# NGC 5128 globular cluster candidates out to 150 kpc: a comprehensive catalog
from Gaia and ground based data 111This paper includes data gathered with the
6.5 m Magellan Telescope at Las Campanas Observatory, Chile.

Allison K. Hughes Steward Observatory, University of Arizona, 933 North Cherry
Avenue, Tucson, AZ 85721, USA  David J. Sand Steward Observatory, University
of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA  Anil Seth
Department of Physics & Astronomy, University of Utah, Salt Lake City, UT,
84112, USA  Jay Strader Center for Data Intensive and Time Domain Astronomy,
Department of Physics and Astronomy, Michigan State University, East Lansing,
MI 48824, USA  Karina Voggel Universite de Strasbourg, CNRS, Observatoire
astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France  Antoine
Dumont Department of Physics & Astronomy, University of Utah, Salt Lake City,
UT, 84112, USA  Denija Crnojević University of Tampa, 401 West Kennedy
Boulevard, Tampa, FL 33606, USA  Nelson Caldwell Center for Astrophysics,
Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Duncan A.
Forbes  Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn VIC 3122, Australia  Joshua D. Simon  Observatories of
the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA
91101, USA  Puragra Guhathakurta UCO/Lick Observatory, University of
California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA  Elisa
Toloba Department of Physics, University of the Pacific, 3601 Pacific Avenue,
Stockton, CA 95211, USA

###### Abstract

We present a new catalog of 40502 globular cluster (GC) candidates in NGC 5128
out to a projected radius of $\sim$150 kpc, based on data from the Panoramic
Imaging Survey of Centaurus and Sculptor (PISCeS), Gaia Data Release 2, and
the NOAO Source Catalog. Ranking these candidates based on the likelihood that
they are true GCs, we find that approximately 1900 belong to our top two
ranking categories and should be the highest priority for spectroscopic
follow-up for confirmation. Taking into account our new data and a vetting of
previous GC catalogs, we estimate a total GC population of $1450\pm 160$ GCs.
We show that a substantial number of sources previously argued to be low-
velocity GCs are instead foreground stars, reducing the inferred GC velocity
dispersion. This work showcases the power of Gaia to identify slightly
extended sources at the $\sim 4$ Mpc distance of NGC 5128, enabling accurate
identification of GCs throughout the entire extended halo, not just the inner
regions that have been the focus of most previous work.

Globular star clusters (656), Optical identification (1167), Galaxy evolution
(594)

††facilities: Magellan:Clay (Megacam), Gaia††software: Source Extractor
(Bertin & Arnouts, 1996), SWarp (Bertin, 2010), The IDL Astronomy User’s
Library (Landsman, 1993)

revtex4-1Repair the float

##  1 Introduction

Globular clusters (GCs) are an essential tool for understanding the formation,
structure, and evolution of galaxies beyond the Local Group, where
spectroscopy of individual stars is typically difficult or impossible (see the
reviews of Harris 1991; Brodie & Strader 2006; Beasley 2020). These old,
massive ($\gtrsim 10^{4}M_{\odot}$) star clusters are found in all but the
least luminous galaxies. The majority of GCs are associated with the stellar
halo, where they serve as luminous beacons of the underlying low surface
brightness stellar population. With modern wide-field imagers and
spectrographs, GCs can be used to measure the mass and structure of dark
matter halos (e.g., Alabi et al. 2016; Wasserman et al. 2018) and trace
individual accretion events (e.g., Mackey et al. 2010).

Historically, NGC 5128 (Centaurus A) has been a leading target for
extragalactic GC studies, due to its richness and proximity. NGC 5128 is the
central elliptical galaxy in a small group of galaxies at a distance of
$3.8\pm 0.1$ Mpc (Harris et al., 2010). Since the first discovery of GCs in
NGC 5128 in the 1980s, many photometric and spectroscopic surveys have been
conducted, leading to the identification of 557 confirmed GCs and thousands of
GC candidates (Graham & Phillips, 1980; van den Bergh et al., 1981; Hesser et
al., 1986; Harris et al., 1992, 2004, 2012; Holland et al., 1999; Harris et
al., 2002, 2006; Peng et al., 2004; Martini & Ho, 2004; Woodley et al., 2005,
2007, 2010a, 2010b; Gómez et al., 2006; Rejkuba et al., 2007; Beasley et al.,
2008; Georgiev et al., 2009, 2010; Taylor et al., 2010, 2015, 2017; Mouhcine
et al., 2010; Sinnott et al., 2010; Voggel et al., 2020; Fahrion et al., 2020;
Müller et al., 2020). The majority of these studies have focused on the inner
$\sim$ 40 kpc of the galaxy. Both the presence of halo substructures out to
$\gtrsim$ 100 kpc (Crnojević et al., 2016, 2019) and the fact that the total
GC population of NGC 5128 is likely in the range of $\sim$ 1000–2000 clusters
(e.g., Harris et al. 2006; Harris 2010; Taylor et al. 2017) illustrate that
there is substantial room for novel studies of the NGC 5128 GC system,
especially in the outer halo.

While the proximity of NGC 5128 aids in the identification and follow-up of GC
candidates, this close distance also provides several challenges. First, the
halo of NGC 5128 is spread across $\gtrsim$ 20 deg2 of sky (Crnojević et al.,
2016), requiring large area searches for a comprehensive accounting of the
stellar halo and GC system. NGC 5128 is also relatively close to the Galactic
plane (with a Galactic latitude of $b\sim 19^{\circ}$), leading to significant
contamination from foreground stars as well as foreground extinction
($E(B-V)\sim 0.12$ mag; Schlafly & Finkbeiner 2011). An additional issue is
that with a modest systematic velocity of 541 km s-1 (Hui et al., 1995) and a
velocity dispersion of $\sigma\sim 150$ km s-1 (Wilkinson et al., 1986; Silge
et al., 2005), there is some overlap in radial velocity of NGC 5128 GCs and
Milky Way foreground stars: radial velocity _alone_ cannot definitively give
membership for every object, especially on the low-velocity end of the
distribution (see Appendix B).

The Panoramic Imaging Survey of Centaurus and Sculptor (PISCeS) produced a
wide-field resolved stellar map of NGC 5128 out to a projected galactocentric
radius of $\sim$ 150 kpc (Crnojević et al., 2016). The PISCeS data are
invaluable in searching for GCs because of the survey’s wide angular coverage
and good seeing (median FWHM of $0.66\arcsec$), which allows GCs at the
distance of NGC 5128 to be marginally resolved and hence separated from
foreground stars.

Here we take advantage of this exquisite dataset to build a new wide-field
catalog of GC candidates, focusing especially on the outer halo (projected
radii $\sim 40$–150 kpc) that is nearly unexplored with spectroscopy. We
supplement our high-quality PISCeS imaging with other data from Gaia DR2 and
the NOAO Source Catalog to refine our sample, with a future goal of
comprehensive spectroscopic follow-up.

The PISCeS data are well-suited to identify typical GCs outside the central
regions of NGC 5128. In a companion paper (Voggel et al., 2020), hereafter
V20, our team focuses on the related question of constructing a complete
sample of the most luminous GCs and stripped galaxy nuclei in NGC 5128. This
requires a distinct approach as many of these sources are saturated or crowded
in the PISCeS data.

This paper is organized as follows. Section 2 outlines the key datasets used
in our GC candidate search. In Section 3 we identify a fiducial sample of
known radial velocity confirmed NGC 5128 GCs which we use to define our GC
candidate selection methodology, which we describe in Section 4. Our final
catalogs are presented in Section 5, and further results are discussed in
Section 6. We summarize and conclude in Section 7. In the Appendix, we present
a collected catalog of all confirmed NGC 5128 GCs as a resource for the
community. We additionally provide information detailing foreground stars,
identified by their Gaia parallax or proper motion measurements, that were
previously mis-reported as NGC 5128 GCs, and report and resolve other
discrepancies in the NGC 5128 GC literature, when possible. Throughout this
work we adopt a distance modulus for NGC 5128 of $(m-M)_{0}=27.91$ mag,
corresponding to a distance of $D=3.82$ Mpc (Harris et al., 2010). The
physical scale at this distance is 18.5 pc arcsec-1 (1.1 kpc arcmin-1).

##  2 Key Datasets

###  2.1 The PISCeS Survey

The foundational dataset of our GC search is deep NGC 5128 Magellan/Megacam
imaging from the PISCeS survey. Here we briefly describe the relevant aspects
of the survey strategy and observational methods; for further details see
Crnojević et al. (2014, 2016, 2019).

The goal of the PISCeS survey is to image the halos of the nearby massive
galaxies NGC 5128 and NGC 253 (NGC 253 is not covered in this paper; see Sand
et al. 2014 and Toloba et al. 2016) out to a projected radius of $R\sim$ 150
kpc. The data are deep enough to reach $\sim$ 1–2 mag below the tip of the red
giant branch ($r\sim 25.5$–26.5 mag). These uniquely deep wide-field maps
enable discovery of faint dwarf galaxies and other halo substructures, such as
tidal streams and shells, allowing comparisons with similar observations in
the Local Group (e.g. McConnachie et al., 2009).

The PISCeS survey uses the Megacam imager (McLeod et al., 2015) on the 6.5-m
Magellan Clay telescope. With the f/5 secondary, Megacam has a $\sim$ 24′
$\times$ 24′ field-of-view with a binned (2$\times$2) scale of 0.16″ per
pixel. We tiled the halo of NGC 5128 with individual pointings of this size,
as illustrated in Figure 1. The typical exposure times were 6$\times$300 s in
both the $g$ and $r$ bands, but were adjusted depending on the seeing and sky
conditions to try to achieve a similar depth in poorer seeing or non-
photometric conditions.

The data were reduced in the standard manner at the Smithsonian Astrophysical
Observatory Telescope Data Center, including bias subtraction, flat fielding,
and cosmic ray rejection. As part of this reduction, an ICRS astrometric
solution based on the 2MASS point source catalog (Cutri et al., 2003) was
applied and the images of a given field and filter were stacked with SWARP
(Bertin, 2010). Subsequent to this processing, the release of Gaia DR2 allowed
us to check this astrometry. Cross-matching found a mean PISCeS–Gaia DR2
offset of ($\alpha$ cos $\delta$, $\delta$) of ($0.1300\pm 0.0002\arcsec$,
$0.0634\pm 0.0002\arcsec$). These values are consistent across fields and
subsamples of PISCeS. We do _not_ correct the self-consistent astrometry of
PISCeS to the Gaia DR2 frame.

Photometric calibration was done by observing Sloan Digital Sky Survey (SDSS;
Ahumada et al. 2020) equatorial fields on photometric nights at a variety of
airmasses. We designed intentional $\sim 2\arcmin$ overlaps between NGC 5128
fields to allow for cross-calibration of the entire survey, leveraging data
taken on photometric nights. All photometry is on the AB mag system. This
paper includes data from 95 pointings around NGC 5128 obtained between 2010
and 2017, as illustrated in Figure 1. The footprint includes nearly full
coverage of the area out to $\sim$ 150 kpc from the center of the galaxy, and
an arm extending in the north-west direction out to $\sim 260$ kpc.

For GC candidate photometry, we ran Source Extractor (Bertin & Arnouts, 1996)
on the $g$ and $r$ stacked images. Aperture photometry was done using aperture
diameters of 3 and 6 pixels (0.48″and 0.96″, respectively), with the intention
of using the differences between these magnitudes to select extended
sources—including GCs. We also measure the “total” magnitudes for each source
in our catalog at a diameter of 6$\times$FWHM (for the median seeing, this is
a radius $\sim 12.4$ pixels = 2.0″), with an aperture correction determined on
a field-by-field basis. When relevant, we correct the photometry for
foreground Galactic extinction using the maps of Schlafly & Finkbeiner (2011)
on a source-by-source basis. We are explicit about when a correction for
extinction is (or is not) made throughout this work, and all absolute
magnitudes are extinction-corrected. Finally, we combine the $g$ and $r$
catalogs using a matching radius of $1\arcsec$. Our use of PISCeS data to
select GC candidates is detailed in §4.1–4.3.

GCs are luminous: the peak of the lognormal GC luminosity function (GCLF) is
expected to occur at $M_{r}\sim-7.7$ (Pota et al., 2015) with $\sigma\sim 1.3$
mag (Jordán et al., 2007), corresponding to an observed peak near $r\sim
20.5$. This means that the PISCeS survey, designed for depths of $r\sim
26$–26.5, is quite effective at photometry of _typical_ GCs around NGC 5128.
However, we have issues with recovering the most luminous GCs and ultra-
compact dwarfs, which are up to $\sim 10$ mag (a factor of 10000) brighter
than our targeted individual red giants. PISCeS data start to saturate for
point sources with $r\lesssim 18$ ($M_{r}\lesssim-10.2$) in the median field,
with this limit pushed to $r\lesssim 18.6$–18.8 ($M_{r}\lesssim-9.6$ to –9.4)
for the few pointings with the best seeing or highest background. For this
reason, in our companion paper V20, we take a different approach to making a
complete catalog of the most luminous sources, which relies only partially on
the PISCeS data.

Figure 1: Footprint of the PISCeS survey around NGC 5128, using data from
2010-2017 and comprising 95 separate Magellan/Megacam fields and oriented such
that north is up and east is left. The dashed circle marks a radius of 150 kpc
from the center of NGC 5128, located at $\alpha$=$201.362540^{\circ}$,
$\delta$=$-43.033627^{\circ}$, which is marked by the central black ‘x’. The
blue dots mark the positions of known confirmed GCs around NGC 5128, which are
largely confined to the central $\sim$40 kpc. Note that several pointings in
this map were not presented in the dwarf galaxy luminosity function analysis
of Crnojević et al. (2019) but are included here: an extension to the
northwest, two pointings to the south centered on known dwarfs KK203 and
KK196, and data that was not high enough quality for a dwarf search but is
sufficiently deep for our GC search.

###  2.2 Gaia Data Release 2

Gaia is an ongoing all-sky astrometric space mission. Its second data release
(DR2) presents at least some astrometric and photometric measurements for over
a billion sources down to a broadband $G\sim 21$ mag (Gaia Collaboration et
al., 2018b).

Gaia DR2 is a useful adjunct to the PISCeS data in two areas. First, through
its measurements of proper motion and parallax, it allows us to identify and
remove a large fraction of Galactic foreground stars that would otherwise
contaminate our GC candidate sample. Second, with an effective angular
resolution of $\sim 0.4\arcsec$ (Evans et al., 2018), Gaia DR2 includes
astrometric and photometric statistics that can be used to pinpoint even
marginally extended sources such as GCs in NGC 5128.

We explain our use of Gaia DR2 to identify NGC 5128 GCs in §4.4. The newly
available Gaia Early Data Release 3 (Gaia Collaboration et al., 2020) and
other future updates will provide additional and higher quality data for
sources, increasing the accuracy with which we can identify nearby
extragalactic GCs.

###  2.3 NOAO Source Catalog

The NOAO Source Catalog (NSC) is a unified collection of nearly all of the
public data taken on the Dark Energy Camera (DECam) on the Blanco 4-m
telescope at CTIO as well as the Mosaic3 imager on the 4m Mayall telescope at
KPNO (Nidever et al., 2018). It includes our area of interest around NGC 5128,
with typical depths of $u\sim$ 23.3, $g\sim$ 21.7, $r\sim$ 21.2, $i\sim$ 21.2,
and $z\sim 21.0$. For this work we have used Data Release 1 of the NSC,
although Data Release 2 has recently become available (Nidever et al., 2020).

GCs have spectral energy distributions that are distinct from both individual
foreground stars and from background galaxies with extended star formation
histories. However, the single color available from PISCeS ($g-r$) does an
inadequate job at separating these populations. The multi-color photometry
available in the NSC provides yet another method to identify and remove Milky
Way foreground stars that would otherwise contaminate our GC candidate sample.
We explain the use of the NSC to identify NGC 5128 GCs via their color in
§4.5.

To bring together data obtained under different protocols and by multiple
PI’s, Nidever et al. (2018) reprocessed the raw data with consistent quality
control, selection, and calibration. Astrometric calibration with $Gaia$ DR1
was done for each chip independently. Photometric calibration was done with
model magnitudes constructed for their filters from public all-sky catalogs
and the Schlegel et al. (1998) reddening map for the extinction term. There is
a fairly consistent, color-dependent offset between the PISCeS and NSC
photometry, between $\pm$ 0.1 mag in the $r$-band and 0.05 and 0.17 mag in the
$g$-band. We provide information about both PISCeS and NSC photometry in our
final catalog of GC candidates.

The NSC includes the same data that comprises the Survey of Centaurus A’s
Baryonic Structures (SCABS), a wide-field $ugriz$ imaging survey of NGC 5128
using DECam (Taylor et al., 2016, 2017), hereafter T17. T17 provides a list of
likely NGC 5128 GC candidates out to $\sim$140 kpc based on color and some
structural information. We do not use the SCABS data catalogs directly
because: (i) the PISCeS data generally have higher image quality (median FWHM
= $0.66\arcsec$) than the SCABS data (FWHM $\sim 0.8\arcsec$–1.2″); (ii) it is
clear from intercomparisons of PISCeS, NSC, and SCABS that the latter suffers
from field edge effects and significant, inconsistent magnitude offsets; and
(iii) the NSC has a higher completeness for known GCs than SCABS. We also note
in passing that Table 2 of T17 appears to be extinction corrected, despite the
statements in the table caption and text that it has not been (we hope this
information helps future researchers using these data). Within the PISCeS
footprint, the NSC contains the reprocessed raw data from SCABS and other
surveys with consistent quality control, selection, and calibration that
results in a catalog with higher quality than SCABS alone.

##  3 A fiducial sample of radial velocity-confirmed globular clusters

To help guide and assess the fidelity of our GC candidate selection, we first
build a fiducial sample of radial velocity-confirmed GCs in NGC 5128. We find
an initial set of 630 “confirmed” GCs by cross-matching published samples
(Graham & Phillips, 1980; van den Bergh et al., 1981; Harris et al., 1992,
2002; Peng et al., 2004; Woodley et al., 2005; Harris et al., 2006; Rejkuba et
al., 2007; Woodley et al., 2007; Beasley et al., 2008; Georgiev et al., 2009;
Woodley et al., 2010a, b; Taylor et al., 2010; Georgiev et al., 2010; Fahrion
et al., 2020; Müller et al., 2020; Voggel et al., 2020). The most common way
to confirm a GC is based on its radial velocity, though some studies instead
rely on morphological parameters or visual classification with Hubble Space
Telescope (HST) imaging. Updated Gaia DR2 and radial velocity measurements for
many of these sources show that 73 objects are not actually GCs in NGC 5128;
see Appendix B for details. Removing this contamination leaves a cleaned list
of 557 confirmed GCs around NGC 5128, which we discuss and provide in Table 4
in Appendix A.

For the specific goals of this paper, we select a subset of these confirmed
GCs to guide our selection process. Each GC in this fiducial sample: (i) is
$>10\arcmin$ from the center of NGC 5128; (ii) has a radial velocity $>250$ km
s-1; (iii) is in the Gaia DR2 catalog and does not have proper motion and
parallax values consistent with being in the foreground; (iv) has not been
marked as a foreground star or background galaxy in any catalog; and (v) has
photometry in our PISCeS Source Extractor catalogs and in the NOAO Source
Catalog. This leaves a set of 69 fiducial GCs, as noted in Table 4 that can be
used to test all of the criteria we use for selecting GCs outside the central
regions of NGC 5128. We think nearly all of the GCs in the larger, cleaned
sample of 557 confirmed objects are true GCs associated with NGC 5128, and use
this broader list to assess the completeness of our sample in Section 6.3.

In addition to our fiducial sample of GCs, we also construct similar sets of
foreground stars and background galaxies that have been confirmed via radial
velocity measurements or HST imaging, as found by previous studies of NGC 5128
(Peng et al., 2004; Woodley et al., 2005; Harris et al., 2006; Gómez et al.,
2006; Beasley et al., 2008). These confirmed contaminant samples allow
independent tests of the precision of our GC selection techniques.

##  4 Identifying Globular Cluster Candidates

This section describes the process of finding GC candidates within the 95
calibrated images from the PISCeS survey, incorporating data from Gaia DR2 and
NSC. A summary is given in Section 4.6. .

To assess the effectiveness of each step of our selection process, we compare
our results with our fiducial sample of confirmed GCs and catalogs of known
foreground stars and background galaxies. Information from each part of our
selection process is used to calculate a final GC likelihood score between 0
and 1 for each candidate, where a score of 1 corresponds to those most likely
to be true GCs in NGC 5128. Where possible, we prioritize completeness over
purity in each step of our selection process, though we recognize the
limitations that our datasets have in regards to the brightest and faintest
GCs.

###  4.1 Initial Cuts

At the bright end, we remove saturated or nearly saturated sources, which
typically have $r\lesssim 18$ mag (see also §4.2). We use a faint magnitude
limit of 22 mag in the band ($g$ or $r$) with better seeing. A magnitude of
$g=22$ mag is $\sim 0.7$ mag (a factor of $\sim 1.9$ in luminosity) beyond the
turnover of the GCLF. Fainter than this limit, contamination grows
substantially, and ancillary information from Gaia DR2 and NSC is either
absent or of lower quality. We use the same limit with the $r$ band ($r<22$
mag) to help remove spurious sources, since essentially all true GCs have
$g-r>0$. Finally, we restrict our study to projected distances greater than
$10\arcmin$ from the center of NGC 5128, as crowding strongly affects our
photometry in this inner region. Much of this central area is already covered
by high-quality _HST_ data and other GC surveys.

We do not include in our candidate catalog any objects that have been
confirmed in previous NGC 5128 studies as background galaxies or foreground
stars via radial velocity measurements or HST imaging, unless specifically
noted in Table 6 in Appendix B.2.

###  4.2 Concentration Index

Figure 2:  The concentration index ($C_{3-6}$) for fiducial sample GCs (green
squares) and all sources between 10–30′ of the center of NGC 5128 (black
dots). The left panel shows $r$-band data and the right panel shows $g$-band
data. Objects with a larger $C_{3-6}$, such as GCs and background galaxies,
are extended compared to point source foreground stars. Objects plotted in
gray have been removed due to saturation/near saturation at brighter
magnitudes.

Milky Way GCs range in half-light radius from 1–20 pc (with a mean of $\approx
3$ pc), corresponding to 0.05–1.08″ at the distance of NGC 5128. In the
excellent seeing of the PISCeS data (median FWHM of $0.66\arcsec$), this means
that GCs are slightly extended compared to point sources. The most massive and
largest GCs can be readily identified by the resolved stars along their
outskirts (see also V20).

We can utilize the extended nature of GCs in NGC 5128 to separate them from
foreground stars in the Milky Way using a concentration index–magnitude
diagram. This method has been commonly used in previous extragalactic GC
studies to separate candidate GCs from foreground stars or background
galaxies, both from the ground and with _HST_ (Whitmore et al., 1999; Peng et
al., 2011; Durrell et al., 2014; Peng & Lim, 2016; Beasley & Trujillo, 2016;
Ko et al., 2019).

To calculate the concentration indices, for each field we measure the
difference in magnitudes at diameters of 3 and 6 pixels (0.48″ and 0.96″,
respectively) for each source. These aperture sizes were chosen to be
effective at separating true GCs from contaminants under a range of crowding
and signal-to-noise conditions. Because the image quality differs among the 95
fields, the mean magnitude difference for foreground stars varies between 0.72
and 1.28 mag, with a standard deviation in the range 0.01–0.07 mag. To create
a concentration index that can be compared among fields, we select unsaturated
point sources with magnitudes between 18.5 and 20.0, and normalize the
distribution of magnitude differences to a mean of 0 and a standard deviation
of 1 on a per field basis after trimming outliers.222Using the IDL code
resistant$\\_$mean. All robust means and standard deviations calculated in
this paper use the same code. Figure 2 shows the concentration index–magnitude
diagram for all sources between 10 and 30′ of NGC 5128, highlighting the
separation of the fiducial sample GCs from foreground stars. We use the symbol
$C_{3-6}$ to represent these normalized values, where larger $C_{3-6}$ values
correspond to more extended sources.

Assuming that point sources are distributed in a Gaussian distribution
centered around $C_{3-6}=0$, concentration_likelihood for each GC candidate is
defined as 1 minus the probability that the candidate’s $C_{3-6}$ value is
consistent with a point source. For this calculation, we use data from the
observing band ($g$ or $r$) with better seeing. As an example, if a candidate
has $C_{3-6}=2.0$, it lies 2$\sigma$ above the point source average for that
field, and we assign it a concentration_likelihood of $0.977$.

Stars that are nearly saturated lead to $C_{3-6}$ values above zero at bright
magnitudes even for true point sources (see stars with $r\lesssim 18$ in
Figure 2). We exclude these saturated (or nearly saturated) objects. Reliably
identifying the most luminous GCs and ultra-compact dwarfs requires a separate
set of selection criteria, discussed in V20.

All of the fiducial sample GCs have $C_{3-6}$ values greater than 1.3 in the
$r$-band and greater than 1.7 in the $g$-band, corresponding to
concentration_likelihood values greater than 0.912 and 0.958, respectively.
The average $C_{3-6}$ value of the fiducial GCs is 3.9 in the $r$-band, and
5.2 in the $g$-band. For each candidate we use the band with better seeing to
calculate its likelihood, noting that the fiducial sample is recovered with
high purity in both bands.

We compiled all available size information for GCs in NGC 5128 (McLaughlin et
al., 2008; Rejkuba et al., 2007; Taylor et al., 2010, 2015) Only 16 of the 69
fiducial sample GCs have physical size information, with half-light radii
between $\approx$ 2.1–4.9 pc and an average of 3.0 pc. The smallest of these
has a concentration index of 1.7 in the $r$-band and 4.1 in the $g$-band.
Because most searches are not sensitive to the most compact GCs and our
selection cuts are based on previously known GCs, our final catalog may also
not include the smallest GCs (half-light radius $\approx$ 1–2 pc) in NGC 5128.

All sources in the 95 PISCeS fields that passed the initial cuts and have a
concentration_likelihood $>$ 0.84 ($C_{3-6}>1.0$) are passed as GC candidates
to the next stage of the selection process.

###  4.3 Removing Galaxies and Blends

Figure 3: Examples of extended objects with $C_{3-6}>$ 3\. In the left panel,
starting in the upper left subpanel and going clockwise is: (a) A confirmed,
luminous GC (KV19-442) that is partially resolved, with red giants apparent in
its outskirts; (b) a good GC candidate that is not resolved into stars, but
which is extended compared to a point source; (c) a pair of foreground stars
that are close enough that they are photometered as a single source with a
large $C_{3-6}$ value; and (d) a very extended galaxy that is cut during the
galaxy removal process (§4.3). Each image is $\approx 1^{\prime}\times
1^{\prime}$. In the right panel, we show an example of how a GC can be
distinguished from a background galaxy by using a brightness profile compiled
from a series of concentric apertures with 12, 20, 28, and 36 pixel diameters
(yellow circles). The smaller, red circles show the 3 and 6 pixel diameter
apertures used for the concentration index measurements.

Besides GCs, there are other types of extended sources in the PISCeS data.
Among objects with higher values of concentration index ($C_{3-6}>3$), there
is a substantial contribution from background galaxies, especially toward
fainter magnitudes. Due to the relatively low Galactic latitude of NGC 5128
($b=19^{\circ}$) blends or near-blends of foreground stars are also common.
Figure 3 shows visual examples of both true GCs and common contaminants.

The process described in this section aims to reduce contamination from
background galaxies and stellar blends in our final GC candidate catalog by
analyzing the shape and brightness profile of each of our potential GC
candidate targets.

We build an algorithm that produces a binary output, identifying a source as
being either: (1) too elliptical and/or too extended to be a GC in NGC 5128,
in which case it is given a structure-based likelihood (structure_check) of 0,
or (2) round and only slightly extended, as expected for GCs, in which case it
is given structure_check = 1. This algorithm was designed empirically such
that a majority of visually identifiable galaxies receive structure_check = 0,
while the fiducial sample GCs receive structure_check = 1.

The galaxy/blend assessment that produces this final binary output is a three-
step process. For each source, we first take the Source Extractor flux_radius
parameter, which measures the circular-equivalent effective radius (the
circular aperture radius enclosing half the total flux of an object) in units
of pixels. We then compare this to a conservative limit, which is a robust
average flux_radius of foreground stars in the field + 3 pixels, tuned to pass
even marginal GC candidates and exclude the more obvious galaxies. Objects
above this critical value are given structure_check = 0, while those with
flux_radius values below the limit continue to the next step.

We next check the ellipticity of the candidates, motivated by the fact that
true GCs are mostly round, while background galaxies (and blends) have a
broader ellipticity distribution. The ellipticity $\epsilon$ is defined as
$\epsilon=1-b/a$, where $a$ and $b$ are the semi-major and semi-minor axes
measured by Source Extractor. We reject the source (set structure_check = 0)
if $\epsilon>0.35$ in one of $g$\- and $r$-bands and $\epsilon>0.25$ in the
other. A few of the most massive star clusters around NGC 5128 have
ellipticities up to $\epsilon\sim 0.35$, likely related to their origin as
stripped galaxy nuclei (Voggel et al., 2018). Hence our ellipticity cut could
in principle remove a small number of sources truly associated with NGC 5128.
Since the current paper is focused on typical GCs rather than the most massive
objects, this ellipticity cut represents an important step in removing the
contaminants that are abundant at fainter magnitudes.

As a final evaluation of how extended the brightness profiles of individual
candidates are, in each band we measure the magnitude of each target in
concentric apertures of diameter 12, 20, 28, and 36 pixels, and determine the
magnitude differences between successive pairs (diff_12_20, diff_20_28, and
diff_28_36). For this step, we reject the source (set structure_check = 0) as
too extended if _all_ three of the following conditions are met in either
$g$\- or $r$-band: (i) diff_12_20 is 10 times greater than the aperture
correction value (see Section 2.1); (ii) diff_20_28 $>$ 0.1; and (iii)
diff_28_36 $>$ 0.1. These larger apertures effectively remove extended,
moderately round background galaxies that passed the previous selection steps.
See Figure 3 for a visual example of this process.

As a test of this galaxy/blend removal step, we compare our results with the
velocity-confirmed background galaxies from several previous spectroscopic
studies of GCs around NGC 5128 (Peng et al., 2004; Woodley et al., 2005; Gómez
et al., 2006; Beasley et al., 2008). These sources were originally selected in
a variety of ways, but generally had colors and magnitudes consistent with
those expected for GCs. We find that the steps in this subsection identify 58
out of 95 (61%) unique background galaxies from these previous studies. It is
reasonable to assume that a subset of the more obvious background galaxies
were culled prior to spectroscopy in these studies. Therefore, our selection
steps can be expected to successfully flag and remove a large fraction of
background galaxies in our magnitude range.

By examining the confirmed background galaxies _not_ identified by our
selection steps, we find that these are marginally extended and circular and
hence visually similar to true GCs. As we discuss below, additional
photometric or spectroscopic information is needed to reliably reject these
remaining background galaxies.

In total, 66% of the possible GC candidates that meet the criteria detailed at
the end of §4.2 are given structure_check = 1, and the other 34% are given
structure_check = 0 and removed from the GC candidate sample.

###  4.4 Gaia DR2

Section 2.2 briefly introduced the possibility of using Gaia DR2 to improve
our GC catalog both in relatively straightforward ways (by removing foreground
stars) and in a more unexpected fashion (by identifying marginally resolved
sources). Here we discuss how we use a range of astrometric and photometric
Gaia DR2 measurements in our GC candidate selection process.

First, we note that 305 of the 557 confirmed NGC 5128 GCs (55%) are in Gaia
DR2. About 80% of the missing objects are faint ($g>20$ in PISCeS or NSC) and
likely below the DR2 completeness limit (Boubert & Everall, 2020). Most of the
rest are within $10\arcmin$ of the galaxy center (where photometry is
difficult), or have conflicting literature classifications (see Appendix B.2
for details).

Of the GC candidates that passed the galaxy/blend removal step in §4.3, we
find that 62% of these sources are in Gaia DR2. If a source is _not_ in DR2,
it is simply passed to the color selection in §4.5. Likewise, if a source is
in Gaia DR2, but has a missing measurement (such as the BP/RP excess factor
discussed below), we simply skip the evaluation of the relevant step.

####  4.4.1 Proper Motion & Parallax

The proper motions and parallaxes of objects associated with NGC 5128 cannot
be measured with Gaia DR2. Therefore, any sources with significant proper
motions or parallaxes can be identified as being in the foreground, and
removed from the GC candidate sample.

We first calculate the total proper motion of an object by adding the right
ascension and declination components in quadrature. Assuming the combined
proper motion has a Chi distribution with two degrees of freedom, it can be
simplified to a Rayleigh distribution. We assign a proper_motion_likelihood of
1–CDF, where CDF is the cumulative distribution function of the Rayleigh
distribution. Sources with lower proper_motion_likelihood values are therefore
more likely to be foreground stars based on their proper motion measurements.
For example, if the proper motion is significant at $2\sigma$, the likelihood
assigned is 1–0.865 = 0.135. We truncate this at $3\sigma$ (0.011): sources
with proper motions more significant than this value are given
proper_motion_likelihood = 0 and removed from the candidate list.

We also calculate a similar parallax_likelihood based on the significance of
the parallax, here assuming the measurement has a Gaussian distribution. For
example, if the parallax is significant at $2\sigma$, the likelihood assigned
is $1-0.954=0.046$. Sources with $>3\sigma$ parallax measurements are given
parallax_likelihood = 0 and removed from the candidate list. Since significant
parallax measurements are much less common than significant proper motion
measurements in Gaia DR2, it is rare to have an object with a significant
parallax but not a significant proper motion.

Of the GC candidates in Gaia DR2 that passed the galaxy/blend removal step in
§4.3, we find that 68% are removed for having proper motion and/or parallax
measurements consistent with being foreground stars.

Of the 391 confirmed foreground stars in previously published papers, 313
(80%) are identified using these proper_motion_likelihood and
parallax_likelihood criteria. The remainder have insignificant proper motions
or parallaxes or are not in Gaia DR2, primarily because they are faint. This
comparison shows that Gaia is an effective tool to identify and remove
foreground stars from our GC candidate sample.

####  4.4.2 Astrometric Excess Noise

Figure 4: Left: Plot of Gaia’s AEN parameter versus G band magnitude. Right:
Plot of Gaia’s $BR_{\rm excess}$ parameter versus G band magnitude. In both
plots, the black dots are all Gaia DR2 sources between 10–60′ of NGC 5128, the
green squares are fiducial sample GCs, blue diamonds are foreground stars
based on their proper motion (discussed in Appendix B.1), and orange triangles
are radial velocity confirmed foreground stars. The fiducial sample GCs are
distinct from the general population of foreground stars in both parameter-
spaces, and so we can use the AEN and $BR_{\rm excess}$ parameters to identify
GC candidates. The lines denoting 3$\sigma$ are given by Equations 1 and 2.
Confirmed foreground stars with AEN or $BR_{\rm excess}$ values greater than
3$\sigma$ are stellar blends, visible in PISCeS images.

Gaia DR2 reports the astrometric excess noise (AEN) as a statistic that
quantifies the goodness-of-fit of their five-parameter astrometric model to
the astrometry for each target (Gaia Collaboration et al., 2018a). The AEN,
given in units of milli-arcseconds (mas), is equal to 0 for a well-fit star
and has larger values for poorer fits. Objects that are extended compared to
point sources have large AEN values, and in V20 we showed that this can be
used to select marginally resolved objects such as GCs around NGC 5128.

In Figure 4 we plot AEN-Gaia DR2 $G$ mag for sources around NGC 5128. Most of
these are foreground stars and therefore have low AEN values ($\lesssim 1$),
especially at brighter magnitudes where the random uncertainties are smaller.
This figure also plots the fiducial sample GCs, showing that they have larger
AEN values and are largely distinct from foreground stars. Much like the
concentration index $C_{3-6}$, AEN is more valuable for rejecting foreground
stars than for rejecting extended objects such as background galaxies or
foreground star blends, which like GCs will have higher AEN values.

Because the AEN distribution depends on the Gaia DR2 $G$ mag, we determined
robust AEN mean and standard deviation for point sources in 0.1 mag bins. We
then calculate a candidate’s aen_likelihood as 1 minus the probability that
its AEN value is consistent with a point source at that magnitude, truncating
the distribution at $-2\sigma$ (aen_likelihood = 0.023). Rather than an error,
each AEN value is also reported with a corresponding “significance” measure,
where a value greater than 2 indicates that the given AEN is probably
significant. Because a majority of sources with high AEN values are not single
stars, they have bad astrometric fits and therefore high significance values.

As an example calculation, consider a GC candidate with an AEN value of 2.14
mas and Gaia DR2 $G=20.03$ mag. In the bin between $G=20.0$ and 20.1 mag,
foreground stars have an AEN robust mean of 1.465 mas and $\sigma=0.672$ mas.
This GC candidate is $1\sigma$ above the mean for point sources and therefore
has an aen_likelihood of 0.841.

For the convenience of the reader who wishes to have a simple criterion to
find extended sources in other circumstances, we use information from Gaia DR2
for sources in the radial range 10–60′ from the galaxy center to define a line
3$\sigma$ above the mean foreground star AEN value:

$AEN_{3\sigma}=0.297+5.63\times 10^{-8}\,e^{0.895\,G}$ (1)

where $G$ is the Gaia DR2 $G$ mag. This line is plotted in Figure 4. We
emphasize that for this paper we use the likelihood analysis described above.

All of the 69 fiducial sample GCs are greater than 4$\sigma$ above the mean
AEN for foreground stars at their magnitude. Of the 375 confirmed foreground
stars in Gaia DR2, 345 (92%) have AEN values within 3$\sigma$ of the mean for
their $G$ magnitude. Visual inspection using PISCeS imaging shows that the
remaining 30 stars with large AEN values are all close blends. This confirms
the utility of AEN for rejecting single foreground stars from the GC candidate
catalog.

####  4.4.3 BP/RP Excess Factor

As we previously showed in V20, a second Gaia DR2 parameter useful for finding
extended sources is the BP/RP Excess Factor ($BR_{\rm excess}$). This
parameter gives the ratio of the sum of the flux of the Blue Photometer ($BP$,
3300-6800 Å) plus the Red Photometer ($RP$, 6400-10500 Å) with the flux in the
broadband $G$ filter. Its utility comes from the distinct manner in which
these fluxes are determined: the $BP$ and $RP$ magnitudes are measured
directly from the flux within a large aperture of 3.4 $\times$ 2.1 arcsec2,
while the $G$ magnitude is derived from profile fitting with an effective
resolution of $\sim$0.4″ (Evans, D. W. et al., 2018). This difference means
that extended sources have a higher $BR_{\rm excess}$ than point sources,
since fitting an effective point-source profile to an extended source in $G$
misses some of the light. As for the concentration index $C_{3-6}$ and AEN, we
expect all extended objects, including contaminant background galaxies and
foreground star blends, to have large $BR_{\rm excess}$ values, while Galactic
foreground stars will have small values.

Figure 4 (right panel) shows $BR_{\rm excess}$ plotted against Gaia DR2 $G$
mag. Qualitatively the figure is similar to the corresponding one for AEN,
with elevated $BR_{\rm excess}$ values for the fiducial sample of GCs and a
clear point-source track of foreground stars. The fiducial GCs are less
clearly separated from the stars than for AEN, but the data used are
essentially independent and so it serves as a second valuable piece of
information to find extended sources. We calculate a bre_likelihood for each
candidate in the same manner as for aen_likelihood, described in §4.4.2.

We also constructed a similar line 3$\sigma$ above the mean foreground star
$BR_{\rm excess}$ value:

$BR_{excess,3\sigma}=1.26+2.79\times 10^{-8}\,e^{0.853\,G}$ (2)

where G is the Gaia DR2 $G$ mag.

All of the fiducial sample GCs have a $BR_{\rm excess}$ value at least
3$\sigma$ above the mean $BR_{\rm excess}$ for foreground stars at their
magnitude, and 90% of them have a $BR_{\rm excess}$ value above 4$\sigma$,
excluding a single fiducial GC that does not have a $BR_{\rm excess}$
measurement.

Of the 367 confirmed foreground stars with $BR_{\rm excess}$ data, 300 (80%)
have $BR_{\rm excess}$ values within 3$\sigma$ of the mean for their
magnitude. Reflecting what is seen with AEN, the remainder are mostly
foreground star blends.

While both AEN and $BR_{\rm excess}$ measure how extended sources are in Gaia
DR2—and hence are correlated for truly extended sources—the statistics are
largely independent and hence both valuable.

###  4.5 Color Selection

As old stellar populations with typically simple star formation histories, GCs
have a restricted range of spectral energy distributions, governed primarily
by metallicity. A fortunate side effect is that GCs occupy a limited area of
parameter space in optical color–color diagrams, allowing them to be separated
from foreground stars and background galaxies with reasonable fidelity. Hence
color–color diagrams have a long history in the selection of extragalactic GCs
(e.g., Rhode & Zepf 2001; Strader et al. 2011; Jennings et al. 2014; Brodie et
al. 2014; Powalka et al. 2016a; T17). The use of a wide spectral baseline,
such as including the UV, near-IR, or both, improves the purity of the GC
selection (Muñoz et al., 2014; Powalka et al., 2016b).

Since our PISCeS data have only two filters ($g$ and $r$ band), to use the
color selection method we match our catalog with NSC, which has ugriz
photometry for over 100,000 sources within the PISCeS footprint (Nidever et
al., 2018). Following the methods of past GC selection techniques, we use the
$u$, $r$, and $z$ filters to maximise the separation of GCs from foreground
stars.

Figure 5: Optical color-color diagram of all sources at distances between 10
and 60′of NGC 5128 that are in both PISCeS and NSC. Almost all of the fiducial
sample GCs (green squares) lie in a well-defined region that is separate from
the radial velocity confirmed foreground stars (orange triangles). The purple
ellipse marks the elliptical region used to select GC candidates, which was
chosen to bound the fiducial sample GCs and confirmed GCs at a distance
greater than 10′ from the center of the galaxy.

Figure 5 shows the position in ($u-r$)0–($r-z$)0 space of all sources in the
radial range 10′–60′ from the center of NGC 5128 that are in both PISCeS and
NSC. The subscript 0 (e.g., $u_{0}$) denotes that the photometry has been
corrected for foreground galactic extinction. For the purposes of calculating
a likelihood, we define the high-probability GC area as an ellipse centered at
$(u-r)_{0}=2.17$ and $(r-z)_{0}=0.45$, with semi-major axis 0.72 mag, semi-
minor axis 0.15 mag, and a position angle $19^{\circ}$ from the x-axis, as
illustrated in Figure 5. This ellipse encloses most of the fiducial GCs and
the confirmed GCs outside of 10′ from the center of the galaxy. Using
integrated single stellar population magnitudes from Marigo et al. (2008), we
find that the cutoff in color on the blue side of the ellipse corresponds to
GC models with ages $\gtrsim$ 5 Gyr at a [Fe/H] = –2, and $\gtrsim$ 1–2 Gyr
for more metal rich stellar populations.

To calculate the color-based likelihood, we draw 10,000 random samples from
the $u$, $r$, and $z$ bands for each source, assuming Gaussian photometric
uncertainties. The fraction of these samples that lie within the ellipse is
the color_likelihood. If all samples are within the ellipse,
$\textit{color\\_likelihood}=1$. Since a few fiducial objects sit just outside
the ellipse, and a few true GCs could have abnormal colors (e.g., due to a
problem with their photometry in a single band), we set the minimum likelihood
at $2\sigma$ (0.023), as we did for some of the Gaia DR2-based likelihoods.
Candidates not in the NSC do not have their total likelihood values affected
by this step.

As an example calculation, let us look at a typical GC candidate with
$u_{0}=21.42\pm 0.12$, $r_{0}=18.81\pm 0.01$, and $z_{0}=18.28\pm 0.03$. This
candidate’s position in color-color space of $(u-r)_{0}=2.61$ and
$(r-z)_{0}=0.53$ is inside of the color selection ellipse, but only 80% of the
randomly varied samples drawn are within the ellipse. Therefore, it has
color_likelihood = 0.80.

Out of the 69 fiducial sample GCs, 64 (93%) have color_likelihood $>$ 0.95. Of
all the potential GC candidates that pass the concentration index, galaxy, and
proper motion/parallax tests, 29% have NSC photometry, and of this 16% have
color_likelihood $>$ 0.75 and 4% have color_likelihood = 1.0. This suggests
the NSC color information is very effective in reducing remaining contaminants
in the GC candidate catalog.

###  4.6 Summary of GC candidate selection process

To summarize, there are five steps in our GC candidate selection process for
the 95 PISCeS fields. We first exclude the brightest and faintest candidates
and those affected by crowding near the galaxy’s center. We then do a
likelihood-based selection of extended objects using a two-aperture technique
on the PISCeS photometry. In the next step, background galaxies and stellar
blends are rejected using cuts in the effective radius, ellipticity, and the
flux distribution at large radii. The penultimate step uses Gaia DR2 for a
likelihood-based assessment that a source is a GC rather than a foreground
star based on measurements of its astrometric motion (proper motion and
parallax) and whether it is extended (astrometric excess noise and BP/RP
excess). Finally, we use multi-band photometry from the NSC to assign a
likelihood that each source has colors consistent with confirmed GCs.

The above likelihoods are multiplied together to give the total_likelihood of
each candidate. Numbers closer to 1 represent a larger chance that the source
is a GC, while candidates that did not survive a yes/no cut (i.e., those
assigned a likelihood of 0 at any point) have a total_likelihood = 0. These
latter objects do not appear in our final GC catalog.

The different steps do not have their likelihoods normalized, and no penalties
are applied if a target does not appear in a given catalog. For instance, if a
GC candidate is not in the Gaia DR2 catalog because it is too faint, it is
implicitly given a likelihood of 1 at that step. The interpretation of sources
with different supporting data is considered in the next section, where these
likelihoods are discussed in the context of our full PISCeS catalog.

##  5 Catalogs

In this section, we present two catalogs: the first includes all of our GC
candidates and the second includes all PISCeS sources that pass the initial
cuts (see Section 4.1). We discuss these catalogs and how we rank our
candidates based on the amount of data available for each.

###  5.1 GC Candidate and Overall Source Catalogs

Table 1: Header information for the catalog of GC candidates in NGC 5128

Column | Label | Description
---|---|---
1 | ID | unique ‘H21’ ID
2 | Discovery_ID | Discovery ID, if available
3 | RA | PISCeS R.A. in decimal degrees (J2000)
4 | Dec | PISCeS Dec in decimal degrees (J2000)
5 | PISCeS_gmag | PISCeS $g$ band magnitude (mag)
6 | PISCeS_gmag_err | error of PISCeS $g$ band magnitude (mag)
7 | PISCeS_rmag | PISCeS $r$ band magnitude (mag)
8 | PISCeS_rmag_err | error of PISCeS $r$ band magnitude (mag)
9 | C_3_6 | Concentration Index value
10 | Gaia_Gmag | Gaia DR2 $G$ band magnitude (mag)
11 | pm_ra | Gaia DR2 proper motion measurement in R.A. direction (mas/yr)
12 | pm_ra_err | error of Gaia DR2 proper motion measurement in R.A. direction (mas/yr)
13 | pm_dec | Gaia DR2 proper motion measurement in Dec direction (mas/yr)
14 | pm_dec_err | error of Gaia DR2 proper motion measurement in Dec direction (mas/yr)
15 | parallax | Gaia DR2 parallax measurement (mas)
16 | parallax_err | error in Gaia DR2 parallax measurement (mas)
17 | AEN | Gaia DR2 Astrometric Excess Noise (mas)
18 | BR_excess | Gaia DR2 BP/RP Excess Factor
19 | ur_color | NSC $(u-r)_{0}$, with Milky Way dust correction applied (mag)
20 | rz_color | NSC $(r-z)_{0}$, with Milky Way dust correction applied (mag)
21 | concentration_likelihood | candidate likelihood based on $C_{3-6}$
22 | proper_motion_likelihood | candidate likelihood based on proper motion
23 | parallax_likelihood | candidate likelihood based on parallax
24 | aen_likelihood | candidate likelihood basd on AEN
25 | bre_likelihood | candidate likelihood based on BRexcess
26 | color_likelihood | candidate likelihood based on NSC color
27 | total_likelihood | total likelihood of candidate being a GC in NGC 5128
28 | candidate_rank | classification based on data availability in key datasets, see Table 3
29 | confirmed | Is it a confirmed GC in NGC 5128? (y/n)
30 | references | literature references*

  * •

The complete table will be available online.

  * •

*Reference papers: aGraham & Phillips (1980), bvan den Bergh et al. (1981), cHesser et al. (1986) dHarris et al. (1992), eHolland et al. (1999), fHarris et al. (2002), gPeng et al. (2004), hMartini & Ho (2004), iHarris et al. (2004), jWoodley et al. (2005), kGómez et al. (2006), lHarris et al. (2006), mRejkuba et al. (2007), nWoodley et al. (2007), oBeasley et al. (2008), pGeorgiev et al. (2009) qMouhcine et al. (2010), rWoodley et al. (2010b), sWoodley et al. (2010a), tSinnott et al. (2010), uTaylor et al. (2010), vGeorgiev et al. (2010), wHarris et al. (2012), xTaylor et al. (2015), yTaylor et al. (2017), zVoggel et al. (2020), aaFahrion et al. (2020), abMüller et al. (2020)

Table 2: Header information for the catalog of all PISCeS sources in NGC 5128

Column | Label | Description
---|---|---
1 | ID | unique ‘H21’ ID
2 | Discovery_ID | Discovery ID, if available
3 | RA | PISCeS R.A. in decimal degrees (J2000)
4 | Dec | PISCeS Dec in decimal degrees (J2000)
5 | PISCeS_gmag | PISCeS $g$ band magnitude (mag)
6 | PISCeS_gmag_err | error of PISCeS $g$ band magnitude (mag)
7 | PISCeS_rmag | PISCeS $r$ band magnitude (mag)
8 | PISCeS_rmag_err | error of PISCeS $r$ band magnitude (mag)
9 | g_C_3_6 | PISCeS $g$ band Concentration Index value
10 | r_C_3_6 | PISCeS $r$ band Concentration Index value
11 | band_used | PISCeS magnitude band used to calculate concentration_likeliness
12 | Gaia_RA | Gaia DR2 R.A. in decimal degrees (ICRS)
13 | Gaia_Dec | Gaia DR2 Dec in decimal degrees (ICRS)
14 | Gaia_Gmag | Gaia DR2 $G$ band magnitude (mag)
15 | pm_ra | Gaia DR2 proper motion measurement in R.A. direction (mas/yr)
16 | pm_ra_err | error of Gaia DR2 proper motion measurement in R.A. direction (mas/yr)
17 | pm_dec | Gaia DR2 proper motion measurement in Dec direction (mas/yr)
18 | pm_dec_err | error of Gaia DR2 proper motion measurement in Dec direction (mas/yr)
19 | parallax | Gaia DR2 parallax measurement (mas)
20 | parallax_err | error in Gaia DR2 parallax measurement (mas)
21 | AEN | Gaia DR2 Astrometric Excess Noise (mas)
22 | BR_excess | Gaia DR2 BP/RP Excess Factor
23 | NSC_umag | NSC $u$ band magnitude (mag)
24 | NSC_umag_err | error of NSC $u$ band magnitude (mag)
25 | NSC_gmag | NSC $g$ band magnitude (mag)
26 | NSC_gmag_err | error of NSC $g$ band magnitude (mag)
27 | NSC_rmag | NSC $r$ band magnitude (mag)
28 | NSC_rmag_err | error of NSC $r$ band magnitude (mag)
29 | NSC_imag | NSC $i$ band magnitude (mag)
30 | NSC_imag_err | error of NSC $i$ band magnitude (mag)
31 | NSC_zmag | NSC $z$ band magnitude (mag)
32 | NSC_zmag_err | error of NSC $z$ band magnitude (mag)
33 | ur_color | NSC $(u-r)_{0}$, with Milky Way dust correction applied (mag)
34 | rz_color | NSC $(r-z)_{0}$, with Milky Way dust correction applied (mag)
35 | concentration_likelihood | candidate likelihood based on $C_{3-6}$
36 | structure_check | galaxy/blend check
37 | proper_motion_likelihood | candidate likelihood based on proper motion
38 | parallax_likelihood | candidate likelihood based on parallax
39 | aen_likelihood | candidate likelihood basd on AEN
40 | bre_likelihood | candidate likelihood based on BRexcess
41 | color_likelihood | candidate likelihood based on NSC color
42 | total_likelihood | total likelihood of candidate being a GC in NGC 5128
43 | candidate_rank | classification based on data availability in key datasets, see §3
44 | confirmed | Is it a confirmed GC in NGC 5128? (y/n)
45 | references | literature references*

  * •

The complete table will be available online.

  * •

*Reference papers: See Table 1

Candidate Rank | PISCeS |  Gaia DR2 | NSC | Minimum $C_{3-6}$ | Number of Candidates
---|---|---|---|---|---
|  |  |  |  | Total | $\mathscr{L}_{total}>0.85$
gold | $\checkmark$ | $\checkmark$ | $\checkmark$ | 1.0 | 5763 | 181
silver | $\checkmark$ | $\checkmark$ | $\times$ | 1.0 | 13793 | 1750
| $\checkmark$ | $\times$ | $\checkmark$ | 1.0
bronze | $\checkmark$ | $\times$ | $\times$ | 2.0 | 11860 | 11860
copper | $\checkmark$ | $\times$ | $\times$ | 1.0 | 9086 | 8541
Table 3: In addition to providing a total_likelihood, we identify GC
candidates by a rank of ‘gold’, ‘silver’, ‘bronze’, or ‘copper’ based on the
amount of data available for each, and columns 2 – 4 indicate if data is
available ($\checkmark$) or not ($\times$) in the three key datasets. For many
candidates, there is only one source of information (PISCeS) available, and so
we label those with $C_{3-6}\geq$ 2.0 as bronze, and those with 1.0 $\leq$
$C_{3-6}$ $<$ 2.0 as copper, where $C_{3-6}=$ 2.0 corresponds to
concentration_likelihood = 0.977 (see §4.2). For each rank, the final two
columns list the total number of candidates and the number of candidates with
total_likelihood $>$ 0.85.

The first presented catalog includes the 40,502 GC candidates in NGC 5128
found through our GC candidate selection process, as detailed in Section 4. We
consider a PISCeS source to be a viable GC candidate if it has $C_{3-6}>1.0$
and survives applicable yes/no cuts (initial cuts, structure_likelihood,
proper_motion_likelihood, parallax_likelihood; see §4.1, 4.3, 4.4). The
likelihood values for each candidate are multiplied together, and a reported
total_likelihood value closer to 1.0 represents a GC candidate with a larger
chance of being a true GC in NGC 5128.

Table 1 lists the header information for the catalog of GC candidates, which
includes: (1) a unique ‘H21’ ID, which we assign; (2) Discovery ID; (3, 4)
PISCeS R.A. & Dec. in J2000 coordinates; (5 – 8) PISCeS $g$ & $r$ magnitudes
and errors; (9) concentration index ($C_{3-6}$); (10) Gaia DR2 $G$ magnitude;
(11 – 18) proper motion in the R.A. and Dec. directions, parallax, AEN, and
$BR_{\rm excess}$ from Gaia DR2; and (19, 20) NSC $(u-r)_{0}$ and $(r-z)_{0}$
color with Milky Way dust correction applied on a source-by-source basis
(Schlafly & Finkbeiner, 2011). We also list a breakdown of the likelihood
values (21 – 27) concentration_likelihood, proper_motion_likelihood,
parallax_likelihood, aen_likelihood, bre_likelihood, color_likelihood, and
total_likelihood; and (28) gold, silver, bronze, copper rank (see below). For
completeness, we (29) include and note targets that have previously been
confirmed as GCs and (30) list all literature references. All PISCeS and Gaia
DR2 photometry reported here has not been corrected for Galactic extinction.
We do not include any GC candidates from the literature that are outside the
PISCeS footprint or within 10′ from the center of NGC 5128. The full GC
candidate table will be available online in electronic format.

The second catalog includes all PISCeS sources that pass our initial cuts
(§4.1). In addition to GC candidates, this source catalog includes background
galaxies and foreground stars that were removed by various steps in our GC
candidate selection process. Along with the columns listed in the GC candidate
table, we include information about the concentration index from both PISCeS
$g$ and $r$ bands; structure_check; Gaia DR2 R.A. & Dec. in ICRS coordinates;
and un-corrected NSC $u,g,r,i,z$ photometry and errors. The header information
is listed in Table 2. The full PISCeS source table will be available online in
electronic format.

###  5.2 Globular cluster candidate data rank

As a guide for future researchers who may use this GC candidate catalog for
spectroscopic follow-up, we split our candidates into four categories (‘gold’,
‘silver’, ‘bronze’, or ‘copper’) based on the number of our key datasets they
appear in (see Table 3), separate from their quality (i.e. total_likelihood).

Gold GC candidates have data from PISCeS, Gaia DR2, and NSC. This group of GC
candidates is expected to have the least amount of contamination from
foreground stars and background galaxies at high total_likelihood scores,
because they have information from all three key datasets pointing to the same
result. The trade-off is that the gold group does not include faint GCs, as
illustrated by the right panel of Figure 10. This is primarily due to the lack
of Gaia DR2 sources at $G$ $\gtrsim$ 20 mag, which is $\sim$ 0.5 mag brighter
than the NGC 5128 peak of the GCLF (Pota et al., 2015). Of the confirmed GCs
outside of 10’ (see Appendix A), 42% have information in all three datasets.
There are 5,763 GC candidates in the gold category, of which 181 have
total_likelihood $\geq$ 0.85, which we identify as a good threshold in Section
6.1 because it maximizes the number of GC candidates above the background. The
gold sample displays a clear overdensity of candidates near NGC 5128, which we
discuss further below. Of the gold sample candidates between 10–30 arcmin
(32.4 kpc), 15 have total_likelihood $\geq$ 0.85 and have not been been
observed spectroscopically. This suggests that more GCs will be confirmed by
following up this sample both close to and far from the center of the galaxy.

Silver GC candidates have data from PISCeS and one of either Gaia DR2 _or_
NSC. While the contamination in this set of candidates will be higher than the
gold sample, it will also be more sensitive to faint GC candidates. Of the
confirmed GCs outside of 10’, 38% have information in two datasets. The silver
sample has a total of 13,793 candidates, of which 1,750 have total_likelihood
$\geq$ 0.85. Between 10–30′ from the center of the galaxy we find 126 silver
GC candidates with total_likelihood $\geq$ 0.85 that have yet to have
spectroscopic follow-up or confirmation.

Bronze and copper GC candidates have data only from PISCeS, and are absent
from both Gaia DR2 and NSC. The likelihood of these candidates is therefore
only based on our concentration index measurement $C_{3-6}$ and passing our
extended galaxy checks (§4.2, 4.3). Because there is information available
from only one catalog, we raise the minimum $C_{3-6}$ value for the bronze
candidates to 2.0, corresponding to a concentration_likelihood $>$ 0.977. The
bronze sample contains many promising candidates, of which there are 11,860 in
total. The remaining 9,086 candidates with 1.0 $\leq C_{3-6}<$ 2.0 are placed
in the copper sample. These candidates should be treated with caution, but may
contain true NGC 5128 GCs. For reference, 14% of confirmed GCs outside of 10’
have information only in the PISCeS dataset. These groups of candidates are
expected to have the most contamination, and are somewhat susceptible to
image-level issues apparent in a handful of fields. For instance, a changing
FWHM across a Megacam field of view can systematically change the average
concentration index value at a small level.

##  6 Discussion

###  6.1 Globular cluster spatial distributions

Figure 6: Left: The relationship between the number of likely background
contaminants and the number of GC candidates above the background level in the
gold and silver GC candidate samples with different minimum values of
total_likelihood between 0.3 and 0.95. The counts are based on power law fits
to the radial distribution of our candidates (e.g. Figure 7). Darker colored
points correspond to a higher minimum total_likelihood value. Right: The
number of GC candidates above the background as a function of minimum
total_likelihood, where the points are color-coded the same as the left panel.
We highlight the gold and silver GC candidates with total_likelihood $\geq$
0.85 as the most likely to be true GCs based on available information, and
this value is indicated with the purple star on the left and the purple line
on the right.

Our catalog consists both of true GCs as well as contaminants. To separate
these two, and to optimize our catalogs, we assume that the true GCs follow a
decreasing power-law function with radius, while the background level is
uniform across our survey. We therefore fit our radial density profile of GC
candidates using a model with a power-law plus uniform background. We first
use this model to determine what an appropriate total_likelihood threshold is
for analyzing the physical properties of GCs in our catalog. Focusing on the
gold and silver GC candidates, we examine the total number of candidates above
the background as well as the total number of contaminants at a range of
total_likelihood thresholds. As shown in Fig. 6, we find that using a
threshold of total_likelihood $\geq$ 0.85 nearly maximizes the number of GC
candidates above the background, while minimizing the number of contaminants.
Therefore, for this section we focus our analysis on the gold and silver GC
candidates that have total_likelihood $\geq$ 0.85.

Figure 7:  Radial distribution of gold and silver GC candidates with
total_likelihood $\geq$ 0.85. Each bin contains 100 GC candidates for the
combined gold and silver sample, with 32 entries in the final bin, and 40 GC
candidates for the gold-only sample, with 7 entries in the final bin. The
curved solid black lines mark power law fits to the GC candidate distributions
between 10′ and 125′, given by equations 3 and 4, and the dotted lines mark
the constant background values in the same equations.

We break down the radial distributions of our combined gold and silver GC
candidate population as well as the gold-only GC candidate population in
Figure 7, where both populations have total_likelihood $\geq$ 0.85. Each
radial bin contains a constant number of GC candidates: 100 GC candidates for
the combined gold and silver population, with 32 entries in the final bin, and
40 GC candidates for the gold-only population, with 7 entries in the final
bin. The power law fit to the radial distribution of the gold GC candidate
population is given by

$\rho_{g}=0.00141+63.7r^{-2.66\pm 0.30}$ (3)

and fit to the distribution of the combined gold and silver GC candidate
population is given by

$\rho_{g+s}=0.0277+26.6r^{-1.99\pm 0.22},$ (4)

where $\rho_{g}$ and $\rho_{g+s}$ are GC candidate surface densities in N per
square arcminute. These fits are denoted by the curved solid black lines in
Figure 7. The combined gold and silver GC candidate population becomes
dominated by the background at a smaller radius ($\sim$ 1.4 deg; 94 kpc) than
the population with only gold candidates ($\sim$ 1.8 deg; 121 kpc).

The power-law index from the gold sample ($-2.66\pm 0.30$) is comparable to
that found for the radial profile of the globular clusters in the Milky Way:
Bica et al. (2006) find a 3-D radial power-law index of –3.9 (corresponding to
–2.9 in projected radius) for all the clusters beyond 3.5 kpc, and an index
–3.6 (–2.6 in projected radius) for the metal-poor clusters that dominate
beyond 8 kpc. These values are steeper than typical massive elliptical
galaxies, where the projected power law indices for the full GC systems at
large radii are found to range between –1.2 and –2 (Faifer et al., 2011). The
index for the combined gold and silver sample ($-1.99\pm 0.22$) is consistent
with the steeper edge of this range. Overall, the spatial profile appears
intermediate between massive galaxies and the typical $L^{\ast}$, Milky Way-
like galaxy, though it should be revisited once spectroscopy is available.

As a point of comparison, the SCABS catalog GC candidates within 120′,
excluding an overdensity at a radius of $\sim 55$′, are fit with a power law
of slope –1.22 (T17), shallower than our result. This may partially arise from
T17’s use of a model that assumes a total population of GCs based on a “known
GC” population that contains contamination from foreground stars (see §6.3 and
Appendix B).

Figure 8: The two-dimensional density distribution of our gold and silver GC
candidates with a total_likelihood $\geq$ 0.85, where each pixel is
0.15$\times$0.15 degrees. The figure is oriented such that north is up and
east is left. Note the overdensity of GC candidates close to the center of the
galaxy, which is angled similarly to the isophotal major axis of the galaxy
(35∘ E of N, Dufour et al. 1979). We exclude all sources within 10′from our
analysis, leading to a central gap in the GC candidate distribution. The
circle marks a distance of 125′(135 kpc) from the galaxy center, which is
about the extent to which PISCeS has full coverage.

The two-dimensional distribution of our gold and silver GC candidates with
total_likelihood $\geq$ 0.85 is shown in Figure 8. There is a central
overdensity, especially along the diagonal from north-east to south-west out
to a distance of about 30′ (32.4 kpc), which is angled similarly to the
isophotal major axis of the galaxy (35∘ E of N, Dufour et al. 1979). A
majority of the already confirmed GCs in NGC 5128 lie within this radius,
though the position angle overdensity seen here has a broader distribution
than has been found in previous works. Though we see an overdensity in the
one-dimensional GC candidate distribution out to $\sim$ 85′, it is less
apparent in the two-dimensional distribution. While not plotted, we also see a
central (within 40–50′) enhancement of the bronze candidates above background,
consistent with at least some of these being real GCs.

###  6.2 GC total population estimates

Figure 9: An illustration of our process to calculate the total number of GCs
in NGC 5128, using Gaussian functions fitted to the expected GCLF, split at a
radius of 10′. The confirmed GC population within 10′ (left) is assumed to be
complete for $V\lesssim 20.5$ mag. Outside of 10′(right), the known population
of confirmed GCs is combined with a background-subtracted sample of our gold
and silver candidate GCs with total_likelihood $\geq$ 0.85. Plotted here are
100 iterations of these background corrected candidate sampling (in grey), and
their average (in black). Only data to the left of the dashed vertical lines
in both histograms are used in the respective Gaussian fits.

Using a method similar to Harris (2010), we estimate the total size of the GC
population in NGC 5128 by forcing a fit to the standard GCLF and estimating
the number of GCs below our detection limit. Based on values of
$(m-M)_{0}=27.91$ (Harris et al., 2010), $A_{V}=0.35$ (Schlafly & Finkbeiner,
2011), and assuming a mean turnover magnitude $M_{V}=-7.3$ (Harris, 2001), the
GCLF turnover is expected to occur at $V=20.95$ mag with $\sigma$=1.4 mag. We
convert our PISCeS $g$\- and $r$-band magnitudes to $V$-band using
transformation coefficients from Jester et al. (2005).

We split the expected population calculation at a radius of 10′, and assume
that within this radius, all bright ($V\leq 20.5$ mag) GCs have been found.
Outside of 10′, we combine the known confirmed GCs with a sample of our new
gold and silver candidate GCs with total_likelihood $\geq$ 0.85. The sample of
GCs is chosen randomly from our candidates to correct for background
contamination based on the fits shown in Fig. 7. These random samples were
chosen 100 times. For both the inner and outer cluster samples we plot the
GCLF and fit a Gaussian function with values discussed above assuming Poisson
errors. We also varied the faint end limit of the fitting range by 0.5
magnitudes, and incorporate this into our overall uncertainties.

This method results in a population estimate of 1300 $\pm$ 110 GCs, which
closely matches the total predicted by Harris (2010). This should be treated
as a lower limit though, since it does not included any GC candidates from the
bronze or copper classifications (those that have data only from PISCeS), and
it includes only gold and silver clusters with total_likelihood $\geq$ 0.85.
We know that 14% of confirmed GCs outside of 10′ are in the bronze sample,
largely due to the incompleteness of Gaia DR2 and NSC at faint magnitudes.
Another 4% of confirmed GCs are in the gold and silver sample but have
total_likelihood $<$ 0.85. Accounting for this incompleteness, we estimate
that there are a total of 1450 $\pm$ 160 GCs in NGC 5128 within $\sim$ 150
kpc.

Forbes (2017) predicts that half of the GC system of an elliptical galaxy will
lie within a radius $R_{e}$ given by $\log R_{e}=0.97(\pm 0.4)\log
M_{*}-9.76(\pm 4.4)$. For a stellar mass of $5.5\times 10^{11}M_{\odot}$ (Peng
et al., 2004), this result predicts that half of NGC 5128’s GCs will lie
within a radius of $42^{+42}_{-21}$ kpc. We find that half of our estimated
total GC population lies within a radius of 48 $\pm$ 3 kpc. Only three GCs
beyond this radius have been confirmed, further illustrating the need for
spectroscopic confirmation of GCs in the outer halo.

The specific frequency ($S_{N}$) of a galaxy is used to measure the relative
occurrence of GCs across galaxy types and masses, and is defined as
$S_{N}=N_{GC}\times 10^{0.4(M_{V}+15)}$ (Harris & van den Bergh, 1981). Using
our new GC population estimate of $N_{GC}$ = 1450 and an extinction-corrected
V-band magnitude of $M_{V}$ = –21.38 for NGC 5128 (de Vaucouleurs et al.,
1991; Schlafly & Finkbeiner, 2011) results in $S_{N}$ = 4.1. This is somewhat
higher than other recent $S_{N}$ calculations for NGC 5128, including $S_{N}$
= 2.9 (T17) and 1.9 (Harris, 2010). These differences are due both to
different $N_{GC}$ estimates and to different assumed $M_{V}$ values.

Our calculation ($S_{N}$ = 4.1) is consistent with the idea of Graham (1979)
that NGC 5128 experienced a merger between an elliptical galaxy with a
relatively high $S_{N}$, and a second gas-rich galaxy, which would typically
have had a lower $S_{N}$.

###  6.3 Comparison with previous results

Figure 10: Left: Recovery fraction of confirmed GCs with total_likelihood
$\geq$ 0.85, binned by sets of 75 with increasing radial distance from the
center of NGC 5128. The last bin has 72 GCs. Within 10′of the galaxy center
our GC selection process is not effective due to crowding. Right: Recovery
fraction with total_likelihood $\geq$ 0.85 of the confirmed GCs outside of
10′, binned by $r$-band magnitude, without extinction correction applied. The
dashed vertical line indicates where Gaia DR2 begins to become incomplete
(Gaia Collaboration et al., 2018b), and thus where we expect the gold sample
to decrease.

Cross-matching items in our GC candidate catalog with the fiducial sample of
69 confirmed GCs, we find that 65 are recovered with total_likelihood $\geq$
0.85 (this is, of course, largely by construction as we used the fiducial
sample to guide our GC candidate selection methodology). The remaining four
fiducial sample GCs have positions in color-color space near the border of the
color selection ellipse discussed in §4.5, and therefore have lower values for
their final total_likelihood values.

We broaden our comparison sample to include all confirmed GCs; see Appendix A
for a list. Comparisons of recovery fractions for the gold, silver, and bronze
rank classifications as a function of radius and magnitude are shown in Figure
10; no confirmed GCs belong to the copper rank. The requirement for data from
the NSC and Gaia DR2 catalogs causes faint end completeness to drop in the
gold and silver GC candidate populations. We recover a total of 192 out of 198
(97%) confirmed GCs that are outside of 10′ and in PISCeS. Additionally, 155
out of 198 (78%) have total_likelihood $\geq$ 0.85, where 69 GCs are in the
gold sample, 56 GCs are in the silver sample, and 30 GCs are in the bronze
sample. Those confirmed GCs that are not recovered or have low
total_likelihood values typically have low concentration index values or were
identified as galaxies due to close proximity to foreground stars. Within 10′,
we only recover 53% of the confirmed GCs, due to crowding. Recall that because
our methods are tailored to work in the uncrowded regions far from the center
of NGC 5128, we exclude the central-most portion of the galaxy from our
catalogs.

We fail to recover a small number of bright GCs/UCDs, mostly due to saturation
of the PISCeS data, but also because of our cuts on structure that identify
background galaxies. This is why we developed a focused approach in V20 to
obtain a complete sample of the brightest GCs, including cluster candidates
lying outside the PISCeS footprint. Of the 480 candidates from V20 that lie
within the PISCeS footprint, only 102 are also included in our catalog.

Apart from V20, the only other catalog presenting GC candidates at comparably
large radii is the SCABS catalog from T17. We find that 864 of the 2087 GC
candidates from SCABS that are in the PISCeS footprint are recovered as
candidates by our tests, and 511 have total_likelihood $\geq$ 0.85 in our
catalog. An additional $\approx$ 1100 SCABS GC candidates are outside of the
PISCeS footprint or are within 10’ of the center of the galaxy and so are not
included in our catalog. Of the $\approx$ 1450 SCABS candidates with
total_likelihood $<$ 0.85 in our catalog, 67% are found to have stellar-like
concentration index values in our PISCeS data and 37% have high confidence
parallax or proper motion measurements in Gaia DR2. This suggests that the
catalog has a high contamination rate, and that the PISCeS concentration
information provides valuable complementary data to the colors used in the
SCABS candidate selection. Additionally, SCABS recovered only 251 out of their
sample of 643 “confirmed’ GCs 333The sample of “confirmed” GCs used by T17 is
not the same as what we list in Appendix A. T17 does not provide a list of the
confirmed GCs that they use to assess their GC candidate selection technique,
and cite private communication as a source. Their sample likely includes
contamination from foreground stars; see Appendix B. . Before their final step
of deriving GC candidate likelihoods based on color, however, they reported
that they successfully recovered $\sim$90% of confirmed GCs. This low recovery
rate in the final step appears to be caused by their method of modeling the
ratio of stars to GCs, which is controlled by an expected population size. T17
additionally predicts a total of $\sim$ 1100 GCs within a projected 55 kpc
from the center of NGC 5128, and $\approx$ 3200 GCs within $\sim$ 140 kpc.
This is more than double our prediction for the total number of GCs in the
galaxy (§6.2).

###  6.4 Color bimodality

Figure 11:  Distributions of gold and silver GC candidates with NSC
photometric data and total_likelihood $\geq$ 0.85. Left: The bimodal shape of
our GC candidate color distribution closely matches that of the confirmed GCs
outside of 10′ from the center of the galaxy, which is multiplied by 3 to more
clearly show its shape. There is an offset between the color of our GC
candidates and those found with the methods employed by T17. NSC photometry
has been dust corrected. Right: Radial distribution of GC candidates, split
based on color with a critical value of $(u-z)_{0}=2.6$ mag. Each radial bin
contains 30 GC candidates, with 20 in the final blue bin and 28 in the final
red bin. The curved solid lines mark the power law fits to the GC candidate
distributions between 10 and 125′, given by Equations 5 and 6, and the dotted
lines mark the constant background values in the same equations.

In many galaxies, the population of GCs is observed to have a distinctly
bimodal metallicity distribution: though most GCs are metal-poor, the “blue”
GCs in a given galaxy are on average more metal-poor and the “red” GCs are on
average more metal-rich (e.g., Brodie & Strader 2006 for a review). The
difference may be the result of dual halo mode formation, where metal-rich GCs
form in massive progenitors and metal-poor GCs form in low mass satellite
galaxies that are later accreted as part of hierarchical galaxy formation
(e.g., Park & Lee 2013; Lee & Jang 2016; Forbes & Remus 2018; El-Badry et al.
2019). This bimodality is one of the most studied properties of GC systems,
since these subpopulations show differences in their intrinsic
characteristics, such as their spatial distribution and kinematics.

As expected, there is a bimodal color distribution of our gold and silver GC
candidates with total_likelihood $\geq$ 0.85. Figure 11 shows the distribution
in NSC $(u-z)_{0}$ color space of these candidates. The right and left edges
of our candidate color distribution matches the distribution of the confirmed
GCs that have NSC data and are outside of 10′, which has been multiplied by a
factor of three to show the distribution’s shape. This match between the color
ranges of our candidates and the confirmed GCs is largely by construction, as
we used a subset of confirmed GCs to guide the color selection step in our GC
candidate selection process (§4.5).

We also plot the NSC color of the SCABS GC candidates from T17. The offset in
the color distributions between the SCABS GC candidates and the confirmed GCs
may arise because of the high rate of contamination in the SCABS sample, as
discussed in §6.3.

The radial distributions of the same gold and silver GC candidates are plotted
in Figure 11, where GC candidates with $(u-z)_{0}<2.6$ are in the blue sample
and GC candidates with $(u-z)_{0}>2.6$ are in the red sample. The power law
fit to the radial distribution of the blue GC candidates is given by

$\rho_{b}=0.00562+9.72r^{-1.81\pm 0.23}$ (5)

and the fit to the radial distribution of the red GC candidates is given by

$\rho_{r}=0.00664+79.3r^{-2.89\pm 0.64}.$ (6)

The slope obtained for the red subpopulation is steeper than the one obtained
for the blue subpopulation and the one for the entire gold and silver GC
candidate system (Eq. 4), as it is more concentrated towards the center. This
follows what has been observed for many galaxies (e.g., Brodie & Strader 2006;
Faifer et al. 2011; Forbes et al. 2012). At all radii that are include in the
fit, there are more blue than red GCs, further indicating that NGC 5128 has a
rich merger history (e.g., Peng et al. 2004; Beasley et al. 2008).

###  6.5 Milky Way foreground star contamination

Because of the relative proximity of NGC 5128 to the galactic disk there is
significant contamination from foreground stars. We find that nearly all of
the objects that lie within the magnitude range expected for NGC 5128 GCs are
actually Galactic foreground stars. Unfortunately, removing all the foreground
star contamination from GC catalogs is very tricky. Of the 630 GCs identified
in previous studies, 355 have both a measured radial velocity and information
in Gaia DR2. A histogram of the radial velocities of these GCs is plotted in
Figure 12. Overlaid in blue, we show the 50 objects that have non-zero proper
motion and/or parallax measurements with a confidence of 3$\sigma$ or greater.
These objects are contaminant foreground stars with high velocities, not GCs
in NGC 5128 as previously thought, and are listed and discussed further in
Appendix B.

We estimate that up to $\approx$80% of entries with gold or silver rank and
total_likelihood $\geq$ 0.85, and $\approx$42% of entries with gold rank and
total_likelihood $\geq$ 0.85, are not true GCs in NGC 5128, based upon the
density of the background in the fit to the radial distribution of candidates,
shown in Figure 7. We expect this percentage to be dependent on the radial
distance from the center of the galaxy and the amount of information available
for the candidates.

###  6.6 Velocity Dispersion of GCs Around NGC 5128

The systematic velocity of NGC 5128 is 541 km s-1 (Hui et al., 1995) with a
velocity dispersion of $\sigma\sim 150$ km s-1 (Wilkinson et al., 1986; Silge
et al., 2005). Based on a sample of 605 identified GCs, Woodley et al. (2010a)
calculated a mean GC radial velocity of $517\pm 7$ km s-1 with $\sigma=160\pm
5$ km s-1. They note that because this value is lower than the accepted
systematic velocity of the galaxy, their catalog may be contaminated on the
low velocity end. We have found and removed contaminant foreground stars from
the confirmed GC population (see Appendix B), and have redone the calculation.
Of the cleaned list of confirmed GCs (see Table 4 in the Appendix), 507 have
radial velocity measurements, with a mean radial velocity of 537 km s-1 and
$\sigma$ = 148 km s-1. Figure 12 shows radial velocity histograms for the
cleaned list of confirmed GCs, the contaminant Milky Way foreground stars that
were previously mis-identitified as GCs, and the combination of these two
populations. Removing the contaminant foreground stars makes the distribution
of the GC radial velocity measurements more symmetric about the mean value and
brings the mean velocity measurement of the GC system closer in line with that
of the galaxy as a whole, as is seen in other galaxies (e.g. Pota et al.
2015). We defer a thorough kinematic and dynamical analysis to a future paper
that will also incorporate new radial velocities.

Figure 12:  Histogram of 507 confirmed GCs with radial velocity measurements.
The dashed line marks the newly measured mean radial velocity value of 537 km
s-1 and the dotted lines mark $\pm 1\sigma$, where $\sigma$ = 148 km s-1. The
standard critical radial velocity for GC confirmation in NGC 5128 is 250 km
s-1. Targets with velocities below this value were typically confirmed via
structural parameters or visual resolution into component stars from HST
images. The filled blue histogram shows the 50 objects that were identified by
a past NGC 5128 survey as ‘GCs’ that have non-zero proper motion measurements
in Gaia DR2 of 3$\sigma$ or greater. These mis-identified ‘GCs’ are actually
Milky Way foreground stars, and are listed and discussed further in Appendix
B.1. By removing these contaminants, the distribution of radial velocities
becomes more symmetric about the mean value.

###  6.7 Future work

Now that we have a new catalog of NGC 5128 candidate GCs out to $\sim$150 kpc,
further observations are required to confirm which are true GCs in NGC 5128.
We have begun taking spectroscopic observations to measure candidate GC radial
velocities using Magellan/Megacam, AAT/2DF, and SOAR. For brighter GCs we will
also be able to estimate metallicities, providing further information on NGC
5128’s accreting substructures. The results will be published in an upcoming
paper.

Once we have a larger population of confirmed GCs at large radii we will be
able to identify specific GCs that are associated with streams and shells
around NGC 5128, similar to the work done for M31 (Veljanoski et al., 2014;
Mackey et al., 2019). The kinematics of GCs associated with NGC 5128’s streams
and shells will provide important constraints on the accreted systems’ orbit,
mass, and concentration while the velocity dispersion, number, and color of
the non-associated GCs can provide complementary constraints on the host
galaxy mass. It is also possible that many of NGC 5128’s past merger/accretion
events may not have visible remnants in the PISCeS RGB map, but could be
detectable kinematically via its GCs. Additionally, using GCs at larger radii
we will be able to calculate the galaxy’s enclosed mass at a larger radius.

The release of Gaia Early Data Release 3 and the upcoming full Gaia Data
Release 3 include information on additional targets around NGC 5128, to a
fainter limiting magnitude of $G\approx 21$ and with higher precision proper
motion and parallax measurements than Gaia DR2 (Gaia Collaboration et al.,
2020). This will allow for the removal of additional contaminant foreground
stars from the silver, bronze, and copper GC candidate categories and a more
confident total_likelihood score that takes into account structural parameters
(ex. AEN and $BR_{\rm excess}$) given to those candidates that now have Gaia
data available for them.

##  7 Summary

We present a new technique for identifying GCs in the Local Volume using a
combination of ground- and space-based observations. We combine data from Gaia
Data Release 2 with the the ground-based PISCeS and NOAO Source Catalog
datasets to select 40,502 GC candidates in NGC 5128 out to a projected radius
of $\sim$ 150 kpc, as presented in Table 1. We highlight the 1,931 candidates
in the gold and silver rank with total_likelihood $\geq$ 0.85 as the most
likely to be true GCs in NGC 5128, and therefore the most promising targets
for followup spectroscopic confirmation.

Our GC candidate selection process identifies extended objects using a
concentration index vs. magnitude relationship, and then rejects foreground
star and background galaxy contaminants based on astrometric motion and
structural parameters from Gaia DR2, and color from NSC. To assist in
selecting extended objects, we provide 3$\sigma$ confidence lines in Gaia AEN
and BRexcess vs. $G$-mag space, and a color selection ellipse in NSC ($u-r$)0
vs. ($r-z$)0 space. Each GC candidate in our catalog has a total_likelihood
value between 0 and 1 (where numbers closer to 1 represent a larger chance
that the source is a GC) as well as a gold, silver, bronze, or copper rank (to
indicate the amount of information available). Our selection technique
recovers 155 out of 198 (78%) confirmed GCs that are outside of 10′ and in
PISCeS with a total_likelihood $\geq$ 0.85.

Our sample of gold and silver GC candidates exhibit a clear central
overdensity. The one-dimensional radial distributions of the gold and combined
gold and silver GC candidate populations can be fit by power laws with
exponents of $-$2.66 and $-$2.01, respectively. Using expected parameters to
fit a GCLF to the combined confirmed and candidate samples, we estimate that
there are a total of 1450 $\pm$ 160 GCs in NGC 5128 within $\sim$ 150 kpc, and
that half of the GCs lie within a radius of 48 $\pm$ 3 kpc.

Our GC candidates exhibit a bimodal color distribution matching that of the
confirmed GCs outside of 10′. The metal-rich subpopulation is more centrally
concentrated, with a power law exponent of $\sim-2.9$, though the metal-poor
subpopulation, with a power law exponent of $\sim-1.8$, is larger at almost
all radii.

We cull contaminant objects from the list of known confirmed GCs and provide
an updated mean radial velocity for confirmed GCs of 537 km s-1 with
$\sigma=148$ km s-1, which is closer in line with the values for the galaxy as
a whole. The cleaned list of confirmed GCs can be found in Table 4.

Once GCs at large radii have been confirmed, we will be able to identify those
that are associated with streams and shells around NGC 5128, providing
information about the accreted systems and host galaxy, as has been done in
M31 (Veljanoski et al., 2014; Mackey et al., 2019). We will additionally apply
these techniques combining Gaia with ground-based observing to identify
slightly extended GCs in further galaxies in the Local Volume.

This research uses services or data provided by the NOAO Data Lab. NOAO is
operated by the Association of Universities for Research in Astronomy (AURA),
Inc. under a cooperative agreement with the National Science Foundation. This
work has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. AKH and DJS acknowledge
support from NSF grants AST-1821967 and 1813708. ACS acknowledges support from
NSF grant AST-1813609. JS acknowledges support from NSF grants AST-1514763 and
AST-1812856 and from the Packard Foundation. JDS acknowledges support from NSF
grant AST-1412792. Research by DC is supported by NSF grant AST-1814208. We
thank Pauline Barmby for supplying globular cluster structural properties from
McLaughlin et al. (2008). Lastly, we thank the anonymous reviewer whose
comments and suggestions helped improve and clarify this manuscript.

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Based upon new observations and data, we can show that only 557 of the 630
objects that have been identified as NGC 5128 globular clusters (GCs) in the
literature are genuine confirmations. In this Appendix, we present a cleaned
catalog of GCs in NGC 5128. We also provide additional notes on objects that
we have “demoted”.

It has been nearly a decade since an up-to-date comprehensive catalog of
confirmed GCs around NGC 5128 has been published. Recent papers have either
studied a subset of candidates and known GCs or have relied on “private
communication” as one of their data sources. With decades of observations and
a multitude of naming conventions and selection criteria, we hope to aid in
future studies by providing information about all confirmed GCs known at this
time in a clear way.

##  Appendix A Table of Confirmed GCs

We present a compilation catalog of the 557 confirmed GCs around NGC 5128. The
most common way to confirm that a candidate GC is associated with NGC 5128 is
to measure its radial velocity, since most GCs at that distance are too small
to visually resolve into component stars with ground-based data. NGC 5128 has
a systematic velocity of 541 km s-1 (Hui et al., 1995), and a central stellar
velocity dispersion of $\sim$150 km s-1 (Wilkinson et al., 1986). Therefore,
to avoid contamination from Milky Way foreground stars, past surveys have
considered a GC to be confirmed if its radial velocity is greater than 250 km
s-1. Three studies confirm select GCs based on morphological parameters if
their radial velocity measurement is below this critical value (Woodley et
al., 2010b, a; Mouhcine et al., 2010). Additionally, Harris et al. (2002,
2006) list new GCs found via their resolved stellar outskirts in HST STIS and
ACS imaging, respectively, and some of these GCs do not currently have radial
velocity measurements. We consider all of these “confirmed” GCs of NGC 5128,
unless there exists evidence to the contrary.

For each confirmed GC around NGC 5128, Table 4 first lists the ID from the GC
candidate catalog in this paper, the discovery ID, and all references in the
literature. Also listed are the right ascension and declination in degrees
(J2000) as well as the $g$ and $r$ band magnitudes. These measurements are
from the PISCeS dataset to provide uniform astrometric and photometric
systems, and the magnitudes have not been extinction corrected. Next we
include the most recently published radial velocity and error (km s-1), along
with its reference. In the final column, we note which GCs are in our fiducial
sample (§3) and two GCs that have slightly incorrect positions in followup
surveys. For completeness, if a GC is not in PISCeS or is within the 10’ from
the center of NGC 5128, we still include it in this catalog using its most
recent astrometry and without PISCeS photometry.

Table 4: Confirmed GCs around CenA

ID | Discovery ID | references* | R.A. | Decl. | radial distance | $g$ | $r$ |  vr |  vr Reference | Notes
---|---|---|---|---|---|---|---|---|---|---
(H21) |  |  | (J2000) | (J2000) | (arcminutes) | (mag) | (mag) |  (km s-1) |  |
H21-069900 | Fluffy | z | 199.545349 | -44.157249 | 103.8 | 19.42 | 18.73 |  719 $\pm$ 6 | z |
H21-154980 | KK197-01 | p;aa | 200.499166 | -42.535139 | 48.37 |  |  |  636 $\pm$ 16 | aa |
H21-156130 | KK197-03 | p;aa | 200.510634 | -42.536913 | 47.90 | 21.41 | 20.75 |  642 $\pm$ 3 | aa |
H21-159794 | H12-556 | w;y;v | 200.552063 | -42.753072 | 39.41 | 21.29 | 20.63 |  |  |
H21-160341 | KKs55-02 | ab | 200.557787 | -42.734733 | 39.66 |  |  |  531 $\pm$ 15 | ab |
H21-183480 | KV19-212 | z | 200.790878 | -43.874443 | 56.25 | 18.28 | 17.53 |  535 $\pm$ 2 | z | 1
H21-194226 | 32 | i;k;n;o;y | 200.909700 | -42.773027 | 25.31 | 18.86 | 18.22 |  497 $\pm$ 33 | o | 1
H21-195812 | C40 | f;g;i;k;n;o;y | 200.926424 | -43.160459 | 20.56 | 19.37 | 18.64 |  443 $\pm$ 48 | o |
H21-196535 | VHH81-01 | b;c;g;i;n;o;r;s;x;y | 200.934075 | -43.186591 | 20.89 | 18.12 | 17.38 |  645 $\pm$ 10 | s | 3
H21-196891 | GC0563 | r;y | 200.937603 | -43.019830 | 18.65 | 19.67 | 18.85 |  533 $\pm$ 35 | r | 1

  * •

The complete table will be available online.

  * •

*See Table 1 for annotation references

  * •

Notes: 1) GC is in our fiducial sample (see Section 3);

  * •

2) The position of GC pff-gc-028 is originally listed in Peng et al. (2004) in
HMS coordinates as 13:25:01.16, $-$42:56:51.05. In their Table 1, Woodley et
al. (2007) gives the position of this GC as 13:20:01.16, –42:56:51.05, which
due to an unfortunate change in one digit of right ascension minutes, points
to an empty patch of sky.

  * •

3) The position of C01/GC0005 is listed in Taylor et al. (2010) as 200.93333,
–43.187083, which is 2.65” away from the position indicated by all other
studies that noted this GC.

##  Appendix B Mis-Classified Objects

In building a catalog of known GCs around NGC 5128, it is important to note
instances of 73 targets that have been erroneously confirmed as GCs. We find
50 targets that we reclassify as foreground stars based on Gaia DR2 proper
motion and/or parallax measurements. These are discussed in Section B.1 and
listed in Table 5. Additionally, there are also 32 occurrences when followup
measurements of velocity, spectra, or structure do not agree with a target’s
initial classification (of which an additional 23 are objects that have been
reclassified as foreground stars). These are discussed in Section B.2 and
listed in Table 6.

There is one additional case in which the position listed for an identified GC
points to an empty patch of sky that cannot be readily matched with a nearby
known or candidate GC. The position for GC0472 from Woodley et al. (2010b) is
given as $\alpha$=201.42908∘, $\delta$=$-$43.00056∘. This is only 3.6′from the
center of NGC 5128, a region crowded with stars and dust. The position could
refer to a source at $\alpha$=201.42822∘, $\delta$=$-$43.00056∘ (a distance of
2.3″away), but we do not want to make that assumption here, as no other NGC
5128 GC surveys have published observations of this object. We note that there
is a very good match between the astrometry used in Woodley et al. (2010b) and
the PISCeS data used here, and so this mismatch is unique.

###  B.1 Foreground stars with measured proper motions in Gaia DR2

With the modest systematic velocity and velocity dispersion of NGC 5128, there
is some overlap in the radial velocity measurements of NGC 5128 GCs and Milky
Way foreground stars: a radial velocity measurement greater than 250 km s-1
_alone_ cannot definitively give membership for every object. Of the $\simeq$
600 identified GCs in NGC 5128, 355 can also be found in Gaia DR2, and 50 of
these have recorded proper motions and/or parallax with significance greater
than 3$\sigma$. Their velocities are plotted as the blue histogram in Figure
12. Because these objects have high-confidence apparent motion measurements,
we can infer that they are Galactic foreground stars, rather than GCs in NGC
5128. These foreground stars can also be seen as distinct from the fiducial
sample GCs in AEN–magnitude space and $BR_{\rm excess}$–magnitude space, as
seen by the blue diamonds in Figure 4, showing that all of these objects match
better to Gaia’s standard astrometric model of a star than our fiducial sample
of confirmed GCs do. Five of these stars also have HST imaging and do not have
the characteristic resolved stellar outskirts of true GCs. The stars with
$\gtrsim$ 500 km s-1 radial velocities are possibly being ejected from the
Milky Way, although the uncertainties on many of these measurements are
relatively large ($\approx$ 100 – 200 km s-1) and so warrant further
observations.

For each foreground star that was previously thought to be a GC in NGC 5128,
Table 5 first lists the right ascension and declination in degrees (J2000).
The position measurements are all from the PISCeS dataset to provide a uniform
astrometric system. Next we list the most recent reported radial velocity and
error (km s-1) along with its reference. Columns 5–7 list the right ascension
proper motion and error (mas yr-1), the declination proper motion and error
(mas yr-1), and the parallax motion and error (mas yr-1) from Gaia DR2.
Finally we include the various names each has had in the literature, along
with references. In the list of names we give preference to the earliest
naming convention when small differences are found, such as the removal or
addition of preceding “0” digits or the removal, addition, or slight
alteration of prefixes.

We identified two authentic GCs that have high apparent motion measurements in
Gaia DR2 (see Notes 10 and 18 in Table 6). Because Gaia DR2 is designed to
observe stars in the Milky Way, it does not always provide accurate
measurements of sources that are extended or in very crowded regions. We urge
caution and follow-up observations of the objects in Table 5, especially those
within 10′of the center of NGC 5128.

Table 5: Foreground stars that were previously mis-classified as GCs

RA | Dec |  vr |  vr Ref.* | $\mu_{\alpha}$ | $\mu_{\delta}$ | $\varpi$ | Names* | Notes
---|---|---|---|---|---|---|---|---
(deg J2000) | (deg J2000) | (km/s) |  | (mas/yr) | (mas/yr) | (mas/yr) |  |
200.858796 | -42.924206 |  235 $\pm$ 43 | r |  -4.81$\pm$0.42 |  -0.79$\pm$0.35 |  0.73$\pm$0.26 |  GC0560r; T17-0955y |
200.867666 | -42.795083 |  181 $\pm$ 68 | r |  -8.67$\pm$0.16 |  -0.08$\pm$0.13 |  0.27$\pm$0.09 |  GC0561r; T17-0962y |
200.868472 | -42.886790 |  238 $\pm$ 26 | r |  -4.86$\pm$0.49 |  -3.69$\pm$0.40 |  0.44$\pm$0.30 |  GC0562r; T17-0964y |
200.977151 | -43.333608 |  274 $\pm$ 49 | r |  -8.72$\pm$1.59 |  0.51$\pm$1.14 |  -0.10$\pm$0.74 |  GC0007n,r; AAT301956o; T17-1035y |
200.994011 | -42.954703 |  590 $\pm$ 144 | r |  -11.7$\pm$0.99 |  -0.34$\pm$0.74 |  0.44$\pm$0.57 |  GC0009n,r; AAT101931o; T17-1048y |
200.998369 | -42.922017 |  293 $\pm$ 83 | o |  -3.35$\pm$1.03 |  0.28$\pm$0.82 |  -1.03$\pm$0.61 |  GC0012n; AAT102120o; T17-1054y |
201.024844 | -43.065200 |  277 $\pm$ 67 | o |  -6.15$\pm$1.09 |  -8.05$\pm$0.86 |  -0.24$\pm$0.72 |  GC0016n; AAT103195o; T17-1068y |
201.027472 | -42.882931 |  285 $\pm$ 29 | r |  -9.81$\pm$0.35 |  -2.19$\pm$0.31 |  0.19$\pm$0.23 |  GC0565r; T17-1071y |
201.035905 | -43.274189 |  305 $\pm$ 56 | n |  6.09$\pm$1.01 |  -5.08$\pm$0.73 |  0.72$\pm$0.63 |  GC0017n; T17-1081y |
201.040767 | -42.748422 |  173 $\pm$ 117 | r |  -6.87$\pm$0.46 |  -2.66$\pm$0.30 |  0.49$\pm$0.21 |  GC0566r; T17-1084y |
201.137766 | -43.312476 |  344 $\pm$ 58 | n |  -2.96$\pm$0.96 |  -4.63$\pm$0.83 |  1.60$\pm$0.56 |  pff-gc-010g,i,l; GC0035n; T17-1180y | 1
201.181460 | -43.145317 |  465 $\pm$ 38 | o |  -4.66$\pm$0.52 |  -1.55$\pm$0.43 |  -0.13$\pm$0.32 |  GC0047n,u; AAT109380o; T17-1216y |
201.199229 | -43.145415 |  353 $\pm$ 29 | r |  -3.25$\pm$1.40 |  -3.98$\pm$1.14 |  -1.07$\pm$0.88 |  GC0575r,u; T17-1240y |
201.216990 | -43.075755 |  195 $\pm$ 29 | q |  -6.81$\pm$1.24 |  -2.84$\pm$0.88 |  -0.19$\pm$0.64 |  C100f,q; GC0068n,r,u; T17-1269y |
201.220601 | -43.198898 |  302 $\pm$ 166 | o |  -10.1$\pm$1.39 |  -6.18$\pm$1.23 |  0.07$\pm$0.92 |  GC0069n; AAT111033o; T17-1270y |
201.224941 | -43.073484 |  466 $\pm$ 87 | o |  -5.11$\pm$1.08 |  -7.67$\pm$0.84 |  -0.78$\pm$0.59 |  GC0071n,u,x; AAT111185o; T17-1278y |
201.228369 | -43.147004 |  197 $\pm$ 29 | r |  -12.9$\pm$0.71 |  -3.60$\pm$0.58 |  0.74$\pm$0.43 |  GC0577r,u; T17-1289y |
201.235562 | -42.658724 |  158 $\pm$ 50 | r |  0.14$\pm$0.36 |  -2.75$\pm$0.28 |  0.78$\pm$0.16 |  GC0579r; T17-1306y |
201.237909 | -42.648595 |  170 $\pm$ 45 | r |  -1.41$\pm$0.54 |  -1.61$\pm$0.40 |  0.08$\pm$0.23 |  GC0580r; T17-1311y |
201.269183 | -43.122730 |  456 $\pm$ 118 | o |  1.89$\pm$0.78 |  -4.51$\pm$0.72 |  0.67$\pm$0.47 |  GC0118n,u; AAT112964o; T17-1385y |
201.287915 | -42.400245 |  456 $\pm$ 52 | o |  -3.57$\pm$0.52 |  -3.26$\pm$0.57 |  0.03$\pm$0.28 |  pff-gc-039g,i,o; GC0133n; T17-1422y |
201.292702 | -42.919294 |  576 $\pm$ 12 | r |  1.11$\pm$1.14 |  -1.43$\pm$1.02 |  -2.24$\pm$0.69 |  GC0137n,r,u; K-033o,q; T17-1429y |
201.296247 | -42.967546 |  330 $\pm$ 61 | o |  0.09$\pm$0.62 |  -14.0$\pm$0.48 |  0.18$\pm$0.32 |  HGHH-G348d,g,i,o; GC0142n,u; T17-1437y |
201.308075 | -42.961843 |  373 $\pm$ 36 | o |  -8.33$\pm$0.51 |  -0.37$\pm$0.42 |  0.09$\pm$0.27 |  HGHH-G271d,g,i,j,o; GC0155n,u; T17-1464y |
201.311756 | -43.686271 |  502 $\pm$ 53 | o |  -4.20$\pm$0.65 |  1.67$\pm$0.49 |  0.65$\pm$0.31 |  pff-gc-046g,i,o; GC0159n; T17-1472y |
201.318460 | -43.059162 |  352 $\pm$ 136 | n |  -8.97$\pm$1.81 |  -2.93$\pm$2.38 |  -0.01$\pm$1.07 |  AAT114993l; GC0170n,u; T17-1487y | 1
201.329612 | -43.201107 |  453 $\pm$ 232 | o |  -18.9$\pm$1.11 |  -1.72$\pm$0.93 |  0.56$\pm$0.61 |  GC0183n; AAT320656o; T17-1515y |
201.339502 | -43.324865 |  163 $\pm$ 57 | r |  -25.6$\pm$1.14 |  -2.48$\pm$0.85 |  0.62$\pm$0.72 |  GC0427r; T17-1533y |
201.357052 | -42.627947 |  404 $\pm$ 74 | o |  -16.7$\pm$1.33 |  2.30$\pm$1.14 |  1.72$\pm$0.53 |  GC0198n; AAT204119o; T17-1557y |
201.358160 | -43.057139 |  269 $\pm$ 27 | q |  -8.33$\pm$0.73 |  -0.81$\pm$0.73 |  0.40$\pm$0.42 |  HGHH-46d,g,i,o; GC0200n,u; GC0462q; T17-1560y; T17-1561y | 2
201.358752 | -43.189572 |  243 $\pm$ 19 | r |  -5.34$\pm$0.41 |  -2.25$\pm$0.38 |  -0.19$\pm$0.27 |  GC0519r; T17-1562y |
201.370066 | -43.072667 |  553 $\pm$ 155 | r |  -4.23$\pm$0.32 |  -2.76$\pm$0.31 |  0.16$\pm$0.20 |  C145l; GC0207n,r,u; T17-1578y | 3
201.376149 | -43.698210 |  297 $\pm$ 40 | n |  -2.61$\pm$1.64 |  -5.08$\pm$1.23 |  -0.96$\pm$0.77 |  pff-gc-054g; GC0216n; T17-1593y |
201.394333 | -43.054556 |  585 $\pm$ 97 | r |  -6.55$\pm$0.29 |  0.44$\pm$0.27 |  0.31$\pm$0.18 |  C152l; GC0241n,r; T17-1634y | 3
201.396764 | -43.200422 |  243 $\pm$ 61 | n |  -12.3$\pm$0.73 |  1.40$\pm$0.57 |  0.27$\pm$0.33 |  58i; WHH-21j; GC0247n; T17-1644y |
201.408318 | -43.283137 |  257 $\pm$ 59 | o |  -15.1$\pm$1.07 |  -5.93$\pm$1.07 |  -0.98$\pm$0.75 |  GC0256n; AAT118314o; T17-1665y |
201.410147 | -43.084056 |  28 $\pm$ 9 | r |  -4.19$\pm$0.36 |  -0.96$\pm$0.35 |  0.59$\pm$0.24 |  C156l; GC0258n,r,u; T17-1668y | 3
201.434215 | -42.983167 |  550 $\pm$ 34 | q |  -5.57$\pm$1.71 |  1.58$\pm$1.49 |  1.05$\pm$1.05 |  HHH86-35c,g,i,q; GC0286n,u; T17-1724y |
201.443677 | -42.581676 |  293 $\pm$ 115 | o |  -8.23$\pm$0.76 |  -0.76$\pm$1.05 |  -0.05$\pm$0.44 |  GC0294n; AAT208206o; T17-1745y |
201.466443 | -43.204605 |  187 $\pm$ 41 | r |  -9.60$\pm$0.50 |  -0.72$\pm$0.49 |  -0.18$\pm$0.26 |  GC0592r; T17-1797y |
201.519553 | -42.793058 |  336 $\pm$ 160 | o |  -0.49$\pm$1.32 |  -5.68$\pm$1.46 |  0.46$\pm$0.66 |  GC0363n; AAT122794o; T17-1914y |
201.550553 | -42.817643 |  225 $\pm$ 35 | r |  -2.88$\pm$0.70 |  -5.63$\pm$1.02 |  0.82$\pm$0.38 |  GC0443r; T17-1964y |
201.566173 | -42.916896 |  582 $\pm$ 10 | s |  -2.83$\pm$0.74 |  -2.05$\pm$0.88 |  -0.33$\pm$0.42 |  f1.GC-22i; R122m; GC0382n,r,s,x; T17-1974y |
201.599416 | -42.788083 |  343 $\pm$ 43 | n |  -10.9$\pm$0.15 |  -4.85$\pm$0.15 |  2.26$\pm$0.07 |  HGHH-51g; GC0398n; T17-2015y |
201.599715 | -43.295681 |  277 $\pm$ 158 | o |  -6.07$\pm$1.47 |  -1.01$\pm$2.46 |  -1.06$\pm$0.84 |  GC0399n; AAT335187o; T17-2017y |
201.657114 | -42.981575 |  276 $\pm$ 22 | r |  -5.66$\pm$0.54 |  -13.0$\pm$0.60 |  -0.17$\pm$0.31 |  GC0553r; T17-2063y |
201.674875 | -43.129149 |  271 $\pm$ 20 | n |  -50.3$\pm$0.20 |  -11.7$\pm$0.28 |  0.92$\pm$0.11 |  HHH86-39c,g,i,j,o; GC0406n,u; T17-2078y |
201.712004 | -43.122378 |  372 $\pm$ 42 | r |  -10.1$\pm$3.23 |  2.25$\pm$4.16 |  2.13$\pm$1.55 |  GC0557r,u; T17-2104y |
201.839971 | -42.644833 |  252 $\pm$ 71 | o |  8.28$\pm$0.49 |  -9.16$\pm$0.59 |  0.29$\pm$0.25 |  pff-gc-101g,i,o; GC0414n; T17-2180y |
201.753258 | -42.360852 |  594 $\pm$ 102 | o |  -10.7$\pm$1.26 |  -3.20$\pm$1.30 |  0.17$\pm$0.74 |  AAT223403o |

  * •

*See Table 1 for annotation references

  * •

Notes: 1) This object was found to be a star based on Hubble Space Telescope
(HST)/Advanced Camera for Surveys (ACS) imaging by Harris et al. (2006).

  * •

2) See Appendix C for information about the naming history of this object.

  * •

3) This object was identified as a GC based on HST ACS imaging by Harris et
al. (2006). It also has large ($\sigma\geq 4$) proper motion and/or parallax
measurements in Gaia DR2, and careful re-inspection of its HST imaging
confirms it to be a point source.

###  B.2 Conflicting measurements

Thirty-two of the identified GCs in NGC 5128 have conflicting classifications
in the literature. A majority of these conflicting classifications occur
because the target was measured to have a radial velocity within the standard
acceptable range of $\approx$ 250 – 1000 km s-1 by one group, but outside this
range by another. Additionally, two objects were identified as GCs based on
their radial velocities, but later found to be stars based on HST/Advanced
Camera for Surveys (ACS) imaging (see note 9 in Table 6). Another object was
subsequently identified as a star because of its spectrum (see note 5 in Table
6). These objects with conflicting measurements have been matched between
studies based on position, and in many cases by their ID as well. When
examining these objects with PISCeS data, several of them can be visually
identified as background galaxies. We believe seven of these objects are
indeed true GCs, because a majority of their measurements classify them as
such and they do not visually look like galaxies, so they are included in
Table 4.

For each object with conflicting measurements, Table 6 first lists the right
ascension and declination in degrees (J2000). The position measurements are
from the PISCeS dataset to provide a uniform astrometric system. Next we list
the conflicting radial velocities and errors (km s-1) along with their
sources, if applicable. We also include our classification of each object, as
well as further information indicated by the “Notes” column.

Many sources experience a discrepancy between Woodley et al. (2007) and
Beasley et al. (2008). It appears that between sharing data with the Woodley
group and publishing their own paper, the Beasley group updated measurements
on several targets. We note that one of these objects has a mismatch in both
its velocity measurement and coordinates. Woodley et al. (2007) gives an
incorrect position for HH-048 as $\alpha$=200.68900∘, $\delta$=$-$43.119111∘,
with a radial velocity of 856 $\pm$ 56 km s-1, citing Beasley et al. (2008) as
the reference for this radial velocity measurement. Beasley et al. (2008),
however, lists HH-048 as a background galaxy ($v_{r}$ = 16000 km s-1) with the
same right ascension but a declination of $\delta$=$-$43.011917∘ (note the
single difference in the digit following the decimal point). Based upon visual
inspection, the position listed in the Beasley catalog is correct, and is
listed in Table 6

Table 6: Previously Classified Objects with Conflicting Measurements

RA | Dec |  vr #1 | Source #1* |  vr #2 | Source #2* | Our Classification | Notes
---|---|---|---|---|---|---|---
(deg J2000) | (deg J2000) | (km/s) |  | (km/s) |  |  |
200.689000 | -43.011917 |  856 $\pm$ 56 | m | 16000 | n | galaxy | 1, 2
200.926424 | -43.160459 |  357 $\pm$ 42 | f |  | j | GC | 3
200.986186 | -43.000083 |  798 $\pm$ 49 | m | 13000 | n | galaxy | 1
201.011383 | -42.809021 |  775 $\pm$ 75 | m | 5000 | n | galaxy | 1
201.035905 | -43.274189 |  305 $\pm$56 | m |  | n | star | 4, 5
201.099937 | -42.902944 |  582 $\pm$ 81 | i | 46000 | n | unknown | 6
201.117323 | -42.884562 |  835 $\pm$ 83 | m | 13000 | n | unknown | 7
201.134014 | -43.182469 |  636 $\pm$ 78 | i |  | j | GC | 8
201.137766 | -43.312476 |  344 $\pm$ 58 | f |  | k | star | 4, 9
201.144203 | -43.214044 |  7717 $\pm$ 194 | i |  517 $\pm$ 123 | m | unknown |
201.188363 | -43.388845 |  998 $\pm$ 250 | m | 17000 | n | galaxy | 1
201.203346 | -43.271446 | 42000 | n |  426 $\pm$ 41 | r | unknown |
201.232175 | -43.379980 |  921 $\pm$ 146 | m | 9000 | n | galaxy | 1
201.263696 | -43.137316 | 31000 | n |  690 $\pm$ 31 | r | unknown |
201.318460 | -43.059162 |  | k |  352 $\pm$ 136 | n | star | 4, 9
201.347769 | -42.890588 |  2017 $\pm$ 78 | i |  545 $\pm$ 64 | m | unknown |
201.376149 | -43.698210 |  317 $\pm$ 43 | f |  169 $\pm$ 108 | n | star | 4
201.406112 | -43.095806 |  | l |  | this work | GC | 10
201.415196 | -43.067039 |  510 $\pm$ 33 | f |  32124 $\pm$ 253 | i | GC | 11
201.440728 | -42.571614 |  998 $\pm$ 250 | m | 15000 | n | galaxy | 1
201.455161 | -43.000611 |  7349 $\pm$ 87 | i |  465 $\pm$ 30 | q | unknown | 12
201.455309 | -43.039000 |  384 $\pm$ 30 | f |  9942 $\pm$ 113 | i | GC | 13
201.543947 | -43.018297 |  231 $\pm$ 143 | n |  311 $\pm$ 81 | r | unknown |
201.550553 | -42.817643 |  117 $\pm$ 80 | n |  225 $\pm$ 35 | r | star | 4, 14
201.572047 | -43.110904 |  24742 $\pm$ 79 | i |  513 $\pm$ 183 | m | unknown |
201.574090 | -42.770562 | 64000 | n |  178 $\pm$ 51 | r | galaxy | 1
201.585963 | -42.896082 |  271 $\pm$ 64 | r |  | this work | unknown | 15
201.592072 | -43.152950 |  505 $\pm$ 78 | i | 21000 | n | unknown | 16
201.660454 | -42.762675 |  474 $\pm$ 65 | f | 2000 | n | GC | 17
201.705431 | -43.082693 |  839 $\pm$ 63 | m | 15000 | n | galaxy | 1
201.748983 | -42.924119 |  833 $\pm$ 32 | m | 13000 | n | galaxy | 1
202.076936 | -42.553438 |  410 $\pm$ 42 | f |  | this work | GC | 18

  * •

*See Table 1 for annotation references

  * •

Notes: 1) Based on visual inspection with PISCeS data, this object is a
galaxy.

  * •

2) See discussion in Section B.2 about the position of this object in the
literature.

  * •

3) This object also has a radial velocity measurement of 443 $\pm$ 48 km s-1
from Beasley et al. (2008), no parallax or proper motion and a high $\sigma$
AEN value in Gaia DR2. We believe that the previous classification of this
object as a foreground star is inaccurate (based on the shape of its PSF
subtracted residual by Gómez et al. (2006)), and so include it in our
confirmed GC sample.

  * •

4) Based on Gaia DR2 proper motion and parallax data, we find this object to
be foreground star. It is also listed in Table 5.

  * •

5) This object was identified as a star by Beasley et al. (2008) because it
exhibits strong molecular bands in its spectrum that are characteristic of an
M-type star.

  * •

6) This object is also measured with $v_{r}$ = 606 $\pm$ 33 km s-1 in Woodley
et al. (2010a), but they still list the older velocity measurement of $v_{r}$
= 582 $\pm$ 81 as their “new weighted radial velocity”. It was also noted as a
background galaxy in Gómez et al. (2006) based on the shape of its PSF
subtracted residual.

  * •

7) Based on visual inspection with PISCeS data, at this position there is a
galaxy and an unknown, point-source-like object projected onto each other.

  * •

8) This object also has a radial velocity measurement of 775 $\pm$ 74 from
Beasley et al. (2008) and 813 $\pm$ 40 from Woodley et al. (2010a), and no
parallax or proper motion and a high $\sigma$ AEN value in Gaia DR2. We
believe the classification as a background galaxy by Gómez et al. (2006) based
on the shape of its PSF subtracted residual is inaccurate, and so include it
in our confirmed GC sample.

  * •

9) This object was found to be a star based on HST ACS imaging by Harris et
al. (2006).

  * •

10) This object was initially identified as a GC based on HST ACS imaging by
Harris et al. (2006), and it has two radial velocity measurements of 575 $\pm$
36 (Woodley et al., 2007) and 524 $\pm$ 18 (Woodley et al., 2010b). In Gaia
DR2, it has a proper motion measurement with $\sigma$ = 4.12, but in Gaia EDR3
it has a proper motion measurement with only $\sigma$ = 1.5. Because it is
very close to the center of the galaxy, we believe the Gaia DR2 measurements
to be inaccurate, and so include it in our confirmed GC sample.

  * •

11) This was also measured by Beasley et al. (2008) with $v_{r}$ = 557 $\pm$
49 km/s. We believe the classification as a galaxy is inaccurate, and so
include it in our confirmed GC sample.

  * •

12) This object is also measured with $v_{r}=475\pm 134$ in Woodley et al.
(2010a), but they still list the older velocity measurement of $v_{r}$ = 465
$\pm$ 30 as their “new weighted radial velocity”.

  * •

13) This object was also measured by Beasley et al. (2008) to have
$v_{r}=420\pm 51$, and by Woodley et al. (2010a) to have $v_{r}$ = 371 $\pm$
28\. We believe the classification as a galaxy is inaccurate, and so include
it in our confirmed GC sample.

  * •

14) Woodley et al. (2010a) classified a small number of candidates as GCs with
low velocities based on their structural parameters, many of which we find to
actually be foreground stars.

  * •

15) This object has one radial velocity measurement of 271 $\pm$ 64 km s-1,
but also has stellar AEN and $C_{3-6}$ values. It has no reported proper
motion or parallax in Gaia DR2. We recommend that further study of this GC to
more confidently reinforce or oppose its status as a GC of NGC 5128.

  * •

16) This object is also measured with $v_{r}$ = 357 $\pm$ 35 km s-1 in Woodley
et al. (2010a), but they still list the older velocity measurement of $v_{r}$
= $505\pm$ 78 as their “new weighted radial velocity”.

  * •

17) The position of this target is listed by Peng et al. (2004); Beasley et
al. (2008) as 201.65829, $-$42.763861, which is 7” away from the position we,
and other followup studies, find for this GC. It also has additional radial
velocity measurements of 492 $\pm$ 37 km s-1 in Woodley et al. (2007) and 627
$\pm$ 21 km s-1 in Woodley et al. (2010a).

  * •

18) This object has a Gaia DR2 proper motion measurement of 13.47 $\pm$ 2.68
mas yr-1. We do not include it in the HVFS table, however, because it has AEN,
parallax, color, and $C_{3-6}$ values and two independent radial velocity
measurements consistent with its status as a GC in NGC 5128. Therefore, it is
is recorded in Table 4, but is not included in the fiducial sample, Figure 12,
or Table 5.

##  Appendix C An object with too many names

During our literature review, we found an instance where two confirmed GCs
with different names shared the same position. The objects identified most
recently as GC0462/T17-1560 and GC0200/T17-1561 have the same position in the
Sinnott et al. (2010) catalog, and positions that differ by 0.24” in the T17
catalog. Upon visual inspection, both objects seem to correspond to the GC
originally identified as HGHH-46 in the Harris et al. (1992) catalog. The