11institutetext: Departamento de Ciencias Físicas, Facultad de Ciencias
Exactas, Universidad Andres Bello, Fernández Concha 700, Las Condes, Santiago,
Chile 22institutetext: Vatican Observatory, Vatican City State, V-00120, Italy
33institutetext: Centro de Astronomía (CITEVA), Universidad de Antofagasta,
Av. Angamos 601, Antofagasta, Chile 44institutetext: Millennium Institute of
Astrophysics , Nuncio Monseñor Sotero Sanz 100, Of. 104, Providencia,
Santiago, Chile

# Physical characterization of recently discovered globular clusters in the
Sagittarius dwarf spheroidal galaxy

II. Metallicities, ages and luminosities

E.R. Garro 11 D. Minniti 1122 M. Gómez 11 J. Alonso-García 3344

(Received April 13, 2021; Accepted July 21, 2021)

###### Abstract

Context. Globular clusters (GCs) are important tools to rebuild the accretion
history of a galaxy. In particular, there are newly discovered GCs in the
Sagittarius (Sgr) dwarf galaxy, that can be used as probes of the accretion
event onto the Milky Way (MW).

Aims. Our main aim is to characterize the GC system of the Sgr dwarf galaxy by
measuring its main physical parameters.

Methods. We build the optical and near-infrared color-magnitude diagrams
(CMDs) for 21 new Sgr GCs using the VISTA Variables in the Via Lactea Extended
Survey (VVVX) near-infrared database combined with the Gaia Early Data Release
3 (EDR3) optical database. We derive metallicities and ages for all targets,
using the isochrone-fitting method with PARSEC isochrones. We also use the
relation between RGB-slope and metallicity as an independent method to confirm
our metallicity estimates. In addition, the total luminosities are calculated
both in the near-infrared and in the optical. We then construct the
metallicity distribution (MD), the globular cluster luminosity function
(GCLF), and the age-metallicity relation for the Sgr GC system.

Results. We find that there are 17 metal-rich GCs with $-0.9<[Fe/H]<-0.3$,
plus 4 metal-poor GCs with $-2.0<[Fe/H]<-1.1$ in the new Sgr GC sample. There
is a good agreement between the metallicity estimates using isochrones and RGB
slopes. Even though our age estimates are rough, we find that the metal-poor
GCs are consistent with an old population with an average age of $\sim$13 Gyr,
while the metal-rich GCs show a wider age range, between $6-8$ Gyr and $10-13$
Gyr. Additionally, we compare the MD and the GCLF for the Sgr GC system with
those of the MW, M31 and Large Magellanic Cloud (LMC) galaxies.

Conclusions. We conclude that the majority of the metal-rich GCs are located
within the main body of Sgr galaxy. We confirm that the GCLF is not a
universal distribution, since the Sgr GCLF peaks at fainter luminosities
($M_{V}\approx-5.5$ mag) than the GCLFs of the MW, M31 and LMC. Also, the MD
shows a double-peaked distribution, and we note that the metal-rich population
looks like the MW bulge GCs. We compared our results with the literature
concluding that the Sgr progenitor could have been a reasonably large galaxy
able to retain the supernovae ejecta, thus enriching its interstellar medium.

###### Key Words.:

Galaxies: dwarf – Galaxy: halos – Galaxies: luminosity function, mass function
– Galaxy: stellar content – (Galaxy:) globular clusters: general – Infrared:
stars – Surveys

##  1 Introduction

The main accepted galaxy formation paradigm predicts that galaxies grow
hierarchically through mergers with other galaxies (e.g., Searle & Zinn 1978;
White & Rees 1978), and thus the accretion of diffuse gas and dark matter
occur especially into the halo. There are different types of mergers, but
broadly we can distinguish major mergers from minor mergers, depending on the
mass ratio of the two objects. In the first case, the masses of the two
colliding galaxies are comparable, while in the second case a galaxy of lower
mass is accreted into a more massive galaxy. Obviously, when a galaxy is
observed, evidence of substructures and deviations from symmetry are
indicative of past or/and ongoing mergers. Clues can be detected within
galaxies themselves in different forms, such as streams, bridges, density
waves, overdensities of stars, substructure in galaxy’s gas, different
globular cluster populations as well as changes in kinematics. Proofs of
merging events are found both in the Galaxy (Newberg et al. 2002; Belokurov et
al. 2006; Martin et al. 2014) and in external galaxies (i.e., Einasto et al.
2012; Cohen et al. 2014; Abraham et al. 2018), like e.g. the Andromeda galaxy
(M31, Ibata et al. 2001). Therefore, the history of our Milky Way is a history
of accretion. At least seven past accretion events can be singled out: Kraken
(Kruijssen et al. 2019, 2020), Sequoia, (Myeong et al. 2019) Sagittarius
(Ibata et al. 1994), Helmi stream (Helmi et al. 1999) and Gaia-Enceladus
(Helmi et al. 2018), and both Large and Small Magellanic Clouds (LMC and SMC)
will infall towards the MW, we know that the Magellanic system is likely on
its first passage about the Milky Way (Kallivayalil et al. 2006; Besla et al.
2010; Kallivayalil et al. 2013).

The most representative example of a satellite galaxy being accreted by our
Milky Way is the Sagittarius dwarf spheroidal galaxy (Sgr dSph). Discovered by
Ibata et al. (1994), it is located behind the Galactic bulge at heliocentric
distance $D\approx 26.5$ kpc (Monaco et al. 2004; Hamanowicz et al. 2016;
Vasiliev & Belokurov 2020) and at about 6.5 kpc below the Galactic plane. The
Sgr dSph represents an excellent laboratory, since the tidal destruction
process is still ongoing (Majewski et al. 2003; Law & Majewski 2010; Belokurov
et al. 2014). The infall into the MW has been estimated to occur $8\pm 1.5$
Gyr ago by Dierickx & Loeb (2017) and $9.3\pm 1.8$ Gyr ago by Hughes et al.
(2019). However, many questions about its formation and evolution before and
after its accretion inside the Galactic halo still remain unanswered.

The mass of the Sgr progenitor and the present-day mass of the remnant are
still topics of active discussion. The stellar mass of the main body is
$M_{\ast}\sim 2\times 10^{7}\ M_{\odot}$ (Ibata et al. 2004) and the dynamical
mass is $M_{dyn}\sim 2\times 10^{8}\ M_{\odot}$ (Grcevich & Putman 2009).
However, the subsequent census of its stellar content revealed that its total
mass could be as high as $10^{11}\ M_{\odot}$ including its dark matter halo
(Niederste-Ostholt et al. 2012; Laporte et al. 2018; Vasiliev & Belokurov
2020), indicating that this was a major merging process between our Galaxy and
the Sgr dSph. Nevertheless, the accretion event of the progenitor of the Sgr
dwarf was a minor merger with mass ratio of $1:104^{+70}_{-43}$. Indeed, the
accretion has occurred at $z<1$, when already the MW was completely formed and
its stellar mass was $M>10^{10}M_{\odot}$ (Kruijssen et al. 2020; see their
Fig. 9).

Although this satellite appears to be quite elongated out to $\sim 100$ kpc
(Majewski et al. 2003; Law & Majewski 2010), its main body contains an
overdensity of stars, which is concentrated in its centre, where the massive
and metal-poor globular cluster NGC 6715 (M 54) is located. It is also
coincident in position with the nucleus of the dwarf galaxy (e.g., Bassino &
Muzzio 1995; Layden & Sarajedini 2000), although Bellazzini et al. (2008) have
argued, from measurements of velocity dispersion profiles, that M 54 is not
the core of Sgr but instead it may have formed independently and plunged to
the core of Sagittarius due to dynamical friction. Although a large number of
star clusters would be expected in these regions, there are only 9 known and
well-characterized GCs associated with Sgr. Besides NGC 6715, there are Arp 2,
Terzan 7, and Terzan 8 located in the main body, and Palomar 12, Whiting 1,
NGC 2419, NGC 4147, and NGC 5634 situated in the extended tidal streams
(Bellazzini et al. 2020). We may expect that stars and globular clusters in
the stream exhibit a different age-metallicity relation (AMR) to those formed
in the central galaxy (Forbes & Bridges 2010; Leaman et al. 2013; Kruijssen et
al. 2019). Indeed, the stellar population seems to be divided into three
groups. It is dominated by a metal-rich and intermediate-age ($[Fe/H]=-0.4$ to
$-0.7$ dex, $t=5$ to $8$ Gyr; e.g., Layden & Sarajedini 2000; Bellazzini et
al. 2006) population in the central part of the galaxy. Additionally, hints of
a young metal-rich population ($[Fe/H]=-0.4$ and $t=2.5$ Gyr) have been found,
including also stars of solar-abundance (e.g., Monaco et al. 2005; Chou et al.
2007). On the other hand, there is also an old and metal-poor ($t=10$ to $13$
Gyr, $[Fe/H]\sim-2.2$; Momany et al. 2005) counterpart.
In addition, Mucciarelli et al. (2017), analysing 235 giant stars, detected a
metallicity gradient within the Sgr nucleus. They found two peaks of the
metal-rich population, indicating that the stars in the metal-rich component
formed outside in over a few Gyr with $[Fe/H]=-0.58$ ($38\leq R\leq 70$ kpc),
with each subsequent generation of stars more centrally concentrated with
$[Fe/H]=-0.38$ ($R\leq 19$ kpc). They also mentioned that some memory of its
formation may still be detectable since the stellar population is not
dynamically mixed. Also, they suggested that Sgr was affected by a strong gas
loss occurring 7.5 Gyr to 2.5 Gyr ago, presumably starting at the first peri-
Galactic passage of the dwarf after its infall into the Milky Way.

In all cases, it is crucial to complete the census of the GC system in the Sgr
dSph in order to put formation and evolution constrains. The first step was
done by Minniti et al. (2021b), who identified 23 GC candidates that may
belong to the Sgr dSph, using the VVVX survey, and already confirm from their
further analysis 12 of them as bona-fide members. Additionally, Minniti et al.
(2021a) later discovered 18 more GCs which might belong to the Sgr galaxy,
confirming 8 of them already as bona-fide members. In both papers (hereafter
M21, for simplicity), physical parameters such as reddening, extinction, and
distance for each cluster have been estimated. In this follow-up paper, we
calculate other important parameters: metallicities, luminosities and, where
possible, we give a rough estimate of the ages, in order to explore the AMR.

In Section 2, we briefly describe the observational data. In Section 3, we
explain the methods used to estimate the physical parameters and the resulting
values for each Sgr GC. In Section 4, we show the metallicity distribution
(MD) and luminosity function (LF) for all the GCs in the Sgr dSph, including
both new detections from M21 and previously known ones, and we compare these
distributions with the MD and LF of the MW, M31, and LMC. In Section 5, a
summary and conclusions are given.

##  2 Observational datasets: VVVX, 2MASS and Gaia EDR3

We use the deep near-infrared (IR) data from the VISTA Variables in the Via
Lactea (VVV; Minniti et al. 2010; Saito et al. 2012) and its eXtention (VVVX;
Minniti 2018) surveys, acquired with the VISTA InfraRed CAMera (VIRCAM) at the
4.1m wide-field Visible and Infrared Survey Telescope for Astronomy (VISTA;
Emerson & Sutherland 2010) at ESO Paranal Observatory. Both VVV and VVVX data
are reduced at the Cambridge Astronomical Survey Unit (CASU; Irwin et al.
2004) and further processing and archiving is performed with the VISTA Data
Flow System (VDFS; Cross et al. 2012) by the Wide-Field Astronomy Unit and
made available at the VISTA Science Archive and ESO Archive. In our analysis,
we use a preliminar version of the VVVX photometric catalogue (Alonso-García
et al, in prep.), which extracts the point-spread function (PSF) photometry
from the VDFS-reduced images. To build this photometric catalogue, a similar
analysis to that described in Alonso-García et al. (2018) for the VVV original
footprint was followed. In order to increase the dynamic range of our near-IR
photometry, we merged111To merge the catalogs, first we transform the VVVX
catalogs, which are in the VISTA magnitude system, into the 2MASS magnitude
scale by applying the recipee from http://casu.ast.cam.ac.uk/surveys-
projects/vista/technical/photometric-properties . our deep VVVX photometry
with the fainter catalogues from the Two Micron All Sky Survey (2MASS;
Skrutskie et al. 2006). We are able to provide in this way accurate photometry
also for bright stars ($K_{s}<11$ mag) that are saturated in the VVVX images.
We also use the $K_{s}$-band photometry from McDonald et al. (2013) and
McDonald et al. (2014) for only Minni327 that is located outside the VVVX
area.
On the other hand, we use the recent optical photometry from the Gaia Early
Data Release 3 (EDR3) (Gaia Collaboration et al. 2021) in order to take
advantage from the more precise astrometry and proper motions (PM), which were
employed especially in the first part of the work (M21) to discriminate the
nature of the candidates and the inclusion to the Sgr galaxy. In this work, by
matching the Gaia EDR3 and VVVX datasets, we construct optical and near-IR
colour-magnitude diagrams (CMDs) in order to obtain the metallicity, age and
luminosity for each target.

##  3 Estimation of parameters for the new Sgr GCs

We focus on the 21 GCs that are recognized as confirmed Sgr members in M21. We
list them and summarize their main physical properties in Table 4.
Along the line of sight to the Sgr dwarf galaxy, high contamination from the
nearby Milky Way disk and from the more distant bulge field stars may
represent an obstacle, however M21 applied a PM decontamination procedure that
allows us to work on clean catalogues. Summarizing, M21 performed two tests in
order to estimate the statistical significance of the stellar overdensities in
the Sgr main body. First, following the procedure of Koposov et al. (2007),
they calculated the number of stars in excess with respect to the background
field, whose random fluctuations are assumed to be Poissonian. After that,
they compared that excess with the statistical error on the background number
counts, and finally they revealed the cluster detection if the significance is
larger than $3\sigma$. Whereas, the second method concerns the variation of
the background. In this case, M21 computed the number counts of sources
included within several adjacent circles ($r<3^{\prime}$) around a wider area
from each cluster centre coordinates. Subsequently, they calculated the
standard deviation of the distribution of these number counts to derive the
signal-to-noise, and considered as significant all candidate GCs with
detections larger than $3\sigma$.

Our main goals are to derive reliable values of metallicity, age and
luminosity in order to build up an ”updated” LF as well as a MD for this
satellite galaxy.
First, we have built the optical and near-IR CMDs for all the GCs in our
sample (Fig. 8), confirming that our targets are not bulge GCs, which should
be $\sim 2.5$ magnitudes brighter in the mean, as demonstrated by previous
works (Minniti et al. 2010, 2017a, 2017b, 2018; Palma et al. 2019; Garro et
al. 2021). Additionally, we have made a comparison between the Sgr GCs and
bulge fields CMDs. Summarizing, we first selected five bulge fields at the
same latitude but $\sim 7^{\circ}$ away from the Sgr main body. As done for
our objects, we constructed the Gaia-VVVX catalogues, properly decontaminated
applying parallax and PM cuts. Figure 1 shows the comparison between these
five bulge fields and Minni332 (taken as representative of the Sgr GCs) CMDs.
This proves that Sgr GCs, shown in Fig. 8, are not affected by the bulge
population, and obviously it demonstrates that the Sgr GCs here investigated
are not bulge GCs.

Figure 1: Comparison between the Gaia EDR3 optical CMDs of Minni332, taken as
a representative of the Sgr GCs (Minniti et al. 2021a), and five bulge fields
located at similar latitudes but away from the Sgr main body.

Following the same strategy as in Garro et al. (2020, 2021), we prefer the
isochrone-fitting method in order to obtain robust results. We favour the
PARSEC alpha-enriched isochrones (Bressan et al. 2012; Marigo et al. 2017),
and adopt the reddening, extinction and distance modulus values, previously
calculated by M21. Briefly, M21 derived appropriate reddening corrections
using the maps of Schlafly & Finkbeiner (2011) and adopting the following
relations for the extinctions and reddenings: $A_{Ks}=0.11\times A_{V}$,
$A_{Ks}=0.72\times E(J-K_{s})$, $A_{G}=0.79\times A_{V}$ and $A_{G}=2.0\times
E(BP-RP)$, obtaining a fairly uniform reddening. Additionally, M21 employed
the RC absolute magnitudes and intrinsic colour by Ruiz-Dern et al. (2018), in
order to compute distances for each individual cluster. Thereafter, we fit in
particular the position of RC, BHB and brighter stars. The best fitting age
and metallicity was obtained by comparing our data with isochrones generated
with different ages and metallicities and selecting the best by-eye fit. We
first fixed the age and varied the metallicity. Then we fixed the metallicity
and searched for the best fitting age. The variations of the age and
metallicity have different effects along the evolutionary stages. Especially,
changing metallicity strongly affects the RGB and the RC, conversely changes
in ages modify the position of the MS-TO regions. In this way, we assign an
error to age and metallicity, changing simultaneously both the metallicity and
age values until the fitting-isochrones did not reproduce all evolutionary
sequences in both optical and near-IR CMDs.

We find 17 metal-rich GCs, specifically ten with $[Fe/H]=-0.3$ to $-0.5$ dex,
and seven with $[Fe/H]$ between $-0.6$ and $-0.9$ dex, whereas other four GCs
are metal-poor with $[Fe/H]=-1.1$ to $-2.0$ dex. Indeed, inspecting the
luminosity function for each GC (Fig. 10), we single out the RC as a peak in
the histogram, confirming that the stellar population is metal-rich. Giving
some examples, we can appreciate a clear excess in Minni324, 330, 340, 342,
344 histograms. Also, metal-poor clusters show blue horizontal branch stars
(BHBs) as well as RR Lyrae variable stars (Section 3.1), e.g. Minni01, 147,
and 335.

Using the same method, we have tried to derive the age, but the absolute
estimate of this parameter results to be a challenge when the magnitude of the
main sequence turn-off (MSTO) is below the detection limit. However, there are
a variety of works (e.g., Rosenberg et al. 1999; Gratton et al. 2003),
adopting relative age determination (instead of absolute ages) from the
observable CMDs, although less accurate. We can therefore obtain a solid lower
limit for the age because the differences $\Delta K_{s}$(HB-MSTO) $>1.80$ mag
and $\Delta G$(HB-MSTO) $>3$ mag, meaning that the clusters are not young with
an $Age\gtrsim 7$ Gyr. This could be improved upon by measuring the extension
of the giant branch, as the presence of bright and red stars in an extended
AGB is indicative of an intermediate-age system (e.g., Freedman et al. 2020,
and references therein). Even so, it is hard to distinguish AGB stars from RGB
stars in such sparse CMDs. In addition, for the clusters containing RR Lyrae a
more stringent age limit can be derived from the typical ages of these
variable stars, that are older than about 10 Gyr see Section 3.1).

Taking into account the lower limit found for the age and the RR Lyrae cluster
membership, but also comparing our clusters with known Sgr GCs and their
observable CMDs, we obtain more constrained ages for Minni 01, 146, 148, 147,
148, 311, 326, 330, 335, 338 and 343, finding all of them to be old GCs.
Additionally, we note that Minni 144, 145, 324, 325, 328, 329, 332, 340, 341,
342, and 344 are intermediate/old globular clusters with an age $t>8$ Gyr.
Hence, deeper observations are necessary to better constrain the ages of these
GCs.

It is well-known that the position and the morphology of the RGB in the CMD
strongly depend on the metal content of the stellar population: the higher the
metal content, the cooler the effective temperature $T_{eff}$ and the redder
the RGB stars (e.g., Ferraro et al. 2000; Valenti et al. 2005). Therefore, a
series of empirical parameters (i.e., RGB colours at fixed level of magnitude,
RGB magnitude at fixed colour, and the RGB slope) can be used to derive a
photometric estimate of the global metallicity of the considered stellar
population. Indeed, we preferred to use the slopeRGB as another independent-
method to constrain our metallicity estimates. Specifically, we adopted the
$slope_{RGB}-[Fe/H]$ linear relation by Cohen et al. (2015) in the near-IR
passband. We have derived the RGB slope as the line connecting two points
along the RGB at the HB level and $\sim$2.5 mag brighter. The resulting
values, listed in Table 4 (column 9 and 10), are in very good agreement to
those derived through isochrone-fitting.

Finally, we estimate the total luminosity $M_{K_{s}}$ of all the GCs in our
sample. Certainly, the total luminosity varies from GC to GC, as it depends on
several factors, such as the luminosity of the brightest stars, the
distribution of members along the isochrones and the presence of red giants.
We first measured the flux for each star and consequently the total flux for
the target, and derived the absolute magnitude converting the total flux. All
resulting $M_{Ks}$ are listed in Table 4. We also derive the equivalent
absolute magnitude in $V-$band, assuming that the mean $(V-K_{s})=2.5\pm 0.5$
mag for observed GCs in systems like the MW and M31 (e.g., Barmby et al. 2000;
Cohen et al. 2007; Conroy & Gunn 2010). Although this could be a rough
approximation, studies (e.g., Pessev et al. 2008) have demonstrated that the
smallest spread in intrinsic colours is found for clusters with ages $\gtrsim
10$ Gyr, whereas the larger spread in colour is found for clusters in the age
range $2-4$ Gyr. On the other hand, comparing the intrinsic colour with M31 GC
system, Wang et al. (2014) found a good correlation between $(V-K_{s})$ and
metallicity (with a mean value $\sim 2.5$), even if the relation shows a
notable departure from linearity with a shallower slope toward the redder end
($[Fe/H]\gtrsim-0.1$). Additionally, the $V-$band total luminosities should be
trusted only to $1-1.5$ mag, which is the scatter in these mean integrated
colour. Hence, the use of a mean $(V-K_{s})=2.5$ is an acceptable compromise
for our targets.
These luminosities, calculated in this way, are an underestimate of the total
luminosity since the faintest stars are missing. Even though Kharchenko et al.
(2016), analysing MW star clusters, noted that the cluster luminosity profiles
show similar features, such as a relatively fast rise in the luminosity at
small $\Delta K_{s}$222Kharchenko et al. (2016) defined $\Delta K_{s}$ as the
magnitude difference between a given cluster member and the brightest cluster
member.  owing to the dominant contribution of a few bright stars and a much
slower increase by successively including fainter stars. As a rule, the first
10–12 brighter members accumulate more than half of the integrated luminosity
of a cluster, which no longer changes at $\Delta K_{s}>10$.
Consequently, we derived the total luminosity in $V-$band ($M_{Vtot}$),
comparing our GC luminosities with other known GCs with similar metallicity,
in order to estimate the fraction of luminosity that comes from low-mass
stars. We explain the main steps computed to estimate the total luminosity for
each Sgr GCs in the Appendix A.
We find that all new Sgr GCs are low-luminosity objects, at least $\sim 1.3$
mag less luminous than the MW GC luminosity function peak ($M_{V}=(-7.4\pm
0.2)$ mag from Harris (1991); Ashman & Zepf (1998)).

Once obtained the absolute magnitudes in $K_{s}-$ and $V-$bands, we are able
to estimate their masses. We first assume a typical GC mass-to-light ratio
$M/L_{K}\approx 1$, equivalent to $M/L_{V}\approx 2$ (Haghi et al. 2017;
Baumgardt et al. 2020). Subsequently, since Haghi et al. (2017) exhibited the
$M/L-$[Fe/H] relations (see their Fig.2), we derive the $M/L$ values,
depending on our metallicity estimates, in order to obtain more rigorous
results. In both cases, we find low-mass GCs, with the same order of magnitude
$M\approx 10^{3}$ to $10^{4}\ M_{\odot}$ (see Table 4). Additionally, we
calculate the mass for each known Sgr GC listed in Table 5, finding a good
agreement between our values and those listed in the Galactic Globular Cluster
Database version 2333https://people.smp.uq.edu.au/HolgerBaumgardt/globular/ by
Hilker et al. (2020). Clearly, the difference are due to the large scatter in
the Haghi’s relations ($\Delta(M/L_{K})\approx\pm 0.5$ and
$\Delta(M/L_{V})\approx\pm 1.0$).

All these parameters are summarized in Table 4. We also marked with an
asterisk symbol all GCs that do not show well-populated RGBs, as they could
have less accurate parameters. However, we include them in our analysis
because they have no effect on the final results.

Cluster ID L B $[Fe/H]_{iso}$ $M_{Ks}$ $M_{Vtot}$ Ageaa$a$We highlight the age
used in the fit of the isochrones (Fig. 8) in square brackets. $slope_{RGB}$
$[Fe/H]_{slope}$bb$b$Calculated using the $slope_{RGB}-[Fe/H]$ relation by
Cohen et al. (2015). $M/L_{K}$cc$c$Mass estimated by the present work,
adopting different values of $M/L_{K}$ from Haghi et al. (2017), depending on
our metallicity values. Mcc$c$Mass estimated by the present work, adopting
different values of $M/L_{K}$ from Haghi et al. (2017), depending on our
metallicity values. $S_{RR}$ [deg] [deg] [dex] [mag] [mag] [Gyr] [dex]
[$M_{\odot}$] Minni01∗ 5.3706 -9.3482 $-1.2\pm 0.2$ $-5.8\pm 0.8$ $-3.4$
$[12]10-13$ -0.08 -1.22 0.9 $3.8\times 10^{3}$ 43.65 Minni144 4.1693 -11.1990
$-0.9\pm 0.2$ $-7.0\pm 0.7$ $-5.1$ $[11]10-13$ -0.09 -0.90 0.8 $1.0\times
10^{4}$ 9.12 Minni145 7.2695 -12.9988 $-0.8\pm 0.3$ $-6.8\pm 1.1$ $-4.4$
$[10]10-13$ -0.092 -0.85 0.8 $8.5\times 10^{3}$ 86.89 Minni146∗ 3.9698
-14.1097 $-1.1\pm 0.2$ $-6.9\pm 1.1$ $-4.5$ $[12]7-13$ -0.084 -1.09 0.9
$1.1\times 10^{4}$ 0 Minni147 3.9993 -11.6982 $-2.0\pm 0.2$ $-6.7\pm 1.0$
$-4.4$ $[13]10-13$ -0.07 -1.53 1.1 $1.1\times 10^{4}$ 17.38 Minni148 5.3598
-13.3792 $-0.3\pm 0.2$ $-7.2\pm 1.1$ $-5.4$ $[10]10-13$ -0.11 -0.30 0.4
$6.2\times 10^{3}$ 20.75 Minni311∗ 5.2749 -9.32097 $-0.6\pm 0.3$ $-8.0\pm 1.1$
$-5.7$ $[10]7-13$ -0.09 -0.90 0.7 $2.3\times 10^{4}$ 0 Minni324 5.7821
-11.9392 $-0.5\pm 0.2$ $-6.9\pm 1.1$ $-5.0$ $[13]10-13$ -0.10 -0.60 0.5
$5.8\times 10^{3}$ 20.0 Minni325∗ 4.1172 -14.5024 $-0.4\pm 0.2$ $-6.9\pm 1.3$
$-5.1$ $[10]7-13$ -0.108 -0.36 0.4 $4.7\times 10^{3}$ 0 Minni326 5.7635
-13.0909 $-0.3\pm 0.2$ $-7.3\pm 1.2$ $-5.1$ $[10]10-13$ -0.11 -0.30 0.4
$6.8\times 10^{3}$ 18.93 Minni328 5.2657 -12.3993 $-0.5\pm 0.1$ $-6.9\pm 0.9$
$-5.1$ $[10]10-13$ -0.10 -0.60 0.5 $5.8\times 10^{3}$ 9.12 Minni329 5.0863
-11.8213 $-0.7\pm 0.2$ $-7.4\pm 1.3$ $-5.3$ $[13]7-13$ -0.096 -0.73 0.8
$1.5\times 10^{4}$ 0 Minni330 6.1214 -14.0065 $-0.6\pm 0.2$ $-7.2\pm 1.1$
$-4.9$ $[10]10-13$ -0.096 -0.73 0.7 $1.1\times 10^{4}$ 10.96 Minni332 5.9722
-12.1903 $-0.5\pm 0.2$ $-7.0\pm 1.1$ $-5.1$ $[11]10-13$ -0.101 -0.58 0.5
$6.4\times 10^{3}$ 9.12 Minni335 5.1161 -12.4645 $-1.3\pm 0.3$ $-7.7\pm 1.0$
$-5.5$ $[14]10-14$ -0.076 -1.33 1.0 $2.4\times 10^{4}$ 25.24 Minni338 4.4542
-14.5275 $-0.6\pm 0.1$ $-7.6\pm 1.1$ $-5.3$ $[10]7-13$ -0.096 -0.73 0.7
$1.6\times 10^{4}$ 0 Minni340 5.2576 -13.2629 $-0.5\pm 0.2$ $-8.0\pm 1.1$
$-6.1$ $[10]10-13$ -0.104 -0.48 0.5 $1.6\times 10^{4}$ 7.26 Minni341 5.4627
-13.8907 $-0.5\pm 0.2$ $-8.0\pm 1.2$ $-6.1$ $[10]10-13$ -0.104 -0.48 0.5
$1.6\times 10^{4}$ 7.26 Minni342 4.9365 -14.1964 $-0.5\pm 0.2$ $-7.4\pm 1.1$
$-5.5$ $[10]10-13$ -0.099 -0.64 0.5 $9.3\times 10^{3}$ 6.31 Minni343 5.0578
-14.4441 $-0.8\pm 0.2$ $-7.8\pm 1.1$ $-5.4$ $[13]10-13$ -0.092 -0.85 0.8
$2.2\times 10^{4}$ 20.75 Minni344 5.1483 -14.6487 $-0.4\pm 0.2$ $-8.3\pm 1.3$
$-6.0$ $[10]10-13$ -0.104 -0.48 0.4 $1.7\times 10^{4}$ 3.98

Table 1: Position, metallicity, age, luminosity, mass-to-light ratio, mass and
specific frequency of RR Lyrae stars for all new Sgr GCs, analysed in this
work. We marked with asterisk symbol the GCs that do not show well-populated
CMDs, thus they could have less reliable parameters. We also marked with an
asterisk symbol all GCs that do not show well-populated CMDs, as they could
have less accurate parameters.

444

Cluster ID | L | B | $[Fe/H]$ | $M_{Ks}$ | $M_{V}$ | Age | Maa$a$Mass values by the Galactic Globular Cluster Database version 2 (Hilker et al. 2020) | Mbb$b$Mass estimated by the present work, adopting different values of $M/L_{K}$ from Haghi et al. (2017), depending on our metallicity values.
---|---|---|---|---|---|---|---|---
| [deg] | [deg] | [dex] | [mag] | [mag] | [Gyr] | $[M_{\odot}]$ |
NGC 6715 | 5.6070 | -14.0871 | -1.49 | -12.51 | -9.98 | 13.0 | $1.62\times 10^{6}$ | $2.3\times 10^{6}$
Terzan 8 | 5.7592 | -24.5587 | -2.16 | -7.55 | -5.07 | 13.0 | $5.8\times 10^{4}$ | $2.6\times 10^{4}$
Arp 2 | 8.5453 | -20.7853 | -1.75 | -7.79 | -5.29 | 11.3 | $3.8\times 10^{4}$ | $3.2\times 10^{4}$
Terzan 7 | 3.3868 | -20.0665 | -0.32 | -7.55 | -5.01 | 7.5 | $2.0\times 10^{4}$ | $8.6\times 10^{3}$
Palomar 12 | 30.5101 | -47.6816 | -0.85 | -6.98 | -4.48 | 9.0 | $6.4\times 10^{3}$ | $1.0\times 10^{4}$
Whiting 1 | 161.6160 | -60.6363 | -0.7 | -4.96 | -2.46 | 6.5 | $1.6\times 10^{3}$ | $1.6\times 10^{3}$
NGC 2419 | 180.3697 | 25.2417 | -2.15 | -11.92 | -9.42 | 12.3 | $1.4\times 10^{6}$ | $1.4\times 10^{6}$
NGC 4147 | 252.8483 | 77.1887 | -1.84 | -8.67 | -6.17 | 14.0 | $3.8\times 10^{4}$ | $6.6\times 10^{4}$
NGC 5634 | 342.2093 | 49.2604 | -1.88 | -10.19 | -7.69 | 13.0 | $2.2\times 10^{5}$ | $2.9\times 10^{5}$

Table 2: Position, metallicity, age, luminosity and mass for the previously
known Sgr GCs, used for comparison.

555

##  4 RR Lyrae stars in Sgr GC system

RR Lyrae stars are usually excellent tracers of metal-poor and old populations
in the MW. M21 searched for these stars within $3^{\prime}$ and $10^{\prime}$
from the cluster centres. As expected, they found an excess of RR Lyrae in
some metal-poor GCs, such as in Minni01 ($N_{3^{\prime}}=1$;
$N_{10^{\prime}}=3$), Minni147 ($N_{3^{\prime}}=1$; $N_{10^{\prime}}=6$) and
Minni335 ($N_{3^{\prime}}=4$; $N_{10^{\prime}}=12$). We should suppose the
presence of these variable stars also in GCs with intermediate metallicity,
like in Minni144 ($N_{3^{\prime}}=1$; $N_{10^{\prime}}=7$), Minni145
($N_{3^{\prime}}=5$; $N_{10^{\prime}}=14$) and Minni343 ($N_{3^{\prime}}=3$;
$N_{10^{\prime}}=13$). While, depending on the traditional stellar
evolutionary theory, we do not expect the presence of many RR Lyrae stars in
metal-rich GCs. However, a few metal-rich GCs in the Sgr dwarf show a higher
number of RR Lyrae within $10^{\prime}$ from the cluster centre: Minni148
($N_{3^{\prime}}=3$; $N_{10^{\prime}}=20$), Minni324 ($N_{3^{\prime}}=2$;
$N_{10^{\prime}}=9$), Minni326 ($N_{3^{\prime}}=3$; $N_{10^{\prime}}=17$),
Minni328 ($N_{3^{\prime}}=1$; $N_{10^{\prime}}=9$), Minni330
($N_{3^{\prime}}=1$; $N_{10^{\prime}}=11$), Minni332 ($N_{3^{\prime}}=1$;
$N_{10^{\prime}}=7$), Minni340 ($N_{3^{\prime}}=2$; $N_{10^{\prime}}=22$),
Minni341 ($N_{3^{\prime}}=2$; $N_{10^{\prime}}=11$), Minni342
($N_{3^{\prime}}=1$; $N_{10^{\prime}}=5$), Minni343 ($N_{3^{\prime}}=3$;
$N_{10^{\prime}}=13$) and Minni344 ($N_{3^{\prime}}=1$; $N_{10^{\prime}}=15$).
Even though this may appear to be an inconsistency, there is varied
observational evidence shown the presence of RR Lyrae stars also in some
metal-rich GCs, such as NGC 6388 ($[Fe/H]=-0.44$), NGC 6441 ($[Fe/H]=-0.46$ –
Pritzl et al. 2002; Clementini et al. 2005), NGC 6440 ($[Fe/H]=-0.36$), and
Patchick 99 ($[Fe/H]=-0.20$ – Garro et al. 2021).

We also computed the specific frequency of RR Lyrae stars in the Sgr GCs.
Suntzeff et al. (1991) defined the specific frequency of RR Lyrae stars
$S_{RR}$ as the number of RR Lyrae stars $N_{RR}$ per unit luminosity,
normalised to a typical Galactic globular cluster luminosity of
$M_{V_{t}}=-7.5$ mag:

$S_{RR}=N_{RR}/10^{-0.4(M_{V_{t}}+7.5)}$ (1)

(following the notation of Harris (1996)). Using the $V-$band total
luminosities and considering the RR Lyrae stars within $3$ arcmin, we find
$4\lesssim S_{RR}\lesssim 87$ for the Sgr GCs. Also, they are faint GCs and it
is therefore not surprising that there are low number statistics. Indeed, we
note that $S_{RR}$ are lower limits, because we have not included information
about detection completeness, or counted the candidate variable stars. On the
other hand, in calculating $S_{RR}$ we have normalized the $N_{RR}$ values to
full cluster luminosities. Accounting for this effect is not trivial, because
we do not know the spatial distribution of RR Lyrae stars in any clusters and
given that we have imaged the centre of each cluster, we expect the $N_{RR}$
to be 80–90 per cent complete. Hence, the $S_{RR}$ values may be 10–20 per
cent greater than quoted above. Therefore, the determination of these quite
reliable $S_{RR}$ allow us to give a lower age limit of $Age\sim 10$ Gyr for
all clusters with $S_{RR}>0$. However, the absence of RR Lyrae stars does not
necessary imply a young ages, because RR Lyrae are uncommon in metal-rich GCs
for example.
At this point, we make comparison with the MW from the 2010 compilation of
Harris (1996) catalogue. That catalogue contains only four of the $\sim 150$
Galactic GCs as having $S_{RR}>60$, and only two of these have $S_{RR}>100$.
The largest value, that for Palomar 13, is $S_{RR}=127.5$. According to this
and given our sample incompleteness, it is very likely that Sgr dwarf galaxy
has $S_{RR}$ greater than this. It is certainly intriguing that only a tiny
fraction of Galactic GCs have very high $S_{RR}$ as well as these Sgr GCs
since we find only one GC with $S_{RR}>60$ (Minni145), and any with
$S_{RR}>100$. This may suggest that Sgr GCs follow a similar trend as of MW
GCs.

##  5 Discussion

In the next sections, we highlight the main differences between the GCs within
the Sgr dSph itself, comparing the resulting values for the newly discovered
GCs (Table 4) and the well-known Sgr GCs (Table 5). However, we want also to
broaden the discussion by making the first comparison between the Sgr GC
system and the GC system of neighbouring galaxies: the MW, M31 and LMC.

###  5.1 The Sagittarius globular cluster system

From Bellazzini et al. (2020) at least nine GCs are associated to the Sgr
stream: four clusters in the Sgr remnant – NGC 6715, Terzan 7, Terzan 8, Arp
2; two clusters in the trailing arm – Palomar 12 and Whiting 1; and three
clusters likely associated to an old arm - NGC 2419, NGC 1447 and NGC 5634.
Actually, also Berkeley 29 an Saurer 1, two younger clusters, originally
associated with the Sgr tidal extension, have now been discarded using the
improved Gaia EDR3 PMs (Gaia Collaboration et al. 2021). M21 increased the
number of GCs in the Sgr system. Hence, these discoveries pave the way to
multiple studies on the understanding of Sgr dwarf itself, on chemistry and
dynamics of these systems, especially when compared with other GC systems, and
they can also help to guide theoretical studies and simulations (e.g.,Vasiliev
et al. 2021; Vasiliev & Baumgardt 2021).

We find that the main body of the Sgr galaxy is mainly a metal-rich component
as shown in Fig. 2. Figure 3 shows the relation between the distance to the
Sgr center and the metallicity of its GCs ranging from NGC 6715 (which
coincides with the Sgr nucleus) to the most distant GC NGC 2419. We note that,
apart from NGC 6715, which is metal-poor, the metallicity is
$-0.3>[Fe/H]>-0.9$ in the innermost regions ($R<0.6$ kpc), whereas between
$R\approx 0.6$ kpc and $40$ kpc we can see that there are both metal-rich
(with the same metallicity range as the inner part) and metal-poor GCs, with
$-1.1>[Fe/H]>-2.3$. The spread in the MD of Sgr GCs seems to suggest that the
Sgr dSph had an extended star formation history and therefore now contains
high metallicity clusters (Hughes et al. 2019). It appears that a metallicity
gradient could be hinted at since we do not find metal-poor GCs in the
innermost regions, but we cannot conclude with extreme certainty that this
occurs in the main body of Sgr dSph. Probably the star cluster formation in
the Sgr galaxy occurred in two different episodes. From the AMR diagram (Fig.
4), we see that metal-poor GCs represent the old component with an average age
$\sim 13$ Gyr, while the metal-rich GCs span a wider range of ages from
younger with $t\sim 7-8$ Gyr to older with $t\sim 10-14$ Gyr. This result also
qualitatively agree with the Sgr star formation history by Hasselquist et al.
2021 in preparation, as they demonstrated that Sgr formed its metal-rich
($-0.9<$ [Fe/H] $<-0.3$) GCs some 6-8 Gyr ago. However, we can only speculate
on the probable formation of these clusters, since the epoch of accretion of
the Sgr dwarf is largely uncertain and our GC ages are approximative: the
older objects could be formed in-situ within the Sgr progenitor and have been
consequently accreted onto the MW, whereas the younger ones can be the result
of the merging event with the MW. This could be distorted since when a
satellite galaxy infalls into the main galaxy halo, a subsequent gas stripping
leads to a truncation of the GC formation in the smaller galaxy. However,
there is evidence that some galaxies (i.e., LMC and SMC) continue to form
clusters after they have entered the halo of the main galaxy. Additionally,
Hughes et al. (2019), using the E-MOSAIC simulation, found that more massive
galaxies can continue to form GCs for longer after entering the halo of the
main galaxy. Many of the satellite galaxies in this population produce streams
because the galaxies were accreted later and so the streams survive until
present day. More massive streams host younger and more-metal rich GCs.
Although our age estimates are rough and we need deeper observations in order
to reach the MSTO, Fig. 4 can help us to broadly reconstruct the formation
history of the Sgr galaxy. Indeed, we find similarities with the AMR shown in
Massari et al. (2019) and Forbes (2020). Both these works assumed a leaky-box
age-metallicity relation666The form of the age-metallicity relation used by
Forbes (2020) is $[Fe/H]=-p\ \ln(t/t_{f})$ where $p$ is the effective yield of
the system and $t_{f}$ is the look-back time when the system first formed from
non-enriched gas.. We have reproduced in Fig. 4 the best-fit halo AMR found by
Forbes (2020). We notice that Forbes’ fit follows the red diamonds, which
represent the known Sgr GCs, whereas the new discovered ones are located above
that best-fit. On the other hand, we also compared the Sgr AMR with those of
the MW and LMC, as shown in Fig. 4. We appreciate that the Sgr AMR looks more
like the MW (Leaman et al. 2013; Horta et al. 2021), whereas the halo AMR by
Forbes (2020) shows a similar trend of the LMC AMR by Horta et al. (2021). It
is important to note that when Horta et al. (2021) compared the AMR of massive
clusters for the LMC sample, they argued that the AMR for the satellite
galaxies is systematically above that for the MW as expected from mass
assembly bias. Investigating on the origin of this bias, they found that the
origin of the AMR trend in the stellar populations is a function of the galaxy
mass. This means that higher mass galaxies undergo more rapid enrichments, as
they retain the SNe ejecta and consequently this leads to a rapid enrichment
of the interstellar medium (ISM). Instead, lower mass galaxies grow more
slowly over time, as their potential wells are not deep enough and large
fraction of the SNe ejecta and stellar mass are lost, leading to a slower
metal enrichment process. Therefore, this seems to indicate that the Sgr
progenitor was not a small galaxy, on the contrary it was massive enough to
retain the stellar mass loss to enrich its ISM quickly.

Figure 2: Latitude versus longitude map depicting the position of Sgr GCs in
the main body. The coloured points highlight the cluster metallicity, adopting
red for GCs with $[Fe/H]\geqslant-0.5$, orange for GCs with
$-1.0\leqslant[Fe/H]\leqslant-0.6$, and blue for GCs with
$[Fe/H]\leqslant-1.1$ for our convention. We included NGC 6715, Terzan 7,
Terzan 8 and Arp 2 for comparison.  Figure 3: Radial dependence of the
metallicity for Sgr GCs. We consider the projected distance from the centre of
Sgr, adopting $D=26.5$ kpc for this galaxy. The new discovered Sgr GCs are
marked with black points, while the known Sgr GCs are represented as red
diamonds.

Figure 4: Age-metallicity relation for the Sgr GC system. The newly discovered
Sgr GCs are marked with black points, while the known Sgr GCs are represented
as red diamonds. On the top panel: the green line reproduces the AMR for the
MW halo GCs shown in Forbes (2020) (see their Fig. 3). On the bottom panel:
the solid lines reproduce the median star cluster AMR relation for LMC
(orange) and Milky Way-mass (black) galaxies in the E-MOSAICS simulations by
Horta et al. (2021) (see their Fig. 3).

Figure 5: Sagittarius metallicity distribution (top panel) and luminosity
function (bottom panel), including both new and known GCs.

###  5.2 Metallicity distribution

The metallicity distribution (MD) can provide important clues as to the
process and conditions relevant to galaxy formation. Therefore, comparison
with other systems can lay out a wider view.
For these purposes, we build-up the MD for the Sgr GC system as shown in Fig.
5. We notice two separate peaks, one metal-rich at $[Fe/H]_{MR}^{Sgr}=-0.56\pm
0.18$ dex and the second metal-poor at $[Fe/H]_{MP}^{Sgr}=-1.75\pm 0.35$ dex.
Additionally, we construct the MD for the MW GC system based on the 2010
compilation of the McMaster Milky Way Globular Cluster catalogue Harris
(1996), including 157 GCs. We also involve the M31 GC system, including 504
GCs by Fan et al. (2008). Finally, we also considered the LMC satellite
galaxy, but in this case we did not find a complete catalogue, so we preferred
to make it ourselves by referring to Mackey & Gilmore (2004); McLaughlin & van
der Marel (2005); Lyubenova et al. (2010); Colucci et al. (2011); Noël et al.
(2013); Jeon et al. (2014); Wagner-Kaiser et al. (2017); Piatti & Koch (2018);
Piatti et al. (2019); Horta et al. (2021). We selected 41 LMC GCs, listed in
Table 3, where we summarized: cluster ID, observed $V$ magnitude, reddening,
metallicity, age, absolute magnitude in $V-$band and references. Although many
additional star clusters have been catalogued by Palma et al. (2016), we did
not consider them as most of these objects show very young age and a mean
metallicity value of $\sim-0.3$ dex, and also because they have not been
clearly categorized as open or globular clusters.

Cluster ID Vmag $E(B-V)$ [Fe/H] Age $M_{Vtot}$ References [mag] [mag] [dex]
[Gyr] [mag] NGC 1466 $11.59$ $0.09$ $-1.70$ $11.00$ $-7.25$ Wagner-Kaiser et
al. (2017); Jeon et al. (2014) (WK17, J14) NGC 1711 $10.11$ $0.09$ $-0.57$
$0.05$ $-8.73$ Colucci et al. (2011) (C11) NGC 1754 $11.57$ $0.07$ $-1.50$
$12.96$ $-7.21$ Piatti & Koch (2018); Piatti et al. (2019); Lyubenova et al.
(2010) (P18, P19, L10) NGC 1786 $9.50$ $0.07$ $-1.75$ $12.30$ $-9.28$ P18, P19
NGC 1718 $12.25$ $0.10$ $-0.40$ $2.0$ $-6.62$ Horta et al. (2021); Kerber et
al. (2007) (H21,K07) NGC 1835 $10.60$ $0.14$ $-1.72$ $13.37$ $-8.40$ P18, P19
NGC 1841 $11.43$ $0.14$ $-2.02$ $12.57$ $-7.57$ P18, P19, H21, Grcevich &
Putman (2009) (G09) NGC 1866 $9.89$ $0.06$ $-0.51$ $0.13$ $-8.86$ C11 NGC 1898
$11.86$ $0.07$ $-1.32$ $13.50$ $-6.92$ P18, P19 NGC 1916 $10.38$ $0.13$
$-1.54$ $12.56$ $-8.58$ P19, C11 NGC 1928 $12.47$ $0.08$ $-1.30$ $13.50$
$-6.34$ P19, Mackey & Gilmore (2004) NGC 1939 $11.83$ $0.16$ $-2.00$ $13.50$
$-7.23$ P19, Mackey & Gilmore (2004) NGC 1978 $10.74$ $0.09$ $-0.38$ $1.9$
$-8.10$ C11 NGC 2002 $10.10$ $0.20$ $-2.20$ $0.18$ $-9.08$ C11 NGC 2005
$11.57$ $0.07$ $-1.74$ $13.77$ $-7.21$ P18, P19, C11, L09 NGC 2019 $10.95$
$0.07$ $-1.56$ $16.20$ $-7.83$ P18, P19, C11 NGC 2100 $9.60$ $0.26$ $-0.32$
$0.015$ $-9.77$ C11 NGC 2210 $10.94$ $0.10$ $-1.55$ $10.43$ $-7.93$ P18, P19
NGC 2257 $12.62$ $0.05$ $-1.77$ $11.54$ $-6.09$ P18, P19, G06, WK17 ESO
121-SC3 $14.04$ $0.04$ $-1.05$ $8.50$ $-4.64$ P18, P19 Reticulum $14.25$
$0.03$ $-1.47$ $11.9$ $-4.40$ G06, J14, WK17 Hodge11 $11.93$ $0.08$ $-2.00$
$13.92$ $-6.88$ G06,WK17, P18, P19 NGC1651 $12.43$ $0.13$ $-0.70$ $2.0$
$-6.53$ H21, K07, Noël et al. (2013) (N13) NGC 1777 $12.41$ $0.13$ $-0.60$
$1.1$ $-6.55$ H21, K07, N13 NGC 1783 $10.60$ $0.10$ $-0.35$ $1.7$ $-8.26$
H21,Mucciarelli et al. (2008), N13 NGC 1806 $11.12$ $0.08$ $-0.60$ $1.5$
$-7.69$ H21, Mucciarelli et al. (2014), N13 NGC 1831 $10.70$ $0.13$ $-0.10$
$0.7$ $-8.26$ H21, K07, N13 NGC 1856 $9.85$ $0.07$ $-0.40$ $0.3$ $-8.93$ H21,
K07, N13 NGC 1868 $11.14$ $0.13$ $-0.70$ $1.1$ $-7.82$ H21, K07, N13 NGC 2121
$11.84$ $0.17$ $-0.40$ $2.9$ $-7.25$ H21, K07, N13 NGC 2136 $10.20$ $0.10$
$-0.40$ $0.09$ $-8.67$ H21, N13 Mucciarelli et al. (2012) NGC 2137 $11.94$
$0.03$ $-0.40$ $0.09$ $-6.71$ H21, Mucciarelli et al. (2012); McLaughlin & van
der Marel (2005) NGC 2155 $12.27$ $0.14$ $-0.35$ $2.5$ $-6.73$ H21, N13,
Martocchia et al. (2019), NGC 2162 $12.22$ $0.13$ $-0.40$ $1.2$ $-6.74$ H21,
K07, N13 NGC 2173 $11.92$ $0.13$ $-0.60$ $1.6$ $-7.04$ H21, K07, N13 NGC 2209
$12.76$ $0.13$ $-0.50$ $1.2$ $-6.20$ H21, K07, N13 NGC 2213 $12.08$ $0.13$
$-0.70$ $1.7$ $-6.88$ H21, K07, N13 NGC 2249 $11.84$ $0.13$ $-0.40$ $1.0$
$-7.12$ H21, K07, N13 Hodge 6 $--$ $--$ $-0.35$ $2.0$ $--$ H21, Hollyhead et
al. (2019) SL 506 $--$ $0.08$ $-0.40$ $2.2$ $--$ H21, K07 SL 663 $--$ $0.07$
$-0.70$ $3.1$ $--$ H21, K07

Table 3: Properties of the LMC GCs used for comparison.

Figure 6 shows the MD for each sample: Sgr, MW, M31 and LMC. We find that each
MD shows a Gaussian-like distribution. Especially, a bimodal MD is shown for
the Andromeda and MW galaxies, with the metal-poor peaks at
$[Fe/H]_{MP}^{M31}\leavevmode\nobreak\ =\leavevmode\nobreak\ -1.71\pm 0.46$
dex and $[Fe/H]_{MP}^{MW}\leavevmode\nobreak\ =\leavevmode\nobreak\ -1.55\pm
0.35$ dex and metal-rich peaks at $[Fe/H]_{MR}^{M31}=-0.76\pm 0.39$ dex and
$[Fe/H]_{MR}^{MW}=-0.54\pm 0.22$ dex, respectively. Whereas we find a double-
peaked distribution for LMC with $[Fe/H]_{MP}^{LMC}\leavevmode\nobreak\
=\leavevmode\nobreak\ -1.66\pm 0.30$ dex and
$[Fe/H]_{MR}^{LMC}\leavevmode\nobreak\ =\leavevmode\nobreak\ -0.47\pm 0.15$
dex. We expected a bimodal MD, as it is a typical feature of all GC systems
(e.g. Ashman & Zepf 1992).

From the comparisons between these galaxies, many differences can be noted.
First, the total number of metal-poor Sgr GCs is smaller than that of the LMC,
while it is similar when only metal-rich populations are considered. On the
other hand, the Sgr MD seems to follow both the MW and M31 MDs. In particular,
the Sgr metal-rich GCs look more like the MW bulge GCs, showing also similar
wide age range. Therefore at odd with the LMC, all the metal-rich GCs in the
Sgr dwarf are relatively old (Age $>6$ Gyr). This is consistent with the
hypothesis that the Sgr GCs formation occurred after infalling into the MW
halo and thus the progenitor satellite was gas-rich, in accordance with what
is shown in Fig. 4. Kruijssen et al. (2011), based on numerical simulations of
isolated and merging disc galaxies, found that the star clusters that survive
the merger and populate the merger remnants are typically formed at the
moments of the pericentre passage, namely slightly before the starbursts that
occur during a galaxy merger. These clusters constitute a large fraction
($30-60$ per cent per pericentre passage) of the survivors. They survived for
two reasons: firstly, they are formed before the peak of the starbust, and
secondly the formed clusters, during the pericentre passage, are ejected into
the stellar halo, where the disruption rate is low and the survival chance is
high. However, the clusters that are produced in the central regions during
the peak of the starburst are short-lived and disrupt before they can migrate
to the halo.

Figure 6: Metallicity distribution for Sgr (black histogram), MW (blue
histogram), M31 (green histogram) and LMC (magenta histogram) GC systems (in
the left panel). We also show separately: the Sgr and LMC metallicity
distributions (in the right panel) as a zoomed figure of the left panel; while
we use the middle panel in order to emphasize the Sgr MD. The histograms are
constructed adopting a bin size of 0.2 dex.

###  5.3 Luminosity function

The brightness distribution of the GCs, known as the globular cluster
luminosity function (GCLF), is an important tool, which can be used, as a
distance indicator as well as to constrain the theories on the formation and
evolution of GCs (e.g, De Grijs et al. 2005; Nantais et al. 2006; Rejkuba
2012), and more precisely to predict the dynamical processes that come into
play in the destruction of GCs, especially when merging events between
galaxies are involved. The main dynamical processes that can destroy GCs are:
(i) the mass loss due to the stellar evolution (i.e. , supernovae explosions –
Lamers et al. 2010); (ii) dynamical friction (Alessandrini et al. 2014); (iii)
tidal shocks heating by passages through bulge or disk (Gnedin & Ostriker
1997; Piatti & Carballo-Bello 2020); and (iv) evaporation due to 2-body
relaxation (Madrid et al. 2017). All of these processes, especially the last
two, can change the luminosity distribution.
Many works (Rejkuba 2012, and references therein) have demonstrated that the
GCLF is not a Gaussian distribution, nor there is a ”Universal distribution”
in most galaxies (Huxor et al. 2014). Although the Gaussian fit is a useful
parametrization (especially at the brighter end), its use has no physical
motivation. Indeed, the shape of the GCLF deviates from the Gaussian symmetric
distribution for the MW as well as the external galaxies, since it shows a
longer tail towards the faint end. This asymmetry is strongly related to the
dynamical evolution of the initial cluster luminosity function, which is well-
approximated by power laws of the form $dN(L)/dL\propto L^{\alpha}$, with
slopes in the range $-2.4\lesssim\alpha\lesssim-2.0$ as found by i.e. Larsen
(2002). Another reason that could explain why the GCLF deviates from the
symmetry can also be found in the mass function, since mass and luminosity are
related parameters in GCs. So it is expected that as dynamic evolution
modifies the GCLF, it also has an effect on the mass function (e.g. Fall &
Zhang 2001). We suggest that many ”inconclusive” objects, defined by M21
because they require additional data for confirmation or rejection (Minni02,
03, 04, 312, 313, just to name a few), could be widespread or dissolute GCs.

Following the same line as for the MD, we compare the Sgr GCLF with the MW,
M31 and LMC GCLFs.
Briefly, we describe the method used to obtain reliable absolute magnitudes
for the GCs in each sample. We derive the absolute magnitude in $V-$band for
our Sgr GCs as explained in Section 3 and shown in Table 4, and we use the
luminosities for the known Sgr GCs, shown in Table 5. Figure 5 depicts the
final Sgr GCLF. This is a unimodal distribution, which exhibits a prominent
peak at $M_{V}^{Sgr}\leavevmode\nobreak\ =\leavevmode\nobreak\ -5.46\pm 1.46$
mag, and shows a tail toward the brighter end.
To build the MW GCLF, we adopt the $M_{V}$ values from the 2010 compilation of
the Harris (1996) catalogue. For the LMC GCLF, we use again our LMC catalogue
with 41 GCs (Table 3), for which we have also recovered, besides
metallicities, their $V$ magnitudes and their colour excess $E(B-V)$. We adopt
the LMC distance modulus $(m-M)_{0}=18.56$ mag from Di Benedetto (2008). For
the M31 GCLF, we prefer a more complete catalogue: the Revised Bologna
Catalogue (RBC, V.5, August 2012 – Galleti et al. 2006, 2014) of M31 globular
clusters and candidates. This catalogue includes 2,060 objects, but we
selected the 625 confirmed GCs ($flag=1$), with the optical photometry. For
M31 we use a distance modulus $(m-M)_{0}\leavevmode\nobreak\
=\leavevmode\nobreak\ 24.47$ mag (McConnachie et al. 2005). At this point, we
are able to calculate the absolute magnitude in $V-$band for LMC and M31 GC
system, applying the same method as for Sgr GCs (Section 3).
Once obtained the GC luminosities, we can build up the luminosity function for
each sample, thus making comparisons between these galaxies.
In Fig. 7, we can clearly see a double-peaked M31 GCLF with the fainter peak
at $M_{V}^{M31}=-5.71\pm 0.71$ mag and the brighter peak at
$M_{V}^{M31}=-7.95\pm 1.12$ mag. A less pronounced double-peaked is notable
for the MW GCLF, which is shifted by $\sim 0.5$ mag toward fainter
luminosities with respect to that of M31, since the fainter peak is at
$M_{V}^{MW}=-4.01\pm 1.28$ mag and the brighter one is at $M_{V}^{MW}=-7.46\pm
1.04$ mag. On the other hand, we find that the LMC GCLF is a unimodal
distribution peaked at $M_{V}^{LMC}=-7.43\pm 1.17$ mag, based on a sample with
38 GCs for which we recovered both $V$ magnitudes and reddening values.
A plausible reason to explain the observed double-peaked GCLFs in the MW and
M31 could be that many GCs have been accreted by the Andromeda halo as well as
by the MW halo (Peacock et al. 2010; Huxor et al. 2014). This scenario finds
an additional support when we include the Sgr GC system, where the LF shows a
fainter peak. More generally, Mackey & Van Den Bergh (2005) found a similar
fainter peak in the GCLF of the ”young halo” GCs of the MW, which they argued
are most likely accreted objects. Therefore, this seems to hint that accreted
Sgr GCs have survived disruption processes deriving from the merging event,
and those GCs that we see today are the remnants of more massive objects or
the final products of the accretion. However, we note that the faint Sgr
clusters are relatively more numerous than their MW counterparts. Therefore
this can indicate dynamical evolution, such as more efficient destruction in
the larger galaxies, or incompleteness at the fainter peak, since we did not
include many of the low luminosity Galactic GCs recently discovered, nor we
considered that many more faint objects are still to be found.
Finally, the actual LMC LF may be more complex than the one we show in Fig. 7,
since there is evidence for a very complex and still ongoing star formation
activity (Bruzual & Charlot 2003). However based on our data, we can see that
the LMC $M_{V}$ GCLF peak is brighter than the Sgr GCLF peak. This seems to
suggest that LMC forms more massive clusters or that the dynamical processes
in the LMC are different than those undergone by the Sgr dwarf. However, this
could also be due to our results suffering from incompleteness, or to the
overall LMC youth when compared with the Sgr dSph.

Figure 7: Luminosity function for Sgr (black histogram), MW (blue histogram),
M31 (green histogram) and LMC (magenta histogram) GC systems (in the left
panel). We also show separately: the Sgr and LMC luminosity functions (in the
right panel) as a zoomed figure of the left panel; while we use the middle
panel in order to emphasize the Sgr LF. The histograms are constructed
considering a bin size of 0.5 mag.

##  6 Summary and conclusions

We analyse the new 21 GCs recently discovered by M21 in the main body of Sgr
dwarf galaxy. We built their optical Gaia EDR3 and near-IR VVVX CMDs and
proceed to fit isochrone models in order to derive suitable values for their
metallicities and ages. We confirm our metallicity estimates using an
independent method ($slope_{RGB}-[Fe/H]$ relation by Cohen et al. 2015).
Furthermore, we also calculated for each target their total luminosity in the
$K_{s}-$ and $V-$bands, finding all of them to be faint ($M_{V}>-6.2$)
clusters.

Once metallicities and luminosities were obtained, we were able to build up
the MD and the LF for the Sgr GC system (including the new GCs discovered by
M21 and the previously known GCs associated to the Sgr dwarf) for the first
time. We find that the main body of Sgr contains prevalently a metal-rich
component. However, both metal-poor and metal-rich GCs are found, with very
different ages: metal-poor GCs are old with $t\sim 13$ Gyr, whereas metal-rich
GCs show a wider age range from $7-8$ Gyr up to $10-13$ Gyr. Our age estimates
are not very accurate, since the MSTO for the GCs in our sample is below our
detection limit, but we derived minimum ages assigning an Age $>10$ Gyr for
those GCs with $S_{RR}>0$, and also a lower limit of $\sim 7$ Gyr (derived
from $\Delta K_{s}$(HB-MSTO) for all GCs with $S_{RR}=0$. We did not detect a
metallicity gradient, but we find that the innermost regions ($R<0.6$ kpc)
show GCs with metallicities of $\sim-0.5$ dex, while between 0.6 and 40 kpc
from the Sgr nucleus we can find both metal-rich and metal-poor populations.
We have done a comparison with the MD and GCLF of other galaxies: the MW,
Andromeda galaxy and LMC, thus placing constrains on the formation and
evolution of the Sgr dwarf galaxy. Based on this comparison, we suggest that
the Sgr progenitor could have been a gas-rich galaxy, and this gas was
retained and subsequently converted into GCs during the infall into the MW
halo. Many GCs survived the main dynamical processes (i.e. tidal shocks and
two-body relaxation process), probably because they were formed before the
main star formation burst and pulled toward the halo where these processes are
less efficient. If this mechanism occurred, we may believe that some of the
”inconclusive” objects, detected in the main body of Sgr by M21, could be
dissolved GCs associated to the Sgr dwarf. Additionally, when we compare the
GCLFs, since the Sgr distribution peaks at lower luminosities
($M_{V}\approx-5.5$ mag) than all other samples, we can conclude that the
dynamical processes that destroy GCs are more efficient in larger galaxies
than in smaller ones, or that many faint GCs are missed in the present
compilations.

###### Acknowledgements.

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. ERG acknowledges support from an
UNAB PhD scholarship and ANID PhD scholarship No. 21210330. D.M. acknowledges
support by the BASAL Center for Astrophysics and Associated Technologies
(CATA) through grant AFB 170002. J.A.-G. acknowledges support from Fondecyt
Regular 1201490 and from ANID – Millennium Science Initiative Program –
ICN12_009 awarded to the Millennium Institute of Astrophysics MAS.

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##  Appendix A LFs and CMDs for the new Sgr GCs

Figure 8: Near-IR and optical CMDs for all the Sgr GC in our sample. The Hess
diagrams represent the VVVX (on the left) and Gaia EDR3 (on the right)
datasets, the cyan points are the stars from 2MASS catalogue, and the black
dotted lines are the PARSEC isochrones which best fit the evolutionary
sequences.

Figure 9:

Figure 10: The red and blue histograms depict the luminosity function for each
Sgr GC in near-IR VVVX and in optical Gaia EDR3 passbands, respectively. The
histograms are constructed adopting a bin size of 0.1 mag, as we want to
individuate the RC position as a clear excess.

Figure 11:

##  Appendix B Estimation of the total luminosity

As explained in Section 3, the integrated luminosities of the Sgr clusters,
calculated in $K_{s}-$band, do not include the contribution from faint stars,
undetected in our photometry, as we can appreciate in Fig. 8. In order to
better estimate the total luminosities of our clusters, we have therefore used
the following approach.

The main goal of this approach is to quantify the fraction of luminosity that
comes from the faintest stars. To do this, we compare the brightness of Sgr
GCs with known and well-characterized GCs. We recover for the latter both
reddening and distance modulus, listed in Table 7. The main steps adopted to
achieve our intent are:

  1. 1.

we calculate the absolute magnitude $M_{Ks}$ of known MW GCs (Table 7), using
the VVV/VVVX datasets. In this way, we can directly compare the luminosities
found for Sgr GCs and known GCs in the same magnitude range ($10.2\lesssim
K_{s}\lesssim 17.2$, only for Terzan 8 we used 2MASS photometry $12.0\lesssim
K_{s}\lesssim 16.7$);

  2. 2.

the obtained $M_{Ks}$ is converted into the absolute magnitude in $V-$band
($M_{V}$), using the typical GC colour $(V-K_{s})=2.5$ mag (e.g., Barmby et
al. 2000; Cohen et al. 2007; Conroy & Gunn 2010);

  3. 3.

we scaled the $M_{V}$ values to the absolute magnitude listed in the 2010
version of the Harris (1996) catalogue ($M_{V}^{Harris}$). Consequently, we
estimate the fraction of luminosity that comes from the faintest stars for
each known GC, computing $\Delta(M_{V})=M_{V}^{Harris}-M_{V}$;

  4. 4.

we group these GCs according to their metallicities, then we calculate the
average of $\Delta(M_{V})$ fractions for each group;

  5. 5.

finally, we add these averages to the Sgr luminosities. We have considered at
least two known GCs with the same metallicity range as the Sgr GCs (from
$-0.3$ to $-2.0$).

We have therefore achieved an empirical correction to our cluster’s
luminosities under the assumption of similarity with other GCs. The resulting
luminosities are listed in Table 4. We find that the missing luminosity was
smaller than 1.8 mag.

Cluster ID |  $[Fe/H]$aa$a$The [Fe/H] values are taken from the 2010 version of the Harris (1996) catalogue. | $E(B-V)$ | $(m-M)_{0}$ | References
---|---|---|---|---
| [dex] | [mag] | [mag] |
Liller 1 | $-0.33$ | 3.09 | 14.48 |  Valenti et al. (2010) (V10)
NGC 6440 | $-0.36$ | 1.15 | 14.58 |  Valenti et al. (2004) (V04)
NGC 6441 | $-0.46$ | 0.52 | 15.65 | V04
NGC 6624 | $-0.44$ | 0.31 | 17.33 |  Siegel et al. (2011) (S11)
Terzan 6 | $-0.56$ | 2.35 | 14.13 |  Valenti et al. (2007) (V07)
Terzan 12 | $-0.50$ | 2.06 | 12.65 | Ortolani et al. (1998)
NGC 6637 | $-0.64$ | 0.22 | 17.35 | S11
Terzan 2 | $-0.69$ | 1.40 | 14.30 | Christian & Friel (1992)
BH 261 | $-0.76$ | 0.36 | 13.90 | Ortolani et al. (2006)
NGC 6569 | $-0.76$ | 0.49 | 15.40 | V07
UKS 1 | $-0.98$ | 2.2 | 16.01 | Minniti et al. (2011)
NGC 6638 | $-0.95$ | 0.43 | 15.07 | V07
Terzan 9 | $-1.05$ | 1.79 | 13.73 | V10
NGC 6642 | $-1.26$ | 0.42 | 14.30 | Barbuy et al. (2006)
NGC 6626 | $-1.32$ | 0.42 | 13.70 | Kerber et al. (2018)
NGC 6540 | $-1.35$ | 0.66 | 13.57 | V10
NGC 6558 | $-1.32$ | 0.50 | 14.59 | Barbuy et al. (2018)
NGC 6453 | $-1.50$ | 0.69 | 15.15 | V10
NGC 6715 | $-1.49$ | 0.14 | 17.27 | S11
Terzan 8 | $-2.16$ | 0.14 | 17.26 | S11

Table 4: Known and well-characterised GCs used to derive the total luminosity
for each Sgr GCs.

777