# Extended stellar populations in Ultra-Faint Dwarf galaxies

Elisa A. Tau Departamento de Astronomía, Universidad de La Serena, Raúl Bitrán
1305, La Serena, Chile  A. Katherina Vivas Cerro Tololo Inter-American
Observatory/NSF’s NOIRLab, Casilla 603, La Serena, Chile  Clara E. Martínez-
Vázquez Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, HI
96720, USA

###### Abstract

The possible existence of stellar halos in low-mass galaxies is being
intensely discussed nowadays after some recent discoveries of stars located in
the outskirts of dwarf galaxies of the Local Group. RR Lyrae stars can be used
to identify the extent of these structures, taking advantage of the
minimization of foreground contamination they provide. In this work we use RR
Lyrae stars obtained from Gaia DR3, DES, ZTF, and Pan-STARRS1 to explore the
outskirts of $45$ ultra-faint dwarf galaxies. We associate the stars with a
host galaxy based on their angular separations, magnitudes and proper motions.
We find a total of $120$ RR Lyrae stars that belong to $21$ different galaxies
in our sample. We report seven new RR Lyrae stars in six ultra-faint dwarf
galaxies (Hydrus I, Ursa Major I, Ursa Major II, Grus II, Eridanus II and
Tucana II). We found a large number of new possible members in Bootes I and
Bootes III as well, but some of them may actually belong to the nearby
Sagittarius stream. Adding to our list of $120$ RR Lyrae stars the
observations of other ultra-faint dwarf galaxies that were out of the reach of
our search, we find that at least $10$ of these galaxies have RR Lyrae stars
located at farther distances than $4$ times their respective half-light
radius, which implies that at least $33\%$ of the 30 ultra-faint dwarfs with
RR Lyrae star population have extended stellar populations.

galaxies: dwarf — galaxies: halos — galaxies: Local Group — galaxies: stellar
content — stars: variables: RR Lyrae stars

††facilities: Gaia, PS1, Blanco, PO:1.2m

##  1 Introduction

Stellar halos of Milky Way-like galaxies have become objects of interest in
the astronomical community and various studies regarding them have been
carried out in these past years (e.g., Zolotov et al., 2009; Cooper et al.,
2010; Tissera et al., 2014; Peacock et al., 2015; Monachesi et al., 2016a, b;
Rey & Starkenburg, 2022; Vera-Casanova et al., 2022). These halos can be
considered as a consequence of the hierarchical formation of structures of the
$\Lambda$CDM model (Searle & Zinn, 1978; Frenk et al., 1988; Navarro et al.,
1997) because stars can be found in the external regions of these massive
galaxies principally due to the interactions between subhalos. On one hand, if
the interacting subhalos are sufficiently massive in order to have a stellar
component, they can deposit a significant fraction of this material in the
outer regions of the host galaxies during the merging process (Bullock &
Johnston, 2005; Monachesi et al., 2019). On the other hand, during the
interactions between galaxies, stars that were originally located in their
inner regions can be heated up and end up reaching farther orbits (Purcell et
al., 2010; Tissera et al., 2013).

However, when considering dwarf galaxies, the existence of stellar halos
surrounding these low-mass structures is still a debatable subject. Until now
the study of these extended stellar components in dwarf galaxies is limited on
account of many reasons, the main one being that they would be extremely faint
objects if they exist and hence they would be difficult to observe. Another
difficulty relies on not having a well-modeled stellar mass-halo mass relation
for these galaxies as we do in the cases of the Milky Way-like ones (Behroozi
et al., 2013; Moster et al., 2013).

Nevertheless, recently there have been some studies that would favor the case
in which these small galaxies also possess stellar halos. For example, Gilbert
et al. (2022) study the dwarf galaxy M33 and conclude that it has a
significant kinematically hot component that is likely the galaxy’s stellar
halo rather than a population from its thick disk. In addition, Qi et al.
(2022) provide evidence for the presence of extended stellar halos or tidal
debris in the outskirts of six classical dwarf spheroidals (dSphs), some of
which also have RR Lyrae stars (RRL) outside of their King radii. More
recently, Sestito et al. (2023b) found five stars with Gaia ERD3 making use of
an algorithm presented in Jensen et al. (2023) and identified them as new
members of Ursa Minor dSph, at elliptical distances ranging from $5.2$ to
$11.7$ half-light radii ($R_{h}$). They also suggest the existence of a
stellar halo around that galaxy, which would be more extended than previously
thought. Furthermore, Sestito et al. (2023a) discovered two stars that belong
to the Sculptor dSph which are located at $10\,R_{h}$ ($\sim 3$ kpc) from its
center. Some studies focusing on the spatial distribution specifically of RRL
in dSphs have also been undertaken. An example of this is the work of Stringer
et al. (2021), in which the authors found $51$ RRL uniformly distributed
located beyond the tidal radius of Fornax. Another dSph found to have RRL
located outside its tidal radius is Carina (Vivas & Mateo, 2013), which
suggests that the galaxy is undergoing a tidal disruption that led those stars
to reach great distances. Additionally, Muraveva et al. (2020) studied $285$
RRL belonging to Draco with Gaia DR2 and found that those located in the
southwestern region of this dSph seem to be closer to us, which could be
indicating that Draco and the Milky Way are interacting.

Regarding ultra-faint dwarf galaxies (UFDs) specifically, there are also some
recent studies that have searched for extended stellar populations. Vivas et
al. (2020) identified extra-tidal RRL from Gaia DR2 in six UFDs (Bootes I,
Bootes III, Sagittarius II, Reticulum III, Eridanus III, and Tucana III).
Tucana II has been proven to have stars that reach up to $9\,R_{h}$ from its
center, making it a very extended stellar system (Chiti et al., 2021).
Hercules is also known for having stars located in its outer regions: Garling
et al. (2018) identified $3$ RRL that lie outside its tidal radius, and more
recently Longeard et al. (2023) reports $3$ new members of Hercules, one of
them being at $9.5\,R_{h}$ from its center. Another example is Centaurus I, in
which Martínez-Vázquez et al. (2021a) report a blue horizontal branch star at
a distance $>9\,R_{h}$ and a RRL at $6\,R_{h}$. Finally, in a recent work,
Waller et al. (2023) report stars in the outskirts of Ursa Major I (one star
at $3.7\,R_{h}$), Bootes I (one star at $4R_{h}$) and Coma Berenices (two
stars at $2.5\,R_{h}$). The authors suggest a tidal stripping scenario and the
influence of supernovae feedback as the cause of these stars’ locations in the
three UFDs because they find that their chemical abundances are consistent
with the central regions of their respective host galaxies.

There have also been some recent studies from a theoretical point of view that
analyze the possibility of the formation of stellar halos using numerical
models. Two scenarios that have been proposed to affect the morphology of
dwarf galaxies the most and that could lead to the formation of these stellar
structures consist of mergers (Deason et al., 2014) and tidal disruption
(Fattahi et al., 2018). For example, Tarumi et al. (2021) analyze the possible
formation of an UFD with an extended stellar distribution using cosmological
hydrodynamic simulations and conclude that a major merger of two small
galaxies can be responsible for this outcome. This mechanism is proposed as an
explanation for the formation of the observed extended stellar halo of Tucana
II. Deason et al. (2022) also use numerical models (N-body cosmological
simulations) to argue in favor of the possible existence of stellar halos
surrounding low-mass galaxies that could be formed due to this type of
external process, and they analyze the properties of these extended structures
differentiating between those stellar halos of satellite and those of field
dwarf galaxies. In addition, Kado-Fong et al. (2022) use the FIRE-2
simulations to study the formation of extended and round stellar halos around
dwarf galaxies and claim that these are built up by stars that formed in the
galaxy (in-situ stars) and then migrated to the external regions. Moreover,
considering UFDs specifically, Ricotti et al. (2022) present an empirical
model for the shape and mass of stellar halos of UFDs from cosmological N-body
simulations. Their results were then compared to the observations of six
isolated dwarf galaxies but they state that the systematic uncertainty of
their inference on the star formation efficiency at the epoch of reionization
is not negligible, which is mainly due to the lack of observations that extend
to great distances from the center of these galaxies. Additionally, Goater et
al. (2023) use the EDGE simulations to study the ellipticity and extended
light surrounding tidally isolated UFDs and find that they exhibit a wide
range of projected ellipticities, with many having anisotropic extended
stellar halos that mimic tidal tails but are in fact a result of late-time
accretion of lower mass stuctures. The authors also establish a connection
between the final shape of the UFDs and their formation time.

Finding evidence of extended populations in UFDs is challenging due to the
very low density of stars in these stellar systems, which is even more extreme
in their external parts. Foreground stars dominate by large the field of view
of the outskirts of the UFDs. Methods that have been used to observationally
detect the stellar halos of UFDs described above include analyzing together
several properties of the stars such as chemical abundances, kinematics,
positions, proper motions and also their location in the color-magnitude
diagram (CMD) from broad-band photometry. However, obtaining abundances and
radial velocities for large number of stars in extended regions around UFDs is
observationally expensive.

In this work we follow Vivas et al. (2020) and use RRL as tracers of the
stellar population of possible stellar halos in UFDs. The main advantage of
using RRL is to avoid, or minimize, the foreground contamination. RRL are a
type of variable star that are undergoing helium-burning phase in their core.
They are old stars ($>10$ Gyr) and they trace a population that is ubiquitous
in all UFD galaxies. Their pulsation periods are short (less than a day) and
the amplitudes of their lightcurves is large ($0.2-1.5$ mag in optical bands,
Smith, 1995). RRL are considered standard candles (e.g., Bono, 2003) due to
the fact that they have a very well-defined relationship between their period
of variability and their luminosity. This is a clear advantage when it comes
to studying dwarf galaxies and its stellar halos: RRL can be associated with
particular stellar systems based on their distance. Since the field population
of Milky Way RRL decreases with Galactocentric radius, they become very rare
at distances larger than $\sim 50$ kpc (e.g., Vivas & Zinn, 2006; Zinn et al.,
2014; Medina et al., 2018; Stringer et al., 2021). Most of the UFDs that are
satellites of the Milky Way are located at larger distances and thus the
possible contamination by halo field stars is usually negligible. Hence, the
arduous task of excluding non-members of the UFDs that are part of the
foreground population is considerably reduced.

Nowadays, thanks to new large-scale surveys that have been completed in the
last few years, catalogs of RRL up to large distances in the Milky Way ($>80$
kpc) are readily available, including those coming from Gaia DR3 (Clementini
et al., 2022), the Zwicky Transient Facility (ZTF, Huang & Koposov, 2022), the
Dark Energy Survey (DES, Stringer et al., 2021), and the Panoramic Survey
Telescope and Rapid Response System (Pan-STARRS, Sesar et al., 2017). The aim
of this work is to search for RRL in these catalogs and find those associated
to the UFD satellites of the Milky Way. A similar analysis was done by Vivas
et al. (2020) based on Gaia DR2, but here we enhance it by (i) using the
updated catalogs mentioned above, which together cover uniformly the whole sky
to distances beyond 100 kpc, (ii) consistently searching the external regions
of the UFDs in order to trace any possible extended population or halos around
these galaxies, and (iii) considering all UFDs in the Milky Way neighbourhood
and not only those closer to 100 kpc.

This paper is structured as follows: in § 2 we describe the catalogs that were
used in this work. In § 3 we explain the methodology and the selection
criteria to match RRL with UFDs. § 4 presents our results, and finally we
discuss the conclusions in § 5.

##  2 Data

In this section we present the data used in this work. A brief description of
the catalogs of RRL is given in § 2.1 to 2.4, and in § 2.5 we present the UFDs
catalog that was used in this work.

###  2.1 Gaia

Besides providing positional measurements for one billion stars in the Milky
Way, the Gaia mission (Gaia Collaboration et al., 2016) collects multi-epoch
photometry that allows the identification of variable stars such as RRL, down
to a limiting magnitude of $G\approx 21$. Vivas et al. (2020) used the Gaia
DR2 catalog of RRL stars (Clementini et al., 2019) to search for stars
belonging to UFDs. The DR2 catalog contained $140,784$ RRL stars covering
unevenly the whole sky. The mean completeness of that catalogue was $60\%$ but
it had a strong dependence with position on the sky since not all the sky had
been observed with the same frequency and light curves were too sparse to
allow a reliable classification of variable stars in some parts of the sky.
Consequently, it was not clear that the UFDs studied in Vivas et al. (2020)
had indeed a complete census of RRL based in DR2.

With Gaia DR3 (Gaia Collaboration et al., 2022) the sky coverage became more
uniform and the confirmation of RRL is more reliable. In addition, the errors
of the proper motions provided by Gaia DR3 are smaller than those given by
Gaia DR2, which makes it even more trustworthy. The DR3 catalog of RRL by
Clementini et al. (2022) has $270,905$ stars, twice the number in DR2. By
comparing with OGLE-IV (Soszyński et al., 2019a, b) in the Bulge and
Magellanic Clouds regions, the completeness of the RRL catalog in DR3 is
estimated to be between $82-94\%$, with contamination $<8\%$. The completeness
at the faint end of Gaia DR3 is harder to asses since there are not many RRL
stars known at such faint magnitudes, but by comparison with an all-sky
compiled catalog (including stars in globular clusters and satellite
galaxies), the completeness was found to be $\sim 64\%$ (Clementini et al.,
2022).

The Gaia RRL DR3 catalog is the main source used in this work because it is
the most complete catalog available in the literature, covering the whole sky,
with complete light curves which allows a complete characterization of the
RRL, and deeper than most of the other catalogs available.

###  2.2 ZTF

ZTF is a time-domain survey being made with the Palomar $48$-inch Schmidt
Telescope, and a $47$ sq deg field of view, $600$-megapixel camera (Masci et
al., 2019). It scans the entire Northern sky ($\delta\geq-28\arcdeg$) every
two days. In this work we use a recent catalog by Huang & Koposov (2022) that
has $71,755$ periodic variables from ZTF classified as RRL. The most distant
RRL found in this catalog is located at $132$ kpc. Regarding its limiting
magnitudes, the limits in the g, r and i bands are $20.8$ mag, $20.6$ mag and
$19.9$ mag respectively. For heliocentric distances $<80$ kpc, its
completeness is $\gtrsim 80\%$. The depth of this survey is about the same as
Gaia DR3.

###  2.3 DES

DES is an optical and near infrared survey (Flaugher et al., 2015) using the
Dark Energy Camera (DECam) at the 4m Blanco Telescope at Cerro Tololo Inter-
American Observatory in Chile. The survey covers $5,000$ sq deg in the
Southern Hemisphere with limiting magnitudes in the g, r, i, z and y bands of
$24.3$, $24.1$, $23.5$, $22.9$, and $21.5$ mag, respectively. Although DES is
not a variability survey, Stringer et al. (2021) used the few repeated
observations of the same field over the 6-year survey to statistically
identify RRL candidates. Stringer et al. (2021) reports $6,971$ RRL candidates
that are located at distances up to $\sim 335$ kpc and are all type RRab. The
sample of sources provided by this catalog is estimated to be more than $70\%$
complete at distances of $\sim 150$ kpc. This survey is the deepest one of all
of those used in this work.

###  2.4 Pan-STARRS1

The Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) survey
(Chambers et al., 2016) is an optical and near infrared survey that covers all
the sky north to a $-30\arcdeg$ declination. The first phase of the survey,
called Pan-STARRS1 (PS1), was made with a 1.8m telescope at Haleakala
Observatories near the summit of Haleakala in Hawaii. PS1 has only sparse
multi-epoch data, with $\sim 12$ epochs in each of the five bands, taken over
a 4.5-year period. Sesar et al. (2017) used template fitting and machine
learning techniques to identify $\sim 45,000$ RRLs candidates in PS1 with
$90\%$ purity and $80\%$ completeness down to $r_{P1}\sim 20$, or distance to
the Sun of $\sim 80$ kpc. Although not as deep and complete as Gaia DR3, this
catalogue may provide additional RRL for UFDs located north of
$\delta=-30\arcdeg$.

We bear in mind that PS1 and DES catalogs are based on few epochs, and some
degree of contamination (low purity) is expected. Therefore, the stars
selected from these catalogs will be considered as RRL candidates in this
work.

Each of the catalogs used in this work was paired with Gaia DR3 to obtain
proper motions and G magnitudes. The latter is important in order to have a
common magnitude system for all stars. However, this could not be done for the
DES catalog given that it contains a lot of stars that are fainter than those
in Gaia DR3. In consequence, a transformation between magnitude systems was
made. DES magnitudes of selected RRL (see Sec. 3.1) were transformed to G in a
two-step procedure, first transforming to SDSS-based photometry using the
transformation equations presented in DES DR2 (Abbott et al., 2021):

$g_{SDSS}=g_{DES}+0.060(g-i)_{DES}-0.005$ (1)

$i_{SDSS}=i_{DES}+0.167(r-i)_{DES}-0.027$ (2)

Then, we obtained G mag for each RRL using Eq. 3 which was taken from Jordi et
al. (2010), with updated coefficients from Evans et al. (2018):

$G=g_{SDSS}-0.0940-0.5310(g-i)_{SDSS}\\\
-0.0974(g-i)^{2}_{SDSS}+0.0052(g-i)^{3}_{SDSS}$ (3)

###  2.5 UFD catalog

Ultra-faint dwarf galaxies are the smallest structures known to be dark-
matter-dominated up to now, along with being the oldest and most metal-poor
systems (Simon, 2019). Over the past years, the discovery of local UFDs has
been notoriously increasing due to new large-scale photometric surveys such as
DES (Bechtol et al., 2015; Drlica-Wagner et al., 2015). In this work we
compiled a list of UFDs that are satellites of the Milky Way from Table 1 in
Vivas et al. (2020) and Table A1 in Martínez-Vázquez et al. (2019). In
addition, we considered recent UFDs discovery reports, including Centaurus I
(Mau et al., 2020), Eridanus IV (Cerny et al., 2021a), and Pegasus IV (Cerny
et al., 2023). We also included DELVE 2 (Cerny et al., 2021b) although it has
not yet been confirmed as a UFD. The final sample of UFDs used in this work is
listed in Table 1 and consists of $45$ galaxies. The properties of each galaxy
are presented as follows: galaxy name, RA (J2000), declination (J2000); proper
motion and proper motion errors, half-light radius in arcminutes, half-light
radius in kiloparsecs, absolute magnitude in V ($M_{v}$), ellipticity
($\epsilon$), heliocentric distance and position angle.

The values presented in Table 1 were taken from Belokurov et al. (2007); Irwin
et al. (2007); Moretti et al. (2009); Sand et al. (2009); McConnachie (2012);
Torrealba et al. (2016); Medina et al. (2017); Martin et al. (2016); Carlin &
Sand (2018); Li et al. (2018); Homma et al. (2018); Martínez-Vázquez et al.
(2019); Vivas et al. (2020); Mau et al. (2020); Simon et al. (2020); Garofalo
et al. (2021); Martínez-Vázquez et al. (2021b); Cerny et al. (2021b, a); Pace
et al. (2022) and Cerny et al. (2023). However, the proper motion values were
updated with those presented in McConnachie & Venn (2020) and Li et al.
(2021).

The order of magnitude of the stellar mass of the UFDs analyzed in this work
ranges from $\sim 10^{3}\,M_{\odot}$ to $10^{6}\,M_{\odot}$ (e.g.,
M${}^{*}_{\rm DELVE2}=8.8\times 10^{2}\,M_{\odot}$ (Cerny et al., 2021b),
M${}^{*}_{\rm UMaI}=1.4\times 10^{4}\,M_{\odot}$ (McConnachie, 2012),
M${}^{*}_{\rm TucIV}=2.2\times 10^{6}\,M_{\odot}$ Simon et al. (2020)).

Table 1: Parameters of the $45$ UFDs studied in this work.

Galaxy | RA | DEC | $\mu_{\alpha}\cos(\delta)$ | $\sigma\mu_{\alpha}\cos(\delta)$ | $\mu_{\delta}$ | $\sigma\mu_{\delta}$ | $R_{h}$ | $R_{h}$ | $M_{V}$ | $\epsilon$ | Distance | PA
---|---|---|---|---|---|---|---|---|---|---|---|---
| [deg] | [deg] | [mas/yr] | [mas/yr] | [mas/yr] | [mas/yr] | [$\arcmin$] | [kpc] | [mag] |  | [kpc] | ($\arcdeg$)
Draco II | 238.1740 | 64.5790 | 1.011 | 0.115 | 0.956 | 0.126 | 3.00 | 19.00 | -0.80 | 0.23 | 21.50 | 76.00
Tucana III | 359.1075 | -59.5831 | -0.111 | 0.023 | -1.629 | 0.023 | 5.10 | 33.97 | -1.30 | 0.20 | 22.90 | 25.00
Segue I | 151.7504 | 16.0756 | -2.074 | 0.052 | -3.411 | 0.043 | 3.93 | 29.00 | -1.30 | 0.32 | 23.00 | 75.00
Hydrus I | 37.3890 | -79.3089 | 3.775 | 0.027 | -1.513 | 0.027 | 6.60 | 53.00 | -4.71 | 0.20 | 27.60 | 97.00
Carina III | 114.6298 | -57.8997 | 3.082 | 0.068 | 1.394 | 0.072 | 3.75 | 30.00 | -2.40 | 0.55 | 27.80 | 150.00
Triangulum II | 33.3225 | 36.1719 | 0.602 | 0.081 | 0.085 | 0.093 | 2.50 | 32.00 | -4.20 | 0.30 | 28.40 | 73.00
Cetus II | 19.4700 | -17.4200 | 2.840 | 0.060 | 0.460 | 0.065 | 1.90 | 16.58 | 0.00 | 0.00∗ | 30.00 | 0.00∗
Reticulum II | 53.9203 | -54.0513 | 2.391 | 0.029 | -1.379 | 0.032 | 5.41 | 32.00 | -3.88 | 0.56 | 30.00 | 69.00
Ursa Major II | 132.8726 | 63.1335 | 1.701 | 0.120 | -1.845 | 0.128 | 13.90 | 149.00 | -4.25 | 0.55 | 32.00 | -76.00
Segue II | 34.8226 | 20.1624 | 1.425 | 0.061 | -0.313 | 0.052 | 3.64 | 35.00 | -1.86 | 0.21 | 35.00 | 166.00
Carina II | 114.1066 | -57.9991 | 1.887 | 0.043 | 0.164 | 0.043 | 8.69 | 91.00 | -4.50 | 0.34 | 37.40 | 170.00
Willman I | 162.3436 | 51.0501 | 0.295 | 0.086 | -1.074 | 0.131 | 2.52 | 25.00 | -2.53 | 0.47 | 38.00 | 74.00
Bootes II | 209.5141 | 12.8553 | -2.273 | 0.151 | -0.361 | 0.115 | 3.07 | 51.00 | -2.94 | 0.23 | 42.00 | -71.00
Coma Berenices | 186.7454 | 23.9069 | 0.374 | 0.059 | -1.699 | 0.056 | 5.67 | 77.00 | -4.38 | 0.37 | 44.00 | -58.00
Bootes III | 209.3000 | 26.8000 | -1.176 | 0.019 | -0.890 | 0.015 | 33.03 | 446.79 | -5.75 | 0.33 | 46.50 | -81.00
Tucana IV | 0.7170 | -60.8300 | 0.618 | 0.036 | -1.696 | 0.038 | 9.30 | 127.00 | -3.00 | 0.39 | 47.00 | 27.00
Tucana V | 354.3500 | -63.2700 | -0.270 | 0.083 | -1.253 | 0.110 | 1.00 | 34.00 | -1.60 | 0.70 | 55.00 | 30.00
Grus II | 331.0200 | -46.4400 | 0.389 | 0.034 | -1.526 | 0.036 | 6.00 | 94.00 | -3.90 | 0.20† | 55.00 | 0.00∗
Tucana II | 343.0600 | -58.5700 | 0.935 | 0.031 | -1.243 | 0.036 | 7.20 | 165.00 | -3.90 | 0.00∗ | 58.00 | 0.00∗
Bootes I | 210.0200 | 14.5135 | -0.307 | 0.052 | -1.157 | 0.043 | 10.50 | 242.00 | -6.02 | 0.26 | 66.00 | 6.00
Delve II | 28.7720 | -68.2530 | 1.020 | 0.240 | -0.850 | 0.180 | 1.02 | 21.00 | -2.10 | 0.03 | 71.00 | 74.00
Sagittarius II | 298.1663 | -22.0650 | -0.710 | 0.077 | -0.905 | 0.051 | 1.70 | 35.00 | -5.70 | 0.00 | 73.10 | 103.00
Eridanus IV | 76.4380 | -9.5150 | 0.250 | 0.060 | -0.100 | 0.050 | 3.30 | 75.00 | -4.70 | 0.54 | 76.70 | 65.00
Horologium II | 49.1077 | -50.0486 | 0.915 | 0.330 | -0.913 | 0.439 | 2.17 | 47.00 | -1.56 | 0.71 | 78.00 | 137.00
Horologium I | 43.8813 | -54.1160 | 0.865 | 0.047 | -0.601 | 0.048 | 1.17 | 30.00 | -3.55 | 0.32 | 79.00 | 53.00
Virgo I | 180.0400 | -0.6800 | -0.320 | 0.140 | -0.620 | 0.090 | 1.50 | 38.00 | -0.80 | 0.44 | 87.00 | 51.00
Eridanus III | 35.6952 | -52.2838 | 1.080 | 0.295 | -0.490 | 0.150 | 0.34 | 8.60 | -2.37 | 0.57 | 87.00 | 73.00
Pegasus IV | 328.5390 | 26.6200 | 0.330 | 0.070 | -0.210 | 0.080 | 1.55 | 41.00 | -4.25 | 0.41† | 90.00 | 115.00
Reticulum III | 56.3600 | -60.4500 | 0.519 | 0.222 | -0.173 | 0.247 | 2.40 | 64.23 | -3.30 | 0.00∗ | 92.00 | 0.00∗
Ursa Major I | 158.7706 | 51.9479 | -0.387 | 0.058 | -0.641 | 0.068 | 8.13 | 319.00 | -5.12 | 0.59 | 97.00 | 67.00
Phoenix II | 354.9928 | -54.4050 | 0.501 | 0.062 | -1.199 | 0.076 | 1.50 | 43.63 | -2.70 | 0.40 | 100.00 | 156.00
Aquarius II | 338.4813 | -9.3274 | 0.647 | 0.588 | -0.298 | 0.548 | 5.10 | 159.00 | -4.30 | 0.40 | 107.87 | 121.00
Centaurus I | 189.5850 | -40.9020 | -0.140 | 0.050 | -0.200 | 0.040 | 2.30 | 79.00 | -5.55 | 0.40 | 116.30 | 20.00
Grus I | 344.1760 | -50.1630 | 0.071 | 0.056 | -0.270 | 0.078 | 1.77 | 62.00 | -3.40 | 0.41 | 127.00 | 4.00
Hercules | 247.7583 | 12.7917 | -0.030 | 0.040 | -0.360 | 0.030 | 6.27 | 330.00 | -5.80 | 0.67 | 133.00 | -72.59
Hydra II | 185.4254 | -31.9853 | -0.576 | 0.280 | -0.101 | 0.212 | 1.70 | 66.00 | -4.60 | 0.00∗ | 151.00 | 0.00∗
Leo IV | 173.2375 | -0.5333 | 0.007 | 0.174 | -0.261 | 0.134 | 3.30 | 206.00 | -5.00 | 0.25 | 154.00 | 355.00
Canes Venatici II | 194.2917 | 34.3208 | -0.138 | 0.111 | -0.320 | 0.082 | 1.85 | 74.00 | -5.20 | 0.23 | 159.00 | 9.45
Leo V | 172.7900 | 2.2200 | 0.118 | 0.212 | -0.387 | 0.151 | 1.00 | 135.00 | -4.40 | 0.43 | 173.00 | -71.00
Pegasus III | 336.1000 | 5.4050 | 0.060 | 0.100 | -0.200 | 0.100 | 0.85 | 53.00 | -3.40 | 0.38 | 174.00 | 0.00∗
Pisces II | 344.6292 | 5.9525 | 0.675 | 0.299 | -0.631 | 0.212 | 1.12 | 58.00 | -4.10 | 0.31† | 175.00 | 0.00∗
Columba I | 82.8542 | -28.0425 | 0.189 | 0.119 | -0.556 | 0.134 | 2.20 | 117.11 | -4.20 | 0.30 | 183.00 | 24.00
Cetus III | 31.3310 | -4.2700 | 0.140 | 0.080 | -0.160 | 0.080 | 1.23 | 89.81 | -2.45 | 0.76 | 251.00 | 101.00
Eridanus II | 56.0880 | -43.5334 | 0.210 | 0.090 | -0.050 | 0.110 | 2.30 | 277.00 | -7.10 | 0.40 | 370.00 | 22.84
Leo T | 143.7225 | 17.0514 | -0.010 | 0.050 | -0.110 | 0.050 | 1.40 | 120.00 | -7.60 |  $\sim$0.00 | 409.00 |  $\sim$0.00

Note. — ∗: values are not measured; †: values are upper limits.

##  3 Methodology

We associate RRL with UFD galaxies in three steps: (i) angular separation,
(ii) heliocentric distance, and (iii) proper motions. The selection
constraints are explained in Secs. 3.1, 3.2 and 3.3 and were applied
separately to each catalog used in this work.

###  3.1 Angular separation selection

The first condition we took into account was that the stars should be located
no farther than a certain radius from the center of the galaxy to be
considered as a member candidate. To consistently search in the external parts
of UFD galaxies, we set up the maximum search radius as a function of the
$R_{h}$ of each galaxy. The maximum separation considered between the stars
and the center of the galaxy was $15R_{h}$, except for very small galaxies
(i.e., if $15R_{h}<1\arcdeg$) where we allowed a search radius of $1\arcdeg$.
This exception was prompted by previous results by Vivas et al. (2020) where
the authors found possible distant members in very small galaxies like
Sagittarius II or Eridanus III (which have $R_{h}$ of $1\farcm 7$ and $0\farcm
34$, respectively).

###  3.2 Magnitude selection

After having made a first cut out considering the separation between the stars
and the center of the UFD, we proceeded to enhance our selection by selecting
only RRL that are at the same distance as the UFD. To do so, we considered the
UFD’s distances (column $11$ in Table 1) to estimate the magnitude $m_{G}$
that the RRL would have in Gaia’s G-band if they belong to the galaxy using
the distance modulus equation:

$m_{G}-M_{G}=5\cdot\log(d)-5$ (4)

where the distance d is the distance to the UFD in pc. The absolute magnitude
of an RRL, $M_{G}$, was assumed to be 0.46, a value obtained using the
Muraveva et al. (2018)’s $M_{G}$ \- [Fe/H] relationship
($M_{G}=0.32{\rm[Fe/H]}+1.1$), and assuming a mean metallicity of [Fe/H]$=-2$
dex, which is typical for UFDs (Simon, 2019). Since not all UFDs have measured
metallicities, we decided to use [Fe/H]=-2.0 as a reference value. However,
the range of metallicities in UFDs is not large, and translates in maximum
differences in $M_{G}$ of only 0.25 mag.

The expected magnitude of RRL found this way are de-reddened. Thus, we proceed
to correct for extinction the $G$ magnitudes of the RRL selected in the
previous step. To do that, we computed the color excess E(B-V) (Schlegel et
al., 1998) using the Python package dustmaps (Green, 2018). We obtained the
reddening correction ($A_{G}$) using the following relation: $A_{G}=2.740\cdot
E(B-V)$ (Casagrande & VandenBerg, 2018).

Finally, we selected RRL having extinction-corrected magnitudes within $\pm
0.5$ mag of the expected magnitude for each UFD. The range allows for
differences arising from different metallicities, photometric errors, and/or
small distance gradients within the searched region. An example of the
selection after this step can be seen in Fig. 1 for four of the galaxies in
our sample.

This cut in magnitude eliminates most foreground/background RRL which will be
brighter/fainter than the RRL in the UFD. The cut also eliminates any possible
contamination by Anomalous Cepheids, whose periods overlap with RRL and have
similar lightcurve shapes. Anomalous Cepheids are however $\sim 0.5–2.5$ mag
brighter than RRL (Catelan & Smith, 2015) and hence will be naturally excluded
with the magnitude cut we applied.

Figure 1: Gaia CMDs showing four galaxies of our sample. All stars enclosed
within $3\,R_{h}$ are plotted in the background, except for Bootes III for
which only those stars enclosed within $1\deg$ are shown. The RRL selected for
each galaxy are located in the horizontal branch as expected. The horizontal
dashed line indicates the G mean value of the selected RRL. In the case of
Grus II, a double horizontal branch is seen (see discussion in the text). The
different symbols represent the catalog where the RRL were selected from.

###  3.3 Proper motion selection

Finally, we considered the proper motion of the previously selected RRL
candidates and the UFDs to dismiss any possible non-member stars that had
passed the other two selection criteria mentioned in Secs. 3.1 and 3.2.

In order to compare the proper motion values of the RRL to those of the UFDs,
we first defined a box for each galaxy inside which the proper motion values
of the RRL candidates should fall to be considered a galaxy member. Example of
these boxes can be seen in Fig. 2. The size of the boxes were based on
confirmed members for each galaxy available in the literature (Simon, 2018;
Pace & Li, 2019; Carlin & Sand, 2018; Longeard et al., 2021; Martínez-Vázquez
et al., 2021a; Cerny et al., 2023; Garofalo et al., 2021; Fabrizio et al.,
2014; Simon et al., 2020; Jenkins et al., 2021; Torrealba et al., 2016; Kirby
et al., 2015). The majority of these confirmed members were based on radial
velocities, and/or proper motions from Gaia DR2 (Gaia Collaboration et al.,
2018). Here we updated the proper motions of all member stars with Gaia DR3
and eliminated some stars that were clearly outliers probably due to large
differences in their proper motion in comparison to those previously reported
in Gaia DR2. In a few cases, there are no list of members available in the
literature. In those cases, we used the reported galaxy’s mean proper motion
as follows: for DELVE 2 and Virgo I we used the values provided in Table 1,
which were obtained from Cerny et al. (2021b) and McConnachie & Venn (2020),
respectively. Note that the proper motion error values stated in Table 1 for
Virgo I is an average between those present in McConnachie & Venn (2020); for
the proper motion box of Eridanus IV, we used the limits presented in Figure 2
of Cerny et al. (2021a); lastly, for the proper motion boxes of Leo T
(Clementini et al., 2012), Pegasus III (Garofalo et al., 2021) and Canes
Venatici II (Vargas et al., 2013) we used the galaxies’ $\mu^{*}_{\alpha}$ and
$\mu_{\delta}$ values as given in those references (which are the same as in
Table 1) without updating the values to Gaia DR3, since these three galaxies
are beyond the Gaia limits.

Figure 2: Proper motion boxes for four galaxies of our sample: Bootes I (upper
left panel), Ursa Major I (upper right panel), DELVE 2 (lower left panel) and
Tucana II (lower right panel). The limits for the boxes of Bootes I, Ursa
Major I and Tucana II were defined according to the spectroscopic members
reported in Simon (2018), while the box of DELVE 2 uses the galaxy’s
$\mu^{*}_{\alpha}$ and $\mu_{\delta}$ values stated in Table 1 obtained from
Cerny et al. (2021b).

Once we had defined the proper motion boxes for each galaxy, we selected those
RRL candidates with proper motion values that would fit in these boxes when
considering their $1\sigma$ errors.

This procedure was only followed for RRL from Gaia DR3, ZTF and PS1. We did
not include the proper motion criterion in the selection of RRL candidates
from DES data because this survey reaches fainter magnitudes than the Gaia
limit. Therefore, the faintest RRL in DES do not have proper motions
available.

##  4 Results

###  4.1 Final RRL sample

Out of the $45$ galaxies analyzed in this work, we find that $21$ of them have
RRL stars according to our selection criteria stated in Sec. 3. The remaining
$24$ galaxies in which no RRL were found can be classified in two groups:
those UFDs that truly do not have RRL and those that may have but the stars
are not found in this work due to the limitations of the catalogs used. This
is further dicussed in Sec. 4.3.

Our final RRL sample consists of $120$ stars which are listed in Table 2. The
information provided for each star in Table 2 is the following: (1) Gaia ID;
(2) RA [deg]; (3) DEC [deg]; (4) GGaia [mag]; (5-6) Gaia proper motion values;
(7) RRL classification; (8) DES ID; (9) ZTF ID; (10) PS1 ID; (11-14) periods
according to DES, ZTF, PS1 and Gaia respectively; (15) angular separation
between the RRL and the host UFD, in $R_{h}$ units; and (16) name of the host
UFD galaxy. The complete list of RRL can be found in the online version of
this work.

Fig. 3 shows four examples of the spatial distribution of the RRL in planar
coordinates centered on each UFD. The different symbols represent the catalog
from which the RRL was selected. We also plotted four ellipses that represent
$R_{h}/2$, $R_{h}$, $2\,R_{h}$ and $4\,R_{h}$ from the center of each galaxy.
The equivalent figures for the rest of the galaxies in which we found RRL are
available in the online version of this paper.

Examples of lightcurves for two of the faintest RRL found in Gaia DR3 are
shown in Fig. 4. The quality of the lightcurves is high even at these faint
magnitudes, reassuring the selection of RRL is clean.

Figure 3: Spatial projection of the RRL found in four galaxies of our sample
in planar coordinates centered on each UFD. Different symbols represent the
catalog they are selected from. Four ellipses are plotted to represent the
galaxy’s size ($R_{h}/2$, $R_{h}$, $2\,R_{h}$ and $4\,R_{h}$). We note that
RRL are located at separations greater than $4\,R_{h}$ in all four cases.
Plots for the remaining 17 UFDs in which we found RRL are available in the
online version of this paper.  Table 2: Final sample of RRL found in $21$
different UFDs.

IDGaia | RA | DEC | $G_{Gaia}$ | $\mu_{\alpha}\cos(\delta)(Gaia)$ | $\mu_{\delta}(Gaia)$ | Type† | IDDES | IDZTF | IDPS1 | $P_{DES}$ | $P_{ZTF}$ | $P_{PS1}$ | $P_{Gaia}$ | Sep/Rh | Galaxy
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| [deg] | [deg] | [mag] | [mas/yr] | [mas/yr] |  |  |  |  | [days] | [days] | [days] | [days] |  |
4918034941751885696 | 1.07229 | -59.37689 | 17.54 | -0.053 | -1.5349 | RRab | 1041991456 | - | - | 0.57282 | - | - | 0.57282 | 14.03 | TucanaIII
4917942612838673024 | 0.99559 | -60.06946 | 19.40 | 0.8997 | -1.7487 | RRc | - | - | - | - | - | - | 0.36598 | 5.32 | TucanaIV
6487761169641710464 | 357.54223 | -62.06401 | 19.30 | 0.8134 | -0.7239 | RRc | - | - | - | - | - | - | 0.29653 | 14.09 | TucanaIV
- | 2.36329 | -60.98564 | 19.23 | - | - | RRab | 1045709754 | - | - | 0.62125 | - | - | - | 8.43 | TucanaIV
6567699405896736384 | 331.10818 | -45.04026 | 19.13 | 0.38 | -0.6487 | RRc | - | - | - | - | - | - | 0.36131 | 14.02 | GrusII
6561357319748782976 | 331.32574 | -46.60868 | 18.74 | 0.4474 | -1.9714 | RRab | - | - | - | - | - | - | 0.62057 | 3.12 | GrusII
6561426485901552640 | 330.87292 | -46.28102 | 19.11 | 0.496 | -1.5272 | RRc | - | - | - | - | - | - | 0.4044 | 2.03 | GrusII
- | 328.87317 | -46.27519 | 18.61 | - | - | RRab | 940908371 | - | - | 0.57105 | - | - | - | 18.61 | GrusII
- | 331.02493 | -46.48205 | 18.64 | - | - | RRab | 947555289 | - | - | 0.41952 | - | - | - | 0.42 | GrusII
- | 330.83239 | -47.92666 | 18.55 | - | - | RRab | 947930606 | - | - | 0.60425 | - | - | - | 14.95 | GrusII
6864048408410304896 | 298.15855 | -22.05848 | 19.76 | 0.3723 | -0.67 | RRc | - | - | - | - | - | - | 0.30785 | 0.34 | SagittariusII
6864423994704275200 | 298.14951 | -22.03330 | 19.68 | 0.0635 | -0.5289 | RRc | - | - | - | - | - | - | 0.31856 | 1.25 | SagittariusII
6864422757758521984 | 298.23647 | -22.06901 | 19.64 | -0.6756 | -0.9773 | RRc | - | - | - | - | - | - | 0.40651 | 2.30 | SagittariusII
6864422993976659968 | 298.18499 | -22.05134 | 19.59 | -0.7179 | -0.9086 | RRab | - | 6864422993976659968 | - | - | 0.66549 | - | 0.66565 | 0.78 | SagittariusII
- | 298.05471 | -21.71638 | 19.44 | - | - | RRab | - | 6865195302117134336 | - | - | 0.54079 | - | - | 12.84 | SagittariusII
87207528534363264 | 34.75026 | 20.10978 | 18.55 | 1.4086 | -0.3918 | RRab | - | 87207528534363264 | - | - | 0.74948 | - | 0.74949 | 1.74 | SegueII
- | 344.19906 | -50.18682 | 20.75 | - | - | RRab | 983283631 | - | - | 0.63549 | - | - | - | 1.22 | GrusI
1243152071642576896 | 208.67327 | 15.30334 | 19.31 | -1.4792 | -0.0398 | RRab | - | 1243152071642576896 | ** | - | 0.62692 | 0.62694 | 0.62691 | 11.26 | BootesI
1226522469372990208 | 211.74214 | 12.52060 | 19.73 | 0.0338 | -1.0351 | RRab | - | 1226522469372990208 | ** | - | 0.64768 | 0.64766 | 0.64766 | 17.80 | BootesI
1229801659723433600 | 210.67042 | 13.05105 | 19.14 | -1.331 | -0.3902 | RRab | - | 1229801659723433472 | ** | - | 0.59843 | 0.59845 | 0.59841 | 9.97 | BootesI
1230741020611316224 | 209.51825 | 14.22200 | 19.44 | -0.5014 | -0.4917 | RRab | - | 1230741020611316224 | ** | - | 0.66164 | 0.6617 | 0.66168 | 4.00 | BootesI
1230772597210842624 | 209.95568 | 14.16816 | 19.43 | 0.1171 | -1.277 | RRc | - | 1230772597210842624 | ** | - | 0.40118 | 0.40118 | 0.40116 | 2.01 | BootesI

Note. — ** Star was found in PS1 but no IDs were not provided in Sesar et al.
(2017)’s catalog.

Note. — ${\dagger}$ DES: all of the RRL reported in this catalog (Stringer et
al., 2021) are type RRab; ZTF: no type is reported in the RRL catalog by Huang
& Koposov (2022), but the authors suggest a classification based on the stars’
periods: type RRab if its greater than $0.45$ days and type RRc if its lower
than $0.45$ days; PS1: Sesar et al. (2017) propose a classification based on
the “score3” parameter of the stars in their catalog: type RRab if
$s_{3,ab}>0.8$ and type RRc if $s_{3,c}>0.55$.

Note. — Only a portion of this table is shown here to demonstrate its form and
content. The complete list of RRL is available in the online version of this
paper.

Figure 4: Examples of Gaia DR3 lightcurves of two of the faintest RRL found in
this work (in the Phoenix II and Ursa Major I galaxies). The red squares and
black x symbols mark measurements flagged in Gaia DR3 as noisy and rejected,
respectively.

###  4.2 Possible Contamination by the Halo and/or Halo Substructures

As discussed before, in general we expect negligible contamination in the
selected RRL around each UFD from the halo field population. However, there
are some special cases in which contamination may be important. Firstly,
although RRL are rare in the distant halo, if the search area is very large
and/or the UFD is not at a large distance from the Galactic center, we may
expect random halo RRL field stars within the selected sample. Most of the
UFDs are very small and consequently the search area is also small. However,
Bootes III is exceptionally large and halo contamination must be addressed.
Secondly, some galaxies are close enough to other stellar systems or halo
substructures, such as the Small Magellanic Cloud (SMC) and stellar streams,
that may also have contamination by RRL from those substructures. We discuss
these special cases in the following subsections.

####  4.2.1 Galaxies Near the Sagittarius Stream: Bootes I, Bootes II, and
Bootes III

Bootes III is a large UFD, which is very likely in the process of being
disrupted (Carlin et al., 2009; Carlin & Sand, 2018). It was discovered by
Grillmair (2009) as a strong overdensity in SDSS data. The same paper reports
a stellar stream, Styx, which passes through Bootes III and has a similar
heliocentric distance (Fig. 5), making a relationship between both structures
very likely. Indications that the galaxy is being disrupted are its large size
($R_{h}=33\farcm 03$, Moskowitz & Walker, 2020), large velocity dispersion,
and an orbit that brings Bootes III as close as 7.8 - 12 kpc from the Galactic
center at pericenter (Carlin & Sand, 2018; Pace et al., 2022).

Figure 5: Equatorial coordinates (x,y=RA,DEC) map of the RRL stars (black
circles) selected as members of the Bootes I, II, III galaxy. The blue
ellipses encloses $4\,R_{h}$ of each galaxy. Bootes III is the largest one at
$\delta=26\fdg 8$, while Bootes II is the smallest and further South one. The
model of the Sgr stream by Vasiliev et al. (2021) is shown with $+$ symbols
whose color scales with the heliocentric distance. Green $+$ symbols are Gaia
DR3 RRL in the Sgr stream selected as a control sample (see text). The solid
line approximately traces the Styx stream (Grillmair, 2009).

Vivas et al. (2020) identified seven RRL in Bootes III based on Gaia DR2 in an
area of $2\arcdeg$ around the galaxy, or about $4R_{h}$. Here we explored a
much larger area around the galaxy, finding $32$ RRL likely associated with
Bootes III since they share the same magnitude (as can be seen in the upper
right panel of Fig. 1) and proper motions as the galaxy. They spread however
in an area as large as the explored region, with quite a uniform distribution
(as shown in the upper right panel of Fig. 3). In particular, the selected RRL
stars do not seem to trace the Styx stream, suggesting Styx is not responsible
for many of these RRL. Although in principle all these RRL stars could be
indeed debris material from Bootes III and/or Styx, we noticed the Sagittarius
(Sgr) stream gets as close as $\sim 10\arcdeg$ to the South of Bootes III
(Vasiliev et al., 2021). Coincidentally, in this part of the sky, the Sgr
stream has a distance of $\sim 35-45$ kpc, not too different than the distance
to Bootes III (Fig. 5). Thus, some contamination by Sgr stream stars may exist
among the candidates to debris from Bootes III. The fact that there seems to
be more RRL stars toward the South of Bootes III compared with the Northern
side, indicates there may be indeed Sgr contamination in our selection. This
can be seen in Fig. 6 which shows that there is overlap between both the G
magnitudes and the proper motions of the selected Bootes III RRL and the ones
in the Sgr stream (control sample, green $+$ symbols in Fig. 5). The RRL in
Bootes III are slightly brighter ($\langle G\rangle=18.76$) than the bulk of
the Sgr stream stars ($\langle G\rangle=18.98$), but there is still enough
overlap to believe some degree of contamination is possible.

Figure 6: Top panel: distribution of G magnitude of RRL selected from Gaia DR3
in the Sgr stream (green $+$ symbols in Fig. 5). Middle panel: distribution of
G magnitudes of RRL selected as possible members of the Bootes I (red), Bootes
II (black), and Bootes III (green) galaxies. Bottom panel: Gaia DR3 proper
motions of the RRL in Bootes I, II and II compared with the control sample in
the Sgr stream.

On the other hand, since Bootes III is relatively close to the Sun ($47$ kpc)
and the search area is very large in this case ($\sim 190$ sq deg), we expect
contamination by random halo stars. By integrating the RRL number density
radial profile Medina et al. (2018) between $37$ and $47$ kpc (the range of
distance of the stars found), we estimate as many as $16$ RRL in the searched
area around Bootes III. Although it is expected that the proper motion cut we
implemented can get rid of some of these Halo contaminants, no clean
separation is seen. Indeed, there were $45$ RRL selected before the proper
motion cut. If $\sim 16$ are halo stars, we expect the excess of stars due to
Bootes III to be $\sim 29$ RRL, confirming that we expect some small degree of
contamination among the $32$ RRL finally selected. Radial velocities would be
needed to confirm the association of the RRL with either Bootes III, Sgr
stream or the Halo. Nevertheless, we expect several of the RRL to be true
members of Bootes III, with some of them extending to large distances from its
center.

Bootes I has a large population of RRL with 15 known from Siegel (2006) and
Dall’Ora et al. (2006), and an additional one found in Gaia DR2 by Vivas et
al. (2020). Two of those previously known stars seem to be extra-tidal stars.
Our search found a total of $27$ RRL around Bootes I, including the $16$
mentioned RRL already reported. The new stars range in distance between $2.47$
and $17.80\,R_{h}$ from the center of the galaxy. We notice however that
Bootes I is just on the edge of the Sgr stream (Fig. 5) and, similar to the
case of Bootes III described above, the proper motions and G magnitudes of the
RRL stars overlap (Fig. 6). The range of G magnitudes of the Bootes I RRL
range from $19.14$ mag to $19.73$ mag, slightly fainter than the range of Sgr
stars ($G=18.5-19.5$ mag). With the current data we are unable to isolate the
true members but we suspect that in this case, most of the stars in the
outskirts of Bootes I are indeed Sgr stream stars. It is possible that the 4
new RRL on the northern side of Bootes I (to the other side of Sgr stream) may
be true members of the galaxy. The spatial distribution of the RRL for this
(and every other) galaxy are provided in the electronic form on this paper
(Fig. 3).

Finally, Bootes II is embedded in the Sgr stream (Fig. 5). We found only one
RRL associated with this star, which was previously known (Sesar et al.,
2014). The star is located well within $1\,R_{h}$ from the center of Bootes
II. This RRL is brighter than the bulk of RRL in the Sgr stream and the proper
motion also separates well from Sgr stars (Fig. 6). Thus, in this case, we are
confident to believe this RRL is indeed a member of the UFD.

####  4.2.2 Galaxies near the SMC: DELVE 2, Tucana IV, and Tucana III

Several UFDs are located in the neighborhood of the SMC as seen in Fig. 7. The
SMC is known to have a very extended population (Massana et al., 2020) and can
contaminate the sample of RRL selected in those UFDs. Of the 5 nearby
galaxies, we found no RRL associated with Tucana V. On the other hand, we
discard contamination from the SMC in Hydrus I and Tucana III because the
distances to those systems are very different to that of the SMC (see Table
1).

Figure 7: Map in equatorial coordinates of UFDs in the neighborhood of the
SMC. The grey background shows all RRL in Gaia DR3 in the neighborhood, with
the large concentration of stars being the SMC. Black circles show the RRL
stars selected as members of the Tucana II, Tucana III, Tucana IV, Hydrus I,
and DELVE 2 galaxies. We found no RRL associated with Tucana V. The blue
ellipses encloses $4\,R_{h}$ of each galaxy, which is very small in the case
of DELVE 2 ($R_{h}=1\farcm 02$), and Tucana V ($R_{h}=1\farcm 0$).

In the upper and middle panels of Fig. 8 we show the distribution of G
magnitudes of RRL in the SMC as well as in DELVE 2, Tucana II, Tucana IV. The
lower panel shows the distribution of proper motions. These plots show that
there is enough overlap in magnitude (i.e. distance) and proper motions to
consider possible contamination from the SMC in those 3 UFDs.

DELVE 2 is located at only $6\fdg 9$ from the SMC. Although the two RRL stars
found in our search are within $1\arcdeg$ from the UFD, the galaxy is tiny and
they are indeed $>35\;R_{h}$ from the center of DELVE 2. In addition, the
magnitudes and proper motions of the two RRL completely overlap with those of
the SMC (Fig. 8). Thus, it is clear in this case that those stars are most
likely members of the SMC rather than of DELVE 2, in agreement with the
conclusions by Cerny et al. (2021b).

Tucana IV may also suffer contamination from the SMC. All the three RRL we
found in this galaxy are far away from its center, at 5, 8, and 14 $R_{h}$.
Those stars also have magnitudes and proper motions overlapping with the SMC
(Fig. 8), which is at an angular distance of $12\fdg 9$ from the UFD. It is
very possible that these three stars are also SMC distant members.

In the case of Tucana II, a possible contamination from the SMC is not that
clear. Not only the galaxy is farther away from the SMC, at $18\fdg 5$, but
out of its 4 RRL, 2 of them are located within $1.1R_{h}$. The most external
ones (at 5 and 12 $R_{h}$) are also the brightest ones in the group
($G=19.07,18.97$ mag), which may be too bright for the SMC. Although
confirmation via radial velocities is needed, we believe that the scenario of
contamination from SMC is weak in the case of Tucana II.

Figure 8: Top panel: distribution of G magnitude of RRL selected from Gaia DR3
in the SMC. Middle panel: distribution of G magnitudes of RRL selected as
possible members of the Tucana II (red), DELVE 2 (black), and Tucana IV
(green) galaxies. Bottom panel: Gaia DR3 proper motions of the RRL in DELVE 2,
Tucana II and Tucana IV compared with the proper motions of RRL in the SMC.

####  4.2.3 Grus II and the Chenab/Orphan Stream

Martínez-Vázquez et al. (2019) searched for RRL in Grus II, finding 3 of them
in the galaxy. However, further analysis made those authors realize that there
may be two substructures overlapping in this part of the sky: Grus II and the
Chenab/Orphan stream (Koposov et al., 2019) that passes several kpc in
projection in front of Grus II. Here we recovered the 3 known stars, and found
3 additional ones, which are located outside the area searched by Martínez-
Vázquez et al. (2019). As in Martínez-Vázquez et al. (2019) we also found a
bimodal distribution in the magnitudes of the RRL (see lower left panel in
Fig. 1), with two stars having a magnitude of $G=19.1$, while the other 4 are
$\sim 0.5$ mag brighter. The two fainter stars are hence associated with Grus
II, while the other 4 are very likely contamination by the Chenab/Orphan
stream.

###  4.3 UFDs with no RRL

We did not find any RRL in $24$ UFDs of our sample. These galaxies are listed
in Table 3 and they are separated in two groups: those galaxies that truly do
not seem to have RRL, and those in which we do not find any but could
nevertheless have some RRL that are outside the limits of the surveys used in
this work.

Table 3: UFDs of our sample with no RRL according to our selecion criteria,
sorted by their distance.

Galaxy | Distance | Expected $m_{G}$
---|---|---
| [kpc] | [mag]
UFDs with no RRL
Draco II | 21.5 | 17.13
Carina III | 27.8 | 17.69
Triangulum II | 28.4 | 17.74
Cetus II | 30.0 | 17.86
Reticulum II | 30.0 | 17.86
Willman I | 38.0 | 18.37
Tucana V | 55.0 | 19.17
Eridanus IV | 76.7 | 19.89
Horologium II | 78.0 | 19.93
Horologium I | 79.0 | 19.96
Virgo I | 87.0 | 20.17
Eridanus III | 87.0 | 20.17
Reticulum III | 92.0 | 20.29
Aquarius II | 107.9 | 20.64
UFDs outside of our detection range
Centaurus I∗ | 116.3 | 20.80
Hercules∗ | 133.0 | 21.09
Hydra II∗ | 151.0 | 21.37
Leo IV∗ | 154.0 | 21.41
Canes Venatici II∗ | 159.0 | 21.48
Leo V∗ | 173.0 | 21.66
Pegasus III∗ | 174.0 | 21.67
Pisces II∗ | 175.0 | 21.69
Columba I | 183.0 | 21.78
Leo T∗ | 409.0 | 23.53

Note. — The third column shows the expected magnitude that the RRL would have
if they were located at distances similar to the UFDs. UFDs with known
population of RRL that we did not recover are marked with an asterisk ($*$):
Centaurus I (Martínez-Vázquez et al., 2021a), Hercules (Garling et al., 2018),
Hydra II (Vivas et al., 2016), Leo IV (Moretti et al., 2009), Leo V (Medina et
al., 2018), Canes Venatici II (Greco et al., 2008), Pegasus III $\&$ Pisces II
(Garofalo et al., 2021), and Leo T (Clementini et al., 2012).

The third column in Table 3 shows the expected magnitude that the RRL would
have if they were located at distances similar to that of the UFD. On one
hand, for those UFDs which have expected magnitudes brighter than $G\sim 21$
mag, Gaia DR3 should have been able to detect them if there were any. Thus, we
can confirm that in these cases the UFDs do not have indeed any RRL. In
agreement with the analysis done by Vivas et al. (2020), we do not find any
RRL in Draco II, Carina III, Triangulum II, Cetus II, Willman I, Tucana V,
Horologium II, Horologium I and Virgo I. Neither Eridanus IV nor Aquarius II
were part of the sample studied by Vivas et al. (2020). Regarding Eridanus III
and Reticulum III, although Vivas et al. (2020) found one RRL in each galaxy
using Gaia DR2, we do not find any in this work. The two stars from Vivas et
al. (2020) do not even exist in the RRL catalog provided by Gaia DR3, which
means that they were likely misclassified in the previous data release.

On the other hand, for those galaxies with expected magnitudes for their RRL
fainter than $G\sim 21$ mag, Gaia is just not able to detect them because they
are too faint. Although DES reaches fainter magnitudes than Gaia, its sky
coverage is limited and only a few UFDs fall within its footprint. The only
one of these distant UFDs that is located within DES footprint is Columba I,
but the expected magnitude for its RRL is very faint ($\sim 21.78$ mag). The
DES RRL survey’s completeness strongly declines at these faint magnitudes
(Stringer et al., 2021), which may be the reason why we do not find any RRL in
this galaxy. All of the other UFDs (Centaurus I, Hercules, Canes Venatici II,
Leo V, Leo IV, Pegasus III, Pisces II and Leo T) are not detected by DES due
to their positions in the sky. However, except Columba I, all of these distant
galaxies have had dedicated searches for variable stars (see Table 3 for
references). A dedicated search for variable stars in Columba I is
recommended. In the case of Centaurus I, the expected magnitude of the RRL is
$\sim 20.80$ mag, within the Gaia’s limits but approaching its limiting
magnitude. Centaurus I is known to have RRL: Martínez-Vázquez et al. (2021a)
report three of them based on their own multi-epoch giz DECam observations of
this UFD. We found none neither in Gaia nor in the other surveys. The
completeness of Gaia decreases as it approached its faint limit and that is
probably the reason why these stars were not detected in this work.

The distant UFDs with known RRL population have had dedicated searches of
variable stars but the coverage is not necessarily large enough to asses the
existence of extended populations. An exception is Hercules. The galaxy has
been reported to have $12$ RRL by Musella et al. (2012) and Garling et al.
(2018), where the latter work showed that Hercules has indeed RRL outside its
tidal radius. We compiled the RRL from these distant galaxies, as well as a
few RRL in nearby galaxies that we did not recover (in Tucana III ($5$ RRL,
Vivas et al., 2020), Sagittarius II ($1$ RRL, Joo et al., 2019), Grus I ($1$
RRL, Martínez-Vázquez et al., 2019) and Eridanus II (62 RRL, Martínez-Vázquez
et al., 2021b)) in a separate list labeled extra RRL. These stars ($96$ RRL in
$13$ galaxies) were included in our analysis of the spatial distribution of
RRL in UFDs discussed in the next section.

###  4.4 Spatial Distribution of the RRL

Of the examples shown in Fig. 3, we note that all of the four galaxies have
RRL located at distances greater than $4\,R_{h}$. In this section we analize
how frequent is to have such extended populations in UFDs. We arbitrarily
adopted $4\,R_{h}$ as the distance to consider if a UFD has an extended
population or not. Our motivation to choose this specific value is driven by
the fact that almost all of the light of the galaxies is expected to be
contained inside a $4\,R_{h}$ radius, so the stellar material found outside of
$4\,R_{h}$ can be considered as stellar halo, or stellar debris. For
comparison, Waller et al. (2023) analizes the outskirts of $3$ UFDs and they
choose distances larger than $\sim 2\,R_{h}$ from the center of their host
galaxies as evidence of extended populations. Here we are more conservative
and push faraway the distance to be considered external population.

In order to understand how common it is to find RRL stars at large angular
separations from the host galaxy, we calculated their elliptical separations,
defined as half the geometrical constant of the ellipse defining the
morphology of the UFD at the location of each individual RRL (Eq. 5):

$S_{\rm ell}=\\{[x\cdot\cos(90\arcdeg-{\rm PA})+y\cdot\sin(90\arcdeg-{\rm
PA})]^{2}+\\\ [-x\cdot\sin(90\arcdeg-{\rm PA})+y\cdot\cos(90\arcdeg-{\rm
PA})/(1-\epsilon)]^{2}\\}^{\frac{1}{2}}$ (5)

where (x,y) are the planar coordinates of the RRL, centered in their
respective UFDs, and $\epsilon$ and PA are the galaxy’s ellipticity and
position angle respectively. The latter values were taken from Table 1. Each
elliptical separation was normalized by the $R_{h}$ of each galaxy. These
normalized values for each RRL are listed in Table 2 (column $15$).

In the left panel of Fig. 9 we show the distribution of the normalized
elliptical separations for all RRL associated with a UFD, including the ones
in the extra RRL list described in the previous section, leaving us with a
total of $216$ RRL. The histogram shows that RRL have elliptical separations
from the center of their host galaxies ranging from $0$ to almost $60\,R_{h}$.
Although our angular distance main criteria (Section 3.1) was to select stars
only within a circle of $15\;R_{h}$, for very small galaxies we allowed a
search area of $1\arcdeg$, which for tiny galaxies such as DELVE 2 means
several tens of $R_{h}$, and that is the reason for finding some very distant
RRL stars in our sample. As we discussed in Sec. 4.2, Bootes I, Bootes III,
Tucana IV, DELVE 2, and Grus II are special cases because there are concerns
that contamination may be affecting the sample of RRL we identified as
members. We excluded the RRL in those galaxies to build a “clean” sample. In
Grus II, we actually know which stars are the contaminants (from the
Chenab/Orphan stream in that case) since the magnitude distribution is
bimodal; thus, we excluded only the 4 brighter RRL originally associated with
this galaxy. In consequence, our clean sample is made of $142$ RRL. A
histogram of the distribution of the normalized $S_{ell}$ of the clean sample
is also shown in Fig. 9. It is clear that although many of the RRL far away
from the center of their UFDs likely come from the galaxies affected by
contamination, we still find several distant RRL in the clean sample of UFDs.

A zoom of the same histogram, including only $S_{ell}<15R_{h}$, is shown in
the right panel of Fig. 9. The histograms show that the majority of the RRL
are located in the central regions of their galaxies, but the number of RRL
located in the outer regions is not negligible. Out of the total of $216$ RRL,
there are $127$ RRL ($\sim 59\%$) inside $2\,R_{h}$ and $156$ RRL ($\sim
72\%$) inside $4\,R_{h}$. On the other hand, there are as many as $60$ RRL
($\sim 28\%$) that are located far away from their host galaxies ($S_{ell}\geq
4\,R_{h}$), $17$ of those belonging to galaxies of the clean sample ($8\%$ of
the clean sample), i.e. galaxies where contamination by other stellar systems
is not suspected.

Figure 9: Left panel: distribution of the elliptical separation of RRL from
their respective host galaxies, using their $R_{h}$ as a normalization. In
blue we show the distribution of the normalized elliptical separation of all
the RRL (those found in this work plus those added as extra RRL as mentioned
in Sec. 4.3), and in orange, we highlight the distribution of the RRL that
belong to our clean sample of UFDs plus the extra galaxies mentioned in Sec.
4.3. . Right panel: zoom of the left panel in the range $S_{ell}<15\arcmin$.

In Fig. 10 we show the cumulative number of UFDs with all of their RRL
enclosed within certain $S_{ell}$. We find that $16$ out of the $30$ UFDs with
RRL ($\sim 53\%$) have all of their RRL within $4\,R_{h}$. On the other hand,
there are $14$ UFDs ($\sim 47\%$) that have at least one RRL located at a
distance $\geq 4\,R_{h}$, and $10$ UFDs ($\sim 33\%$) that have at least one
located at a distance farther than $10\,R_{h}$. If we use only the clean
sample, then there are 10 UFDs ($\sim 33\%$) that have at least one RRL
located at a distance $\geq 4\,R_{h}$, and $6$ UFDs ($\sim 20\%$) that have at
least one RRL located at a distance farther than $10\,R_{h}$. The galaxies in
the clean sample with RRL at $S_{ell}\geq 4\,R_{h}$ are Tucana II, Tucana III,
Grus II, Sagittarius II, Pegasus IV, Hercules, Ursa Major I, Centaurus I, Leo
IV, and Eridanus II. We notice also that Pegasus III, Ursa Major II, Coma
Berenices and Hydrus I have at least one RRL outside $S_{ell}>3.5\,R_{h}$.
These numbers suggest that the existence of extended stellar populations is
not uncommon in UFDs.

Figure 10: Cumulative number of galaxies that have all of their RRL enclosed
within certain times their respective $R_{h}$.

##  5 Discussion and Conclusions

We analyzed a sample of $45$ ultra-faint dwarf galaxies of the Local Group
(see Table 1). We used data from the Gaia DR3, DES, ZTF and PS1 surveys to
search for RRL in these galaxies. Our main goal was to characterize the
spatial distribution of RRL within each galaxy and to study how frequent it is
to have extended stellar populations in UFDs. We found a total amount of $120$
RRL belonging to $21$ different UFDs (Table 2).

Some of these stars are reported for the first time. For Hydrus I we report
one new RRL, bringing the total of known RRL to $5$ after adding those
previously reported by Koposov et al. (2018) and Vivas et al. (2020). For Ursa
Major II, besides the $4$ previously known RRL (Dall’Ora et al., 2012; Vivas
et al., 2020), we report $2$ new RRL. For Grus II we report one new RRL that
adds to the one previously reported by Martínez-Vázquez et al. (2019). For
Tucana II there were $3$ RRL previously known (Vivas et al., 2020) and we
report one new RRL. For Ursa Major I, in addition to the $7$ RRL reported in
Garofalo et al. (2013), we found one new RRL that is located outside the field
of view studied by those authors. For Eridanus II, besides the $67$ RRL
previously found by Martínez-Vázquez et al. (2021b), we report one new RRL
with a location that is outside the region studied in that work. In regard to
Bootes I and Bootes III, we report various new RRL in both galaxies but we
recognize that these UFDs (in particular Bootes I) are affected by
contamination from the Sgr stream. More studies involving the stars’
metallicities and radial velocities are needed to determine the association of
these RRL with either the galaxies or the stream. In the case of Segue I, the
RRL found in this work is the same one reported by Simon et al. (2011), but
here we confirm for the first time its period using PS1 data. On the other
hand, in this work we withdraw the previous claim that Eridanus III and
Reticulum III had one RRL each (Vivas et al., 2020). In both cases, neither
one of the RRL was found in Gaia DR3’s RRL catalog (Clementini et al., 2022),
suspecting a misclassification in the previous DR2.

Figure 11: Eccentricity and pericenter distance of the orbits of UFD galaxies
calculated by Li et al. (2021) with Gaia EDR3 proper motions and assuming a
Milky Way potential that follows an Einasto profile with high mass (their
model PEHM). Red symbols indicate UFD galaxies with extended populations as
identified in this work. Neither Pegasus IV nor Centaurus I are included in
this plot since they were not available at the time of Li et al. (2021) orbit
calculations.

Using Eq. 5 we computed the elliptical separation between these selected RRL
and their respective host galaxies, and normalized them by their respective
$R_{h}$. We found that $14$ UFDs have RRL located at distances from their
center that are $\geq 4\,R_{h}$, and we are certain that $10$ of them do not
have contamination problems. Therefore, we conclude that UFDs can have
extended populations. These $14$ UFDs with RRL in their outskirts are located
at heliocentric distances ranging from $\sim 23$ kpc to $370$ kpc and have
absolute magnitudes ranging from $-1.3$ to $-7.1$, so there does not seem to
be a preference neither in these galaxies’ distance distribution from the
Milky Way nor in their absolute magnitude values. In Fig. 11 we show the
distribution of the pericenter distance, $r_{\rm peri}$ and eccentricity of
the orbits of the Milky Way UFD satellites as calculated by Li et al. (2021).
The orbits of UFDs with extended populations (red symbols) do not have
particularly close approaches to the Milky Way, except for Tucana III, nor
they have particularly eccentric orbits. Galaxies with small pericenter
passages are strong candidates to suffer tidal disruptions that can be
responsible for the presence of extended populations. However, there is a wide
range of pericenter distances in the UFDs that we flagged as having extended
populations, suggesting that other mechanisms besides interaction with the
Milky Way may play a role in the formation of extended stellar populations
around UFDs.

It is important to stress that the number of $10$ UFDs with external
populations is a lower limit. Not only we have at least $2$ more UFDs (Bootes
I and Bootes III) with candidates in the outskirts that need more follow-up in
order to discard contamination by the Sgr stream, but also some of the most
distant UFD galaxies (the ones outside Gaia’s faint limit) may not have wide
coverage for variable stars. Four additional UFDs would have extended
populations if our arbitrary definition is lowered to $S_{ell}\geq 3.5R_{h}$.
It is also important to highlight that RRL are scarce in UFDs, with many of
them hosting just a few (or none) of those variables (Martínez-Vázquez et al.,
2019; Vivas et al., 2020). Thus, there may be cases in which the number of RRL
in a UFD is just not enough to trace the population.

Recently, Waller et al. (2023) studied Ursa Major I, Bootes I and Coma
Berenices with the aim to identify potential members in the outskirts of these
three UFDs using Gaia EDR3 data and the Gemini GRACES spectrograph. Comparing
their work with our results for these same UFDs of our sample, we find them to
be in good agreement. The authors report one star at $3.7\,R_{h}$ in the case
of Ursa Major I, one star at $4\,R_{h}$ in Bootes I and two stars at
$2.5\,R_{h}$ for Coma Berenices, concluding that these galaxies have stars
located in their outskirts. In this work we also identify stars in the outer
regions of Ursa Major I and Bootes I. In the case of Ursa Major I, we found
$1$ RRL in its outskirts according to our criterion (at $8.40\,R_{h}$), but we
do also find one RRL at a distance similar to the one reported for the star
studied in Waller et al. (2023), located at $3.01\,R_{h}$. Regarding Bootes I,
we found $12$ RRL that are possibly in its outer region (raging between at
$4.0-17.8\,R_{h}$), but we bear in mind that this galaxy’s RRL sample is
probably contaminated by some stars that belong to the Sgr stream. Jensen et
al. (2023) also identify $34$ stars that could be part of the outskirts of
Bootes I using their own numerical algorithm (one of them being located at
$9\,R_{h}$), but mention that a spectroscopic analysis would be useful to
better understand this result. As for Coma Berenices, although we do not find
RRL located at distances greater than $4\,R_{h}$, we found one RRL at
$3.98\,R_{h}$ which is even farther away than those identified by Waller et
al. (2023). We also found agreement with previous studies of Tucana II in
which stars up to $9\,R_{h}$ were identified in the external parts of the
galaxy by Chiti et al. (2021). Here we also found 2 distant RRL in Tucana II,
at 5 and 12 $R_{h}$. A more detailed analysis of the RRL found in the
outskirts of the UFDs could be made by studying their abundances, and radial
velocities (e.g. Chiti et al., 2021). These additional data would further
corroborate their association with the UFDs and could help understand if they
were formed in their central regions and then stripped away into farther
distances or if an outside-in star formation scenario explains their current
locations.

These extended stellar populations can also be found in dSphs, such as Fornax
(Stringer et al., 2021; Qi et al., 2022), Carina (Vivas & Mateo, 2013; Qi et
al., 2022) and Ursa Minor (Sestito et al., 2023b; Jensen et al., 2023), so it
is not a an exclusive feature of the UFDs.

Numerical simulations also provide information on the extended population of
dwarf and UFD galaxies. The resolution of cosmological hydrodynamical
simulations has been improving in the past years and this leads galaxy models
towards being more fiducial at low-mass ranges. This type of analysis will
allow us to study the evolution of the modelled galaxies by tracing them
through different redshifts, which could help enlighten the mechanism
responsible for driving the stars of these UFDs to such large distances from
the center of their hosts.

This era of big surveys has facilitated the search for wider regions in the
sky and has allowed us to extend to larger distances. The upcoming large scale
surveys, such as the Vera Rubin Observatory and the Nancy Grace Roman Space
Telescope, will reach farther regions when observing dwarf galaxies in the
Local Group and will be able to get better and more accurate information
regarding their true extent.

We thank the anonymous referee for useful comments and suggestions to this
work. EAT acknowledges financial support from ANID “Beca de Doctorado
Nacional” 21220806. C.E.M.-V. 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. 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.

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