11institutetext:  ESO - European Southern Observatory, Alonso de Cordova 3107,
Vitacura, Santiago, Chile 22institutetext: Instituto de Astrofísica, Depto. de
Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andrés Bello, Av.
Fernandez Concha 700, Las Condes, Santiago, Chile 33institutetext: Vatican
Observatory, Vatican City State, V-00120, Italy 44institutetext: Departamento
de Fisica, Universidade Federal de Santa Catarina, Trinidade 88040-900,
Florianopolis, Brazil 55institutetext: Instituto de Astronomía, Universidad
Católica del Norte, Av. Angamos 0610, Antofagasta, Chile

# Over 200 globular clusters in the Milky Way and still none with super-Solar
metallicity

E. R. Garro 11 D. Minniti 223344 J. G. Fernández-Trincado 55

(Received: XX; Accepted: YY)

###### Abstract

Context. A large number of globular clusters in the Milky Way have been
studied in recent years, especially in hidden regions such as those of the
Galactic bulge.

Aims. The main goal of this work is to understand what we can learn if we
include these new objects into the Milky Way globular cluster (GC) system that
we know today. We compiled a catalog of 37 recently discovered globular
clusters. Most of them are located in the Galactic bulge, but we also included
some of the GCs for comparison.

Methods. We used a range of distributions for investigating the Galactic GC
system based on the metallicity, luminosity function, and age. We considered
three samples. We first treated the new GC sample separately from the known
and well characterized GCs. Consequently, we merged these two samples, thereby
upgrading the Milky Way GC system. Furthermore, we performed a comparison
between our clusters sample and the field star population.

Results. We found a double-peaked distribution for the luminosity function,
which shows an elongated faint end tail. Considering the ”merged” sample, the
luminosity function peaks at $M_{V}^{up}=-7.00\pm 1.3$ mag and at
$M_{V}^{up}=-4.1\pm 0.48$ mag. The metallicity distributions also display a
bimodality trend. In this case, we compare our new sample compilation with
previously published ones, finding that the distributions are in good general
agreement. We also constructed the metallicity distribution for the field star
sample and, by comparing it with that of the GCs, we learned that a high
percentage of field stars show [Fe/H] $>0$; whereas we did not detect any GCs
in the same metallicity range. To understand this inconsistency, we
constructed the age-metallicity diagram for both samples, noting that the old
and metal-poor population (age $\geq 8$ Gyr and [Fe/H] $\leq-1.0$) is
represented by Gcs, while the young and metal-rich population (age $<8$ Gyr
and [Fe/H] $>-1.0$) corresponds to field stars.

Conclusions. From the analysis of the GC luminosity function and metallicity
distribution, we can conclude that many GCs, probably those that are very
faint, have survived strong dynamical processes that are typical of the bulge
regions. Moreover, we cannot exclude the possibility that some of them have
been accreted during past merging events, especially the metal-poor component,
whereas the metal-rich population may be related to the formation of the bulge
and/or disk. Finally, the difference that we notice between the cluster and
field star samples should be explored in the context of the evolutionary
differences among these two stellar populations.

###### Key Words.:

Galaxy: bulge – (Galaxy:) globular clusters: general - Galaxy: formation -
Galaxy: evolution

##  1 Introduction

In a cosmological context, the hierarchical galaxy formation process predicts
that galaxies and their halos have a large number of progenitors at the
formation redshift ($z\sim 3$) of globular clusters (GCs, De Lucia & Blaizot
2007; Lamers et al. 2017). With the advent of new observations from James Webb
Space Telescope, new theories may be formulated and new observational
discoveries can be established, which may change, confirm, or improve our
knowledge. For instance, recent works have uncovered (mini-)quenched galaxies
at redshifts of $z=4.4$ (Looser et al. 2023a) and $z=7.3$ (Looser et al.
2023b); thus, we cannot exclude the fact that GCs have been formed as well at
these redshifts. Also, Mowla et al. (2022) found compact red companions to the
Sparkler galaxy, which may be the first evolved GCs seen at $z_{spec}\approx
1.4$. They infer formation redshift of $z_{form}\sim 7-11$ for these
candidates, corresponding to ages of $\sim 3.9-4.1$ Gyr at the epoch of
observation and a formation time just $\sim 0.5$ Gyr after the Big Bang.
Therefore, as these authors reported, if these ages are confirmed, at least
some GCs appear to have formed contemporaneously with the large-scale
reionization of the intergalactic medium, hinting at a deep connection between
GC formation and the initial phases of galaxy assembly. Nevertheless, there is
a long way to go before we can at least confirm the existence of those
primordial GCs and begin constructing new models that describe these compact
objects. This is especially true because their exact formation redshifts are
somewhat uncertain for these unresolved and red objects, with no spectroscopic
data yet available to offer clues to the real phase of these objects.

Both simulations (e.g., Tonini 2013; Kruijssen 2015) and observations (e.g.,
Horta et al. 2023) have shown that much of the metal-poor GC population in
massive galaxies was mostly accreted from cannibalized dwarf galaxies, whereas
the metal-rich population formed preferentially in situ111We use ”in situ” to
refer to the GCs that formed during the initial collapse of the central
galaxy, and ”ex-situ” for those one that are accreted during the subsequently
mergers. or also likely during merging events (Hughes et al. 2019a; Garro et
al. 2021a; Hasselquist et al. 2021). In this context, debris from accreted GCs
and dwarf galaxies is expected to populate halo regions as well as the central
regions of the MW (Das et al. 2020; Fernández-Trincado et al. 2019, 2021a).
However, the number of confirmed merging footprints in the inner regions is
still smaller than those found in the Galactic halo. For that reason, we want
to investigate the Galactic bulge to collect clues to its formation and
evolution history.

Actually, there are many queries that remain unanswered regarding the bulge.
For instance, it is not completely clear if the bulge is a simple classical
bulge, formed from a monolithic collapse, and then grown up hierarchically by
merging of galaxies (Guedes et al. 2013), or it was formed by secular
evolution (Kormendy & Kennicutt 2004), so it is part of the peanut structure
corresponding to the old Galactic thick disk. This would imply that the MW is
a pure thin+thick disk galaxy, with only a possible limited contribution by a
classical bulge (Di Matteo et al. 2015). Such a mix would represent a compound
bulge (Athanassoula 2005; Erwin et al. 2014; Zoccali et al. 2014). Secondly,
there are also queries about its evolution, such as how many accretions
occurred, how the star formation history and so the chemical evolution
proceeded, and so on.

The main aim of this paper is to take advantage from bulge GC populations,
which can be used as archaeological probes to reconstruct the formation and
evolution of the MW. However, such regions as the Galactic bulge are very
challenging to study, because of the high stellar crowding and differential
reddening, which make the identification of new GCs a complicated task. Wide-
field near-infrared (NIR) photometry such as the VISTA Variables in the Vía
Láctea (VVV; Minniti et al. 2010; Saito et al. 2012) survey and its extension
(VVVX; Minniti 2018) offers a huge advantage to detect several sparse and
faint GCs heavily obscured by interstellar dust in the bulge region. Indeed,
numerous ($\sim 300$) GC candidates have recently been discovered in these
zones (Minniti et al. 2017, 2021c, 2021a; Dias et al. 2022; Garro et al.
2021b, 2022c). It seems that the number of known MW GCs (in total $N_{GC}\sim
170$ \- Vasiliev & Baumgardt 2021), but in particular the MW bulge GCs
($N_{GC}\sim 40$ \- Barbuy et al. 2018b, or maybe more as suggested by Bica et
al. 2016) is too small if we take into account the mass of the MW and if we
compare that number with similar systems, such as M31. In this context, for
example, Abdullah & Kroupa (2018) (see their Figure 6) showed that the MW and
M31 specific frequencies should be similar in their range of masses
($M/M_{\odot}=10^{10}-10^{11}$). Therefore, this may imply that the census of
the MW clusters is still incomplete (Minniti et al. 2017). Indeed, searching
and analysing new GCs in the MW bulge is tricky. They appear as round
concentrations of stars, showing up as overdensities above the background in
the optical and NIR images, but sometimes they are not real clusters but
asterisms, background fluctuations, or possible streams of previously
disrupted GCs. At the distance of the Galactic bulge, their typical half-light
radii would range between 2 pc ($0^{\prime}.80$) for the smallest ones and 10
pc ($4^{\prime}.20$) for the largest ones. Additionally, since many of them
are very faint and small objects, they are experiencing destruction processes,
due to the fact that the deep potential well of the Galactic bulge strengthens
the efficiency of such dynamic processes (Habibi et al. 2014; Khoperskov et
al. 2018). Hence, this is why the Galactic bulge is referred to as the
elephant graveyard (Minniti et al. 2017).

Hence, we want to employ both known and well characterized GCs and the
recently discovered ones for investigating the inner regions, using different
tools: the metallicity distribution function (MD), the luminosity function
(LF), age distributions, and the kinematics information. Additionally, we
prefer expanding this analysis to the bulge field star (FS) populations, since
it is expected that a small fraction of bulge FSs (proposed to be $\sim
5-10\%$ – Kruijssen 2012; Adamo et al. 2015) is born in bound systems, and
then it is lost due to both merging events and/or destruction/dissolution
processes (stellar evolution, two-body relaxation, tidal evaporation, and
tidal shocks – Kruijssen et al. 2011; Madrid et al. 2017). Consequently, a
comparison between these two populations may help us to understand and
constrain the formation and evolution of the inner Galaxy. Nevertheless, these
two populations are usually treated separately.

With respect to what has been done thus far, different studies have reported
that the Galactic bulge shows multiple peaks in its MD, features that are
usually associated with different stellar populations (Ness et al. 2013;
Bensby et al. 2017; Rojas-Arriagada et al. 2020), coexisting in the innermost
regions. The existence of a metallicity gradient is demonstrated adopting
different tracers (Minniti et al. 1995). Gonzalez et al. (2013) using the VVV
photometry confirmed that metal-rich stars ([Fe/H] $\sim 0$) dominated the
inner bulge in regions closer to the Galactic plane ($|b|<5$), while at larger
scale heights, the mean metallicity of the bulge red giant population becomes
significantly more metal-poor. Ness et al. (2013) and Debattista et al. (2017)
found that the metal-rich population is dominant at low latitudes, but drops
off rapidly with increasingly latitude. The metal-poor population instead
follows the opposite trend, increasing toward high Galactic latitudes. The
intermediate-metallicity population dominates everywhere except near the disk,
where the metal-rich population dominates. On the other hand, works by Barbuy
et al. (2018a) and Savino et al. (2020) found a predominance of moderately
metal-poor populations in the innermost Galactocentric regions, which extends
to large distances above the Galactic plane. This is probably related to the
fact that the old and intermediate age RR Lyrae populations were taken into
account and they are not expected to exhibit a strong peanut shape, as red
clump stars (Gonzalez et al. 2015), since they should be older than the
formation of the bar itself (Debattista et al. 2017). On the other side, if we
take into account GCs, we find the metal-rich ones especially in the inner
regions of the Galaxy, while the metal-poor one in the halo.
We may note that the meanings of ”metal-poor” and ”metal-rich” are not
strictly defined and depend on the different contexts where these terms are
used. For instance, for the ”metal-rich” FSs we often refer to solar
metallicity ([Fe/H] $\approx 0$), while for the ”metal-rich” GCs, we consider
values of [Fe/H] $>-0.5$, which might be referred to as ”intermediate-
metallicity” for the field overall. Therefore, in the present work, we broadly
define ”metal-poor” as [Fe/H] $<-1.0$, whereas ”metal-rich” if [Fe/H]
$\geq-1.0$, both for FSs and GCs. Moreover, we refer to ”super metal-rich” or
”super-Solar” to indicate those populations with [Fe/H] $\geq 0$. Various
nomenclatures are often used in the literature, such as ”moderately metal-
poor” (which may correspond to $-2.0\lesssim$ [Fe/H] $\lesssim-1.0$) or
”intermediate metallicity” (which may be equivalent to $-1.5\lesssim$ [Fe/H]
$\lesssim-0.6$); however, this depends once again on the populations involved.
We prefer not to use this nomenclature.

Today, we know of $\sim 170$ well-characterized GCs in the MW (Vasiliev &
Baumgardt 2021). Broadly, the Galactic GC system shows a bimodal metallicity
distribution, which indicates that in the MW coexist two major subpopulations,
but always the metallicity is typically sub-Solar ([Fe/H] $<0$). In spite of
that, there are some GCs that may show [Fe/H] $>0$. This is not completely
demonstrated, and the misgivings are strongly related to the abundance scale’s
calibrations adopted. Therefore, we cannot ignore them. For example, Carretta
et al. (2009) suggested a [Fe/H] $>+0.40\pm 0.09$ for Liller 1 GC. Recently,
Dalessandro et al. (2022) and Crociati et al. (2023) showed a bimodal iron
distribution, with a sub-solar component ([Fe/H] $=-0.48$ dex with
$\sigma=0.22$, and age $\approx 12$ Gyr) and a super-solar component ([Fe/H]
$=+0.26$ dex with $\sigma=0.17$, and age $\approx 1-3$ Gyr) for Liller 1. For
this purpose, they suggested that Liller 1 experienced three main bursts and a
low, but constant, activity of star formation over the entire lifetime. Also,
NGC 6528 may have a super-solar metallicity as found by Carretta et al. (2009)
([Fe/H] $=+0.07\pm 0.08$) and Liu et al. (2017) ([Fe/H] $=+0.04\pm 0.07$), but
in both cases, the uncertainties are greater than the value itself; therefore,
we cannot definitively conclude either way whether we indeed have a case of a
super metal-rich GC. It is clear that the analysis of the bulge MD is very
complex, since this strongly depends on target selection, tracers, and
analysis methods.

Moreover, the $\alpha$-elements are efficient tracers of Galactic evolution,
especially when [$\alpha$/Fe]-[Fe/H] diagrams are used. An $\alpha$-enhanced
plateau at low [Fe/H] is typical both for the MW and external galaxies, this
is due to the fast enrichment from massive ($8<M/M_{\odot}<40$) stars that
explode as type II supernovae (SNII), while a following decline is expected
once low-mass (in binary systems with $1.4<M/M_{\odot}<8$) stars begin to
explode as type Ia supernovae (SNIa). This creates the ”knee” point, which can
move to higher metallicity for higher star formation rates (Matteucci &
Greggio 1986). For example, Queiroz et al. (2021) found an apparent chemical
bimodality in key abundance ratios, such as [$\alpha$/Fe], [C/N], and [Mn/O],
which probe different enrichment timescales, indicating a star formation gap
between the $\alpha$-rich and $\alpha$-poor populations. They also found
signatures of the bar, a thin inner disk, a thick inner disk, and a broad
metallicity population with large velocity dispersion indicative of a
pressure-supported component. Furthermore, they found a group of counter-
rotating stars that could be an accreted metal-poor population originated
during a gas-rich accretion phase in the early formation of the bulge, or of a
clumpy star formation during the earliest phases of the early disk that
migrated into the bulge (Fiteni et al. 2021). In summary, many observations
suggest that the formation of the boxy bulge occurred later, originating from
the vertical instability of the Galactic bulge, formed via secular evolution
from the stellar disk. In this scenario, the old and metal-poor stellar
population dominates at higher scale heights due to the non-mixed orbits of
originally hotter thick disk stars. Lian et al. (2020) derived three-phase
star formation history of the MW bulge, which consists of an initial
starburst, followed by a rapid star formation quenching episode and a lengthy,
quiescent secular evolution phase. In fact, they found that the metal-poor,
high-$\alpha$ bulge stars ([Fe/H] $<0.0$ and [Mg/Fe] $>0.15$) were formed
rapidly ($<2$ Gyr) during the early starburst. The density gap between the
high- and low-$\alpha$ sequences is due to the quenching process. The metal-
rich, low-$\alpha$ population ([Fe/H] $>0.0$ and [Mg/Fe] $<0.15$) then
accumulates gradually through inefficient star formation during the secular
phase. This is qualitatively consistent with the early star formation history
(SFH) of the inner disk. Additionally, this explains why there is a fraction
of young stars with age $<5$ Gyr in the bulge. Indeed, we know that the bulge
mean age is about 10 Gyr, with a lower-limit of $\sim 5$ Gyr (Clarkson et al.
2011), where well-mixed clusters and stellar populations coexist. The typical
age of GCs in the innermost regions is older than 10 Gyr (Harris 1996; Minniti
1995), however GCs with intermediate age ($\approx 7-9$ Gyr) are found by
Garro et al. (2022b) and Garro et al. (2022a), indicating that these objects
are either real members of the bulge or intruders originating from the halo
(Forbes & Bridges 2010; Massari et al. 2019; Romero-Colmenares et al. 2021).
Moreover, spectroscopy of microlensed stars by Bensby et al. (2017) found a
very wide age distribution for the bulge, with several star forming episodes
at 3, 6, 8, and 11 Gyr. Also, they linked the ages to the metallicity of the
microlensed stars. At [Fe/H] $\approx-0.5$ all stars appear to be older than
10 Gyr. At higher metallicities, the age ranges spans from the youngest one
with $\sim 1$ Gyr to the oldest with $\sim 12-13$ Gyr. Additionally, the
authors indicated that their age becomes younger with increasing metallicity.
Below [Fe/H] $\approx-0.5$ essentially all stars are old, below solar but more
metal-rich than $-0.5$ dex, the fraction is around 20%, and above solar
metallicity more than one third of the stars are younger than 8 Gyr. Moreover,
Bensby et al. (2017) found that Galactic bulge properties (MFD, star formation
episodes, abundances trends) are similar to those of the MW thin and thick
disks. However, it seems that the bulge star formation rate was slightly
faster than that of the local disk, as also proposed by Lucertini et al.
(2022). Finally, their results again strengthen the observational evidence
that supports the idea of a secular origin for the Galactic bulge, formed out
of the other main stellar populations present in the central regions of our
Galaxy.

To summarize, it really is difficult to understand which of the three theories
(hierarchical scenario, secular evolution, or a combination of these two) best
explains the formation and evolution of the bulge, as well as that of the
entire galaxy. Therefore, we prefer to use the GC population in our attempts
to provide constrains, since these objects trace the Galaxy’s properties from
the innermost regions toward the outskirts. In particular, we analyzed
numerous low-luminosity GCs, which probably survived strong dynamical
processes. We employ them in this paper to see what we can learn if we include
this sample in the typical MW GC system.

##  2 Sample of selected bulge GCs

As mentioned previously, many new GCs are recently discovered and
photometrically analyzed both in NIR and optical wavelengths in the MW bulge
and disk. We have cataloged these objects in Table 2, where we listed their
main physical parameters: positions, mean cluster proper motions (PM),
heliocentric and Galactocentric distances, metallicities, ages, extinction,
and integrated luminosities. We also list the references from which we have
taken all the information. The majority of the clusters are located inside the
Galactic bulge at $R_{G}\lesssim 3$ kpc; other clusters, namely Garro 01,
Riddle 15, and Gaia 2, are situated in the disk at $R_{G}>11$ kpc. Notably,
clusters, located in the innermost regions, are very obscured and heavy
embedded by the dust, where the differential reddening and extinction
($0.1<A_{Ks}<1.0$ mag, equivalent to $0.9<A_{V}<9.1$ mag - see Table 2) can
play an important role both for the detection and the characterization of
these new objects. Moreover, Figure 1 displays the position of the GCs
analyzed in Galactocentric coordinates, and we highlight the metallicity
(changing the color of the points) in order to show that both metal-poor and
metal-rich GC populations are present inside the bulge (see also Section 4).
The spatial distribution of the new sample seems to be asymmetric,
preferentially toward $X>0$ kpc. This is due to the fact that most clusters
present in our compilation were discovered in the VVV-VVVX footprints, but
this does not mean that on the opposite side ($X<0$ kpc), other small GC
candidates could live. Likely, they have not been detected yet.

Figure 1: Galactocentric distribution (XY on the left, and XZ on the right) of
the GCs analyzed in the present work (colored points), highlighting clusters
in the inner regions of the bulge. The known Galactic GCs positions are drawn
in grey points. X measured the system’s ”east-west” location, Y measured its
”north-south” location, and Z measured its distance above or below the
galactic plane. The marker’s color changes depending on the cluster’s
metallicity, as indicated by the color bar. The black cross represents the
position of the Galactic centre, while the blue star indicates the position of
the Sun.

Furthermore, we selected the clusters depending on their mean cluster PMs
(where available), and we compare our sample with well-known Galactic GCs
studied by Vasiliev & Baumgardt (2021). As shown in Figure 2, our PM values
are indeed consistent with the Galactic GCs sample. We can easily distinguish
VVV-CL160 with $(\mu_{\alpha_{\ast}},\mu_{\delta}=-2.90,-16.47$) mas yr-1,
which is separated from the bulk of the points. The origin of VVV-CL160 is
still debated (Minniti et al. 2021a), since it was found that its orbit is one
of the most eccentric between the Galactic GCs (Garro et al. 2023).

It is important to mention some important limitations of our work. First, most
of the clusters in this new catalog have been only identified photometrically
as GC candidates, therefore they deserve a detailed spectroscopic analysis for
deriving robust [Fe/H] estimates as well as radial velocities and chemical
abundances ([X/H]), in order to further confirm their real nature. For
example, Lim et al. (2022) carried out a spectroscopic analysis of 15 and 10
target stars near Camargo 1103 and Camargo 1106, respectively, two star
clusters that have been recently reported as metal-poor GC candidates in the
bulge (Camargo 2018). They did not find any clear evidence of a grouping in
radial velocity-metallicity space that would indicate the characterization of
either object as metal-poor GCs. Yet, they cannot completely rule out a low
probability that they only observed non-member stars. Another example may be
represented by Garro 01, since its classification is ambiguous. It was
classified as GC with [Fe/H] $=-0.7$ and age $\approx 11$ Gyr (as written in
Table 2) by Garro et al. (2020) and recently as possible open cluster with
[Fe/H] $=-0.3$ and age $=4$ Gyr by Pace et al. (2023). However, they cannot
confirm the Garro 01 cluster nature either. Here, we assume that all these
targets (Table 2) are genuine GCs. Second, incomplete color-magnitude diagrams
(CMDs) that do not reach the main sequence turnoff point (MSTO), affects the
age and luminosity estimates. In particular, in many cases ages are derived
using the vertical method (see for example the work by Garro et al. 2022b) or
identifying RR Lyrae stars belonging to the clusters, thus fixing a lower
limit, but indicating large error bars (Table 2). This also implies that we
cannot aptly classify them as (young) GCs or old open clusters (OCs), even if
a net separation is clearly established between these two classes.

A third caveat is represented by the fact that many of these clusters
(considered in the present work) are located in very obscured regions, where
the differential reddening, high extinction and stellar crowding may
complicate the analysis, introducing uncertainties in the derivation of the
main physical parameters. However, these problems are highly discussed by the
authors of the papers (see Table 2, last column). Finally, taking into account
the errors in the photometry, we can consider that this first work on the
newly updated MW GC system can offer further clues about the GC system itself,
as well as indications about the MW’s history.

This study includes the information collected to date, and the sample
considered here contains both the known and well-characterized GCs and those
from recently studied and confirmed as high-probability GCs (Table 2). In this
way, we are upgrading the MW GC system, therefore we expect that this has an
impact on the MW GC luminosity function (LF, see Sect. 3) and the metallicity
distribution function (MD, see Sect. 4).

Figure 2: Vector PMs diagram for our GC sample. It demonstrates that the
kinematics of the GCs here studied (orange points) are consistent with the
Galactic GCs from Vasiliev & Baumgardt (2021) (blue open squares). Table 1:
Catalog of the 37 recently discovered GCs in the MW. We list (where available)
their main physical parameters: position, mean cluster PMs, extinction in
$K_{s}$ band, distances, metallicity, age, total luminosity, and their
references.

Cluster ID l b $\mu_{\alpha_{\ast}}$ $e_{\mu_{\alpha_{\ast}}}$ $\mu_{\delta}$
$e_{\mu_{\delta}}$ $A_{Ks}$ $e_{A_{Ks}}$ $D_{\odot}$ $e_{D_{\odot}}$ $R_{G}$
[Fe/H] $e_{[Fe/H]}$ Age $e_{Age}$ $M_{Ks}$ $e_{MKs}$ $M_{V}$ $e_{M_{V}}$
Reference [deg] [deg] [mas yr-1] [mas yr-1] [mas yr-1] [mas yr-1] [kpc] [kpc]
[kpc] [dex] [dex] [Gyr] [Gyr] [mag] [mag] [mag] [mag] Garro 01 310.828
$-3.944$ $-$4.68 0.47 $-$1.35 0.45 0.15 0.01 15.5 1.0 11.2 $-$0.7 0.2 11.0 1.0
$-$7.76 0.5 $-$5.26 1.0 (a)(a)footnotemark: $(a)$ (z)(z)footnotemark: $(z)$
Garro 02 12.048 1.646 $-$6.07 0.62 $-$6.15 0.75 0.79 0.04 5.6 0.8 2.90 $-$1.3
0.2 12.0 2.0 $-$7.52 1.2 $-$5.44 0.8 (b)(b)footnotemark: $(b)$ Patchick 99
2.488 $-6.145$ $-$2.98 1.74 $-$5.49 2.02 0.09 0.01 6.6 0.6 2.81 $-$0.2 0.2
10.0 2.0 $-$7.00 0.6 $-$5.20 1.0 (c)(c)footnotemark: $(c)$ FSR 0009 1.856
$-$9.529 $-$1.39 1.10 $-$5.22 0.99 0.11 0.03 6.9 0.2 1.82 $-$1.2 0.3 11.0 2.0
$-$5.80 0.7 $-$3.40 1.0 (d)(d)footnotemark: $(d)$ FSR 1775 354.546 $-$5.779
$-$3.00 0.80 $-$5.53 0.73 0.16 0.01 8.9 0.2 1.37 $-$1.1 0.2 10.0 2.0 $-$8.00
1.7 $-$5.60 1.5 (d)(d)footnotemark: $(d)$ FSR 1767 352.601 $-$2.166 $-$3.02
0.50 $-$4.85 0.50 0.28 0.03 10.6 0.2 2.70 $-$0.7 0.2 11.0 2.0 $-$8.40 1.5
$-$6.30 1.3 (d)(d)footnotemark: $(d)$ VVV-CL131 354.722 $-$2.170 $-$3.24 0.81
$-$5.65 0.07 0.23 0.03 9.0 0.5 1.17 $-$0.6 0.2 10.0 3.0 $-$8.20 1.5 $-$5.90
1.3 (d)(d)footnotemark: $(d)$ VVV-CL143 355.788 $-$2.319 $-$3.18 0.91 $-$6.17
0.85 0.21 0.04 8.9 0.5 1.00 $-$0.6 0.2 10.0 3.0 $-$8.20 1.3 $-$5.90 1.2
(d)(d)footnotemark: $(d)$ VVV-CL160 10.151 0.302 $-$2.90 1.28 $-$16.47 1.31
0.73 0.03 6.8 0.5 1.92 $-$1.4 0.3 13.0 2.0 $-$7.90 1.5 $-$5.50 1.2
(d)(d)footnotemark: $(d)$ (e)(e)footnotemark: $(e)$ ESO 393-12 353.514
$-$2.284 $-$2.86 9.47 $-$5.39 0.44 0.23 0.02 8.2 0.4 0.98 $-$0.6 0.2 10.0 2.0
$-$7.70 1.5 $-$5.30 1.3 (d)(d)footnotemark: $(d)$ ESO 456-09 357.882 $-$3.339
$-$3.41 0.71 $-$4.36 0.75 0.18 0.03 7.6 0.4 0.81 $-$0.6 0.2 10.0 2.0 $-$8.30
1.5 $-$6.00 1.3 (d)(d)footnotemark: $(d)$ Kronberger 49 7.627 $-$2.012 $-$2.84
0.69 $-$5.52 0.71 0.30 0.03 8.3 0.5 1.14 $-$0.2 0.2 11.0 2.0 $-$8.50 1.5
$-$6.70 1.3 (d)(d)footnotemark: $(d)$ Patchick 125 349.756 3.426 $-$3.85 0.50
$+$0.64 0.39 0.33 0.01 10.9 0.5 3.23 $-$1.8 0.2 14.0 2.0 $-$6.10 0.8 $-$3.80
1.0 (f)(f)footnotemark: $(f)$(g)(g)footnotemark: $(g)$ (h)(h)footnotemark:
$(h)$ (z)(z)footnotemark: $(z)$ Patchick 126 340.381 $-$3.826 $-$4.75 0.46
$-$6.68 0.62 0.44 0.01 8.6 0.4 2.94 $-$0.7 0.3 8.0 4.0 $-$5.56 0.8 $-$3.50 1.0
(f)(f)footnotemark: $(f)$ Riddle 15 48.355 2.455 $-$1.03 0.32 $-$1.64 0.27
0.52 0.01 18.10 0.5 14.06 $-$1.4 0.2 13.0 3.0 $-$7.60 0.8 $-$6.20 1.0
(f)(f)footnotemark: $(f)$ Ferrero 54 262.803 $-$2.571 $-$1.33 0.27 $+$1.31
0.34 0.60 0.01 7.10 0.4 11.5 $-$0.2 0.2 11.0 2.0 $-$5.87 1.7 $-$4.10 1.5
(f)(f)footnotemark: $(f)$ Gaia 2 132.155 $-$8.730 $-$1.31 0.18 $+$1.21 0.19
0.10 0.002 4.91 0.5 12.03 $-$0.9 0.2 10.0 1.0 $-$5.40 2.0 $-$3.9 1.7
(f)(f)footnotemark: $(f)$ VVV-CL001 5.267 $0.780$ $-$3.41 0.50 $-$1.97 0.5
0.65 0.03 8.23 0.4 0.76 $-$2.4 0.24 11.9 3.0 (i)(i)footnotemark: $(i)$
(l)(l)footnotemark: $(l)$ (m)(m)footnotemark: $(m)$ FSR 1776 354.720 $-5.249$
$-$2.3 1.10 $-$2.6 0.8 0.12 7.24 0.5 1.39 $+$0.02 0.14 10.0 2.0
In)In)footnotemark: $In)$ Gran 1 -1.233 $-3.978$ $-$8.10 $-$8.01 0.24 7.94
0.64 $-$1.13 0.06 10.0 2.0 $-$5.46 (h,y)(h,y)footnotemark: $(h,y)$ Gran 2
-0.771 $8.587$ $+$0.19 $-$2.57 0.26 16.6 8.58 $-$1.46 0.13 $-$5.92
(h,y)(h,y)footnotemark: $(h,y)$ Gran 4 10.198 $-6.388$ $+$0.51 $-$3.51 1.40
21.9 13.7 $-$1.72 0.32 10.0 $-$6.45 (h,y,z)(h,y,z)footnotemark: $(h,y,z)$ Gran
5 4.459 $1.838$ $-$5.32 $-$9.20 0.43 4.47 3.76 $-$1.56 0.17 $-$5.95
(h,y)(h,y)footnotemark: $(h,y)$ FSR 19 5.499 $6.071$ $-$2.50 0.76 $-$5.02 0.47
0.19 0.07 7.2 0.7 1.48 $-$0.5 11.0 $-$7.72 $-$4.62 (o)(o)footnotemark: $(o)$
FSR 25 7.534 $5.649$ $-$2.61 1.27 $-$5.23 0.74 0.27 0.01 7.0 0.9 1.73 $-$0.5
11.0 $-$7.31 $-$4.21 (o)(o)footnotemark: $(o)$ FSR 1758 349.217 $-3.292$
$-$2.85 0.05 $+$2.47 0.05 0.26 0.07 8.8 2.1 1.79 $-$1.4 0.05 11.6 1.3
(p)(p)footnotemark: $(p)$ Minni 48 359.35 $2.79$ $-$3.50 0.5 $-$6.0 0.5 0.45
0.05 8.4 1\. 0 $-$0.2 0.30 10.0 2.0 $-$9.04 0.7 (q)(q)footnotemark: $(q)$ FSR
1716 (Minni 22) 356.828 $-2.729$ 0.38 0.02 7.4 0\. 3 $-$1.3 0.3 11.2 2.0
$-$6.2 0.5 (r)(r)footnotemark: $(r)$ VVV-CL002 359.559 $0.889$ $-$2.80 $-$0.5
0.98 0.29 7.3 0\. 9 0.70 $-$0.54 0.2 ¿6.5 $-$3.4 (s)(s)footnotemark: $(s)$
(t)(t)footnotemark: $(t)$ (w)(w)footnotemark: $(w)$ Camargo 1102 359.145
$5.734$ 0.40 0.11 8.2 1\. 2 0.85 $-$1.7 0.2 13.3 1.0 $-$6.3 0.6
(u)(u)footnotemark: $(u)$ Camargo 1103 5.604 $-2.121$ 0.73 0.11 5.0 0\. 8 3.03
$-$1.8 0.3 13.5 1.0 $-$6.9 1.0 (u)(u)footnotemark: $(u)$ Camargo 1104 5.621
$-1.778$ 0.83 0.11 5.4 1\. 0 2.68 $-$1.8 0.3 13.5 0.5 $-$5.7 1.7
(u)(u)footnotemark: $(u)$ Camargo 1105 359.479 $2.017$ 0.90 0.11 5.8 0\. 9
2.18 $-$1.5 0.2 13.0 1.0 $-$6.3 1.0 (u)(u)footnotemark: $(u)$ Camargo 1106
357.351 $1.683$ 0.63 0.11 4.5 0\. 4 3.54 $-$1.5 0.3 12.5 1.0 $-$5.7 1.6
(u)(u)footnotemark: $(u)$ Camargo 1107 357.977 0.956 0.36 0.01 4.0 0.7 4.29
$-$2.2 0.4 13.5 2.0 $-$6.6 0.5 (v)(v)footnotemark: $(v)$ Camargo 1108 357.977
0.956 0.50 0.01 3.3 0.5 5.0 $-$1.80 0.3 13.5 1.5 $-$8.4 0.5
(v)(v)footnotemark: $(v)$ Camargo 1109 2.165 0.844 0.36 0.01 4.3 0.6 3.97
$-$1.50 0.2 12.0 1.5 $-$6.4 0.7 (v)(v)footnotemark: $(v)$

222 $a$$a$footnotetext: Garro et al. (2020) $b$$b$footnotetext: Garro et al.
(2022c) $c$$c$footnotetext: Garro et al. (2021b) $d$$d$footnotetext: Garro et
al. (2022b) $e$$e$footnotetext: Minniti et al. (2021a) $f$$f$footnotetext:
Garro et al. (2022a) $g$$g$footnotetext:  Fernández-Trincado et al. (2022)
$h$$h$footnotetext:  Gran et al. (2022) $i$$i$footnotetext: Minniti et al.
(2011) $l$$l$footnotetext: Fernández-Trincado et al. (2021b)
$m$$m$footnotetext: Olivares Carvajal et al. (2022) $n$$n$footnotetext: Dias
et al. (2022) $o$$o$footnotetext: Obasi et al. (2021) $p$$p$footnotetext:
Romero-Colmenares et al. (2021) $q$$q$footnotetext: Minniti et al. (2021c)
$r$$r$footnotetext: Minniti et al. (2017) $s$$s$footnotetext: Moni Bidin et
al. (2011) $t$$t$footnotetext: Minniti et al. (2021b) $u$$u$footnotetext:
Camargo (2018) $v$$v$footnotetext: Camargo & Minniti (2019)
$z$$z$footnotetext: Pace et al. (2023) $y$$y$footnotetext: Gran et al. (2023)
wwfootnotemark: $w$Minniti et al. (2023)

##  3 Milky Way globular cluster luminosity function

Until now, all the information that we have about the MW GC system were based
on the known and well-characterized Galactic GCs, listed in previous
compilations such as the catalogs from Harris (1996) and Vasiliev & Baumgardt
2021. Discovering and identifying these clusters has been easy over time, as
most of them are very bright, massive, highly concentrated, and hosting a
larger number of stars. On the other hand, new GCs (Table 2) are mainly faint,
widespread, embedded in very obscured regions. Therefore, the detection of
low-luminosity GCs, possible thanks to powerful surveys, is only able within
our Galaxy, while they are not visible in external galaxies. Hence, this may
allow us to explore a region of the LF not accessible before, going toward the
tail of this feature and increasing statistics at these luminosity ranges.

The MW GC LF can be used as a distance indicator (Rejkuba 2012) or to
constrain the GC history (Kruijssen & Zwart 2009). In our case, we employ it
for the second scope. As mentioned earlier in this paper, many dynamical
processes can destroy a GC, and all these events can have an effect on the MW
GC LF, affecting in particular the faint end tail of the distribution. We
investigate this in order to see how the known MW GC LF changes if we include
all the recently discovered GCs.

As we can see from Table 2 and Figure 3 (orange lines), the LF for the new GCs
extends toward much lower luminosities. Actually, we found a double peaked
distribution: the first peak at $M_{V}^{new}\leavevmode\nobreak\
=\leavevmode\nobreak\ -6.06\pm 0.80$ mag and a second one at
$M_{V}^{new}\leavevmode\nobreak\ =\leavevmode\nobreak\ -3.83\pm 0.62$ mag
(this is a tentative one since the $1\sigma$ Poisson error is $\pm 2$ GCs,
therefore the statistical significance of this peak is very low). Moreover, we
constructed the LF for all known and well-characterized GCs (blue lines),
using the $M_{V}$ values from the 2010 compilation of the Harris (1996)
catalog. A less pronounced double-peak is present for this sample at
$M_{V}^{old}=-7.46\pm 0.20$ and $M_{V}^{old}=-4.35\pm 0.20$, in agreement with
the literature (e.g., Garro et al. 2021a). At this point, if we merge the two
samples, thus upgrading the ”typical” GC LF (green lines), we find that the
distribution is slightly shifted toward lower luminosities, with the bright
peak at $M_{V}^{up}=-7.00\pm 1.30$ mag and the faint one at
$M_{V}^{up}=-4.10\pm 0.49$ mag, with an indication of elongated faint end
tail. However, the significance and physical meaning of the LF peaks must be
taken with caution, because it is well known that the GCLF is asymmetric when
plotted in magnitude bins (see, e.g., very similar histograms in Fall & Zhang
2001). In this instance, the statistical significance of the second peak is
not as robust, given the limited number of clusters within that range
(specifically, at $-5<M_{V}<-3$, there are 26 objects with Poisson error for
each bin of $\pm 2-3$); however it does not disappear even when we include the
Poisson error. Hence, this observation might imply the existence of numerous
other faint clusters yet to be discovered, likely obscured by the considerable
challenges in their detection. This study could serve as an initial step in
delving into the analysis of this faint segment of the MW GC LF.
Additionally, we can note that the uncertainties on the GCLF peak magnitudes
seem large, even for the brighter peak, when instead other studies usually
find uncertainties of 0.1-0.2 mag (as reviewed, for example, by Rejkuba 2012).
However, in our case, the uncertainties are greater due to the large
uncertainties in the luminosities of each cluster (refer to Table 2). This is
attributed to the methodology used in calculating luminosities in prior
literature. Colour-magnitude diagrams indicate that main sequence stars are
missing in their compilation, resulting in lower-limit luminosity values.
Consequently, this leads to significant uncertainties, thereby contributing to
higher uncertainties in the MW LF peak.

As demonstrated by several works, the GC LFs is not Gaussian nor universal for
all galaxies (Rejkuba 2012). The shape of the GC LF deviates from the Gaussian
symmetric distribution, since it shows a longer tail toward the faint end.
This trend is related to the main dynamical processes that can destroy a GC
(which can be amplified especially when galaxy merger events are involved),
which are: (i) the mass loss due to stellar evolution, such as the supernova
explosions (Lamers et al. 2010); (ii) dynamical friction (Alessandrini et al.
2014); (iii) tidal shock heating by passages through the bulge or disk (Piatti
& Carballo-Bello 2020); and (iv) evaporation due to two-body relaxation
(Madrid et al. 2017). Moreover, Kruijssen & Zwart (2009) suggested that the
efficiency of the dynamical evolution are linked to the initial cluster LF and
mass function, which depend on the M/L parameter differently. In turn, M/L
depends on the cluster mass dependent mass-loss rate (dissolution time
$t_{dis}\propto M^{0.7}$ and $t_{dis}\propto t_{rh}^{0.75}$, where $t_{rh}$ is
half-mass relaxation time, Kruijssen & Zwart 2009). This indicates that if M/L
increases with mass and luminosity, the low-mass, and low-luminosity GCs,
present in our compilation, are more strongly depleted in low-mass stars. This
because the massive stars are more segregated in the central regions, whereas
the low-mass stars are preferentially located in the cluster’s outskirts,
where the cluster’s potential well is less strong than the central regions;
thus, the chance of losing stars is most probable in the external regions of
the cluster. Hence, the estimation of the luminosity, which we are using (see
Table 2, and reference there in) is reliable, since it mainly comes from
evolved and brighter stars. Nonetheless, a dependence of M/L on mass is not
obvious, since it is still not the impact of the mass function can change
depending on the cluster’s metallicity, as suggested by Baumgardt (2016).

Another important feature that we have to include is the fact that the MW GC
LF may be bimodal, even if the second peak does not contain a high number of
clusters. However, we want to compare the obtained MW GC LF with the M31
galaxy’s LF (Peacock et al. 2010; Huxor et al. 2014; Garro et al. 2021a) –
which shows a double peaked distribution – to see if we can deduce some
important clues about our Galaxy. By this comparison, we can deduce that the
second peak may be related to GCs, which have been accreted or survived
disruption processes (Huxor et al. 2014). This may be supported by the fact
that the new clusters that are very faint ($M_{V}>-5.0$), they are also
younger than 11 Gyr, more metal-rich than -1.0, and located in the bulge,
where dynamical processes are very strong (Figure 4). Precisely, Ferrero 54
and Gaia 2 located at larger $R_{G}$ are disk-like GCs, and Patchick 125 is
the ancient clusters in our compilation. If this is true, our targets have
lost a high percentage of their stars, therefore likely those low-luminosity
(and low-mass) GCs may be what remains of more massive progenitors. This
result is in agreement with recent studies that suggest that the Galactic
stellar halo has assembled from tidally disrupted dwarf galaxies (see e.g.,
Belokurov et al. 2018; Conroy et al. 2019; Kruijssen et al. 2019). However,
most of the stellar streams, or the accretion events in general, have been
discovered across the Galactic halo (Ibata et al. 2001; Odenkirchen et al.
2001; Mateu 2023). This may represent a ”selection effect,” given that
studying the halo is easier than exploring the bulge, just because the stellar
crowding and extinction are irrelevant there. Finding new objects in the
bulge, which may be what remains of disrupted GCs, and considering why they
were not accreted, could pave the way for the study of ex situ populations
also in the bulge. Nonetheless, we need numerical simulations and
spectroscopic analysis that can confute this hypothesis. For that, we can
speculate that this new MWGC LF may be the result of different processes, such
as a higher number of accreted objects, efficient destruction due to the
above-mentioned dynamical processes that occurred both in the Galactic halo
and in the bulge, and/or incompleteness of our catalog since many other faint
and obscured objects still remain to be identified. In particular, we suspect
that with the discovery and confirmation as real GCs of other candidates,
which are also of low luminosity, it may be possible that the LF can change
once completeness is achieved.

figurec

Figure 3: Luminosity functions (LFs). The left panel shows three histograms
depicting the LFs for the known MW GC system by Harris (1996) (2010 edition),
using the dashed blue line, for the GCs analyzed in this work and listed in
Table 2, using a dashed orange line and the sum of the two mentioned
distributions in the green line. In the right panel, we show the LFs using the
KDE technique for the three samples. Figure 4: [Fe/H]-$M_{V}$ (left panel),
$M_{V}$-Age (middle-left panel), [Fe/H]-Age (middle-right panel), and
$M_{V}$-$R_{G}$ diagrams for the new GC sample. With red squares, we selected
only very faint clusters with $M_{V}>-5.0$.

##  4 Metallicity distribution

The metallicity distribution (MD) is an important tool for obtaining
information about the age and formation history of a stellar system,
especially when this is investigated in different environments. As shown in
Figure 5, we compared the new GC MD (green line) with the MDs of known GCs
using three samples: the 2010 compilation of the Harris (1996) catalog (blue
line), the Mészáros et al. (2020) catalog (orange line), which includes, in
particular, the halo+disk GCs, and our compilation of bulge GCs listed in
Table 2. The first sample contains 157 GCs and their [Fe/H] values are both
spectroscopic and photometric estimates333Extensive references are given for
the Harris’ catalog at https://physics.mcmaster.ca/%7Eharris/mwgc.ref, whereas
the second includes 31444Mészáros et al. (2020) excluded from their catalog
GCs exhibiting significant differential reddening (E(B-V) $>0.4$), which
introduces errors in estimations of atmospheric parameters and, consequently,
the chemical abundance estimates. known GCs and the [Fe/H] is taken from SDSS-
IV APOGEE-2, while the third catalog is created using [Fe/H] and [Mg/Fe] taken
from the literature, as specified in the fourth column.
Mészáros et al. (2020) found that the [Fe/H] metallicities that they derived
are on average 0.162 dex higher than those from the Harris catalog, so we
subtracted this quantity from their [Fe/H] to bring the MDs to the same scale.
Due to the fact that the histograms depend on the bin size, we also preferred
to construct a kernel density estimation (KDE) diagram, using the epanechnikov
kernel, a smoothing of 0.25, and normalized per area. The KDE code provides us
the highest peak of the metallicity distributions.Independently, to better
identify the peaks of the distributions, we overplotted a densogram for each
sample, using the acos scaling555We constructed the densogram with TOPCAT, and
we used the acos scaling only because the peaks of the distributions were more
marked than the linear scaling. in agreement with the previous method. A third
and more robust method that we implemented is the Gaussian mixture model
(GMM). We tested different Gaussian components and that the best fit came from
a two-Gaussian fit, from which we obtained the following peaks and errors. In
addition, these results are in agreement within the errors with the previous
estimations. In all cases, we found double-peaked distributions (see Figure
5): (i) for the Mészáros et al. (2020) sample, the metal-poor peak is at
[Fe/H] $=-1.49\pm 0.40$ dex and the metal-rich peak is at [Fe/H]
$\leavevmode\nobreak\ =-0.56\pm 0.46$ dex. The latter is not clearly visible
in the histogram distribution, due to the choice of bin size, but it is clear
in the KDE diagram. Finally, a third peak at very metal-poor range is
detectable at [Fe/H] $\leavevmode\nobreak\ =-2.20\pm 0.38$ dex; (ii) for the
Harris (1996) (2010 edition) sample, the metal-poor peak is at [Fe/H]
$=-1.59\pm 0.36$ dex and the metal-rich peak is at [Fe/H]
$\leavevmode\nobreak\ =-0.59\pm 0.35$ dex, in agreement with the literature
(e.g., Minniti 1995; Carretta et al. 2009; Smith 2000; Ness & Freeman 2016;
Dias et al. 2016; Garro et al. 2021a); (iii) for the bulge GCs sample (see
Table 2), the metal-poor peak is at [Fe/H] $=-1.03\pm 0.20$ and the metal-rich
peak is at [Fe/H] $=-0.38\pm 0.20$; (iv) for the new sample containing
clusters in Table 2, metal-poor peak is at [Fe/H] $=-1.38\pm 0.35$ dex and
metal-rich is at [Fe/H] $\leavevmode\nobreak\ =-0.59\pm 0.23$ dex, with
another tentative peak at [Fe/H] $\leavevmode\nobreak\ =-0.12\pm 0.20$ dex.

Table 2: Parameters for bulge GCs. We construct our compilation of 20 bulge GCs, collecting [Fe/H] values from the literature. Cluster ID | [Fe/H] | References
---|---|---
Terzan 2 | $-0.85\pm 0.04$ | Geisler et al. (2021)
Terzan 4 | $-1.40\pm 0.05$ | Geisler et al. (2021)
HP 1 | $-1.20\pm 0.10$ | Geisler et al. (2021)
Terzan 9 | $-1.40\pm 0.16$ | Geisler et al. (2021)
Djorg 2 | $-1.07\pm 0.09$ | Geisler et al. (2021)
NGC 6540 | $-1.06\pm 0.06$ | Geisler et al. (2021)
NGC 6642 | $-1.11\pm 0.04$ | Geisler et al. (2021)
NGC 6558 | $-1.17\pm 0.01$ | Barbuy et al. (2018b)
NGC 6522 | $-1.05\pm 0.20$ | Barbuy et al. (2021)
NGC 6316 | $-0.50\pm 0.06$ | Dias et al. (2016)
NGC 6355 | $-1.46\pm 0.06$ | Dias et al. (2016)
NGC 6401 | $-1.12\pm 0.07$ | Dias et al. (2016)
Palomar 6 | $-0.85\pm 0.11$ | Dias et al. (2016)
NGC 6440 | $-0.24\pm 0.05$ | Dias et al. (2016)
NGC 6528 | $-0.13\pm 0.07$ | Dias et al. (2016)
NGC 6539 | $-0.55\pm 0.06$ | Dias et al. (2016)
NGC 6553 | $-0.13\pm 0.01$ | Dias et al. (2016)
NGC 6441 | $-0.46$ |  Carretta et al. (2009), Harris (1996)
NGC 6171 | $-0.87\pm 0.13$ | Mészáros et al. (2020)
NGC 6388 | $-0.41\pm 0.16$ | Mészáros et al. (2020)

Figure 5: Metallicity distributions. Right and in the middle panels we show
the KDEs and histograms for the known MW GCs for the Mészáros et al. (2020)
(orange lines), Harris (1996) (2010 edition - blue lines), bulge GCs (Table 2
\- magenta lines), and our work (green lines) samples, respectively. In the
right panel, we also show the densograms in order to better discriminate the
higher peaks (yellower colors) of the distributions. On the left panel, we
show histograms for different samples of bulge FSs, as specified by the
legend. The grey areas, in the middle and left panels, are used to point out
that at metallicity [Fe/H] $>0$ we do not have any GCs, while a higher
percentage of bulge FSs is located at that range.

Basically, the distributions, obtained using these different samples, are in
agreement between them, since both metal-rich and metal-poor peaks show
similar values. In this way, we can confirm the metallicity bimodality of GCs
as expected, since it is well studied in the literature (e.g., Tonini 2013).
However, we can use the MDs in order to (i) understand something more about
our compilation and (ii) apply known models in order to draw conclusions
regarding the nature of our sample.

Figure 6 displays that the new GCs sample, which are mainly situated in the MW
bulge, follows the same trend as the inner (bulge) GCs. In addition, we can
see a farther tentative peak at [Fe/H] $\approx-0.1$. This may suggest that
our sample may be contaminated by younger stellar systems, which should be
more metal-rich than older population, as GCs are. This might be expected
given that age estimates are approximate for all our targets, and OCs may be
included in our sample. Examples could be: Ferrero 54, which was classified as
MW disk GC by Garro et al. (2023), with an age $=11$ Gyr and [Fe/H] $=-0.2$;
and Kronberger 49 located at $R_{G}=1.14$ kpc, with an age $=11$ Gyr and
[Fe/H] $=-0.2$. For that reason, we need both spectroscopic analysis and
deeper CMDs to constrain their parameters.

Moreover, comparing all distributions, we can see that the number density of
the metal-poor part is in better agreement, whereas the metal-rich one is
shifted to higher values for the new and bulge GC samples than the other two.
We can expect this effect because the metal-rich component is concentrated
more toward the inner regions of the Galaxy, where the majority of our new
targets are located, while the metal-poor one becomes more significant at
larger Galactocentric distances. Indeed, as found by Tonini (2013) model
(their Figure 2), the metal-rich distribution was formed locally in the main
progenitor at $z\sim 2$, while the metal-poor component was formed in
satellites at an epoch $z\sim 3-4$, and then merged with the main progenitor.
Therefore, connecting to the discussion made in Section 3, and comparing our
distribution with the Tonini’s model, the metallicity bimodaly is a direct
prediction of a hierarchical clustering scenario. In consequence, we argue
that the metal-poor component is mainly the contribution due to the tidal
disruption of dwarf-like objects, whereas the metal-rich population is related
to the formation of the bulge and/or disk (see e.g., Mouhcine 2006). This may
imply that many of our targets may be formed in situ, and they might be
classified as main progenitors, following the nomenclature from Massari et al.
(2019).
Moreover, the height of the MD’s peaks can give us clues about the star
formation histories. Figures 5 and 6 show that metal-poor and metal-rich peaks
are similar, especially if we include in the total compilation the new GC
sample. Therefore, based on Tonini’s model, this trend suggests that the MW
experienced a balanced star formation ($M_{SF}/M_{0}=0.2$) and merger history
($M_{1}/M_{0}=0.3$)666Where $M_{0}$ is the final stellar mass, $M_{SF}/M_{0}$
star formation history parameter, and $M_{1}/M_{0}$ is assembly histories
parameter.. Moreover, we know that multiple components, with different ages
and metallicity, co-exist in the bulge, suggesting that star formation does
not stop at $z\sim 2$; father, the final stellar mass is formed at later (or
$z<2$) time, hinting that younger (e.g., age of $\sim 10$ Gyr) GCs may have
formed later in the MW bulge, due to an increasing in gas and so a burst in
star formation due to merging events. Once the age of our targets has been
confirmed, our young candidates might belong to this younger populations, and
this can help confirm whether the formation of GCs may occur later in the MW
bulge, indicating a strong presence of gas at that stage; otherwise this could
be linked to accretion events, which enriched our Galaxy and formed a new
generation of star clusters. However, this is a speculation until this
statement is confirmed observationally as well as via simulations and models.

Finally, we want to highlight the fact that spectroscopic analysis should be
performed to recover orbital parameters and chemical abundances, thus
constraining the real nature of these systems. Furthermore, it is likely that
many other GCs are missing from our compilation.

Figure 6: Same details as in Figure 5 (right panel). We split the Harris
(1996) (2010 edition) GC catalog into inner (bulge) GCs located at $R_{G}<3$
kpc (red line) and outer (halo) GCs at $R_{G}>3$ kpc (blue line). The new GCs
sample is drawn in black line. We use this comparison to better understand the
separation between bulge and halo clusters and to show that new GCs sample
follow a similar trend as the inner GCs.

##  5 Comparisons with field stars

Another important comparison we carried out within the framework of this study
considers GCs and FS MDs (see Figure 5). In order to do this, we took into
consideration five bulge FS public samples by Zoccali et al. (2008); Bensby et
al. (2017); Hasselquist et al. (2020); Abdurro’uf et al. (2022). For the
Abdurro’uf et al. (2022) catalog, we applied the typical APOGEE selection
cuts: apo_ps41 $<3.5$, ASPCAPFLAG $=0$, STARFLAG $=0$, SNR $>70$, LOGG $<3.6$,
TEFF $<5500$, VSCATTER $<1$, and ruwe $<1.4$. Also, for comparison, we
included Galactic disk FSs, using the catalog from Casali et al. (2020).
Even though they come from widely different surveys (this was done
intentionally since we need high statistics), these are all in good agreement,
exhibiting metallicity peaks between -0.5 and 0.0, with a long tail toward the
metal-poor regime. In addition, we can see that both bulge and disk FS
catalogs seems to follow the same behavior. From Figure 5, we can see that
$\sim 30-40\%$ of stars in all those catalogs show metallicities higher than
Solar value, while a very low percentage of stars have [Fe/H] $<-1.0$. Even
though a large number of very metal-rich stars have been observed, we still do
not know of any GCs in the super-Solar metallicity regime today. So, we
consider the question of where the super metal-rich bulge GCs reside and
whether they can feasibly form and exist. Alternatively, we explore whether
there might be a physical process that preferentially destroyed them in the
past.

To gain clarity in these areas, we need to understand if there is a connection
between GCs and isolated FSs. We could resort to a range of possible
explanations, such as different star formation scenarios that may have
occurred for these two populations, in addition to scenarios related to the
formation of the bulge and disk during the early phases of the Universe
(Costantin et al. 2021). Evolutionary effects, such as cluster disruption,
mass loss, interactions, merging events may also play a role (Minniti et al.
2017, 2019). It is likely that all of these properties and effects have had an
effect on the ratio of clusters to FSs at a given metallicity range and
location within the Galaxy, and may be responsible for these observed
differences. To date, many studies were focused on the Galactic halo, finding
a good agreement between observations and simulations. For instance, Reina-
Campos et al. (2020), using an E-MOSAIC simulation, found that GCs play a sub-
dominant role in the build-up of the stellar halo. Additionally, these authors
found that the disruption of GCs contributes between $0.3-14\%$ of the bulge
mass, in agreement with observational estimates by Hughes et al. (2019b). It
was also predicted that stars from disrupted GCs in the Galactic bulge show a
higher fraction around [Fe/H] $\approx-1$. A similar fraction was found by
Schiavon et al. (2016) when analysing FSs in the MW bulge in a specific
metallicity range of [Fe/H] $<-1$ and, by finding nitrogen-enriched stars,
concluded that $14\%$ of the stellar mass of the bulge came from disrupted
GCs. Therefore, the contribution of disrupted GCs to the stellar population of
the bulge constitutes only a small percentage. Thus, we suspect that this
factor alone cannot explain this inconsistency in metallicity between clusters
and bulge FSs; it is more likely that the ratio of FSs to GCs varies strongly
in different environments. For instance, as found by Lamers et al. (2017) the
difference between the GC and FS metallicity distributions is not specific to
our Galaxy, but is a well known phenomenon in external galaxies as well and it
changes if outer or inner regions are taken into account. Reporting what they
found: (i) in dwarf galaxies the population is generally metal-poor, but the
GCs are usually more metal-poor than FSs; (ii) in the M31 inner and outer
halo, the cluster-to-star ratio is high at low metallicity and low at high
metallicity; (iii) in both the inner and outer regions the relative
contribution of the clusters at low metallicity is larger than that of the
stars; (iv) in both the inner and the outer regions, the relative
contributions of the clusters at high metallicity is smaller than that of the
stars; and (v) finally, the ratios of Fornax dwarf spheroidal galaxy are more
similar to those in the outer regions of the larger galaxies than to the inner
regions.

##  6 Age-metallicity distribution

Another distribution that we want to take into consideration in order to
understand the main differences between GCs and FSs is the age-metallicity
distribution (Figure 7). We used the catalogs by Bensby et al. (2017) (red
points) and Casali et al. (2020) (cyan points), while we considered only the
new GCs (orange points) by the present compilation, since (in general), these
are low-luminosity and low-mass clusters, so we foresee that they have lost a
fraction of stars during their life (see Section 3). As expected, we can see
that there is an anti-correlation between age and metallicity, since the age
decreases with metallicity. In particular, we may note that the younger and
metal-rich population is represented by FSs, while GCs occupy the right-bottom
part of the diagram, with lower metallicities and older ages. This is also
highlighted by the histograms and cumulative distributions displayed by Figure
7. GCs are more segregated at age $>10$ Gyr and their [Fe/H] spans over all
values, especially at [Fe/H] $<-0.5$. In our compilation, the only two
clusters with age $<10$ are VVVCL002 (age $>6.5$ Gyr) and Patchick 126 (age
$>8$ Gyr). For the first, Minniti et al. (2023) demonstrated that VVVCL0002 is
an old GC, since its high $\alpha$-enhancement ($[\alpha/Fe]>+0.4$) is
connected to rapid chemical evolution dominated by core-collapse supernovae
rather than type Ia supernovae, formed together with other clusters and field
stars present today in the Galactic bulge, rather than a younger open cluster
or the remnants from an (already-disrupted) dwarf galaxy. Patchick 126 is
already classified as an in situ GC by Belokurov & Kravtsov (2023), suggesting
that its formation occurred $\approx 11.7-12.7$ Gyr ago, according to in situ
GC ages. Therefore, we keep these lower limits, even if their ages seem to be
older than those listed in Table 2. On the other hand, FSs are more segregate
at [Fe/H] $>-0.7$, while their ages span over a wide range of values including
intermediate age with age $<6$ Gyr.

Figure 7: Age-metallicity distribution for FSs (using catalogs from Bensby et
al. (2017) as red points and Casali et al. (2020) as cyan points) and for new
GCs (orange points). In the top and right panels, we show the respective
histograms and cumulative distributions for FSs (red and cyan histograms and
dashed black lines, respectively) and for new GCs (orange histograms and
continuous black lines).

##  7 Discussion

The literature extensively addresses differences in metallicity distributions
between FS and GC populations, not only within our Galaxy, but also in
external galaxies. For example, Forte et al. (1981) proposed that the color
variations observed in the spheroidal components of external galaxies (NGC
4374, NGC 4406, NGC 4621, and M87) compared to their GC systems suggest a
disparity in metallicity, indicating that GCs are more metal-poor than the
spheroidal components. This implies a distinct chemical enrichment history for
the GC system and the spheroidal component, suggesting that GCs are likely
form a component that is dynamically and chemically distinct from the
spheroid. More recently, Larsen et al. (2012), in their study of the Fornax
dwarf spheroidal galaxy’s GC system and its metal-poor FSs, suggested that the
primary distinction in the metallicity distribution between FSs and GCs arises
from the ability of each Fornax cluster to accrete a substantial amount of gas
with the same composition as the first-generation stars. In contrast, limited
gas of this composition was available for the formation of additional FSs. In
this section, we want to sum up and attempt to understand whether there is
indeed a verified link between FSs and GCs. We also explore how this might
help answer the questions posed in Section 5.

One caveat is related to the fact that our GC compilation may still be
incomplete, as many other star clusters could remain hidden, due to crowding
and extinction. Furthermore, we predict that the chemical analysis of these
clusters will be performed in order to confirm or refute the nature of the new
GCs included in the present work, as well as to better distinguish between the
natures of GCs and OCs. Finally, we need further support from numerical
simulations to understand whether it is possible to form super-metal-rich GCs,
understand their probable evolution until their extinction, or (on the other
hand) to understand why it is not possible to form them.

However, we find it surprising that there are a high percentage of super
metal-rich FSs, but no GCs in the same metallicity range. For instance,
presuming that we are roughly counting that there are $30-40\%$ of stars with
[Fe/H] ¿ 0, out of $\sim 50$ bulge GCs, we would expect $\sim 20-25$ to have
super-Solar metallicity; however, there are none. This fact is independent of
how the bulge GC is defined, namely: because there is no definitive
classification, the criteria used to describe them can differ among works in
the literature. Again, if we use another sample of fewer bulge GCs, with only
30 bulge GCs in total, there is still not a single super-Solar metallicity GC
present. Therefore, we foresee that the answers to all our questions must be
sought in the evolutionary difference between these two stellar populations.
This is supported by the fact that we found significant differences, as
displayed in Figure 7, where we recognise three evolutionary moments. We can
suppose that young (age $<5-6$ Gyr) and (super) metal-rich FSs may be the
result of a dissolution of old open clusters (OCs), since they are younger,
more metal-rich, less massive, less bound, with shallower potential wells and
therefore with shorter break-up times than GCs (with the caveat that the OC-GC
boundary is not so well defined). This may be supported by the fact that many
OCs can disintegrate, as recently suggested by Bhattacharya et al. (2022). In
fact, they found that many OCs show extended features, such as tidal tails and
extended coronas.

Similar features have also been discovered in MW GCs. For instance, Kundu et
al. (2019, 2021) concluded that some GCs analyzed in the MW halo show the
presence of extra-tidal RR Lyrae stars. So, we can expect (and attempt to
explore in the future) the notion that several small and low-luminosity GCs
analyzed here may be exhibit similar extra-tidal features, as found by Ferrone
et al. (2023) in other Galactic GCs (e.g., NGC 3201, NGC 4590, NGC 5466, Pal
5). However, if a GC’s extra-tidal features are composed of stars such as RR
Lyrae, these, in particular, contribute with old and metal-poor stars.
Therefore, if we speculate on the fact that (super) metal-rich FSs are the
result of OC dissolution or groups of stars formed later from [Fe/H]-enriched
gas, we probably do not see super metal-rich GCs because at the time when GCs
formed (10-13 Gyr ago), the gas did not have enough time to get rich in metals
to form super metal-rich GCs. Thus, we suggest that they never formed in the
first place.

On the other hand, Navarro et al. (2023) also modeled GC destruction for
objects with orbits that bring them close to the Galactic centre, finding that
the least massive clusters are quickly ($<10$ Myr) destroyed. Instead, the
most massive clusters have a lengthy evolution, displaying variations in the
morphology, especially after each passage close to the supermassive black
hole. Therefore, in order to explain why we have not yet detected super metal-
rich GCs, we cannot exclude other options: (i) we have not detected them yet
and that may be because they live in very crowded and reddened regions where
the separation from FSs is impossible or (ii) they have been destroyed,
because they lived in preferentially dangerous regions, or they have orbits
that are prone to efficient dynamical effects; alternatively, (iii) they did
not form, because of some unknown reason, (iv) another possibility is the
accretion of metal-rich elliptical galaxy, such as M32, which is not known to
contain GCs (Rudenko et al. 2009); or (v) finally, a combination of these
tentative answers may serve as an apt approach to explaining why super metal-
rich GCs are not observed today.

##  8 Conclusion

Several dozens of new Galactic GCs have been discovered in the past decade or
so thanks to the advent of new large surveys in the optical and near-IR,
significantly augmenting the MW GC system. Therefore, our aim is to collect
them in a single catalog to show that, in reality, our Galaxy could
potentially host more than 200 GCs. Taking into account all the limitations
described in Section 2, this work allowed us to update the data on the MW GC
system, adding 37 new GC candidates; in addition, we were able to upgrade the
LF and MD data. Independently, Bica et al. (2024) analyzed a similar updated
sample of GCs in the bulge, arriving at analogous conclusions.

One of the main achievements of our work is the fact that we are exploring the
faint tail of the MW GC LF. The ”updated” GC LF is shifted toward slightly
lower luminosities and may indicate a double-peaked distribution. When
comparing the MW GC LF with that of Andromeda’s GC LF and assuming the
authenticity of the second peak, it suggests that the MW may harbour accreted
objects. Alternatively, these objects could be survivors of a dynamical
process that led to their dissolution or disruption. Due to the fact that
their age estimates are approximate, we can only speculate on the fact that
some of these low-luminosity objects could be what remains of those objects
that today the James Webb Space Telescope is observing at high redshift (see
Section 1). Alternatively, there may be a connection between those compact red
objects and diffuse Galactic GCs, present in our compilation. Moreover, the MD
shows a bimodal distribution, with a third tentative peak. We find that new
GCs follow the same behavior as the bulge GC population (as shown in Figure
6), as expected due to their location inside the MW. Furthermore, it seems to
be accepted that bulge GCs may be the first stellar objects formed during the
formation of the bulge and/or disk (an example may be Liller 1 - Dalessandro
et al. 2022), while the metal-poor GCs, located at higher Galactocentric
distances, may represent the accreted component (e.g., Forbes & Bridges 2010
and reference therein). Nevertheless, we cannot exclude the possibility that
the Galactic bulge (as well as the Galactic halo) may contain ex situ clusters
or those formed in a second moment from accreted gas, supporting the scenario
that the bulge was formed first by monolithic collapse and then grew up
hierarchically via merging galaxies. This is a hypothesis that must be
confirmed spectroscopically. Furthermore, no GCs with super-solar metallicity
have been discovered so far. This is perhaps the most important conclusion. To
obtain clues to resolving the questions we consider in Section 5, we
definitely need the support of: (i) spectroscopic analyses to confirm the
nature of these GCs, derive their chemistry, and reconstruct their orbits;
(ii) numerical simulations that can help quantify how many super metal-rich
GCs we can expect in the MW, if they can or cannot exist, if they were
destroyed, and if so, to understand why and how; and, finally, (iii) deeper
observations in order to reach the MSTO and derive robust ages.

The data and conclusions presented in this work are compiled on the basis of
existing surveys, such as VVV-VVVX, 2MASS, and SDSS in the near-infrared
(NIR), as well as the Gaia mission in the optical wavelengths. Hence, more
progress is expected to come with the advent of future instrumentations such
as LSST, MOONS, 4MOST, and others.

###### Acknowledgements.

The authors are grateful to the anonymous referee for providing helpful
comments and suggestions, which have improved the content of this paper. We
thank Dr. Anna Barbara de Andrade Queiroz and Dr. Bruno Dias for their
invaluable suggestions.
We gratefully acknowledge the use of data from the ESO Public Survey program
IDs 179.B-2002 and 198.B-2004 taken with the VISTA telescope and data products
from the Cambridge Astronomical Survey Unit. This work presents results from
the European Space Agency (ESA) space mission Gaia. Gaia data are being
processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding
for the DPAC is provided by national institutions, in particular the
institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia
mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website
is https://archives.esac.esa.int/gaia.
E.R.G. gratefully acknowledges support from ANID PhD scholarship No. 21210330
and ESO Fellowship program. D.M. gratefully acknowledges support from the ANID
BASAL projects ACE210002 and FB210003, from Fondecyt Project No. 1220724, and
from CNPq Project 350104/2022-0. J.G.F-T gratefully acknowledges the grant
support provided by Proyecto Fondecyt Iniciación No. 11220340, and from the
Joint Committee ESO-Government of Chile 2021 (ORP 023/2021).

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# Camera-Pose Robust Crater Detection from Chang’e 5

Matthew Rodda Corresponding author. E-Mail<EMAIL_ADDRESS>The
University of Adelaide, Adelaide, Australia  Sofia McLeod  The University of
Adelaide, Adelaide, Australia  Ky Cuong Pham  The University of Adelaide,
Adelaide, Australia  Tat-Jun Chin  The University of Adelaide, Adelaide,
Australia

###### Abstract

As space missions aim to explore increasingly hazardous terrain, accurate and
timely position estimates are required to ensure safe navigation. Vision-based
navigation achieves this goal through correlating impact craters visible
through onboard imagery with a known database to estimate a craft’s pose.
However, existing literature has not sufficiently evaluated crater-detection
algorithm (CDA) performance from imagery containing off-nadir view angles. In
this work, we evaluate the performance of Mask R-CNN for crater detection,
comparing models pretrained on simulated data containing off-nadir view angles
and to pretraining on real-lunar images. We demonstrate pretraining on real-
lunar images is superior despite the lack of images containing off-nadir view
angles, achieving detection performance of 63.1% $F_{1}$-score and ellipse-
regression performance of 0.701 intersection over union. This work provides
the first quantitative analysis of performance of CDAs on images containing
off-nadir view angles. Towards the development of increasingly robust CDAs, we
additionally provide the first annotated CDA dataset with off-nadir view
angles from the Chang’e 5 Landing Camera, available here.

##  1 Introduction

Accurate pose estimation of spacecraft is increasingly valuable as future
missions aim to hazardous yet scientifically valuable terrain, such as the
lunar south pole. Recent investigations into vision-based navigation systems
have utilized camera measurements cross-referenced with onboard maps to
provide accurate estimations of pose [Christian2021-ts, Maass2020]. A crucial
initial step for vision-based navigation is detection of salient features from
camera measurements [Christian2021-ts]. For planetary bodies without thick
atmospheres (eg. the Moon and asteroids), impact craters provide a valuable
source of detectable and persistent landmarks visible on the surface
[Maass2016]. Techniques to detect such impact craters from imagery are named
crater-detection algorithms (CDAs), with a pipeline shown in Fig. 1.

Existing literature explores CDA performance in a narrow operating scenario,
often using a digital-elevation map (DEM) or strictly nadir-pointing images as
input. In this work, we provide the first analysis of CDA performance on real
optical imagery with off-nadir view angles on a newly annotated dataset from
the Chang’e 5 landing camera.

Figure 1: Steps of CDA pipeline, demonstrating bounding box detection and
ellipse regression on image from the Chang’e 5 landing camera [CE5].

##  2 Related Works

There exists significant literature describing the creation and evaluation of
CDAs under different operating conditions [tewari2023, Woicke2018-lg,
DeLatte2019-ye, Salamuniccar2008-oy]. Typically, CDAs focus on detecting lunar
or Mars craters, towards the goal of increasing completeness of crater
catalogues of these planetary bodies [Benedix2020, Lee2021, AliDib2020]. As
such, many CDAs use DEMs or digital-terrain maps (DTMs) as input, as this data
is free from variation due to lighting or view angle [tewari2023]. However,
for optical navigation, crater detection from a DEM or DTM is constraining as
these maps require many measurements to be accurately defined [LRO-Dataset].
Hence, for optical navigation, it is preferable to detect craters from optical
imagery.

CDAs using real optical imagery are relatively less explored. Yang et al.
applied 7 CDAs to an optical imagery dataset collected from the Lunar
Reconnaissance Orbiter (LRO) Narrow-Angle Camera (NAC), demonstrating state-
of-the-art detection performance of 86.97%$F_{1}$-score with a Faster R-CNN
architecture [CraterDaNet]. Mao et al. applied a Dual U-Net architecture to
optical imagery collected from the LRO Wide-Angle Camera, in addition to a
DEM, demonstrating that this additional data source leads to with improved
performance as compared to 4 CDAs using only the DEM [DualUNet]. While these
CDAs predict from optical imagery, again their relevance to optical navigation
is questionable as images are reconstructed mosaics and strictly nadir-
pointing [Robinson2010].

The only analysis of CDA performance with off-nadir view angles is provided by
Maas et al. using a novel segmentation-based CDA on both simulated images of
the near-earth asteroid Eros in 2016 and real images from Chang’e 3 orbiter in
2020 [Maass2016, Maass2020]. While both datasets contain significant off-nadir
view angles, a quantitative analysis of CDA performance was not performed.

###  2.1 Contributions

In this work, we describe the annotation of the first CDA dataset with
significant off-nadir view angles, using images collected from the Chang’e 5
landing camera [CE5]. Addressing off-nadir view angles constitutes a
significant advancement to existing analyses as these view angles can obscure
already complex surface morphology [Giannakis2024]. We analyze the performance
of Mask R-CNN ($M_{RCNN}$), a previously high-performing CDA from literature,
after pretraining on real and simulated CDA datasets from literature
[AliDib2020, he2018mask]. We demonstrate that, despite the lack of off-nadir
view angles, datasets containing real lunar images achieve best detection and
ellipse-regression performance after finetuning.

##  3 Datasets

###  3.1 CE5-CDA

CE5-CDA is a newly annotated dataset of real lunar images collected by the
Chang’e 5 Landing Camera [CE5]. 132 images were hand-labelled by expert
annotators, describing craters present within the image with a bounding
ellipse of the crater rim. The first 100 images of the Chang’e 5 landing
camera were labelled to create a training set, and every tenth image of the
remaining 313 were labelled to create the testing set.

CE5-CDA, like many CDA datasets, provides an incomplete annotation of visible
craters. This is due to the number of small craters visible in early images,
with the first 150 images containing >300 visible craters. Annotators
prioritised annotating the largest craters for labelling first, then craters
with a well-defined rim. On average, the dataset contains 50 labelled craters
per image, with later images within the dataset containing fewer labelled
craters, as fewer craters are visible as the lander approaches the lunar
surface.

To our knowledge, CE5-CDA is both the first annotated CDA dataset of real-
lunar images containing off-nadir view angles, and the first annotated dataset
of the Chang’e 5 landing camera. Hence, as part of this work, we make the
CE5-CDA dataset available to the research community for further analysis.

###  3.2 CRESENT

CRESENT is a dataset of rendered images of the lunar surface, with crater rims
supervised by a bounding ellipse [McLeod2024]. Images were rendered from 100km
above the surface, with off-nadir view angles ranging between 0 to 60 degrees,
in increments of 10 degrees, mimicking the expected orbital conditions of a
lunar surveillance mission [McLeod2024].

This simulated dataset was valuable as camera pose was known exactly. This
allowed automated supervision of the rendered images by projecting Robbin’s
crater catalogue onto the surface and analysis of CDA performance as off-nadir
view angles varied [LDEM, Robbins2019].

Notably, as no complete lunar-crater catalogue exists, annotation of craters
present within each image is incomplete. As such, many CRESENT images contain
multiple unlabelled instances of craters that appear obvious to the human-eye.
The subset of CRESENT images within 0-75E, 0-30N was used for practical
purposes, with the number of images per off-nadir view angle shown in Table 1.
A 20% random stratified split of images from each off-nadir view angle was
selected as a validation set.

Angle | 0∘ | 10∘ | 20∘ | 30∘ | 40∘ | 50∘ | 60∘
---|---|---|---|---|---|---|---
Images | 461 | 450 | 437 | 415 | 381 | 325 | 225
Table 1: Count of images per off-nadir view angle.

###  3.3 LRO-NAC

LRO-NAC is a manually supervised dataset of 20 images from the LRO NAC,
containing over 20 000 annotated craters [CraterDaNet]. While the LRO-NAC is
the smallest dataset utilized in this work, it is a valuable source of real
lunar image mosaics, containing images under a range of lighting conditions.
Similarly to CE5-CDA and CRESENT, LRO-NAC is incomplete, however it provides
the most complete annotation of visible craters of the three datasets, with
hundreds of annotations per image. The dataset consists of 12 800x800
resolution images used for training, and 8 1000x1000 resolution images used
for validation.

##  4 Methodology

In this section, we describe the training and evaluation process of
$M_{RCNN}$. $M_{RCNN}$ is a specialization of Faster R-CNN, a two-stage object
detection architecture that has exhibited high performance across a large
range of computer vision tasks, including state-of-the-art performance in
crater detection [ren2016faster, CraterDaNet]. $M_{RCNN}$ uses a specialized
head to predict a segmentation mask, a binary mask with the same resolution as
the input image, where masked pixels represent the presence of an object in
the original image. After training, the near-elliptical segmentation mask
produced by $M_{RCNN}$ is fit with an ellipse using a least-square fitting
algorithm[Pilu, OpenCV].

###  4.1 Training

All training was performed in Pytorch with a stochastic gradient descent
optimizer until validation loss plateaued, at which point the best performing
weights were restored [Pytorch]. Training was performed on a g4dn.16xlarge AWS
instance, with GPU acceleration using a Tesla T4. Training time for both
architectures were similar, taking $<3$ hours to train on CRESENT, $<40$
minutes on LROC-NAC and $<15$ minutes on CE5-CDA.

###  4.2 Evaluation

CDA performance was evaluated for detection and ellipse-regression separately.
Detection performance is evaluated using precision (P), recall (R) and
$F_{1}$-score, where true positive ($T_{P}$) predictions are determined by the
intersection-over-union (IoU) of predicted and ground-truth bounding boxes
being greater than 0.5. Ellipse-regression performance of each $T_{P}$ is then
evaluated, again using IoU. Ellipse IoU ($E_{\text{IoU}}$) of a $T_{P}$ was
approximated by projecting the ellipses onto an image at the same resolution
of the input sample. The intersection and union were then calculated at pixel
resolution on the projected ellipses.

##  5 Results

Detection and ellipse-regression performance of $M_{RCNN}$ was evaluated after
training on different subsets of the datasets described in Sec. 3. Best
detection and ellipse-regression performance is achieved by pretraining on
LRO-NAC, before finetuning on the CE5-CDA dataset, as shown in Table 2.
Despite CRESENT’s number of training images and inclusion of images with off-
nadir view angles, bridging the domain gap between the simulated images and
real CE5-CDA images during finetuning was challenging. In fact, training on
CE5-CDA alone outperformed the model pretrained on CRESENT in both detection
and ellipse-regression.

While LRO-NAC lacked images with off-nadir view angles, it supplied real-lunar
images and the highest completeness of annotated craters, which may have
resulted in its best performance.

CDA performance without finetuning was also evaluating, yielding poor results.
This suggests that existing datasets are not sufficient for generalizing to
the real images and off-nadir view angles present in CE5-CDA.

Pretraining | P(%) | R(%) | F1(%) | $E_{\text{IoU}}$ | E($T_{P}$)
---|---|---|---|---|---
CRESENT | $5.3$ | $4.4$ | $6.9$ | $0.557$ | $1.3$
LRO-NAC | $12.3$ | $27.3$ | $16.6$ | $0.549$ | $8.0$
None | $63.1$ | $56.3$ | $60.0$ | $0.687$ | $18.7$
CRESENT | $52.4$ | $55.3$ | $54.3$ | $0.674$ | $18.3$
LRO-NAC | $57.0$ | $68.4$ | $63.1$ | $0.701$ | $22.2$
Table 2: CDA performance on CE5-CDA test set. The pretraining column denotes
what dataset, if any, was used to initially train the CDA, and bolding denotes
whether the CDA was then finetuned on the CE5-CDA training set. The expected
number of $T_{P}$ predictions is included as many pose estimation algorithms
require a minimum of 5 to function.

Fig. 2 shows ellipse-regressions from each of the 5 CDAs evaluated. Many false
positive predictions visible in these samples appear to be real-unlabelled
instances, demonstrating the affect of incompleteness in annotation. While the
incompleteness of CE5-CDA is a limitation of the dataset, it is representative
of the incompleteness of real-lunar crater catalogues. In operation, a CDA may
produce detections of visible craters that are not catalogued, which may be
considered false positives as they are useless of pose estimation.

Figure 2:  Sample images from CE5-CDA, with CDA-regressed ellipses. Rows show
two different samples from the CE5-CDA test set, while columns separate
inference from each CDA. Blue ellipses denote ground truth, while green and
red ellipses show true positive and false positive predictions respectively.

As the Chang’e 5 lander approached the surface, the landing camera recorded
images from both decreasing altitudes and off-nadir view angles [CE5]. Fig. 3
shows the CDA pretrained on LRO-NAC demonstrated the best generalization from
the training set to this new scenario, in both detection and ellipse-
regression.

Figure 3: Reduction in detection and ellipse-regression performance over frame
number of finetuned CDAs. The end of the training-set and beginning of the
test-set is denoted with a grey line.

##  6 Discussion

In Sec. 5, we demonstrate that simulated images are not sufficient for
pretraining a CDA despite a greater number of training samples and closer
replication of operating conditions of the final task. Future work may explore
how domain adaptation could bridge the simulated-to-real domain gap to improve
performance after finetuning on real lunar images.

Future work may additionally explore automated labelling of real lunar images
by projecting known crater catalogues onto existing mosiacs, using annotated
position information. As demonstrated in this work, real lunar images are
necessary for best CDA performance, however manual labelling of large datasets
is infeasible. Automating labelling of nadir-pointing image mosiacs could
allow manual labelling efforts be focused towards annotating the previous
Chang’e 3 and recently launched Chang’e 6 mission data, containing off-nadir
view angles.

Future work may also investigate the affect of illumination conditions in
tandem with camera-pose on CDA performance. Such analysis could inform whether
strategic collection of images in a power-constrained environment may result
in best crater-detection performance and consequently higher quality pose
estimations.

##  7 Conclusion

In this work, we provide the first quantitative analysis of CDA performance on
real lunar images containing off-nadir view angles. We demonstrate that an
existing state-of-the-art CDA achieves poor performance in this operating
scenario, but can be improved through finetuning. While pretraining on
simulated images containing off-nadir view angles yields no improvement,
pretraining on real nadir-pointing lunar mosiacs improved both detection and
ellipse-regression performance, achieving 63.1% $F_{1}$-score
$0.701E_{\text{IoU}}$ respectively. For development of robust CDAs, we show
that inclusion of off-nadir training images is necessary for sufficient
detection performance in this operating scenario.