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# DELVE 6: An Ancient, Ultra-Faint Star Cluster on the Outskirts of the
Magellanic Clouds

W. Cerny Department of Astronomy, Yale University, New Haven, CT 06520, USA
A. Drlica-Wagner Fermi National Accelerator Laboratory, P.O. Box 500, Batavia,
IL 60510, USA  Kavli Institute for Cosmological Physics, University of
Chicago, Chicago, IL 60637, USA  Department of Astronomy and Astrophysics,
University of Chicago, Chicago IL 60637, USA  T. S. Li Department of Astronomy
and Astrophysics, University of Toronto, 50 St. George Street, Toronto ON, M5S
3H4, Canada  A. B. Pace McWilliams Center for Cosmology, Carnegie Mellon
University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA  K. A. G. Olsen NSF’s
National Optical-Infrared Astronomy Research Laboratory, 950 N. Cherry Ave.,
Tucson, AZ 85719, USA  N. E. D. Noël  Department of Physics, University of
Surrey, Guildford GU2 7XH, UK  R. P. van der Marel Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Center for
Astrophysical Sciences, Department of Physics & Astronomy, Johns Hopkins
University, Baltimore, MD 21218, USA  J. L. Carlin Rubin Observatory/AURA, 950
North Cherry Avenue, Tucson, AZ, 85719, USA  Y. Choi Department of Astronomy,
University of California, Berkeley, Berkeley, CA 94720, USA  D. Erkal
Department of Physics, University of Surrey, Guildford GU2 7XH, UK  M. Geha
Department of Astronomy, Yale University, New Haven, CT 06520, USA  D. J.
James ASTRAVEO LLC, PO Box 1668, Gloucester, MA 01931  Applied Materials Inc.,
35 Dory Road, Gloucester, MA 01930  C. E. Martínez-Vázquez Gemini Observatory,
NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, HI 96720, USA  P. Massana
Department of Physics, Montana State University, P.O. Box 173840, Bozeman, MT
59717-3840  G. E. Medina Department of Astronomy and Astrophysics, University
of Toronto, 50 St. George Street, Toronto ON, M5S 3H4, Canada  A. E. Miller
School of Mathematical and Physical Sciences, Macquarie University, Balaclava
Road, Sydney, NSW 2109, Australia  Research Centre for Astronomy, Astrophysics
and Astrophotonics, Macquarie University, Balaclava Road, Sydney, NSW 2109,
Australia  Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte
16, D-14482 Potsdam, Germany  Institut für Physik und Astronomie, Universität
Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, D-14476 Golm (Potsdam), Germany
B. Mutlu-Pakdil Department of Physics and Astronomy, Dartmouth College,
Hanover, NH 03755, USA  D. L. Nidever  Department of Physics, Montana State
University, P.O. Box 173840, Bozeman, MT 59717-3840; NSF’s National Optical-
Infrared Astronomy Research Laboratory, 950 N. Cherry Ave., Tucson, AZ 85719,
USA  NSF’s National Optical-Infrared Astronomy Research Laboratory, 950 N.
Cherry Ave., Tucson, AZ 85719, USA  J. D. Sakowska Department of Physics,
University of Surrey, Guildford GU2 7XH, UK  G. S. Stringfellow Center for
Astrophysics and Space Astronomy, University of Colorado, 389 UCB, Boulder, CO
80309-0389, USA  J. A. Carballo-Bello Instituto de Alta Investigación, Sede
Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren 2477, Iquique,
Chile  P. S. Ferguson Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA  N. Kuropatkin Fermi National Accelerator Laboratory,
P.O. Box 500, Batavia, IL 60510, USA  S. Mau Department of Physics, Stanford
University, 382 Via Pueblo Mall, Stanford, CA 94305, USA  Kavli Institute for
Particle Astrophysics & Cosmology, P.O. Box 2450, Stanford University,
Stanford, CA 94305, USA  E. J. Tollerud Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218, USA  A. K. Vivas Cerro Tololo
Inter-American Observatory, NSF’s National Optical-Infrared Astronomy Research
Laboratory,
Casilla 603, La Serena, Chile

###### Abstract

We present the discovery of DELVE 6, an ultra-faint stellar system identified
in the second data release of the DECam Local Volume Exploration (DELVE)
survey. Based on a maximum-likelihood fit to its structure and stellar
population, we find that DELVE 6 is an old ($\tau>9.8$ Gyr, at 95% confidence)
and metal-poor ($\rm[Fe/H]<-1.17$ dex, at 95% confidence) stellar system with
an absolute magnitude of $M_{V}=-1.5^{+0.4}_{-0.6}$ mag and an azimuthally-
averaged half-light radius of $r_{1/2}=10^{+4}_{-3}$ pc. These properties are
consistent with the population of ultra-faint star clusters uncovered by
recent surveys. Interestingly, DELVE 6 is located at an angular separation of
$\sim 10{}^{\circ}$ from the center of the Small Magellanic Cloud (SMC),
corresponding to a three-dimensional physical separation of $\sim 20$ kpc
given the system’s observed distance ($D_{\odot}=80$ kpc). This also places
the system $\sim 35$ kpc from the center of the Large Magellanic Cloud (LMC),
lying within recent constraints on the size of the LMC’s dark matter halo. We
tentatively measure the proper motion of DELVE 6 using data from Gaia, which
we find supports a potential association between the system and the LMC/SMC.
Although future kinematic measurements will be necessary to determine its
origins, we highlight that DELVE 6 may represent only the second or third
ancient ($\tau>9$ Gyr) star cluster associated with the SMC, or one of fewer
than two dozen ancient clusters associated with the LMC. Nonetheless, we
cannot currently rule out the possibility that the system is a distant Milky
Way halo star cluster.

star clusters, Magellanic Clouds

††software: numpy (van der Walt et al., 2011; Harris et al., 2020), scipy
(Virtanen et al., 2020), emcee (Foreman-Mackey et al., 2013), HEALPix (Górski
et al., 2005),888http://healpix.sourceforge.net healpy (Zonca et al., 2019) ,
ugali (Bechtol et al., 2015) 999https://github.com/DarkEnergySurvey/ugali,
ChainConsumer (Hinton, 2019), simple (Bechtol et al., 2015; Drlica-Wagner et
al., 2015), astropy (Astropy Collaboration et al., 2013, 2018, 2022)

FERMILAB-PUB-23-271-LDRD-PPD

##  1 Introduction

Recent large-scale digital sky surveys have revolutionized our understanding
of the Magellanic Clouds (MCs) and their environments. In particular,
sensitive surveys with the VISual and Infrared Telescope for Astronomy, (e.g.,
VMC; Cioni et al. 2011), the VLT Survey Telescope (e.g., STEP and YMCA; Ripepi
et al. 2014; Gatto et al. 2021), and the Dark Energy Camera on the 4m Blanco
Telescope (e.g., DES, SMASH, and MagLiteS; DES Collaboration 2005; Nidever et
al. 2017; Bechtol 2017) have provided an unprecedentedly deep view of the
diverse stellar populations of the MCs, enabling detailed characterization of
their star formation histories (e.g., Rubele et al., 2015, 2018; Mazzi et al.,
2021; Massana et al., 2022), 3D geometries (e.g., Ripepi et al., 2017; Choi et
al., 2018a; Ripepi et al., 2022), and substructures (e.g., Pieres et al.,
2017; Mackey et al., 2018; Choi et al., 2018b; Massana et al., 2020; Gatto et
al., 2022a; El Youssoufi et al., 2021; Cullinane et al., 2022). Furthermore,
these surveys have significantly expanded the census of star clusters and
satellite galaxies in the main bodies and outskirts of the Clouds (e.g.,
Bechtol et al., 2015; Koposov et al., 2015; Martin et al., 2016; Drlica-Wagner
et al., 2016; Koposov et al., 2018; Torrealba et al., 2018; Cerny et al.,
2021a; Gatto et al., 2021), allowing for constraints on the MCs’ masses, dark
matter halos, orbits, and interaction histories (e.g., Jethwa et al., 2016;
Kallivayalil et al., 2018; Bitsakis et al., 2018; Erkal & Belokurov, 2020;
Patel et al., 2020; Dias et al., 2021) especially when paired with the precise
phase-space information provided by the Gaia satellite (Gaia Collaboration et
al., 2016; Battaglia et al., 2022; Pace et al., 2022). Lastly, these efforts
to survey and characterize the satellite populations of the MCs have enabled
novel observational tests of hierarchical galaxy formation within the
$\Lambda$CDM paradigm at a lower host mass scale than offered by the Milky Way
(e.g., Sales et al., 2016; Dooley et al., 2017; Jahn et al., 2019).

Figure 1: (Left) $2\arcmin\times 2\arcmin$ false-color image cutout centered
on DELVE 6 based on $griz$ DECam imaging, taken from the Legacy Survey Sky
Viewer. A clustering of faint blue sources is visible amidst a number of
foreground stars and background galaxies. We have increased the brightness of
this cutout image to enhance the visibility of faint cluster member stars.
(Right) Map of star clusters and dwarf galaxies in the Magellanic environment,
plotted in Magellanic Stream coordinate system from Nidever et al. (2008).
Each black point corresponds to a star cluster included in the main cluster
catalogs from Bica et al. (2008, 2020). Recently-discovered ultra-faint star
clusters in this region are shown as red dots, whereas candidate and confirmed
ultra-faint dwarf galaxies potentially associated with the MCs are shown as
blue triangles. We caution that some of these objects have uncertain
classifications and/or tentative associations with the MCs. In addition, we
plot the centroid position of the SMC Northern Overdensity (SMCNOD; Pieres et
al. 2017) in orange. Lastly, DELVE 6 is shown as a yellow star, positioned
near $B_{\rm MS}\sim 0$; this latitude falls along the projected track of the
Magellanic Stream.

In this Letter, we present the newest discovery in this ongoing census of
Magellanic satellites: DELVE 6, an ancient, ultra-faint star cluster in the
distant outskirts of the MCs. This low-mass system was identified through
matched-filter searches over imaging from the Dark Energy Camera (DECam;
Flaugher et al. 2015) processed as part of the second data release of the
DECam Local Volume Exploration survey (DELVE DR2; Drlica-Wagner et al., 2022).
We find that it has an old and metal-poor stellar population, joining the
less-than-two-dozen ancient globular clusters known in the Magellanic
environment, and that it falls at an unusually large separation from its
likely hosts. Thus, DELVE 6 potentially represents an exciting and novel
window into the stellar populations inhabiting the periphery of the LMC/SMC
system. Here, we present an initial characterization of this system’s basic
properties, and briefly highlight possibilities for its origins that can be
tested with deeper imaging and spectroscopic followup.

##  2 Discovery and Characterization

###  2.1 Identification in DELVE DR2 and the Legacy Surveys DR10

In Cerny et al. (2022), we presented the results of an extensive search for
ultra-faint stellar systems in the Milky Way halo using DECam data processed
as part of DELVE DR2 (Drlica-Wagner et al., 2022). Briefly, this search
involved applying the open-source simple search
code111https://github.com/DarkEnergySurvey/simple, which implements an
isochrone matched-filter in color–magnitude space to identify overdensities of
resolved stars in the Milky Way halo consistent with an old, metal-poor
stellar population. Over the entire DELVE DR2 footprint ($\sim$ 21,000 deg2),
this search resulted in $\mathcal{O}(10^{4})$ overdensities, six of which we
confirmed as bona fide ultra-faint stellar systems in Cerny et al. (2022) on
the basis of deeper follow-up imaging.

During the late stages of preparation of the aforementioned work, new multi-
band co-added images built from the DECam data became available through an
early version of the Legacy Surveys Data Release
10.222https://www.legacysurvey.org/dr10/description/ Motivated by the new
availability of these images, we performed a visual inspection of a subset of
the initial high-significance ($>5.5\sigma$) satellite candidates that resided
in regions where comparable color images were not previously available. The
primary goal of this effort was to identify systems that were clearly
identifiable as overdensities of blue stars in these images, but may have
initially been missed due to their marginal signals seen in their smoothed
spatial distribution and observed color–magnitude diagrams (CMDs) generated as
part of simple’s diagnostic plots. One such candidate, DELVE J0212-6603 (DELVE
6), was identified at high significance ($\sim 5-7\sigma$; comparable to the
candidates presented in Cerny et al. 2022) in our multi-pronged search, but
was initially passed over during prior inspection due to its sparse CMD.
However, as seen in Figure 1, this system is visible as a tight clustering of
faint blue sources in the color images provided by the Legacy Surveys DR10 and
was easily identified during our visual inspection.

After confirming that the system has not been reported in literature catalogs
of star clusters and dwarf galaxies in the environment of the MCs (e.g., Bica
et al., 2008, 2020; Gatto et al., 2020), we proceeded to characterize the
newly-discovered system’s structure and stellar population, as described in
the following subsection. In the absence of timely deeper follow-up imaging,
we continued to use the photometric catalogs provided by DELVE DR2 for our
analysis. The DELVE DR2 data coincident with DELVE 6 are relatively deep,
reaching (extinction-corrected) $\rm S/N=10$ magnitude limits of $g_{0}\sim
24.0$ mag and $r_{0}\sim 23.8$ mag. These limits are roughly 0.5 mag and 0.8
mag deeper than the median DELVE DR2 depth in the $g$ and $r$ bands,
respectively (see Drlica-Wagner et al. 2022 for specific information about
this public dataset). This depth was therefore found to be sufficient to
characterize the newly-discovered system despite its low luminosity.

Throughout the analyses described below, we separated stars from galaxies
based on the selection $0\leq\texttt{EXTENDED\\_CLASS\\_G}\leq 2$, matching
our DECam analyses described in Cerny et al. (2022). This broadly allowed for
a higher degree of stellar completeness at the cost of increased galaxy
contamination at fainter magnitudes (Drlica-Wagner et al. 2022).

Figure 2: (Left) Spatial distribution of stars in a $0.12{}^{\circ}\times
0.12{}^{\circ}$ ($7.2\arcmin\times 7.2\arcmin$) field centered on DELVE 6.
Stars are colored by their probability of being a member of the candidate
system, as determined through our ugali fit described in Section 2.2; stars
with probabilities $p<0.1$ are shown in grey. (Center) CMD for the stars shown
in the left panel. The best-fit isochrone with $Z=0.0001$ and $\tau=13.5$ Gyr
is shown in black, although see the discussion in Section 2.2 and see Figure 3
for caveats about this model. (Right) Radial stellar density profile for DELVE
6. The best-fit Plummer model is shown as a solid blue curve, assuming the
half-light radius reported in Table 1 and an ellipticity $\epsilon=0$. This
ellipticity is approximately matched to the mode of the marginalized posterior
distribution for $\epsilon$ derived from our MCMC analysis; however, our
constraint on the system’s ellipticity ($\epsilon<0.56$ at 95% confidence) is
relatively weak due to the small number of observed member stars.

###  2.2 Structural and Stellar Population Fit

Table 1:  Properties of DELVE 6

Parameter | Value | Units
---|---|---
IAU Name | DELVE J0212$-$6603 | …
Constellation | Hydrus | …
$\alpha_{2000}$ | $33.070^{+0.003}_{-0.004}$ | deg
$\delta_{2000}$ | $-66.056^{+0.002}_{-0.002}$ | deg
$r_{\text{h}}$ | $0.43^{+0.18}_{-0.12}$ | arcmin
$r_{1/2}$ | $10^{+4}_{-3}$ | pc
$\epsilon$ | $<0.56$ | …
$\mathrm{P.A.}$ | $14^{+40}_{-63}$ | deg
$M_{V}$aaOur estimate of $M_{V}$ was derived following the procedure from Martin et al. (2008) and does not include uncertainty in the distance. | $-1.5^{+0.4}_{-0.6}$ | mag
$\tau$ | $>9.8$ | Gyr
$\rm[Fe/H]$ | $<-1.17$ | dex
$(m-M)_{0}$ |  $19.51^{+0.04}_{-0.12}\rm\ (stat.)\ \pm 0.1\tablenotemark{b}$ (sys.) | mag
$D_{\odot}$ | $80^{+2}_{-4}\rm\ (stat.)\ ^{+4}_{-4}\ (sys.)$ | kpc
$D_{\rm GC}$ | $78^{+2}_{-4}\rm\ (stat.)\ ^{+4}_{-4}\ (sys.)$ | kpc
$D_{\rm LMC}$ | $35^{+2}_{-3}\rm\ (stat.)\ ^{+3}_{-3}\ (sys.)$ | kpc
$D_{\rm SMC}$ | $20^{+2}_{-3}\rm\ (stat.)\ ^{+3}_{-3}\ (sys.)$ | kpc
$E(B-V)$ccThis $E(B-V)$ value is the mean reddening of all sources within $r_{1/2}$, as determined via the maps of Schlegel et al. (1998) with the recalibration from Schlafly & Finkbeiner (2011) | 0.036 | mag
$\mu_{\alpha}\cos\delta$ | $\ \ 0.93^{+0.39}_{-0.39}$ | mas yr-1
$\mu_{\delta}$ | $-1.28^{+0.38}_{-0.38}$ | mas yr-1

Note. — Uncertainties for each parameter were derived from the highest-density
interval containing 68% of the marginalized posterior distribution. For the
ellipticity, metallicity, and age, the posterior distribution peaked at the
boundary of the allowed parameter space. Therefore, we quote the upper, upper,
and lower bound for these three parameters (respectively) at 95% confidence.

We fit DELVE 6’s morphological and stellar population properties using the
Ultra-faint Galaxy LIkelihood software toolkit (ugali), which implements an
unbinned Poisson maximum-likelihood approach based on the statistical
formalism presented in Appendix C of Drlica-Wagner et al. (2020). We modelled
DELVE 6’s structure with an elliptical Plummer (1911) radial stellar density
profile, and we fit a PARSEC isochrone (Bressan et al., 2012) to its observed
$g,r$-band CMD. The eight free parameters for these models were the centroid
coordinates ($\alpha_{\rm 2000}$ and $\delta_{\rm 2000}$), extension
($a_{h}$), ellipticity ($\epsilon$), position angle (P.A.) of the Plummer
profile, and the age ($\tau$), metallicity ($\rm[Fe/H]$), and distance modulus
($(m-M)_{0}$) of the isochrone model. All eight of these parameters were
constrained simultaneously by sampling their posterior probability
distribution functions using the affine-invariant Markov Chain Monte Carlo
ensemble sampler (Goodman & Weare, 2010) implemented in the Python package
emcee (Foreman-Mackey et al., 2013). This sampling was performed with 80
walkers each taking 35,000 steps, with the first 12,500 steps discarded as
burn-in; these parameters were set to ensure dense sampling of the
age–metallicity bimodality described later in the next subsection.

We report the best-fit values of each parameter and their associated
uncertainties in Table 1. These results were derived from a fit assuming a
nominal magnitude limit of $g_{0},r_{0}=23.8$ mag, and with the size of the
concentric annulus used by ugali to construct the foreground/background model
used for its joint fit of stellar color, magnitude, and spatial distributions
set to $0.5{}^{\circ}<r<1.5{}^{\circ}$. To assess whether these fit
hyperparameters might affect our results given the complex, spatially-variable
foreground/background stellar density associated with the MCs, we explored the
sensitivity of our derived estimates of DELVE 6’s properties to variations in
the assumed magnitude limit and outer radius of the background annulus.
Specifically, we re-ran the full ugali MCMC procedure for magnitude limits in
the interval [23.6 mag, 24.0 mag] and background annulus radii in the interval
[1.0∘,2.0∘]. In these tests, we found that all fits that converged resulted in
parameter estimates consistent within uncertainties with those reported in
Table 1; this was true for all parameters except the position angle, which is
mostly unconstrained due to the negligible ellipticity of DELVE 6. However, we
did need to apply a weak prior on the extension (sizes
$0.001{}^{\circ}<a_{h}<0.1{}^{\circ}$) in order to avoid convergence to non-
physical results. Our fiducial results presented in Table 1 were derived with
this prior applied.

###  2.3 Properties of DELVE 6

As depicted in Figure 2–3, we find that DELVE 6 is a compact
($r_{1/2}=10^{+4}_{-3}$ pc), ultra-faint ($M_{V}=-1.5^{+0.4}_{-0.6}$ mag)
stellar system with a round morphology ($\epsilon<0.56$ at 95% confidence).
These properties place DELVE 6 in a region of the $M_{V}$–$r_{1/2}$ plane that
is dominated by the population of ultra-faint Milky Way halo star clusters
discovered by recent surveys, which are generally fainter and more compact
than their ultra-faint dwarf galaxy counterparts (see Figure 4). We do observe
that DELVE 6 is among the more extended (candidate) ultra-faint star clusters
discovered to date, though. We tentatively classify DELVE 6 as an ultra-faint
star cluster on the basis of its small physical size, although a future
spectroscopic measurement of its velocity and/or metallicity dispersion will
provide a more definitive classification for the system.

In addition, we find that DELVE 6 is most consistent with an ancient stellar
population, as evident from the clear main-sequence turnoff, extended subgiant
branch, and (sparse) red giant branch seen in its observed CMD (Figure 2–3).
The best-fit isochrone favored by our ugali fit was consistent with the
maximum age and the minimum metallicity of our isochrone grid ($\tau=13.5$ Gyr
and $\rm[Fe/H]=-2.19$ dex, respectively) although the marginalized posterior
distribution for these two parameters was found to be bimodal, with a
secondary peak at $\tau\sim 10$ Gyr and $\rm[Fe/H]\sim-1.2$ dex (see left
panel of Figure 3). These modes appear to depend on whether the single blue
horizontal branch (BHB) star candidate shown in the right panel of Figure 3 is
a true member, or alternately whether the star positioned near the red
horizontal branch (RHB) of the second model is a true member. In our nominal
best-fit parameter constraints, the BHB star is included as a high-confidence
member, driving the fit toward the lower-metallicity mode (blue isochrone in
Figure 3). Removing the BHB star from our photometric catalog and re-running
the fit resulted in the secondary mode becoming the favored best-fit solution
(red isochrone in the same figure). If we instead removed the candidate RHB
star, the results are qualitatively similar to those shown in Figure 3.

Using the BHB–blue straggler separation technique introduced in Li et al.
(2019), we found that the BHB star’s $(g-r)_{0}$ and $(i-z)_{0}$ color is
consistent with a classification as a bona fide BHB star. Furthermore, the
star’s ${\it Gaia}$ DR3 proper motion (Gaia Collaboration et al., 2022) is
sufficiently small that we cannot clearly identify it as a foreground star,
and its parallax is consistent with zero within errors; we therefore cannot
rule out its membership in the distant DELVE 6 system. By contrast, the RHB
candidate’s proper motion of ($\mu_{\alpha}\cos\delta,\mu_{\delta})=(-3.0\pm
0.4,-12.2\pm 0.3$) implies a tangential velocity that is inconsistent with
that of a typical star in a bound orbit at DELVE 6’s distance; this suggests
the star is not a member of DELVE 6. We have opted to present our ugali fit
results from a fit with both stars included in our catalog. This decision
fully specifies the age/metallicity solution that we report for DELVE 6 due to
the strong impact of the BHB candidate, but the upper/lower limits presented
in the Table 1 encompass both plausible solutions for these two parameters.
Despite the uncertainty in the age and metallicity, we found that the
structural properties presented in Table 1 are consistent within uncertainties
with the results derived from fits with either one of the two stars in
question removed.

Although we cannot conclusively determine which age/metallicity is most
appropriate for DELVE 6 until deeper imaging and/or a spectroscopic
metallicity measurement becomes available, both of these isochrone fits
strongly suggest that the system is ancient ($\tau>9.8$ Gyr). DELVE 6’s old
age, as well as its position in the outskirts of the LMC and SMC, raises
interesting questions about its formation and evolution. We study the systemic
proper motion of DELVE 6 below and then explore several possibilities for its
origin in Section 3.

Figure 3: (Left) 2D posterior probability distribution for the metallicity and
age of DELVE 6. The blue shaded contours denote the $1\sigma,\ 2\sigma$, and
$3\sigma$ 2D confidence regions in this plane. (Right) CMD for all stars
within $2r_{1/2}$ of DELVE 6’s centroid. Two isochrone models are shown. The
blue model depicts an isochrone with ${\rm[Fe/H]}=-2.19$ and $\tau=13.5$ Gyr,
consistent with the posterior mode shown in the bottom-righthand corner of the
left panel, whereas the red model depicts a younger, more metal-rich isochrone
corresponding to a fit lying within the medium-blue $2\sigma$ contour near the
top-center of the left panel. Here, both models are fixed to the distance
modulus reported in Table 1, despite small differences in distance between the
corresponding samples. We highlight that one BHB candidate lies along the
older, more metal-poor (blue) model, and one (likely non-member) star lies
near the RHB of the younger, more metal-rich (red) model.

###  2.4 Systemic Proper Motion of DELVE 6

In addition to the aforementioned BHB and RHB candidates, we identified one
additional nearby member candidate with a Gaia proper motion measurement. This
star (Gaia DR3 source_id: 4698076296289956352) is the brightest RGB star
consistent with our best-fit isochrone in Figure 2 and was identified as a
high-probability member in our ugali fit ($p_{\texttt{ugali}}=0.99$; see
Appendix A, Table 2). Notably, this RGB star’s proper motion is consistent
with the BHB star at the $1.3\sigma$ level.333Here, the confidence level
calculated appropriately for the case of two-dimensional Gaussians was
converted to the equivalent $\sigma$-distance for a one-dimensional Gaussian;
however, this calculation neglects the covariance between proper motion
components. The adequate agreement in proper motion supports the
interpretation that the BHB and RGB stars may both be members of DELVE 6, as
the joint probability of having these two stars by chance lying on a single
isochrone while also sharing a statistically consistent non-zero proper motion
is small. It is thus reasonable to derive the proper motion of DELVE 6 from
these two stars, which we find to be
$(\mu_{\alpha}\cos\delta,\mu_{\delta})=(0.93\pm 0.39,-1.28\pm 0.38)$ mas yr-1
through a simple two-parameter fit.

Although this measurement is tentative and should be interpreted cautiously,
DELVE 6’s kinematics are singularly important for unravelling its origins.
Therefore, we briefly explored what this measurement might tell us about the
connection of DELVE 6 to possible host systems. To do so, we calculated its
azimuthal and polar velocity components in Galactocentric spherical
coordinates (hereafter $v_{\phi}$ and $v_{\theta}$) by sampling from the
posterior distributions for the available 5D phase-space measurements and
sampling the unknown radial velocity from a uniform distribution on the
interval [$-500$ km $\rm s^{-1}$, 500 km $\rm s^{-1}$]. We then compared the
values of these velocitity components to those expected from stars belonging
to the distant MW halo and the MCs.

Using galpy (Bovy, 2015) to carry out the velocity transformation, we find
$v_{\phi}=-50\pm 150$ km $\rm s^{-1}$, $v_{\theta}=-430\pm 150$ km $\rm
s^{-1}$, where the best-fit values and the upper/lower uncertainties
correspond to the median and 16th/84th percentiles across 100,000 random 6D
samples. This value of $v_{\phi}$ is uninformative, as it is consistent with
the expected velocity distributions of all three hosts. However, we do observe
that DELVE 6’s estimated polar velocity $v_{\theta}$ is approximately
consistent with that of the LMC ($v_{\theta}\sim-305$ km $\rm s^{-1}$) and SMC
($v_{\theta}\sim-260$ km $\rm s^{-1}$). The polar velocity distribution of MW
halo tracers at 80 kpc is expected to be a Gaussian centered near
${v_{\theta}}=0\rm~{}km~{}^{-1}$ with dispersion $\sigma_{v_{\theta}}\lesssim
100$ km s-1 (see Fig. 4 of Bird et al. 2019), and thus DELVE 6 appears to be
kinematically distinct from typical stars in the outer halo in this velocity
component. We therefore conclude that DELVE 6’s proper motion, taken at face
value, would argue in favor of a Magellanic association. This conclusion only
weakly depends on the unknown line-of-sight velocity but is limited by the
large error on DELVE 6’s proper motion. Reduced proper motion errors (e.g.,
from future Gaia data releases) will provide more definitive kinematic
evidence for an association with one host or another.

##  3 Discussion

At its projected sky position (Figure 1) and Galactocentric distance ($D_{\rm
GC}=78$ kpc), DELVE 6 is located $20$ kpc from the center of the SMC and $35$
kpc from the center of the LMC.444We assume Galactocentric distances for the
LMC, SMC, and Galactic center from Pietrzyński et al. (2013); Graczyk et al.
(2020) and GRAVITY Collaboration et al. (2019), respectively. We neglect the
uncertainties on these distances and on each object’s centroid coordinates
when calculating $D_{\rm LMC}$, $D_{\rm SMC},D_{\rm GC}$ because they are
subdominant relative to the uncertainty on DELVE 6’s heliocentric distance.
Despite this relative proximity, DELVE 6 is located beyond the tidal radius
($r_{t}$) of the LMC due to the MW ($r_{t}\sim 22$ kpc; van der Marel &
Kallivayalil 2014) and the tidal radius of the SMC due to the LMC ($r_{t}\sim
5$ kpc; Massana et al. 2020), suggesting that these two possible hosts have a
weak gravitational influence on DELVE 6. It is therefore not immediately
evident based on its position alone whether this system is associated with
either of the Clouds. On the basis of its separation from the LMC and SMC, as
well as the possible ages and metallicities discussed above, we speculate that
DELVE 6 is most likely described by one of three scenarios: (1) a distant
ultra-faint Milky Way halo star cluster coincidentally located near the MCs;
(2) a LMC cluster residing in its host’s outer halo in a weakly-bound or
unbound orbit, or (3) a cluster formed within the SMC that has been stripped
from its host and now orbits in the MW+LMC potential.

Figure 4: Absolute magnitude ($M_{V}$) vs. azimuthally-averaged half-light
radius ($r_{1/2}$) for a large sample of classical globular clusters,
candidate and confirmed Milky Way satellite galaxies, and recently-discovered
ultra-faint halo star clusters. The location of DELVE 6 in this plane is
indicated by a yellow star. A complete reference list for this figure is
available in Appendix B.

The first of these scenarios is supported by the similarity between DELVE 6’s
age and metallicity to the properties of the MW’s “classical” globular
clusters and the growing population of ultra-faint MW halo star clusters. This
scenario also mitigates the need for an explanation of DELVE 6’s apparently
large separation from the LMC and SMC. Roughly a dozen MW star clusters are
known at $D_{\odot}>70$ kpc, suggesting that an LMC/SMC origin is not
necessary to explain DELVE 6’s large Galactocentric distance.555This number
includes ultra-faint systems, but excludes clusters in the MW’s dwarf
satellites (e.g. Fornax and Eridanus II). This all being said, our exploration
of DELVE 6’s tentative proper motion (Section 2.4) suggests that its overall
kinematics may be more consistent with the LMC/SMC system and inconsistent
with MW halo tracers at its distance.

On that note, the second of our proposed scenarios – namely that the system
was formed in the LMC and remains in a weakly-bound or unbound orbit around
its host – may also explain the ancient age of DELVE 6 given the $\sim 15$
known LMC globular clusters with ages $>9$ Gyr (e.g., Mackey & Gilmore, 2004),
but does not directly explain the system’s present-day Galactocentric distance
and 3D separation. Indeed, if confirmed to be an LMC satellite, DELVE 6 would
reside at a larger separation from the LMC than all but two star clusters
believed to be associated with the MCs.666The two candidate LMC/SMC clusters
at larger separations are DES 1 (Luque et al., 2016) and Eridanus III (Bechtol
et al., 2015); both are included in Figure 1. Conn et al. (2018) argue in
favor of a Magellanic association for both, although their analysis did not
rely on any kinematic evidence. Nevertheless, there is evidence that the LMC
dark matter halo extends $>50$ kpc in radius (e.g., Koposov et al., 2022),
making it plausible that DELVE 6 lies in the outskirts of the LMC halo.
Furthermore, we note that at least two ultra-faint dwarf galaxies that are
likely to be associated with the LMC lie at larger separations from their
(original) host compared to DELVE 6: Horologium I and Phoenix II (see Pace et
al., 2022). Detailed modelling of the MW and LMC dark matter halo structures
(including the LMC’s dynamical friction wake) and these satellites’ orbits
within the associated potential suggests that the former of these two ultra-
faint dwarfs is unbound from the LMC, while the latter is likely bound
(Garavito-Camargo et al., 2021). By analogy, we conclude that DELVE 6 could
plausibly be either weakly bound to the LMC or unbound given its current
position.

The last possibility is that DELVE 6 was initially formed within the SMC, but
was stripped from its host due to interactions between the LMC and the SMC.
The strongest (and arguably only) observational evidence for this conclusion
is DELVE 6’s large present-day Galactocentric distance and its on-sky
location. These properties place the system in a 3D position where a
relatively high density of SMC satellites/debris is expected based on
numerical simulations (Jethwa et al., 2016). In further support of this
possibility, we highlight that a similar stripping scenario has also been
proposed for the recently-discovered ultra-faint star cluster YMCA-1 on the
basis of its proper motion (Piatti & Lucchini, 2022); like DELVE 6, this
system lies well beyond the SMC’s tidal radius.

Disfavoring this stripping scenario is the fact that DELVE 6’s age and
metallicity from our nominal best-fit solution are inconsistent with the known
SMC globular cluster population, which includes only a single comparably old
system with a robustly-measured age (NGC 121, at $\tau\sim 11$ Gyr; Glatt et
al. 2008). Indeed, our measurement suggests that DELVE 6 would be the second
or third oldest star cluster associated with the SMC, depending on the status
of the aforementioned YMCA-1 system, which has a somewhat uncertain age
($\tau\sim 9.6-11.7$ Gyr; Piatti & Lucchini 2022; Gatto et al. 2022b) and only
a tentative association with the SMC. Nonetheless, such a stripping scenario
has been proposed as one explanation for the apparent dearth of old-aged star
clusters associated with the SMC. By tracing the orbits of star clusters
throughout a period of dynamical interaction between the LMC and SMC,
Carpintero et al. (2013) found that for large eccentricities ($e>0.5$), $\sim
15\%$ of SMC star clusters are captured by the LMC and an additional $\sim
20-50\%$ of clusters are ejected into the intergalactic medium. We believe
that either of these two capture scenarios is more likely than the possibility
that DELVE 6 inhabits a weakly-bound orbit in the outer halo of the SMC
(analogous to the case above for the LMC) given that the system lies at $\sim
4r_{\rm t,SMC}$ compared to $\sim 1.6r_{\rm t,LMC}$.

Spectroscopic follow-up will be critical for distinguishing between these
scenarios. Specifically, a radial velocity measurement would enable the
possibility of rewinding DELVE 6’s orbit in the combined MW+LMC+SMC potential,
elucidating its origins. If an LMC or SMC origin can be robustly established
on the basis of its orbit, DELVE 6 may provide a significant constraint on its
host’s age-metallicity relation at a very large radius. Deeper imaging
reaching the main-sequence turnoff feature of DELVE 6’s color–magnitude
diagram will be necessary to realize this possibility and robustly confirm
this system’s ancient age, and a spectroscopic metallicity measurement would
aid in breaking the age-metallicity degeneracy inherent to isochrone fitting.

Lastly, we highlight that the discovery of DELVE 6 emphasizes that the
observational census of ultra-faint systems in the Magellanic environment is
incomplete. Considering the continual discovery of similar ultra-faint star
cluster systems near the MCs in recent years, we speculate that a more
extensive population of old, metal-poor ultra-faint star clusters may exist
around the LMC, SMC, and perhaps even other low-mass galaxies in the Local
Group, waiting to be uncovered by current and future surveys.

##  4 Acknowledgments

Codes and data products associated with this work are available online at
https://github.com/wcerny/DELVE6_Paper.

This project is partially supported by the NASA Fermi Guest Investigator
Program Cycle 9 No. 91201. This work is partially supported by Fermilab LDRD
project L2019-011. W.C. gratefully acknowledges support from a Gruber Science
Fellowship at Yale University. CEMV is supported by the international Gemini
Observatory, a program of NSF’s NOIRLab, which is managed by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation, on behalf of the Gemini partnership of
Argentina, Brazil, Canada, Chile, the Republic of Korea, and the United States
of America. JAC-B acknowledges support from FONDECYT Regular N 1220083.

This project used data obtained with the Dark Energy Camera, which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the DOE and NSF (USA), MISE (Spain), STFC (UK),
HEFCE (UK), NCSA (UIUC), KICP (U. Chicago), CCAPP (Ohio State), MIFPA (Texas
A&M University), CNPQ, FAPERJ, FINEP (Brazil), MINECO (Spain), DFG (Germany),
and the collaborating institutions in the Dark Energy Survey, which are
Argonne Lab, UC Santa Cruz, University of Cambridge, CIEMAT-Madrid, University
of Chicago, University College London, DES-Brazil Consortium, University of
Edinburgh, ETH Zürich, Fermilab, University of Illinois, ICE (IEEC-CSIC), IFAE
Barcelona, Lawrence Berkeley Lab, LMU München, and the associated Excellence
Cluster Universe, University of Michigan, NSF’s National Optical-Infrared
Astronomy Research Laboratory, University of Nottingham, Ohio State
University, OzDES Membership Consortium University of Pennsylvania, University
of Portsmouth, SLAC National Lab, Stanford University, University of Sussex,
and Texas A&M University.

Based on observations at Cerro Tololo Inter-American Observatory, NSF’s
National Optical-Infrared Astronomy Research Laboratory (2019A-0305; PI:
Drlica-Wagner), which is operated by the Association of Universities for
Research in Astronomy (AURA) under a cooperative agreement with the National
Science Foundation.

The Legacy Surveys consist of three individual and complementary projects: the
Dark Energy Camera Legacy Survey (DECaLS; Proposal ID 2014B-0404; PIs: David
Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID
2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy Survey
(MzLS; Prop. ID 2016A-0453; PI: Arjun Dey). DECaLS, BASS and MzLS together
include data obtained, respectively, at the Blanco telescope, Cerro Tololo
Inter-American Observatory, NSF’s NOIRLab; the Bok telescope, Steward
Observatory, University of Arizona; and the Mayall telescope, Kitt Peak
National Observatory, NOIRLab. Pipeline processing and analyses of the data
were supported by NOIRLab and the Lawrence Berkeley National Laboratory
(LBNL). The Legacy Surveys project is honored to be permitted to conduct
astronomical research on Iolkam Du’ag (Kitt Peak), a mountain with particular
significance to the Tohono O’odham Nation.

NOIRLab is operated by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. LBNL is managed by the Regents of the University of California
under contract to the U.S. Department of Energy.

BASS is a key project of the Telescope Access Program (TAP), which has been
funded by the National Astronomical Observatories of China, the Chinese
Academy of Sciences (the Strategic Priority Research Program “The Emergence of
Cosmological Structures” Grant # XDB09000000), and the Special Fund for
Astronomy from the Ministry of Finance. The BASS is also supported by the
External Cooperation Program of Chinese Academy of Sciences (Grant #
114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant #
12120101003, # 11433005).

The Legacy Survey team makes use of data products from the Near-Earth Object
Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet
Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by
the National Aeronautics and Space Administration.

The Legacy Surveys imaging of the DESI footprint is supported by the Director,
Office of Science, Office of High Energy Physics of the U.S. Department of
Energy under Contract No. DE-AC02-05CH1123, by the National Energy Research
Scientific Computing Center, a DOE Office of Science User Facility under the
same contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOAO.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

This work made use of Astropy:777http://www.astropy.org a community-developed
core Python package and an ecosystem of tools and resources for astronomy.

This manuscript has been authored by Fermi Research Alliance, LLC, under
contract No. DE-AC02-07CH11359 with the US Department of Energy, Office of
Science, Office of High Energy Physics. The United States Government retains
and the publisher, by accepting the article for publication, acknowledges that
the United States Government retains a non-exclusive, paid-up, irrevocable,
worldwide license to publish or reproduce the published form of this
manuscript, or allow others to do so, for United States Government purposes.

Blanco, Gaia.

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##  Appendix A Candidate DELVE 6 Members Identified in GAIA DR3

In Table 2, we summarize the properties of the three potential DELVE 6 member
stars that we identified in Gaia DR3. We refer the reader to Section 2.2 for a
more detailed discussion of these sources.

Table 2:  Properties of Candidate Proper-Motion Members of DELVE 6

Gaia Source ID | R.A. (deg) | Dec. (deg) |  $\varpi$ (mas) |  $\mu_{\alpha}\cos\delta$ (mas yr-1) |  $\mu_{\rm\delta}$ (mas yr-1) | $p_{\texttt{ugali}}$ | Comment
---|---|---|---|---|---|---|---
4698076296289954048 | 33.0582 | -66.0618 | $0.0\pm 0.4$ | 0.6 $\pm 0.5$ | $-1.1\pm 0.4$ | 1.00 | BHB Candidate
4698076296289956352 | 33.0771 | -66.0579 | 0.2 $\pm$ 0.6 | $2.0\pm 0.8$ | $-2.2\pm 0.9$ | 0.99 | RGB star
4698076296289957248 | 33.0549 | -66.0558 | $0.0\pm 0.3$ | $-3.0\pm 0.4$ | -12.2 $\pm 0.3$ | 0.00 | RHB? Non-member

Note. — The astrometric properties included above are all taken directly from
Gaia DR3. Here, $p_{\texttt{ugali}}$ is the membership probability of each
star (rounded to the nearest hundredth) as determined from our fiducial
results, which favored the isochrone model with $\tau=13.5\mathrm{\,Gyr}$ and
$\rm[Fe/H]=-2.19$ dex.

##  Appendix B References for Literature Data Presented in Figure 4

In Figure 4, we compare DELVE 6’s absolute $V$-band magnitude ($M_{V}$) and
azimuthally-averaged half-light radius ($r_{1/2}$) to the known population of
MW satellite galaxies, globular clusters, and recently-discovered ultra-faint
star clusters. For the MW satellite galaxies, we adopted or derived
measurements of $M_{V}$ and $r_{1/2}$ from McConnachie (2012), Koposov et al.
(2015), Drlica-Wagner et al. (2015), Martin et al. (2015), Kim & Jerjen
(2015a), Drlica-Wagner et al. (2016), Crnojević et al. (2016), Torrealba et
al. (2016a), Torrealba et al. (2016b), Carlin et al. (2017), Homma et al.
(2018), Homma et al. (2019), Koposov et al. (2018), Muñoz et al. (2018),
Mutlu-Pakdil et al. (2018), Torrealba et al. (2018), Wang et al. (2019),
Moskowitz & Walker (2020), Simon et al. (2020), Mau et al. (2020), Ji et al.
(2021), Cerny et al. (2021b), Cantu et al. (2021), Cerny et al. (2022),
Richstein et al. (2022), and Cerny et al. (2023). For the ultra-faint star
clusters, we adopted or derived measurements from Fadely et al. (2011), Muñoz
et al. (2012), Balbinot et al. (2013), Kim & Jerjen (2015b), Kim et al.
(2015), Weisz et al. (2016), Martin et al. (2016), Kim et al. (2016), Longeard
et al. (2018), Luque et al. (2018), Muñoz et al. (2018), Mutlu-Pakdil et al.
(2018), Conn et al. (2018), Torrealba et al. (2019), Longeard et al. (2019),
Homma et al. (2019), Mau et al. (2019), Mau et al. (2020), Cerny et al.
(2021a), Cerny et al. (2022), Gatto et al. (2022b). In cases where the above
studies of ultra-faint systems quote only an elliptical half-light radius, we
have converted these measurements to azimuthally-averaged half-light radii
using these works’ reported ellipticities (where possible). Lastly,
measurements for the classical globular clusters are taken from Harris (2010).
Two ultra-faint star clusters discovered in the Sloan Digital Sky Survey
(Koposov 1 and Koposov 2; Koposov et al. 2007) have been removed from this
catalog to avoid duplication.