent of $\Sigma_{\text{SFR}}$. This constant value is indicated in
Figure 21 as a red horizontal line. They suggested that the variability seen
in the CFE by other authors was caused by using different cluster age
intervals for different galaxies in determination of the CFE. The result was a
biased sampling of the CFE using a cluster age range of 0 - 10 Myr for systems
with high $\Sigma_{\text{SFR}}$, and 10 - 100 Myr for systems with a low
$\Sigma_{\text{SFR}}$. Indeed, we note that of the data points in Figure 21,
Adamo et al. (2015); Lim & Lee (2015); Annibali et al. (2011); Adamo et al.
(2011) use objects with ages of 1 - 10 Myr, while the others use a range of
ages from 1 - 10, 10 - 100, and 1 - 100 Myr in their CFE determinations. Our
use of 1 - 10 Myr matches the majority of the listed studies. Independent of
other studies, however, we find that our sample seems to match the theoretical
model, and shows a trend of decreasing CFE with decreasing
$\Sigma_{\text{SFR}}$.

Table 6: SFRs and CFE for our sample. CFE is determined by comparing the mass of clusters with ages below 10 Myr to the SFR within their respective tidal tail. The SFR is found using GALEX and Swift UV data, converted to a SFR (Kennicutt & Evans, 2012). System | SFR | SFR${}_{\text{density}}$ | CFE | A${}_{\text{in}}$ | $\Sigma_{\text{SCC}}$
---|---|---|---|---|---
| ($10^{-2}$ M⊙ yr-1) | ($10^{-3}$ M⊙ yr-1 kpc-2) | (%) | (kpc2) | (kpc-2)
ESO 376-28 | $0.55\pm 0.25$ | $0.062\pm 0.028$ | $2.1^{+1.3}_{-0.6}$ | 88.9 | $-0.015\pm 0.013$
NGC 2993 | $2.31\pm 0.15$ | $0.129\pm 0.008$ | $1.11^{+0.70}_{-0.30}$ | 179.1 | $0.050\pm 0.017$
NGC 2992 | $3.75\pm 0.21$ | $0.163\pm 0.009$ | $3.5^{+2.3}_{-1.0}$ | 229.5 | $0.070\pm 0.022$
NGC 3256E | $6.30\pm 0.12$ | $0.256\pm 0.005$ | $2.0^{+1.2}_{-0.5}$ | 246.0 | $0.034\pm 0.014$
NGC 3256W | $6.42\pm 0.11$ | $0.321\pm 0.006$ | $0.17^{+0.11}_{-0.05}$ | 199.9 | $0.103\pm 0.025$
NGC 1487E | $0.428\pm 0.030$ | $0.345\pm 0.024$ | N/A | 12.4 | 0
NGC 1487W | $0.493\pm 0.033$ | $0.360\pm 0.024$ | N/A | 13.7 | $0.073\pm 0.073$
NGC 1614S | $17.45\pm 0.40$ | $0.532\pm 0.012$ | $5.0^{+3.2}_{-1.4}$ | 327.8 | $0.078\pm 0.019$
NGC 6872 | $65.4\pm 3.0$ | $0.734\pm 0.033$ | $5.7^{+3.7}_{-1.6}$ | 890.3 | $0.15\pm 0.016$
MCG-03-13-063 | $0.98\pm 0.33$ | $0.77\pm 0.26$ | $6.6^{+4.2}_{-1.8}$ | 12.8 | $0.76\pm 0.25$
NGC 1614N | $48.68\pm 0.14$ | $1.598\pm 0.005$ | $0.66^{+0.42}_{-0.18}$ | 304.6 | $0.046\pm 0.017$
AM1054-325 | $33.0\pm 3.1$ | $2.55\pm 0.24$ | $6.9^{+4.4}_{-1.9}$ | 129.5 | $1.016\pm 0.090$
Figure 21: Cluster formation efficiency (CFE) plotted against the log star
formation rate density. Included are several similar measurements gathered in
Adamo et al. (2015), as well as a theoretical curve from Kruijssen (2012) in
solid black. Dotted lines indicate a factor of 2 variation in the theoretical
model. We include a modified version of the Kruijssen (2012) curve, using the
$\Sigma_{\text{gas}}$ vs $\Sigma_{\text{SFR}}$ relation from Bigiel et al.
(2008), as a dashed line. The dot-dash lines indicate upper and lower limits
on this relation as defined by Johnson et al. (2016). The red solid line
corresponds to the 24% value of CFE from Chandar et al. (2017).

###  4.3 Spatial distribution

SCC age and mass are plotted against distance from the center of the
interacting system in Figures 3 \- 14. The central point of each system is
obtained as coordinates from SIMBAD. The median distance is marked with a
dashed vertical line. We perform KS tests on the age and mass distributions
for our SCCs as separated by the median distance to the center, with results
shown in Table 7. We find statistically significant results beyond 2$\sigma$
in only two tails, NGC 1614S, and AM1054-325. NGC 1614S shows significant
results in both its age and mass distributions, with p-values of 0.0011 and
0.0052 for its age and mass distributions, respectively. From Figure 4 we see
there is a clump of young objects near the base of the tail, with masses
$\approx 10^{5}$ M⊙. KS results for its companion tail, NGC 1614N, produce
p-values of 0.18 and 0.06 for the age and mass distributions, respectively. We
do not claim either of these results for NGC 1614N to be significant.
AM1054-325 shows significant results in the mass distribution, but not in age.

For the majority of our sample, we see that the general trend shows a
relatively even distribution of ages though the tidal debris; young objects
are not concentrated in any particular region, but are found throughout the
tidal tails.

Table 7: KS results for age and mass distributions of SCCs in tails, between objects interior and exterior to the median distance to the centre of the system. System | KS${}_{\text{Age}}$ | KS${}_{\text{Mass}}$
---|---|---
NGC 1614N | 0.18 | 0.06
NGC 1614S | 0.0011 | 0.0052
AM1054-325 | 0.92 | 0.018
ESO 376-28 | N/A | N/A
NGC 2992 | 0.27 | 0.56
NGC 2993 | 0.96 | 0.96
MCG-03-13-063 | 0.44 | 0.99
NGC 6872 | 0.68 | 0.89
NGC 3256E | 0.85 | 0.45
NGC 3256W | 0.91 | 0.66
NGC 1487E | N/A | N/A
NGC 1487W | N/A | N/A

###  4.4 Dynamical age

The dynamical age of a cluster ($\Pi$), introduced by Gieles & Portegies Zwart
(2011), offers a method for estimating if a cluster is gravitationally bound
at the current time. It is defined as the ratio of the age of a cluster to the
crossing time of the cluster ($T_{\text{cr}}$):

$\Pi\equiv\frac{t_{\text{cluster}}}{T_{\text{cr}}}.$ (2)

$T_{\text{cr}}$ is defined as:

$T_{\text{cr}}\>(\text{s})\equiv
10\left(\frac{r_{\text{h}}^{3}}{GM}\right)^{1/2},$ (3)

where $G$ is the gravitational constant, $M$ is the mass of the cluster, and
$r_{\text{h}}$ is the half-light radius of the cluster. A cluster is said to
be gravitationally bound if $\Pi\geq 1$. At this dynamical age, the stars in
the cluster have evolved for longer than a crossing time, and as such are not
likely to escape from the cluster, meaning the cluster is gravitationally
bound. Objects with $\Pi<1$ are not necessarily unbound, but as the stars have
not yet evolved for longer than a crossing time, they still have time to
escape before then, and we cannot determine if they are bound to the cluster.
Unbound associations will expand with time, causing $T_{\text{cr}}$ to
increase as well, and remain at or below $\Pi=1$. Bound objects, on the other
hand, will remain bound and compact with time, causing $\Pi$ to increase with
time. Data for our SCCs are shown in Figure 22.

The determination of a cluster as bound or unbound remains an estimate, as
several factors will influence the evolution of a cluster. If the natal gas of
a cluster is expelled too quickly, on a timescale comparable to the crossing
time, the cluster is more susceptible to disruption, for a given star
formation efficiency (Baumgardt & Kroupa, 2007; Hills, 1980). Similarly, it is
not possible for us to determine if a cluster, even with $\Pi>1$, will remain
bound throughout the lifetime of the merger, as this calculation does not take
into account external forces. Clusters which pass nearby GMCs or through the
disk or nucleus of the merging galaxies are subject to gravitational tidal
forces which can disrupt them (e.g. Krumholz et al., 2019; Kim et al., 2018;
Tacconi et al., 2008; Spitzer, 1958). However, as these objects exist in the
diffuse regions of tidal debris, their chances of survival is increased as
they will not experience the strong gravitational forces seen in the nuclear
regions.

Figure 22: Dynamical ages of SCCs, following the prescription set by Gieles &
Portegies Zwart (2011). The vertical dashed line marks the limit for
gravitationally bound objects; those to the right of the line are
gravitationally bound, while those to the left are unbound. Gray boxes
indicate counts per bin for each system as a whole, while coloured lines
represent individual tails (where applicable).

###  4.5 Age and mass as related to half-light radii

There is debate on the relation between cluster age and mass on their physical
sizes. The initial half-light radius of a cluster is predicted, from an
analytic model, to depend on the mass and gas surface density (Choksi &
Kruijssen, 2021). As clusters evolve, mass loss and stellar interactions
within the cluster will cause its expansion (Portegies Zwart et al., 2010).
Gieles et al. (2011) suggest two stages of radii evolution for clusters in
tidal fields: expansion, driven by mass loss, followed by contraction. They
find that two-thirds of the Milky Way’s globular clusters are in the expansion
phase.

Several studies of extragalactic clusters have found a slight dependence of
age on radius (Ryon et al., 2017; Bastian et al., 2012; Lee et al., 2005),
while others have found none (Brown & Gnedin, 2021; Scheepmaker et al., 2007;
Larsen, 2004). There is a similar debate on the relation between mass and
radius, and it is not clear that observational studies have found a
relationship between these cluster properties (Brown & Gnedin, 2021; Ryon et
al., 2017). There is considerable scatter in the distribution of cluster
radius, hiding any clear signals.

We plot the ages and masses of our SCCs against their radii in Figure 23. We
include both objects which are determined to be gravitationally bound and
those which are not. We again find considerable scatter in our radii
distribution, complicating any clear conclusions. On the left side of Figure
23 we compare the ages of our SCCs to their radii. There are only a small
number of objects at ages $<10$ Myr, as a result of our selection criteria,
namely that we look for isolated objects. Star clusters are formed in
clustered fashion (Grasha et al., 2015; Gouliermis et al., 2015; Bastian et
al., 2009a; Gieles et al., 2008), meaning our young SCCs will be in crowded
regions which have been removed from our ISHAPE catalogue. This effect is seen
in the fact that the young, unbound objects have large, extended radii,
indicating blending. Thus, while Figure 23 suggests that cluster radius
increases with age, we have a small and biased sample at ages around 10 Myr.

Looking at the right panel of Figure 23 we see the relation between our masses
and radii. We again see a large amount of scatter in our data, with no clear
trend. Recent work by Brown & Gnedin (2021) looked at the cluster radii of 31
galaxies from the Legacy Extragalactic UV Survey (LEGUS). LEGUS galaxies are
nearby ($<12$ Mpc) spiral and irregular galaxies, with few interacting systems
and no major mergers. Their work finds a power-law relation between mass and
radius extending up to 105 M⊙. Above this mass limit, the relation appears to
flatten, though this may be the result of low numbers of clusters with these
large masses. We overplot their fit in Figure 23, continuing their trend to
higher masses. We find our data are consistent with their fit, though there is
large scatter.

Figure 23: Half-light radii for our sources, as a function of age (Left) and
mass (Right). Filled circles represent bound objects, while diamonds are
unbound objects, using the definition set in Section 4.4. On the right, we
include the mass-radius relation from Brown & Gnedin (2021). Our data are
consistent with their model, but there is a large amount of scatter in our
data.

###  4.6 NGC 1487 Objects

NGC 1487 stands out from the rest of the mergers in our sample: it is three
times closer than our next closest galaxy, there is only one SCC between the
two tidal tails, and it has been classified as both a merger between two disk
galaxies (Aguero & Paolantonio, 1997) and a merger between dwarf galaxies
(Buzzo et al., 2021; Bergvall et al., 2003). Despite the lack of SCCs, visual
examination of the tails shows an abundance of objects within the debris. This
suggests the debris host faint, low-mass objects which belong to the merging
system, but are not luminous, high-mass clusters with $M_{V}<-8.6$. The
absence of high-mass objects may arise if this is indeed a merger between
dwarf galaxies. Massive star clusters and high SFRs require high gas pressure
(Maji et al., 2017; Zubovas et al., 2014; Blitz & Rosolowsky, 2006), and these
required pressures may not be produced in a dwarf galaxy merger. Lahén et al.
(2019) were able to simulate a merger between two equal sized dwarf galaxies,
which produced clusters with masses $\geq 10^{5}$ M⊙. Pressures in these
clusters was found to be $\sim 10^{7}$ $k$(K cm-3)-1, smaller than the
$10^{8}-10^{12}$ $k$(K cm-3)-1 values seen in simulations of major mergers
(Maji et al., 2017).

To consider this scenario of low-mass cluster formation, we construct a
stacked mass function with objects from both tails. We eliminate our magnitude
limit, but still require that sources are fit to our SSP models with
$\chi^{2}\leq 3$ and V${}_{\text{606}}$ \- I${}_{\text{814}}$ < 1.43. We only
include objects with an age $\leq$ 10 Myr as before; results are shown in
Figure 24 for 58 objects which meet our requirements. We fit our data to the
mass turnover at log Mass = 3.1, and find that our data shows a slope of
$\beta=-2.06\pm 0.31$. This is consistent with our results at higher masses
for our SCCs, where the completeness limit only allowed a fit down to log Mass
= 4.6.

Our SED modelling assumes a continuously populated IMF, which is a reasonable
assumption for our clusters with masses $>10^{4}$ M⊙. Below this mass limit,
the stochastic sampling of the stellar IMF can affect photometric measurements
(Larsen, 2011). The low numbers of stars can mean that a cluster can host only
single digit numbers of supergiants, or none at all. The overall colour of the
cluster would become bluer in the absence of supergiants, causing us to
underestimate the age; consequently, the mass can decrease as well, as younger
clusters are more luminous than older ones. This can result in a bi-modality
of colours in clusters (Popescu & Hanson, 2010; Silva-Villa & Larsen, 2011).
Despite this, the effect on the slope of the mass function $\beta$ is small
(Fouesneau et al., 2012), and eliminating sources with poor fits to models
will reduce this effect (Fouesneau & Lançon, 2010).

Figure 24: Mass function for sources in NGC 1487E and NGC 1487W. The dashed
vertical line indicates our mass cut at log Mass = 3.1.

We plot the cumulative fraction of objects in Figure 25, again using the
mspecfit.pro code to search for a truncated power law. We find for NGC 1487 a
value of $N_{0}=3.7\pm 3.6$, giving marginal significance ($\approx 1\sigma$)
for a truncated power law. We plot both a standard power law and a truncated
power law to our cumulative mass distribution in Figure 25.

Figure 25: Cumulative fraction of sources in NGC 1487E and NGC 1487W. We
overplot a power law function as a solid black line, and a truncated power law
as a dotted line.

The similarities in slopes of our mass functions of NGC 1487 and stacked
systems (see Figures 19 and 24, and Figures 20 and 25) imply we are observing
the low-mass end cluster formation. We suggest that the pressure in NGC 1487
is too low to reach the threshold for massive clusters, as it is the result of
mergers between dwarf galaxies, and not a major merger.

We look at the cluster radii of these objects as well, using ISHAPE. Neither
tail in NGC 1487 contains enough foreground stars to produce a PSF image; we
generate a PSF for each of the five B${}_{\text{438}}$-band images in our
sample (NGC 3256W, NGC 3256E, NGC 6872, AM1054-325, and MCG-03-13-063), run
ISHAPE five separate times, using each PSF once. Our final derived
$r_{\text{h}}$ value is the mean value from each run. We find the dynamical
ages for these objects as well, as in Section 4.4. Results are shown in Figure
26. All objects except for one in these tails are gravitationally bound,
following Portegies Zwart et al. (2010). Figure 27 shows the age and mass of
these objects plotted against their radii. We again include the relation of
Brown & Gnedin (2021) between mass and radius. Our data points show similar
scatter as our SCCs, in Figure 23.

Objects in NGC 1487 are more compact than in our other tails. The median half-
light radius for bound sources in NGC 1487 is 3.03 pc, compared to 6.78 pc for
all our other systems. We do not see the large, 10 pc clusters that exist in
NGC 3256 or NGC 2992/3.

Figure 26: Half-light radii (left) and dynamical ages (right) for sources in
NGC 1487W and NGC 1487E. Figure 27: Same as Figure 23, but for combined
sources in NGC 1487E/W. We again include the mass-radius relation from Brown &
Gnedin (2021).

##  5 Summary

We have analyzed 425 SCCs in 12 tidal tails, across seven merging systems. We
summarize our findings as follows:

  1. 1.

Many objects in tidal tails show signs of line emission in colour-colour
diagrams, indicating young ages $<10$ Myr. Clusters at these ages will have
strong emission in H$\alpha$, which falls in our V${}_{\text{606}}$-band
filter. The effect of this emission impacts our colour-colour diagrams. These
colours indicate current, ongoing star formation in tidal debris. The age and
mass distributions (Figure 17) suggest that previous star formation episodes
produced many more SCCs, as evidenced by high-mass objects seen at older ages.

  2. 2.

The mass function of our SCCs has a consistent shape as compared to YMCs in
other systems. Conventionally, the mass function of YMCs takes the form of a
power-law with a slope of $\beta\approx-2.0$. Other studies have found
evidence of a high-mass cut-off, suggesting the mass function follows a
Schecter function instead. We do not find evidence for such a mass cut-off,
and find our data fit well to a power law with slope $\beta=-2.02\pm 0.15$
using binned data, and $\beta=-2.16\pm 0.09$ for a cumulative distribution
fit.

  3. 3.

The CFE in tidal tails increases as the SFR density increases. We use GALEX
and Swift UV imaging to determine the SFR in our tails. When compared to
previous observations and theoretical predictions using a reformulation of the
Kennicutt-Schmidt law from Bigiel et al. (2008) and Johnson et al. (2016), we
find good agreement, implying the gas in the tidal debris is primarily Hi and
that the CFE depends on the local environment. Our data pushed this link to
lower SFR densities than previously observed for cluster formation.

  4. 4.

Little dependence on galactic radii is seen for ages or masses of SCCs. Our KS
tests reveal only NGC 1614S has significant differences in age or mass
distributions with regard to galactocentric distance, while AM1054-325 shows
significance in mass and distance only. Our other systems show that young
clusters are distributed throughout the tails.

  5. 5.

Cluster radii of gravitationally bound objects, as determined using
calculations from Portegies Zwart et al. (2010), fall in the range of 2 – 32
pc, with a median value of 7 pc. We do not see a relation between age and
radius, or mass and radius. Work by Brown & Gnedin (2021) suggests cluster
radius increases with mass; we include their power-law determination, which is
consistent with our data.

  6. 6.

Low-mass objects in NGC 1487, which fall below our magnitude limit of MV <
-8.5, show a mass function with a slope of $\beta=-2.00\pm 0.28$ using binned
data. We find minimal significance ($\approx 1\sigma$) for a truncated power
law with slope $\beta=-2.07\pm 0.22$, and a slope of $\beta=-2.37\pm 0.18$ for
a pure power law, using a cumulative distribution fit. Though the
uncertainties are large, these values are consistent with our stacked SCC mass
function, suggesting cluster formation is consistent down to low masses.

##  6 Acknowledgments

We would like to thank the anonymous referee for helpful comments which have
improved the quality and content of this paper. This research is based on
observations made with the NASA/ESA Hubble Space Telescope obtained from the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5–26555.
These observations are associated with programs GO-7466, GO-10592, GO-11134,
GO-14066, GO-14937, and GO-15083. Support for this work was provided by grant
HST-GO-14937.002-A and HST-GO-15083.001-A. The Digitized Sky Survey was
produced at the Space Telescope Science Institute under U.S. Government grant
NAG W–2166. The images of these surveys are based on photographic data
obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK
Schmidt Telescope. The plates were processed into the present compressed
digital form with the permission of these institutions. This research is based
on observations made with GALEX, obtained from the MAST data archive at the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5–26555.

##  7 Data Availability

HST, GALEX, and Swift data are publicly available through the MAST portal at
https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. The derived
data generated in this research will be shared on reasonable request to the
corresponding author.

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##  Appendix A Notes on Individual Tails

###  A.1 NGC 1614N/S

This is our furthest merger in our sample, at a distance of 65.6 Mpc. The
tidal debris are the youngest of our systems, forming 50 Myr after the second
passage of the two galaxies (Väisänen et al., 2012). It boasts two tidal
tails, with the northern tail wrapping back onto the centre of the merger, and
the southern tail extended radially outward. This system has a large IR
luminosity, with L${}_{IR}=4\times 10^{11}$ L⊙, classifying it as a Luminous
Infrared Galaxy (LIRG). The large IR luminosity appears to be driven through
star formation. A 300 pc ring surrounding the nucleus shows evidence of
luminous Hii regions as revealed in Pa-$\alpha$ observations. This ring also
coincides with 3 micron PAH emission and radio continuum (Väisänen et al.,
2012).

X-ray observations initially suggested the presence of an obscured AGN
(Risaliti et al., 2000). However, L-band observations of the nucleus do not
show any enhanced emission (Väisänen et al., 2012) as is characteristic of an
AGN (Sani et al., 2008). The X-ray emission can be explained through low-mass
x-ray binaries (LMXBs) Olsson et al. (2010). Most notably, high resolution
VLBI observations do not find a compact source in the nucleus (Herrero-Illana
et al., 2017). Should an AGN exist in NGC 1614, it is faint and turned off.

Figures 3 and 4 show the colour-colour diagrams of the SCCs in each tail. At a
glance, the two tails in the same system appear different from each other. The
Southern tail has several objects with blue colours at V${}_{\text{606}}$ \-
I${}_{\text{814}}$ $<0$, which do not appear in the Northern tail. This is
reflected somewhat in the age distributions for the two tails, as the Southern
tails has several more young ($<10$ Myr) SCCs than seen in the Northern tail.
However, the difference in V${}_{\text{606}}$ \- I${}_{\text{814}}$ colour can
be explained if internal extinction is affecting the Northern clusters.

A KS test between the two tails for their SCC U${}_{\text{336}}$ \-
B${}_{\text{435}}$, B${}_{\text{435}}$ \- V${}_{\text{606}}$, and
V${}_{\text{606}}$ \- I${}_{\text{814}}$ colours gives p-values of 0.71, 1.3
$\times 10^{-5}$, and 5.2 x $10^{-9}$, respectively. A KS test between their
ages and masses gives p-values of 0.049 and 0.69, respectively.

KS test results for NGC 1614S between in-tail and out-of-tail SCCs for
U${}_{\text{336}}$ \- B${}_{\text{435}}$, B${}_{\text{435}}$ \-
V${}_{\text{606}}$, and V${}_{\text{606}}$ \- I${}_{\text{814}}$ colours give
$p$\- values of 0.65, 0.045, and $1.2\times 10^{-4}$, respectively. For NGC
1614N, we find $p$\- values of 0.17, 0.19, and $7.2\times 10^{-3}$, for
U${}_{\text{336}}$ \- B${}_{\text{435}}$, B${}_{\text{435}}$ \-
V${}_{\text{606}}$, and V${}_{\text{606}}$ \- I${}_{\text{814}}$. Cluster
excess for NGC 1614S and NGC 1614N are 0.078 $\pm 0.019$ kpc-2, and 0.046 $\pm
0.017$ kpc-2, respectively. NGC 1614S has a cluster excess above 3$\sigma$,
though NGC 1614N does not.

###  A.2 AM1054-325 and ESO 376-28

AM1054-325 and ESO 376-28 are an interacting pair in a relatively early stage
of their merger history, with an interaction age of 85 Myr. AM1054-325 is a
spiral galaxy with an elongated spiral arm extending to the North and a tidal
dwarf galaxy (TDG) candidate to the NE (Weilbacher et al., 2003).
Spectroscopic measurements find Hii regions in AM1054-325, created by shocked
gas (Krabbe et al., 2014), including some within the tidal dwarf galaxy, as
well as in the outer disk and extended spiral arm. Its interacting companion,
ESO 376-28, is a lenticular galaxy. Krabbe et al. (2014) finds emission lines
indicative of Hii regions within this galaxy as well.

ESO 376-28 contains only one SCC, with an age of 106.5 yr and a mass of 104.75
M⊙, about 3.6 kpc from the centre of the galaxy. Unfortunately, we cannot
derive a radius due to its low S/N in ISHAPE.

While ESO 376-28 is devoid of SCCs, its companion, AM1054-325, hosts the
largest excess of SCCs in our sample, at 1.016 $\pm$ 0.090 kpc-2. A KS test of
colours for in-tail and out-of-tail SCCs gives $p$-values of 0.166, 4.5
$\times 10^{-3}$, and 2.0 $\times 10^{-8}$, for U${}_{\text{336}}$ \-
B${}_{\text{438}}$, B${}_{\text{438}}$ \- V${}_{\text{606}}$, and
V${}_{\text{606}}$ \- I${}_{\text{814}}$ respectively. We find $p$-values less
than 0.04 for our B${}_{\text{438}}$ \- V${}_{\text{606}}$ and
V${}_{\text{606}}$ \- I${}_{\text{814}}$ colours, indicating our in-tail and
out-of-tail SCCs are drawn from differing distributions. This is largely due
to the young ages of the in-tail SCCs, as seen in the colour-colour diagram in
Figure 5. Many objects have evidence of emission from recombination lines of
hydrogen, notably H$\alpha$, strongly influencing the V${}_{\text{606}}$-band
magnitudes. The spatial distribution in Figure 5 shows that the young, < 10
Myr SCCs are distributed through the length of the tidal tail. Mixed in with
the young SCCs, we see a group of older and more massive objects, with ages
between 10${}^{8}-10^{8.5}$ and masses between $10^{5.5}-10^{6}$ M⊙. These
appear clustered around the TDG candidate, with ages similar to the age of the
interaction of the system; this region may have seen the first burst of star
formation from the encounter.

From Figure 5, there appear to be two groupings of ages, one at 6.7 and one at
7.9. It is tempting to interpret this as two isolated bursts of star
formation; however, it is possibly an indication of continuous star formation
since the encounter, and we are instead seeing artificial effects due to age
fitting. Similar artifacts are seen in other cluster studies (see Section
3.3).

The system is at a distance of 52.9 Mpc and is compact, with each galaxy
filling one quadrant of the WFC3 FOV. This causes crowding to be a concern
when fitting radii, and we eliminated about a third of our SCCs. SCCs which
were fit show radii between $\sim 3-10$ pc. All but one of the 13 sources are
gravitationally bound.

###  A.3 NGC 2992/3

NGC 2992 and 2993 are disk galaxies in the initial stages of merging. This
interaction has produced a tidal tail in NGC 2993 and a tidal dwarf galaxy at
the northern tip of NGC 2992. A tidal bridge, connecting the two main
galaxies, is not imaged in our data. Our HST observations fall on the tidal
tail of NGC 2993, and the TDG and associated tidal debris, North of the main
body of NGC 2992.

NGC 2992 contains an AGN and is classified as a Seyfert 1.9. The
classification has changed over time, as the AGN has shown variability, though
observations from 2007 – 2014 indicate it may have become stable. The
luminosity in the nuclear region appears to be dominated by the AGN, with low
contributions from star formation. Dynamical models from Duc et al. (2000)
place the interaction at 100 Myr.

This system was observed in parallel observing mode, with ACS
B${}_{\text{435}}$ and WFC3 U${}_{\text{336}}$ imaging. Due to the observing
constraints, our U${}_{\text{336}}$-band imaging is not as deep as our other
systems (see Section 2.6) and has several more undetected objects in
U${}_{\text{336}}$, resulting in upper limits in Figures 7 and 8.

A KS test between the SCCs for the two tails for their U${}_{\text{336}}$ \-
B${}_{\text{438}}$, B${}_{\text{438}}$ \- V${}_{\text{606}}$, and
V${}_{\text{606}}$ \- I${}_{\text{814}}$ colours gives p-values of 0.011,
0.16, and 1.2 $\times 10^{-3}$, respectively. A KS test between their ages and
masses gives p-values of 0.40 and 0.47, respectively. This indicates the SCCs
in both tails are consistent with being drawn from the same distribution. The
difference in KS results between colours and masses/ages can be explained if
the SCCs have internal extinction, resulting in different colours, but similar
masses and ages.

A KS test between SCC colours for in-tail and out-of-tail SCCs in NGC 2992
finds $p$-values of 0.73, 0.87, and 0.50 for U${}_{\text{336}}$ \-
B${}_{\text{435}}$, B${}_{\text{435}}$ \- V${}_{\text{606}}$, and
V${}_{\text{606}}$ \- I${}_{\text{814}}$ respectively. The fact that none of
these values are below 0.04 means we cannot say that SCCs are drawn from
different populations. However, the SCC excess is $0.070\pm 0.022$ kpc-2,
above 3$\sigma$. Thus, while the colours of in-tail and out-of-tail SCCs are
similar, the strong excess of objects inside the tidal debris lends us
confidence that these are not containment sources. NGC 2993 shows no SCCs out-
of-tail, with 9 in-tail SCCs. While there are no out-of-tail SCCs to compare
to, visual examination of Figure 8 shows an absence of detected objects (SCCs
and non-SCCs) in the out-of-tail region, above U${}_{\text{336}}$ \-
B${}_{\text{438}}$= -0.5, suggesting objects in NGC 2993 are real.

The median SCC radius for the two tails is 5.6 pc, with all but one of our
objects being bound. At the tip of the tail in NGC 2993 we find a massive,
extended cluster, with age of 108.1 yr, mass of 106.0 M⊙, and a radius of 9.5
pc.

###  A.4 MCG-03-13-063

MCG-03-13-063 is a disturbed spiral with no optical companion. Little data
exists on this system. It features an extended spiral arm, hosting beads of
clusters. The SCCs are recently formed, with ages $<10$ Myr. The arm is thin,
with clusters located in well-defined regions Mullan et al. (2011).

Our KS tests for U${}_{\text{336}}$ \- B${}_{\text{438}}$, B${}_{\text{438}}$
\- V${}_{\text{606}}$, and V${}_{\text{606}}$ \- I${}_{\text{814}}$, find
$p$-values of 2.1 $\times 10^{-3}$, 0.35, and 1.7 $\times 10^{-3}$,
respectively, for in-tail and out-of-tail SCCs. The SCC excess in this system
is $0.76\pm 0.25$ kpc-2, significant beyond 3$\sigma$.

###  A.5 NGC 6872

NGC 6872 is a disturbed barred spiral galaxy merging with the nearby, smaller
galaxy IC 4970. It is located in the Pavo Group with 12 other members. The
interaction has produced two elongated spiral arms which span a distance of
160 kpc from East to West (Eufrasio et al., 2014). Our study here focuses only
on the Eastern tidal arm of the system; we do not image the Western tail. An
X-ray view of the Pavo Group found a trail of x-ray emission between NGC 6872
and the large, dominant elliptical galaxy NGC 6876. The origin of this trail
is unlikely to be related to tidal interactions, as the morphology of NGC 6876
does not show any disturbances. Furthermore, no Hi is seen associated with the
x-ray emission (Horellou & Koribalski, 2007). Rather, it is likely due to a
Bondi-Hoyle wake; as NGC 6872 passes through the IGM, gas is gravitationally
focused in its wake, and is compressed and heated (Horellou & Koribalski,
2007; Machacek et al., 2005).

NGC 6872 has been modeled by Mihos et al. (1993) and Horellou & Koribalski
(2007), finding that the tidal arms can be reproduced in an interaction with a
small companion, at a mass ratio of 5:1. While models from Mihos et al. (1993)
predict enhanced star formation in the nucleus of the galaxy, H$\alpha$
observations show a lack of star formation in the interior; rather, the star
forming regions are located in the tidal arms.

An isolated blue clump can be seen at the Northern tip of the Eastern tail in
GALEX imaging, which unfortunately falls outside our FOV. This clump is a
possible TDG, though spectroscopic analysis is needed to confirm that it is
gravitationally bound (Eufrasio et al., 2014).

NGC 6872 hosts the largest numbers of SCCs in our sample, with 158 in the
tail, and an excess of $0.150\pm 0.016$ kpc-2. KS tests between in-tail and
out-of-tail SCCs find $p$-values of 0.026, 0.049, and 0.025 for
U${}_{\text{336}}$ \- B${}_{\text{438}}$, B${}_{\text{438}}$ \-
V${}_{\text{606}}$, and V${}_{\text{606}}$ \- I${}_{\text{814}}$,
respectively. Young SCCs are found throughout the tail, from the base to the
tip, suggesting this system is currently undergoing a burst of star formation.
Our KS tests show that there is no statistical difference between ages or
masses of SCCs with distance. However, we see a visual trend for SCCs with
ages > 108, where older SCCs are preferentially within our 41 kpc median
distance. To a lesser extent, this extends to masses > $10^{6}$, with more
massive clusters located closer to the centre. Radii are difficult to
determine as with NGC 1614, due to the large distance (62.6 Mpc) and crowding.
We find radii for seven SCCs, with only two of them being bound objects.

Our results are similar to a ground-based study of the entire body of NGC
6872, which found young clusters (< 10 Myr) and objects around $10^{6}$ M⊙ in
both of the tidal tails of the system (Bastian et al., 2005a). They also did
not find any objects older than 145 Myr in the tails; these resided in the
interior of the galaxy. Although we have found SCCs older than this in our
tidal tail, the majority are less than this age: 18 out of the 158 SCCs are
older than 145 Myr.

###  A.6 NGC 3256E/W

NGC 3256 has an IR emission of L${}_{\textrm{IR}}$ = 3.3 x
10${}^{11}L_{\odot}$ (Lípari et al., 2004), classifying it as a Luminous
Infrared Galaxy (LIRG). This is a starbursting galaxy with two prominent tidal
tails.

The central 5 kpc of the system shows three compact knots, one at optical
wavelengths and the other two in IR, as well as an asymmetric spiral arm
associated with each individual source, suggesting this system is the result
of three galaxies merging together. The likely scenario involves two disk
galaxies merging first, followed by a smaller, satellite galaxy merging
(Lípari et al., 2004, 2000).

The interior shows prodigious amounts of star formation, powering a galactic
wind and the system’s large IR luminosity (Lípari et al., 2000). This is
visualized in bright Hii regions (English & Freeman, 2003; Lípari et al.,
2000) and numerous young, blue clusters (Mulia et al., 2016; Goddard et al.,
2010; Zepf et al., 1999). Broadband analysis of such objects shows the age
distributions have an overdensity of objects with ages less than 10 Myr (Mulia
et al., 2016; Goddard et al., 2010). Spectroscopy of several of these internal
clusters also shows they have a high metallicity, at Z $\sim$ 1.5 Z⊙ (Trancho
et al., 2007b). Similarly, three clusters in the Western tidal tail studied
spectroscopically show similar elevated metallicity levels of Z $\sim$ 1.5 Z⊙
(Trancho et al., 2007a).

SCCs for both NGC 3256W and NGC 3256E do not show the large numbers of young
objects seen in the nucleus. There are only four in the Eastern tail and one
in the Western tail that fall below an age of 10 Myr. Populations of SCCs in
both tails have ages comparable to the interaction age of 400 Myr, suggesting
they formed in the interaction. Rodruck et al. (2016) find similar results for
ages of the diffuse light as well. This is also seen in Mulia et al. (2015),
who looked at clusters in NGC 3256E, at the base of the tail, near the
nucleus. The ages of these objects were weakly clustered around 250 Myr.

A KS test between the SCCs for the two tails for their U${}_{\text{336}}$ \-
B${}_{\text{438}}$, B${}_{\text{438}}$ \- $V$, and $V$ \- $I$ colours gives
p-values of 0.017, 2.2 $\times 10^{-4}$, and 8.3 $\times 10^{-3}$,
respectively. A KS test between their ages and masses gives p-values of 0.05
and 2.0 $\times 10^{-4}$, respectively. The KS tests show differences between
the masses of the clusters, though not the ages. NGC 3256E appears to be
currently forming clusters, as also seen in Rodruck et al. (2016).

KS tests for in-tail and out-of-tail SCCs give similar results for both tails.
For NGC 3256E, we find $p$-values of 0.92, 0.17, and 0.23 for
U${}_{\text{336}}$ \- B${}_{\text{438}}$, B${}_{\text{438}}$ \- $V$, and $V$
\- $I$, respectively. For NGC 3256W, we find $p$-values of 0.97, 0.33, and
0.18 for U${}_{\text{336}}$ \- B${}_{\text{438}}$, B${}_{\text{438}}$ \- $V$,
and $V$ \- $I$, respectively. The cluster excess for NGC 3256E is 0.034 $\pm
0.014$ kpc-2, and 0.103 $\pm 0.025$ kpc-2 for NGC 3256W. The excess in NGC
3256W is above 3$\sigma$.

SCCs in NGC 3256 show a median radius of 8.5 pc, larger than the typical radii
of clusters in extragalactic observations, which generally peak around 3 – 5
pc (Ennis et al., 2019; Ryon et al., 2017; Chandar et al., 2016; Bastian et
al., 2012; Jordán et al., 2007). However, these other studies still see
objects with large radii, and such large objects are expected to form in
galaxy mergers (Renaud et al., 2015). All sources for which we have a measured
radius appear to be bound, from Figure 22. Of particular note is a massive
object located near the tip of the tail, with age $10^{8.3}$ yr, mass
$10^{6.3}$ M⊙, and a radius of 10.7 pc. This is our fourth largest SCC in NGC
3256W, and is 50 kpc from the centre of the merging system. This object could
evolve to become similar to a present day globular cluster. Clusters formed in
tidal tails can migrate outwards and become isolated globular clusters (Matsui
et al., 2019).

NGC 1487 stands out from the rest of the mergers in our sample: it is three
times closer than our next closest galaxy, there is only one SCC between the
two tidal tails, and it has been classified as both a merger between two disk
galaxies (Aguero & Paolantonio, 1997) and a merger between dwarf galaxies
(Buzzo et al., 2021; Bergvall et al., 2003). Despite the lack of SCCs, visual
examination of the tails shows an abundance of objects within the debris. This
suggests the debris host faint, low-mass objects which belong to the merging
system, but are not luminous, high-mass clusters with $M_{V}<-8.6$. The
absence of high-mass objects may arise if this is indeed a merger between
dwarf galaxies. Massive star clusters and high SFRs require high gas pressure
(Maji et al., 2017; Zubovas et al., 2014; Blitz & Rosolowsky, 2006), and these
required pressures may not be produced in a dwarf galaxy merger. Lahén et al.
(2019) were able to simulate a merger between two equal sized dwarf galaxies,
which produced clusters with masses $\geq 10^{5}$ M⊙. Pressures in these
clusters was found to be $\sim 10^{7}$ $k$(K cm-3)-1, smaller than the
$10^{8}-10^{12}$ $k$(K cm-3)-1 values seen in simulations of major mergers
(Maji et al., 2017).

###  A.7 NGC 1487E/W

NGC 1487 is our nearest merging system in our sample, at 10.8 Mpc. This is a
peculiar system in that it has been called a disk merger (Aguero &
Paolantonio, 1997) and a dwarf merger (Buzzo et al., 2021; Bergvall et al.,
2003). Aguero & Paolantonio (1997) classify it as a merger between disk
galaxies due to emission line strength, which gives a SFR higher than seen in
isolated galaxies. Lee & Lee (2005) give an age for the merger at 500 Myr, as
BI-band photometry of star clusters in the nucleus suggests they are 500 Myr.
This age estimate is supported by integral field spectroscopy (Buzzo et al.,
2021). However, these estimates are based on the assumption that the age of
the interaction is correlated to the number density peak in cluster age,
implying that they formed due to the interaction. It is possible that the
present tidal tails could have formed in a secondary encounter between the
galaxies, and thus have a younger age than the quoted value.

Evidence of a dwarf merger is seen in its low mass ($4.6\pm 1.2\times 10^{9}$
M⊙) and low mass of nuclear concentrations ($\sim 1.5-0.2$ $\times$ 109 M⊙),
similar velocity fields between concentrations, and low SFRs (Buzzo et al.,
2021).

Tidal debris extends to the East and West. Most interestingly, it is the only
galaxy in our sample not to contain high-mass clusters. As discussed in
Section 4.6, NGC 1487 may be a dwarf galaxy merger, and not able to produce
the necessary pressures to form massive clusters, as seen in major mergers. We
find only one SCC in NGC 1487W, and none in NGC 1487E. The rest of the
detected objects fall below our magnitude cut of $M_{V}<-8.5$. This does not
mean that it does not contain star clusters, but rather it does not contain
high-mass clusters. Despite the lack of SCCs, both regions of debris show
clear excesses of detected objects, as compared to their respective out-of-
tail regions. The cluster excesses for in-tail vs out-of-tail sources is 4.2
$\pm$ 0.6 for NGC 1487W, and 3.3 $\pm$ 0.6 for NGC 1487E, which are
statistically significant for each tail.

The mass function for objects in the debris shows a similar slope as our SCCs
(Figure 24), though with smaller radii (Figure 26). The implication is that we
are seeing the low-mass regime of cluster formation in NGC 1487. We are able
to see these objects despite their faintness as NGC 1487 is relatively nearby
(10.8 Mpc). Three clusters in the central region observed by Mengel et al.
(2008) show similar properties to what we see in the tidal tails, with radii
between 1 – 3 pc and masses betwen 7 – 15 $\times 10^{4}$ M⊙. Hi observations
show high densities, at 2.55 $\pm 0.51\times 10^{7}$ M⊙ kpc-2, but Mullan et
al. (2011) suggest this may be an inclination effect.

The ages of objects found in the tails closely resemble previous studies of
star formation in NGC 1487. Lee & Lee (2005) found a bimodal distribution in
the colours of star clusters, which correspond to ages of 15 Myr and 500 Myr.
Buzzo et al. (2021) find the star formation history of the system to have
peaks at $\sim 10$ and $\sim 300$ Myr. Our data in the tails show objects with
ages $<10$ Myr, as well as a clustering of objects at 500 Myr, matching the
star formation history of the tails to the interior.