# Stellar Metallicities from DECam $u$-band Photometry: A Study of Milky Way
Ultra-Faint Dwarf Galaxies

Yue Pan  Department of Astronomy & Astrophysics, University of Chicago, 5640 S
Ellis Avenue, Chicago, IL 60637, USA  Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA  Anirudh Chiti  Department of
Astronomy & Astrophysics, University of Chicago, 5640 S Ellis Avenue, Chicago,
IL 60637, USA  Kavli Institute for Cosmological Physics, University of
Chicago, Chicago, IL 60637, USA  Alex Drlica-Wagner  Department of Astronomy &
Astrophysics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637,
USA  Kavli Institute for Cosmological Physics, University of Chicago, Chicago,
IL 60637, USA  Fermi National Accelerator Laboratory, P.O. Box 500, Batavia,
IL 60510, USA  Alexander P. Ji  Department of Astronomy & Astrophysics,
University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637, USA  Kavli
Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637,
USA  Ting S. Li  David A. Dunlap Department of Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON, M5S3H4 Canada
Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St
George Street, Toronto, ON M5S 3H4, Canada  Guilherme Limberg  Department of
Astronomy & Astrophysics, University of Chicago, 5640 S Ellis Avenue, Chicago,
IL 60637, USA  Kavli Institute for Cosmological Physics, University of
Chicago, Chicago, IL 60637, USA  Universidade de São Paulo, IAG, Departamento
de Astronomia, SP 05508-090, São Paulo, Brazil  Douglas L. Tucker  Fermi
National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, USA  Sahar
Allam  Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510,
USA

###### Abstract

We conducted an in-depth analysis of candidate member stars located in the
peripheries of three ultra-faint dwarf (UFD) galaxy satellites of the Milky
Way: Boötes I (Boo1), Boötes II (Boo2), and Segue I (Seg1). Studying these
peripheral stars has previously been difficult due to contamination from the
Milky Way foreground. We used $u$-band photometry from the Dark Energy Camera
(DECam) to derive metallicities to efficiently select UFD candidate member
stars. This approach was validated on Boo1, where we identified both
previously known and new candidate member stars beyond five half-light radii.
We then applied a similar procedure to Boo2 and Seg1. Our findings hinted at
evidence for tidal features in Boo1 and Seg1, with Boo1 having an elongation
consistent with its proper motion and Seg1 showing some distant candidate
stars, a few of which are along its elongation and proper motion. We find two
Boo2 stars at large distances consistent with being candidate member stars.
Using a foreground contamination rate derived from the _Besançon_ Galaxy
model, we ascribed purity estimates to each candidate member star. We
recommend further spectroscopic studies on the newly identified high-purity
members. Our technique offers promise for future endeavors to detect candidate
member stars at large radii in other systems, leveraging metallicity-sensitive
filters with the Legacy Survey of Space and Time and the new, narrow-band Ca
HK filter on DECam.

##  1 Introduction

Over the last two decades, large digital sky surveys such as the Sloan Digital
Sky Survey (SDSS), the Dark Energy Survey (DES), and PanSTARRS have allowed
astronomers to identify many more low surface brightness stellar systems
surrounding the Milky Way (e.g. Simon, 2019). Among these faint stellar
systems, ultra-faint dwarf galaxies (UFDs), which were first detected in SDSS
data two decades ago (Willman et al., 2005a, b), have generated particular
interest due to their extremely faint luminosities ($L<10^{5}L_{\odot}$),
chemically primitive compositions ($[\rm{Fe}/\rm{H}]\lesssim-2.0$), large dark
matter contents ($\gtrsim 100\ M_{\odot}/L_{\odot}$; Simon & Geha, 2007), and
old ages ($\sim$ 13 Gyr; e.g. Brown et al., 2014; Simon, 2019).

As per the hierarchical structure formation theory of galaxies, smaller
galaxies are formed before larger ones (White & Frenk, 1991; Cole et al.,
2000). Therefore, UFDs are presumably the building blocks of more massive
galaxies, and particularly interesting probes of the early chemical evolution
of the universe since they are thought to have undergone only a few cycles of
chemical enrichment (Frebel et al., 2014). The number and distribution of UFDs
can constrain dark-matter models (e.g. Kim et al., 2018; Nadler et al., 2021;
Mau et al., 2022). Moreover, the resolved kinematics of their member stars
link to a number of questions related to dark matter and can be used to put
constraints on the dark-matter annihilation cross-sections and the dark-matter
distribution on small scales (Calore et al., 2018; Abdallah et al., 2020;
Malhan et al., 2022).

More than 50 UFDs have been discovered around the Milky Way (MW). While their
relative proximity ($<200$ kpc) makes them suitable for in-depth
investigations, it is still extremely hard to study their resolved stellar
populations due to their faint nature. Traditionally, member stars of MW UFDs
are identified by low- and medium-resolution spectroscopy, through the
clustered radial velocities and low metallicities of UFD members.
Subsequently, one can derive the dynamical mass from the velocity dispersion
of member stars (Walker et al., 2009; Wolf et al., 2010) and use the estimated
mass-to-light ratio to distinguish UFDs from globular clusters (GCs; Willman &
Strader, 2012). One can also distinguish UFDs from GCs through metallicity
measurements since UFDs show significant metallicity spreads (e.g. Frebel et
al., 2014), whereas GCs show minimal spreads ($\lesssim 0.05$ dex; e.g.
Carretta et al., 2009).

However, spectroscopy of UFDs is primarily devoted to their central regions
($\lesssim 2$ half-light radii), since member stars in the outskirts are
sparsely distributed (Muñoz et al., 2018) and dominated by MW foreground
stars. Simulations suggest that UFDs are formed within extended dark-matter
halos and may be shaped by early galaxy mergers and supernova feedback (Deason
et al., 2014; Munshi et al., 2019; Wheeler et al., 2019). Signatures of these
effects would primarily reside in the outer regions of UFDs. Thus, a more
efficient method to identify member stars in the outer regions of dwarf
galaxies is needed to understand early dwarf galaxy evolution and probe the
nature of their small-scale dark-matter halos.

It is possible to greatly improve the efficiency of spectroscopy by
determining metallicities and identifying candidate member stars through
photometry. Early research by Anthony-Twarog et al. (1991) demonstrated the
efficacy of using photometry to detect metal-poor stars. More recently, Pace &
Li (2019) showed that the use of metallicity-sensitive broadband colors from
DES can enhance the efficiency of identifying member stars of UFDs, and recent
studies have been successful in generalizing this technique with intermediate
and narrow-band filters to identify UFD stars (Chiti et al., 2020, 2021;
Longeard et al., 2021, 2022, 2023; Fu et al., 2023). Current iterations of
photometric metallicity work typically determine the metallicity by
establishing a relation between a star’s metallicity and its brightness in a
narrowband imaging filter that encompasses a prominent metal absorption
feature (e.g., Ca ii K line; Keller et al., 2007; Starkenburg et al., 2017).
This technique offers the advantage of determining metallicities for all stars
within the camera’s field-of-view (FOV), unlike spectroscopy, which has to be
more targeted and is constrained by factors like slit arrangements and the
number of fibers.

In this paper, we combine targeted $u$-band observations from the Dark Energy
Camera (DECam) with additional broad-band photometry from DECam Local Volume
Exploration Survey (DELVE) Data Release 2 (DR2, Drlica-Wagner et al., 2022)
and astrometry from the _Gaia_ DR3 catalog (Gaia Collaboration et al., 2016,
2022) to identify candidate member stars of three MW UFDs: Boötes I (Boo1),
Boötes II (Boo2), and Segue I (Seg1). The DECam $u$-band covers the prominent
Ca ii K metal absorption line, and thus can be used to derive photometric
metallicities. Since Boo1 is the most widely studied MW UFD in our sample, we
start by identifying candidate member stars of Boo1 and comparing our
photometric catalog to existing spectroscopic catalogs. We then statistically
evaluate the purity and completeness of our sample and generalize our method
to the other two systems to identify new candidate member stars out to large
radii. We demonstrate the power of DECam $u$-band photometry to identify low-
metallicity stars, we identify low-metallicity stars in the outskirts of each
UFD, and we publicly release our selected low-metallicity UFD candidate member
stars to facilitate spectroscopic follow-up work.

This paper is organized as follows. Section 2 outlines our DECam $u$-band
observations, data reduction, and zero-point calibration. Section 3 presents
our candidate member star selection process, which combines an isochrone
selection, a proper motion selection, and a photometric metallicity selection.
Section 4 presents our investigation of stars in the outskirts of Boo1, Boo2,
and Seg1, along with a discussion of the completeness and purity of the
sample. Finally, Section 5 discusses the relation of the candidate member star
spatial distribution to the evolution nature of UFDs, and Section 6 summarizes
our main findings.

##  2 Observations and data reduction

In this section, we discuss our observations and the process of producing
source catalogs used in our subsequent analysis. We present the DECam $u$-band
observations in Section 2.1, the data reduction and generation of source
catalogs from individual $u$-band exposures in Section 2.2, and the procedure
for calibrating $u$-band zero-points and generating a combined source catalog
in Section 2.3. Our final, combined $u$-band catalog is then cross-matched
with DELVE DR2 (Drlica-Wagner et al., 2022) for broadband $g,i$ photometry
that is used in subsequent analyses.

Table 1:  Observations of Boo1, Boo2, and Seg1 Name | RA | DEC | UT Observation Dates | Instrument | Filter | Seeing | Exposure time
---|---|---|---|---|---|---|---
| h:m:s | d:m:s |  |  |  |  | s
Boo1 | 14:00:06.0 | +14:30:00 | 12 Mar 2021 | DECam | $u$ | 1$\farcs$0 |  $20\times 300$ s
Boo2 | 13:58:00.0 | +12:51:00 | 10 Jun 2021 | DECam | $u$ | 1$\farcs$0 |  $20\times 300$ s
Seg1 | 10:07:04.0 | +16:04:55 | 10 Jun 2021 | DECam | $u$ | 1$\farcs$0 |  $20\times 300$ s
Table 2:  Properties of Boo1, Boo2, and Seg1

Name | $r_{h}(^{\prime})$ |  $\mu_{\alpha}\cos\delta$ (mas yr-1) |  $\mu_{\delta}$ (mas yr-1) | $(m-M)_{o}$ | $\theta(^{\circ})$ | $\epsilon$ | References1
---|---|---|---|---|---|---|---
Boo1 | $9.97\pm 0.27$ | $-0.39\pm 0.01$ | $-1.06\pm 0.01$ | 19.11 | $6.0\pm 3.0$ | $0.30\pm 0.03$ | a, b, b, c, a, a
Boo2 | $3.17\pm 0.42$ | $-2.33^{+0.09}_{-0.08}$ | $-0.41\pm 0.06$ | 18.10 | $-68.0\pm 27.0$ | $0.25\pm 0.11$ | a, b, b, d, a, a
Seg1 | $3.62\pm 0.42$ | $-2.21\pm 0.06$ | $-3.34\pm 0.05$ | 16.80 | $77.0\pm 15.0$ | $0.33\pm 0.10$ | a, b, b, e, a, a

11footnotetext: References: a. Muñoz et al. (2018); b. McConnachie & Venn
(2020); c. Dall’Ora et al. (2006); d. Walsh et al. (2008); e. Belokurov et al.
(2007)

###  2.1 Observations

We obtained $u$-band photometry of Boo1, Boo2, and Seg1 using DECam (Flaugher
et al., 2015) on the 4 m Blanco Telescope located at Cerro Tololo Inter-
American Observatory (CTIO) in Chile (PI: Ji, PropID: 2021A-0272). The DECam
hosts 62 $2048\times 4096$ pixel science CCDs that have a pixel scale of
$\sim$0$\farcs$26/pixel. This grants DECam a large field-of-view ($\sim$3 sq.
degrees, $\sim$2.2 degrees across), making it ideally suited for wide-field
photometric studies. We observed each of the aforementioned dwarf galaxies
using sequences of 300 s exposures dithered by 30$\farcs$ to cover chip gaps.
Total exposure times were calculated to target 0.03 mag precision at $u=23$.
Conditions were clear and the seeing was stable at $\sim$1$\farcs$0 throughout
observations. Table 1 displays the full details of our observations.

###  2.2 DECam $u$-band data reduction & photometry

The DECam data were processed with the DES Data Management Final Cut pipeline
(Morganson et al., 2018). This pipeline includes includes bias subtraction,
non-linearity corrections, bad pixel masking, gain correction, brighter-fatter
correction, and flat fielding. Bias corrections and flat-fielding made use of
“super-cal” assembled by combining flats and biases taken over several nights
developed for $u$-band data processing for the DES Deep Fields (Hartley et
al., 2022). In addition, the DES Final Cut pipeline includes identification
and masking of cosmic rays, bleed trails from saturated stars, and trails from
artificial satellites was performed. Sky background estimation is performed
through principal component analysis decomposition over the entire focal plane
following Bernstein et al. (2017), and then adjusted CCD-by-CCD during source
extraction and measurement.

Astronomical source detection and measurement were performed on a per CCD
basis using the PSFEx and SourceExtractor routines (Bertin & Arnouts, 1996;
Bertin, 2011). As part of this step, astrometric calibration was performed
with SCAMP (Bertin, 2006) by matching objects to the Gaia DR2 catalog (Gaia
Collaboration et al., 2018). The SourceExtractor source detection threshold
was set to detect sources with S/N $>5$. Photometric fluxes and magnitudes
refer to the SourceExtractor Point Spread Function (PSF) model fit.

###  2.3 DECam $u$-band zero-point calibration

We calibrate the photometric zero-points for the DECam $u$-band source
catalogs generated in Section 2.2 by comparing instrumental DECam $u$-band
magnitudes with predicted DECam $u$-band magnitudes derived from $u$-, $g$-,
$r$\- band photometry from the SDSS DR16 catalog (Ahumada et al., 2020).
Specifically, DECam $u$-band magnitudes can be related to SDSS $u$-, $g$-,
$r$-band magnitudes using the following equation (Allam, Tucker, et al., in
prep.) :

$u_{\rm{DECam}}=u_{\rm{SDSS}}-0.479+0.466\cdot(g-r)_{\rm{SDSS}}-0.35\cdot(g-r)_{\rm{SDSS}}^{2}$
(1)

for objects with $0.2\leq(g-r)_{\rm{sdss}}\leq 1.2$. This process is similar
to the SDSS $g$-, $r$-, $i$-, $z$-band magnitude conversion to DES magnitudes
in Appendix B.1 of Abbott et al. (2021), but with a second order term. The
zero-point can then be estimated to be the median difference between the DECam
$u$-band magnitudes in our catalogs and the DECam $u$-band predicted from SDSS
photometry.

To obtain the SDSS $u$-, $g$-, $r$-band magnitudes for sources in our
catalogs, we crossmatch our catalogs from Section 2.2 with the SDSS DR16
catalog (Ahumada et al., 2020) using R.A. and Decl. with a radius of
1$\farcs$. To ensure a clean estimate of the zero-point, we (1) retain objects
that have a $u$-band magnitude error of less than 0.1 mag in both our catalog
and the SDSS DR16 catalog, (2) retain objects with no photometric flags in
either catalog (FLAGS = 0, FLAGS_WEIGHT = 0, and IMAFLAGS_ISO = 0), and (3)
exclude galaxies with
$|\texttt{SPREAD\\_MODEL}|<0.003+\texttt{SPREADERR\\_MODEL}$, (Koposov et al.,
2015; Slater et al., 2020). After this selection, we calculate a first-pass
$u$-band zero-point offset for each individual chip in each exposure by taking
the median offset between the $u$-band magnitudes in Section 2.2 and those
predicted by SDSS photometry. We then clip all sources that are $>3$ $\sigma$
outliers relative to this zero-point and re-calculate as before to obtain
zero-points for each chip and exposure. The median (${\rm{ZP}_{i}}$) and
standard deviation (${\rm{ZP}}_{\rm{err,i}}$) of zero-points after sigma
clipping are the zero-point value and error for each exposure. The typical
number of stars on each chip used for the zero-point estimate is $\sim 30-40$.
Figure 1 shows the distribution of inferred zero-points from individual stars
over all chips for one 300s exposure. There are some variations across
different chips for a given exposure time due to different responses, and
across exposures due to e.g., weather condition.

For each source in our catalog, we take the weighted average of its zero-point
corrected magnitude across 20 exposures to obtain a final $u$-band magnitude.
Note that this is just a weighted average of the measured magnitudes for each
star instead photometering a coadded image. To start with, for each exposure,
we concatenate the catalog of all sources in each chip. We then crossmatch
between the 20 exposures to generate a final catalog. We note that not every
star may be detected in each exposure, due to varying weather conditions at
the time of each exposure, pixel artifacts, or statistical fluctuations for
sources near the detection threshold.

We calculate the calibrated DECam $u$-band magnitude based on the zero-point
correction in each exposure ($\tt{MAG\\_PSF}$+${\rm{ZP}_{i}}$) for each
selected star in all 20 exposures. Typical values of $\rm{ZP}_{i}$ varies
between $\sim$5.1 and $\sim$5.3 depending on the weather condition. The random
uncertainty associated with this calibrated magnitude is computed as the
quadratic sum of the uncertainties from the DECam $u$-band measurement
($\tt{MAG\\_PSF\\_ERR}$) and the zero-point calculation
(${\rm{ZP}}_{\rm{err,i}}$) for each exposure. In the bright limit $g<18.5$,
the stars’ $u$-band magnitude error will be dominated by the zero-point
calibration precision. We find the standard deviation of $u$-band magnitudes
in this regime to be $\sim 0.035$ mags across the 20 exposures. We take this
to be our zero-point calibration uncertainty, and we add this value in
quadrature to our random $u$-band magnitude uncertainty to derive a total
photometric uncertainty, which will be propagated when computing photometric
metallicity uncertainties.

We compute the mean of the calibrated magnitudes for all selected objects
across all exposures using the inverse-variance weighting method (Strutz,
2010):

$\mu=\frac{\sum_{i=1}^{20}x_{i}/\sigma_{i}^{2}}{\sum_{i=1}^{20}1/\sigma_{i}^{2}}$
(2)

where $x_{i}$ and $\sigma_{i}$ are the calibrated DECam $u$-band magnitude
($\tt{MAG\\_PSF}$+${\rm{ZP}_{i}}$) and the quadratic sum of
$\tt{MAG\\_PSF\\_ERR}$ and ${\rm{ZP}}_{\rm{err,i}}$, respectively, for each
exposure. The variance among all weighted average is then computed as in
Strutz (2010):

$\sigma^{2}(\mu)=\frac{1}{\sum_{i=1}^{20}1/\sigma_{i}^{2}}$ (3)

Figure 1: Zero-point distribution inferred from individual stars in the Boo1
FOV across all 60 chips in a single exposure. The zero-point is defined as the
theoretical DECam $u$-band magnitude from SDSS DR16 catalog minus the observed
DECam $u$-band magnitude. Each histogram represents the zero-point
distribution for all stars on one chip at a single exposure. The distribution
is fairly narrow for most chips, but for some chips there are individual stars
with large deviations which are sigma-clipped before computing the zeropoint.
Figure 2: An illustration of why the DECam $u$-band is sensitive to
metallicity. _Left:_ a synthetic spectrum generated by Turbospectrum (Alvarez
& Plez, 1998; Plez, 2012) for a sample cool red giant star with metallicity
[Fe/H] = $-1$ overlaid with the bandpass of the DECam $u$ filter. _Right:_ the
synthetic spectrum for a sample star with the same surface gravity and surface
temperature but with metallicity [Fe/H] = $-3$. The Ca ii K metal absorption
lines are more prominent for more metal-rich stars (left), and the DECam
$u$-band filter completely covers this feature. Therefore, the more metal-rich
a star is, the dimmer it appears in the DECam $u$-band. This correlation
provides a way to associate the DECam $u$-band magnitude of a star with its
metallicity, as shown in Figure 4. Figure 3: _Top_ : Isochrone and proper
motion selection of candidate member stars. Top left: The CMD of all stars in
our catalog for Boo1 (light blue) and selected stars (dark blue) using the
isochrone cuts illustrated in Section 3. The isochrone of metallicity [Fe/H] =
$-2.49$ and age = 13 Gyr is shown as purple. Top middle: Proper motion of Boo1
candidate member stars selected using proper motion and isochrone cuts. Top
right: Stars that pass the isochrone cut but not the proper motion cut. The
proper motion of Boo1 is shown as a triangle. _Bottom_ : spatial distribution
of all stars in our original catalog (left), stars that pass the isochrone cut
(middle), and stars that pass the isochrone and proper motion cut (right)
centered at the position of Boo1.

##  3 Selecting candidate member stars using photometric metallicity

After obtaining the calibrated DECam $u$-band magnitudes for all objects in
our catalog, we apply several selection criteria to identify a reasonably pure
sample of potential UFD member stars. First, we apply parallax_over_error$<3$
to weed out sources with resolved parallax values (i.e., nearby foreground
stars); second, we perform an isochrone cut along the color-magnitude diagram
(CMD) of each UFD using DELVE DR2 photometry (Drlica-Wagner et al., 2022)
(Section 3.1); third, we apply a proper motion cut using the Gaia DR3 catalog
(Gaia Collaboration et al., 2022) to identify stars with kinematics similar to
each UFD (Section 3.2); and finally, we identify low-metallicity stars using
the DECam $u$-band magnitude and corresponding $g,i$ magnitudes since UFD
stars are more metal-poor compared to Milky Way foreground stars (Section
3.3). Figure 2 illustrates a synthetic spectrum overlaid with the DECam
$u$-band, showing that the DECam $u$-band total throughput covers the
prominent Ca ii K absorption feature at 3933 Å. Therefore, the higher a star’s
metallicity, the fainter it will appear in the DECam $u$-band at a given
effective temperature and surface gravity.

To relate the metallicity of a star to its DECam $u$-band magnitude, we
utilize a grid of synthetic spectra similar to Chiti et al. (2020), who used
such a grid to establish the relationship between a star’s metallicity and
SkyMapper $v$-band magnitude with $g,i$ photometry. They noted that for a
given surface gravity, a star’s metallicity can be interpolated from its
$v-g-0.9\times(g-i)$ color. In this study, we use a comparable grid of
synthetic spectra to establish the relationship between a star’s metallicity
and $u-g-0.9\times(g-i)$ color. A detailed discussion of this is presented in
Section 3.3. In this section, we outline the steps of our selection technique
on Boo1 as an illustrative example. The same steps were performed for Boo2 and
Seg1.

###  3.1 Isochrone cut

We begin by applying an isochrone cut to select stars that exhibit a
consistent color-magnitude diagram (CMD) with that of an old, metal-poor
population at the distance of Boo1 (see Table 2). We first use STILTS to
crossmatch the final catalog obtained in Section 2.3 with the DELVE DR2
catalog (Drlica-Wagner et al., 2022) to obtain precise DECam $g$\- and $i$\-
band magnitudes ($\tt{MAG\\_PSF\\_g},\ \tt{MAG\\_PSF\\_i}$). To determine the
reddening correction for each star, we use dust maps from Schlegel et al.
(1998) to obtain $E(B-V)$ value. The reddening coefficients for $u$-, $g$\-
and $i$\- bands are taken as $R_{u}=3.995$111taken from
https://www.legacysurvey.org/dr8/catalogs/, $R_{g}=3.186$ and $R_{i}=1.569$,
respectively, following Abbott et al. (2018) to convert $E(B-V)$ to the
reddening corrections $A_{g}$ and $A_{i}$. We apply this correction to the
DELVE magnitudes to obtain the dereddened $g$\- and $i$\- band magnitudes. We
perform the same procedure to get dereddened $u$\- band magnitudes.

After obtaining dereddened $g$\- and $i$-band magnitudes for all selected
stars, we fit the $g,g-i$ CMD with an isochrone of [Fe/H] = $-2.49$ and age =
13 Gyr from the Dartmouth Stellar Evolution Database (Dotter et al., 2008) at
a distance modulus of $m-M=19.1$ (McConnachie, 2012), which has been shown to
represent the stellar population of Boo1 well. We then select stars that have
a $g-i$ color within 0.2 mag of this isochrone. The left panel of Figure 3
illustrates the selection procedure based on the isochrone.

Figure 4: $u-g-0.9\times(g-i)$ as a function of $g-i$ color for three
different surface gravity bins, color coded by metallicity [Fe/H]. We manually
shift the contours down by 0.07 to match our photometric metallicity with
spectroscopic results (Section 3.3.1). Stars (triangles) are selected
candidate member stars (non-member stars) that pass (do not pass) our
isochrone, proper motion, and metallicity cuts. In general, the grid shows
that for stars with surface gravity $\log g=1,2$, a higher $g-i$ color is
associated with a higher $u-g-0.9\times(g-i)$ value, and stars with a higher
metallicity tends to have higher $u-g-0.9\times(g-i)$ values. The
$u-g-0.9\times(g-i)$ vs $g-i$ parameter space cleanly separates metal-poor
stars from metal-rich ones.  Figure 5: The distribution of photometric
metallicity for candidate member (blue) and non-member stars of Boo1 (orange).
It is evident that the two groups are clearly distinguished by their
metallicity, with candidate member stars having low-metallicity ([Fe/H] $\leq
1.5$) and non-members having high metallicity ([Fe/H] $\geq 1.5$). However, it
should be noted that some non-member stars appear in the low-metallicity
range. In Section 3.3, we discuss that this might be due to those non-member
stars being off-grid in the parameter space shown in Figure 4, and the
photometric metallicity calculation is inaccurate for off-grid stars. Such
off-grid stars can be seen in the build-up at [Fe/H] = $-4.0$ in both
histograms. Figure 6: _Left:_ The distribution of photometric metallicity for
our selected candidate member stars (blue), member stars from Jenkins et al.
(2021) (red), and Longeard et al. (2022) (green). Note that we exclude
horizontal branch stars in our analysis, and stars from our catalog and from
the Jenkins et al. catalog are of the same magnitude range ($m_{g}<21.5$).
_Middle:_ The photometric metallicities obtained for Boo1 stars in this work
are compared with the metallicities obtained by Jenkins et al. (2021) for the
same sample of stars. Our error includes both the systematic uncertainty of
our calculation method (0.17 dex) and the uncertainty propagated from the
photometric uncertainty. The points follow a clean one-to-one relationship
with a $1\sigma$ scatter $<0.2$ dex, except for three stars in the bottom left
(open circles). See discussion in Section 3.3.2 on these stars. _Right:_
Comparison between our photometric metallicities and spectroscopic
metallicities from Frebel et al. (2014) of Seg1 stars. The points also follow
a clean one-to-one relationship with minimal scatter, further validating the
accuracy of our photometric metallicity calculation apart from one outlier.
Note that the outlier (at [Fe/H]${}_{\mathrm{phot}}\approx-2$) is Segue 1-7
(Norris et al., 2010), an extremely carbon-enhanced star with [C/Fe] = 2.3 at
[Fe/H] = $-3.57$ (Frebel et al., 2014).

###  3.2 Proper motion cut

To further identify candidate member stars, we select stars that have proper
motions consistent with the systemic proper motion of Boo1. We crossmatch the
catalog of stars that passed our isochrone cut in Section 3.1 with the Gaia
DR3 catalog (Gaia Collaboration et al., 2022) to obtain proper motion data and
corresponding uncertainties for our selected stars. We apply a reflex
correction on both the proper motions of stars and the systemic proper motion
of the UFD from McConnachie & Venn (2020). The systematic proper motion after
our reflex correction is visually consistent with that in Figure 16 of Pace et
al. (2022) for Boo1. We then evaluate the consistency of these proper motions
with the proper motion of Boo1 obtained from McConnachie & Venn (2020) using
the Mahalanobis distance:

$d_{\rm
Mahalanobis}=\sqrt{(\vec{x}-\vec{y})^{T}\cdot\Sigma^{-1}\cdot(\vec{x}+\vec{y})}$
(4)

where $\Sigma$ is the covariance matrix between pmRA and pmDEC obtained from
the correlation matrix and the proper motion errors in Gaia, and
$\vec{x}=(\rm{pm_{RA,Boo1}}$,$\rm{pm_{DEC,Boo1}}),\vec{y}=(\rm{pm_{RA}},\rm{pm_{DEC}})$
for each source. We select stars that have $d_{\rm{Mahalanobis}}<3$. The right
two panels of Figure 3 illustrate this selection procedure.

###  3.3 Photometric metallicities

We outline a photometric method to obtain a star’s metallicity based on its
DECam $u$-band magnitude and $g-i$ color, which is an efficient way to
estimate metallicities for spatially complete samples of stars without
requiring traditional spectroscopy. Such a method has been used in studies of
dwarf galaxies in the past with e.g., the SkyMapper $v$ filter (Chiti et al.,
2020, 2021) and the Pristine Ca HK filter (Longeard et al., 2021, 2022, 2023).
Here we demonstrate that a similar analysis can be performed with DECam
$u$-band photometry due to the Ca ii K absorption feature encompassing a
fraction of the bandpass of the filter (see Figure 2). Consequently, the
strength of the feature (as a function of the metallicity of the star, among
other stellar parameters) affects the brightness of the star in the DECam
$u$-band. We describe our analysis with Boo1 here since it is the most
extensively studied system regarding stellar metallicities among the three
UFDs we focused on in this study and has evidence of extra-tidal features
(Belokurov et al., 2006a; Martin et al., 2007; Norris et al., 2008; Roderick
et al., 2016; Jenkins et al., 2021; Filion & Wyse, 2021; Longeard et al.,
2022).

####  3.3.1 Deriving photometric metallicities

To illustrate how we compute metallicity from photometry, we present a grid in
Figure 4 that shows $u-g-0.9\times(g-i)$ and $g-i$ colors separated by four
different surface gravities, where we determine the surface gravity of each
star by interpolating along the same isochrone as in Section 3.1. This grid is
a modified version of the grid computed by Chiti et al. (2020), with the DECam
$u$-band filter used to generate synthetic photometry as opposed to the
SkyMapper $v$ filter in that study. The general trend of the grid shows that
metallicity decreases as the $u-g$ color and $g-i$ color become bluer at a
fixed surface gravity. The data points of each star are located in this
parameter space for a given surface gravity based on their dereddened DECam
$u$-, $g$-, $i$-band magnitudes. We interpolate the metallicity of each star
using this grid. Note that we adjust the synthetic $u$-band magnitudes down by
0.07 mag to better match our photometric metallicities with spectroscopic
metallicities in the literature. This shift is roughly consistent with the
shift applied in Chiti et al. (2020) to their synthetic SkyMapper $v$
magnitudes, which is an empirically driven correction that accounts for the
difference between photometric and spectroscopic metallicities due to
potential imperfections in the grid of synthetic spectra.

We note also that the photometric metallicities derived for non-member stars
in our catalog are inaccurate because these stars are not located at the
distance of the system and have different surface gravity values than member
stars on the red giant branch. We do not apply any metallicity corrections to
get accurate values for these non-member stars in our catalogs as we need an
accurate measure of their distance to derive a surface gravity. However, we
note that we do extend the stellar parameter range of the MSTO grid of
synthetic spectra in Chiti et al. (2020) to include main-sequence stars (3.5
$<$ log $g\leq 5$) and compute synthetic photometry for those. This main-
sequence grid is later used to adjust for the photometric metallicity
difference when a the star is assumed to be on the red giant branch as opposed
to the main sequence in Section 4.1.3 when we estimate the contamination rate
due to MW foreground main-sequence stars using the _Besançon_ model.

The metallicity distribution of candidate member and non-member stars is shown
in Figure 5, where candidate member stars are defined as those that pass our
proper motion and isochrone cuts in Section 3.1 and Section 3.2, while non-
member stars are defined as those that pass the isochrone cut but not the
proper motion cut. We observe that candidate member stars have significantly
lower metallicities than non-member MW foreground stars, indicating the
accuracy of our photometric metallicities. We further apply a metallicity cut
of [Fe/H] $\leq-1.5$ to select metal-poor candidate member stars. We choose
$-1.5$ to ensure both a more complete and pure sample, and we discuss the
details in Section 4.1.3.

However, there are some non-member stars in the low-metallicity regime. By
plotting their photometric locations in $u-g-0.9\times(g-i)$ vs $g-i$ colors,
we found that they are typically located out of range of the contours in
Figure 5 and thereby off-grid relative to our synthetic photometry, indicating
that their photometric metallicity is likely inaccurate.

####  3.3.2 Validating photometric metallicities

To assess the accuracy of our photometric metallicity calculation, we compare
the photometric metallicities of our candidate member stars with the
spectroscopic metallicities from Jenkins et al. (2021) and Frebel et al.
(2014) for Boo1 and Seg1, respectively. The error of our photometric
metallicities is the quadratic sum of the systematic uncertainty of our method
(0.17 dex, taken from analysis with the same grid from Chiti et al. 2020) and
the error propagated from the photometric uncertainty. The right two panels of
Figure 6 show that the mean offset of the two metallicities is small for both
Boo1 and Seg1 stars, with 1$\sigma\lesssim 0.2$ dex. There are three outliers
from the one-to-one line in the Boo1 sample (open circles), which we find out
to be outliers in the $u-g-0.9(g-i)$ vs $g-i$ grid and thus have biased low
photometric metallicities and higher photometric metallicity errors as can be
seen in the middle panel of Figure 6. The synthetic grid in Figure 4 shows
that contours are more tightly clustered at lower metallicity, so a $u$-band
uncertainty would translate to a larger photometric metallicity uncertainty at
lower metallicity. Thus, low metallicity outliers with correspondingly larger
uncertainties are more likely to appear than metal-rich outliers at the lowest
metallicities, potentially explaining why the three outliers all have
photometric metallicities lower than spectroscopic metallicites. Nevertheless,
for our purposes, the three outliers do not affect our sample because they
pass our metallicity cut and are members. Our goal of this study is to select
potential members using photometric metallicities, as opposed to
characterizing metallicity distribution of the UFD. Note that the outlier in
the Seg1 comparison (right panel of Figure 6) at
[Fe/H]${}_{\mathrm{phot}}\approx-2$ is Segue 1-7 (Norris et al., 2010), an
extremely carbon-enhanced star with $\rm[C/Fe]=2.3$ at $\rm[Fe/H]=-3.57$
(Frebel et al., 2014). These stars are known to have photometric metallicities
biased high due to the CN feature at $\sim 3800$ Å(Starkenburg et al., 2017).
Overall, the comparison demonstrates that our photometric metallicity
calculation is robust.

##  4 Candidate member star catalog and member star validation

In previous sections, we demonstrate that we can effectively select candidate
member stars in the peripheries of UFDs using photometric metallicities from
DECam $u$-band. In this section, we show the spatial distribution of detected
candidate member stars for Boo1, Boo2, and Seg1. To gain a statistical
understanding of our sample, we calculate the purity and completeness of our
selected candidate member stars for all three systems using the _Besançon
model of stellar population synthesis of the Galaxy_ 222https://model.obs-
besancon.fr/modele_home.php (Robin et al., 2003; Czekaj et al., 2014) and
literature samples of members. We also discuss the implications of the
candidate member star spatial distribution considering their proper motions.
Finally, for each identified star, we calculate an estimate of purity and use
this as a measure to guide future spectroscopic follow-up.

###  4.1 Boo1

Figure 7: Spatial distribution of candidate member stars in our catalog for
Boo1 (top), Boo2 (middle), and Seg1 (bottom). We divide the candidate member
stars by three magnitudes: $M_{g}<19.5$ (left), $M_{g}<20$ (middle), and
$M_{g}<20.2$ (right). The dashed grey ellipses denote 1, 2, 3, 4, and 5 half-
light radii of each system with ellipticity and position angle listed as in
Table 2. Each arrow represents the reflex-corrected velocity vector of a star
calculated from its proper motion. For Boo1 (top), our candidate member star
population extends beyond $\sim 5r_{h}$, and they form a streak in the same
direction as the proper motion of the system in the brightest sample (top left
panel), indicating possible tidal disruption. For Boo2 (middle rows), most of
our candidate member stars lie within 2 $r_{h}$. There exists an extension of
stars north-east of the system, but three of them (open black circles) are
outliers in CMD, indicating they may not be members. The other two solid black
points outside 5 $r_{h}$ could be targets for future spectroscopic follow-up.
For Seg1 (bottom), we apply an additional cut of [Fe/H] $<-2$ to weed out
potential 300S member stars (Section 4.2.1). There is also a handful of
candidates south-east of the system, in addition to potential contamination
from the Sagittarius stream or other substructures (Section 4.2.1).  Figure 8:
Spatial distribution of candidate member stars for Boo1 with a metallicity cut
[Fe/H] $<-1.5$ compared with member stars in Longeard et al. (2022) (blue) and
Jenkins et al. (2021) (orange). Other symbols are the same as in Figure 7.
Most of the member stars in the Jenkins et al. catalog are located within 1
half-light radius, while the member stars in the Longeard et al. catalog
extend out to approximately three to 4 half-light radii for stars brighter
than $m_{g}=20.2$. We were able to recover all of the member stars in the
Jenkins et al. and Longeard et al. catalogs except for one that has a
photometric metallicity of $-1.47$ and thus does not pass our $-1.5$
photometric metallicity cut. We discuss the completeness and purity of our
selected candidate member star sample compared to the combined Jenkins et al.
and Longeard et al. catalog in Section 4.1.2.

####  4.1.1 Spatial distribution of Boo1 candidate members

In Figure 7, we present the spatial distribution of candidate member stars in
Boo1 that satisfy our isochrone, proper motion, and metallicity cuts as
described in Section 3. For stars with $m_{g}<20$, we observe that the
majority of them form an inclined streak that aligns with the proper motion of
most stars. This echoes suggestions in the literature that Boo1 is currently
experiencing tidal disruption by the Milky Way (Longeard et al., 2022; Pace et
al., 2022). Moreover, we identify several new candidate member stars located
at distances of $\sim 3-5$ half-light radii from the center.

In Figure 8, we compare the spatial distribution of our selected candidate
member stars to that of member and non-member stars in the Jenkins et al.
(2021) and Longeard et al. (2022) catalogs. We apply our isochrone and proper
motion selections to determine members/non-members in the two catalogs to
enable a fair comparison. For stars with $m_{g}<19.5$, we identify more
candidate member stars at large radii than in previous catalogs. We also
identify more faint stars $(m_{g}<20.2)$ than in previous catalogs; however,
some of these stars may be non-members with large proper motion uncertainty,
allowing them to pass the proper motion cut, or MW foreground stars with low-
metallicity. The contamination rate increases as we go to fainter magnitudes
(e.g. $m_{g}>20.5$), but for our sample of stars with $m_{g}<20.2$, we still
retain an obvious elongated feature in the lower-left panel of Figure 8.

Figure 9: Number of member and non-member stars as a function of $m_{g}$ and
half-light radius $r_{h}$ from the center for three different metallicity
cuts. Stricter metallicity cuts result in a decrease of both candidate member
stars and non-member stars. Looser metallicity cuts result in an increase in
both candidate member stars and non-member stars. As discussed in Section
4.1.3, we choose [Fe/H]$<-1.5$ as our final photometric metallicity cut given
joint completeness and purity considerations.

####  4.1.2 Completeness of Boo1 sample

We now calculate the completeness of our selected star sample, which is an
essential metric for assessing the accuracy of our candidate member star
selection. Boo1 is a particularly suitable target for this analysis, as it is
the only MW UFD that has an extensive sample of literature member stars in
this study. By quantifying the completeness and purity of our selection of
candidate Boo1 member, we can obtain a preliminary estimate of the potential
bias and uncertainty in our selection criteria, which could be applied to
other systems in this study.

The completeness of our selected sample of candidate member stars for Boo1 is
determined by calculating the ratio of the number of stars in our catalog that
are also present in the combined Jenkins et al. (2021) and Longeard et al.
(2022) catalog to the total number of stars in the combined catalog. To
compute this, we first crossmatch the two catalogs, which yields a total of 48
member stars. Subsequently, we crossmatch these 48 catalog member stars with
our selected stars in Section 3 that satisfy the metallicity cuts
${\rm[Fe/H]}<-1$, ${\rm[Fe/H]}<-1.5$, and ${\rm[Fe/H]}<-2$. We obtain 47, 45,
and 42 overlaps, respectively. Hence, the completeness rates are 97.9%, 93.8%,
and 87.5%, respectively. These results indicate that lower metallicity cuts
may exclude more true members. Note that we only consider red-giant branch
(RGB) stars here and exclude horizontal branch stars.

####  4.1.3 Purity of Boo1 sample

Purity is defined as the ratio of the number of our selected candidate member
stars that are actually members in the combined catalog to the total number of
our selected candidate member stars. We first combine all the stars (members
and non-members) in the Jenkins et al. (2021) and Longeard et al. (2022)
catalogs. Next, we crossmatch these stars with our selected stars that pass
the isochrone, proper motion, and metallicity cuts ${\rm[Fe/H]}<-1$,
${\rm[Fe/H]}<-1.5$, and ${\rm[Fe/H]}<-2$ to obtain three different samples. We
compute the purity rate for different metallicity cuts using these overlaps.

As we only have two catalogs available to compute the completeness and purity
rates, and only the Longeard et al. (2022) catalog extends beyond 1 half-light
radius of Boo1, we require an independent method to estimate contamination
rate from MW foreground stars. We use the _Besançon_ model, which enables us
to simulate the number of MW foreground stars within 5 half-light radii from
Boo1. We adopt the SDSS+JHK photometric system in our simulations, and our
field of view encompasses 150 kpc, with the frame centered on Boo1 and a solid
angle of 100 deg2. We use the large field instead of the small field (10 deg2)
since the small field contains only a few foreground stars that satisfy our
selection criteria, leading to a biased estimate of the foreground
contamination rate, particularly at larger radii. We verified that the proper
motion and radial velocity distributions do not show spatial variations in the
100 deg2 field that was selected.

We select all stars with $g$-band magnitudes between g=16 and g=23 and
generate model stars without applying a proper motion error function in the
query. We use the correlation between proper motion uncertainties and the
dereddened g-band magnitudes in our sample of observed non-members and fit an
exponential function $0.01+e^{1.2\cdot m_{g}-25}$, and use this to derive the
proper motion error for simulated stars. The model generates a total of
311,416 stars, and we apply our isochrone, proper motion, and metallicity cut
[Fe/H] $<-1.5$ to obtain 1712 stars that pass all our selection criteria.
Since most of the MW foreground stars are main sequence stars, their
metallicities will be inaccurate if we use the synthetic photometry grid
obtained for giant stars in Section 3.3.1. To get accurate metallicities for
the MW foreground stars, we use the synthetic photometry grid described in
Section 3.3.1 for main sequence stars (3.5 $<$log $g\leq 5.0$). From this
grid, we derive the metallicity differential between assuming a star is on the
main-sequence versus the red giant branch as a function of the star’s
uncorrected metallicity and SDSS $g-r$ color. We apply this correction to the
main-sequence stars in the Besancon catalog to mimic how their metallicities
would appear in our analysis. We further apply a magnitude cut $m_{g}<21.5$,
as all our candidate member stars have $m_{g}<21.5$.

We assume a uniform spatial _density_ distribution of MW foreground stars and
calculate the MW contamination rate as the total number of stars that pass all
our selection criteria (1712) divided by the total FOV (100 deg2). We divide
the area into several radial bins: 0-1 $r_{h}$, 1-2 $r_{h}$, 2-3 $r_{h}$, 3-4
$r_{h}$, etc, and for each bin, the estimated MW contamination number is the
area of the annulus times the contamination rate. For each annulus, we further
divide it into magnitude bins $m_{g}=(16,19.5,20,20.5,21,21.5)$. We record the
number of candidate member stars and MW foreground stars that fall into each
radial and magnitude bin. Then the purity of each star in a specific radial
and magnitude bin is computed as (# of candidate members - # MW foreground)/(#
of candidate members) in that bin. Stars that fall into the same radial and
magnitude bin will have the same purity. We use purity as a guide for
spectroscopic studies to decide which stars should be targets given limited
telescope time.

As shown in Figure 9, both the number of candidate member stars and the number
of MW foreground stars increase from bright to faint magnitudes. From small to
large radial distances, the number of candidate member stars decreases
significantly and the number of foreground stars increases steadily. Going
from metallicity cut [Fe/H] $<-1$ to [Fe/H] $<-1.5$ decreases the foreground
number with minimal decrease of candidate member stars, so to maximize both
completeness and purity, we have chosen the metallicity cut [Fe/H] $<-1.5$ and
apply this metallicity cut on all subsequent analyses.

We fit a function to the number of foreground stars for each system, as a
function of both radius and $g$-band magnitude, and display the color-mesh
interpolator in Figure 10. The number of MW foreground stars increases as the
magnitude becomes fainter and the radius grows larger. For Boo1, at a $g$-band
magnitude of approximately 21 and a radius of around 0.2 degree, approximately
10 foreground stars pass all of our cuts, potentially contaminating our
sample.

To ensure the robustness of our method, we perform one final check by
incorporating the uncertainty in metallicity into our foreground contamination
estimate. We use the same sample of large-field model stars as in Section
4.1.3, where we calculated the theoretical purity rate. We fit an exponential
function of the form $y=0.0001+e^{1.08x-25}$ to the metallicity error and
$g$-band magnitude of our sample of non-member stars. We then use this fitted
function to get the metallicity error ($y$) of model stars based on their
$g$-band magnitudes ($x$). Assuming a Gaussian distribution of metallicity for
each model star with a mean equal to the metallicity returned by the model and
a standard deviation equal to the metallicity error we calculated using the
fit, we generate 1000 ensembles for each star and run 1000 simulation
experiments to estimate, on average, how many stars pass all selection cuts.
The standard deviation of the number of stars passing all selection cuts for
the 1000 runs is approximately 2.5, indicating that there will be a variation
of only around 2.5 stars passing all selection cuts if we include the
metallicity uncertainty. This demonstrates that our selection is robust
against metallicity uncertainties.

We use purity as a measure of how likely our identified star is a true member
to guide future spectroscopic studies, and report this our tables of candidate
members (Tables 3, 4, 5). MEM_FLAG = 0 means this star is an identified member
star in literature. MEM_FLAG = 1 means this star is an identified non-member
star in literature, but we flag it as a candidate member star in our catalog.
MEM_FLAG = 2 means this star is not identified in previous studies, and we
identify it as a bright candidate member star ($m_{g}<20.2$). These are
interesting candidates for future spectroscopic studies. MEM_FLAG = 3 means
this star is not identified in previous studies, and we identify it as a
candidate with lower purity due to its faintness ($m_{g}>20.2$). Note that in
some radial and magnitude bins, the number of predicted foreground stars
exceed the observed number of stars, so we assign a purity of 0 for these
cases. In these tables, we also exclude stars that are $\gtrsim 0.05$ mag from
the edge of our grid of synthetic photometry, have discrepant $g-r$ vs. $r-i$
colors, or have entries in the Gaia DR3 variable source catalog (Rimoldini et
al., 2023). We additionally indicate stars that may be outliers relative to
the CMD under a tighter selection, but still pass our isochrone tolerance in
Section 3.1 through the CMD_outlier_flag column.

In Figure 11, we show a spatial distribution of candidate member stars with
$m_{g}<20.2$ color-coded by their purity. Most of the stars we identified have
high purity $>95\%$, and all stars have purity $>80\%$. We propose these stars
(MEM_FLAG = 2) for future spectroscopic studies. Table 3 shows a
representative sample of identified candidate member stars in our catalog.

Figure 10: A 2D histogram displaying the estimated number of MW foreground
stars for Boo1, Boo2, and Seg1 as a function of radius (in degrees) and
$m_{g}$. The number of MW foreground stars increases as the magnitude becomes
fainter and the radius grows larger. Figure 11: The spatial distribution of
Boo1, Boo2, and Seg1 candidate member stars brighter than $m_{g}=20.2$ color-
coded according to their purity. Purity decreases as the radius increases and
magnitude becomes fainter. We use purity as a measure to guide future
spectroscopic follow-up of the newly found potential member stars. Figure 12:
Spatial distribution of candidate member stars for Boo2 with a metallicity cut
[Fe/H] $<-1.5$ compared with member stars in Koch et al. (2009) (blue), Bruce
et al. (2023) (orange), and Ji et al. (2016) (green). Other symbols are the
same as in Figure 7. We recover all the member stars in all three catalogs,
reaching a 100% completeness rate. For stars with $m_{g}<20.2$ (lower left),
we zoom out to show the entire DECam FOV ($\sim 4$deg2). There is a hint of
metal-poor candidate member stars to the south and to the east of the system,
two of which (solid circles) are not outliers in CMD and thus could be
interesting targets for future spectroscopic follow-up.

###  4.2 Boo2 and Seg1

####  4.2.1 Spatial distribution

In Figure 7, we present the spatial distribution of candidate member stars in
Boo2 that satisfy our isochrone, proper motion, and metallicity cuts. Most of
our identified stars with $m_{g}<20$ lie within 2 $r_{h}$ of the system. For
the sample brighter than $m_{g}=20.2$, we detect 4 stars with consistent
proper motions in the DECam FOV north-east of the system at large radial
distances. Three of them, indicated by hollow circles in Figure 7 appear as
outliers on the CMD despite passing our selection, so we flag them as unlikely
members. The remaining candidate is a potential target for future
spectroscopic follow-up studies.

In Figure 12, we compare the spatial distribution of our selected candidate
member stars of Boo2 to that of member and non-member stars in the Koch et al.
(2009), Ji et al. (2016), and Bruce et al. (2023) catalogs. We apply our
isochrone and proper motion cuts to all members in the three catalogs to
enable a fair comparison. Note that Boo2 has a relatively small size, but we
show the entire DECam FOV ($\sim 3$deg2) for the faint sample with
$m_{g}<20.2$ to include all detected candidate member stars in the DECam FOV.
The four stars north-east of the system are not detected in any previous
spectroscopic studies.

For Seg1, Figure 7 suggests that similar to Boo1, the spatial distribution of
several new candidates in Seg1 suggest an elongation consistent with the
direction of the proper motion. This may indicate signs of Seg1 undergoing
tidal disruption by the MW, but further kinematic studies of distant members
are needed to fully ascertain the dynamical state of the system. By comparing
with the Simon et al. (2011) and Frebel et al. (2014) samples in Figure 13, we
find a handful more candidate member stars outside of 5 $r_{h}$ to the south
and to the east of the system in addition to several directly east and north.
We note that the Sagittarius stream has increasing presence toward the north
of the field (e.g., Belokurov et al., 2006b; Geha et al., 2009) and the 300S
stream passes east-west (Fu et al., 2018), suggesting some distant stars in
these directions may be members of those streams.

####  4.2.2 Completeness & purity

The completeness of our selected sample of candidate member stars for Boo2 and
Seg1 is determined in the same way as in Section 4.1.2. For Boo2, every
candidate member star determined in previous spectroscopic studies is
identified in our photometric sample. For Seg1, to compare with Simon et al.
(2011) and Frebel et al. (2014) catalog, we weed out potential 300S stream
members in the field of view (Fu et al., 2018) by applying an additional
metallicity cut of [Fe/H] $<-2$ (Li et al., 2022; Usman et al., 2024). This
cut also removes all Sagittarius stream members apart from its faint component
(Limberg et al., 2023). Two member stars of Seg1, SDSS J100714+160154 and SDSS
J100710+160623 (Frebel et al., 2014), in the two catalogs that have unusually
high spectroscopic metallicities of $-1.42$ and $-1.67$ respectively, and
photometric metallicities $-1.00$ and $-1.63$, do not show up in our catalog
because they do not pass our [Fe/H] $<-2$ cut.

The purity for Boo2 and Seg1 candidate member stars is calculated in the same
way as in Section 4.1.3. For Boo2, Figure 10 shows that our sample is
essentially clean of contamination across all radii for stars brighter than
20.0 mag, and for Seg1, our sample is essentially clean of contamination
across all radii for stars brighter than 20.0 mag. However, the region of sky
around Seg1 has many substructures like the Sagittarius stream and 300S
stream, so the _Besançon_ model might underestimate the foreground
contamination. Table 4 sand Table 5 show a representative sample of candidate
member stars in our Boo2 and Seg1 catalogs, respectively, with same columns as
in Table 3.

Figure 13: Spatial distribution of candidate member stars for Seg1 with a
metallicity cut [Fe/H] $<-2$ compared with member stars in Simon et al. (2011)
(red) and Frebel et al. (2014) (orange). We recover all but two member star in
the two catalogs, SDSS J100714+160154 and SDSS J100710+160623, which have
unusually high spectroscopic metallicities of $-1.42$ and $-1.67$ respectively
(Frebel et al., 2014), and photometric metallicities $-1.00$ and $-1.63$, so
they are cut off from our photometric metallicity cut of [Fe/H] = $-$2\. We
find a handful more candidate members to the south of the system compared to
previous studies, in addition to a few east and north. As discussed in
Sections 4.2.1 and 4.2.2, the presence of the 300S and Sagittarius streams in
the field-of-view may affect the purity of these candidates.

##  5 Discussion

The processes that drive the formation and evolution of UFDs, including the
prominence of early dwarf-dwarf mergers, the influence of supernova feedback,
and the strength of tidal disruption by a massive host, are still relatively
poorly constrained. Observationally, these phenomena manifest in the outskirts
of these galaxies (beyond $4r_{h}$), which can be probed through detailed
studies of their resolved stellar populations at large distances.
Observational efforts have concentrated on the outskirts of the MW UFDs to
identify distant member stars. This approach has unveiled extended stellar
populations in many UFDs. For example, RR Lyrae (RRL) stars outside of the
tidal radius of fourteen UFDs (Boötes I, Boötes III, Sagittarius II, Pegasus
IV, Reticulum III, Eridanus II, Eridanus III, DELVE 2, Tucana II, Tucana III,
Tucana IV, Hercules, Grus II, and Ursa Major I) have been identified (Garling
et al., 2018; Vivas et al., 2020; Tau et al., 2024). Chiti et al. (2021)
showed that there are member stars of Tucana II out to distances of $\sim 1$
kpc, and Filion & Wyse (2021); Longeard et al. (2022, 2023); Ou et al. (2024)
have shown similar distant members and candidates in Hercules and Boötes I.
Jensen et al. (2024) find evidence for low-density outer profiles in nine
dwarf galaxies, and Martínez-Vázquez et al. (2021) reported a RRL star at
$6r_{h}$ and another blue horizontal branch star at $>9r_{h}$ in Centaurus I.
Here, we report multiple new bright candidate member stars $(m_{g}<20.2)$ of
Boo1 located at $>4r_{h}$, five candidate member stars of Boo2 located at
$>5r_{h}$ (including one promising candidate member), and two candidate member
stars of Seg1 at $>5r_{h}$. These are interesting targets for spectroscopic
follow-up.

Current observations strongly support the conclusion that UFDs host stars at
large distances; however, the physical mechanism that relocates stars from
these low-mass systems to large distances is currently uncertain. One
explanation is tidal disruption, which transports stars to large radii through
interactions with an external, more massive galaxy. Indeed, a number of
studies have found evidence or have suggested that some UFDs are undergoing
tidal disruption by the MW (e.g., Drlica-Wagner et al., 2015; Simon et al.,
2017; Li et al., 2018; Mutlu-Pakdil et al., 2019; Ou et al., 2024). In
particular, the previously known orientation of distant members in Boo1 and
its velocity gradient strongly suggest the system is undergoing tidal
disruption (Filion & Wyse, 2021; Longeard et al., 2022; Filion & Wyse, 2021;
Pace et al., 2022). This is consistent with our finding of a larger number of
candidates in Boo1 at large distances. The orbital parameters of Boo1, such as
a comparison of half-light radius and tidal radius from modeling (i.e., Fig 5
and 6 in Pace et al., 2022), also indicates Boo1 as potentially being tidally
disrupted, although it has a pericenter of $\sim 38$ kpc. For Seg1, it is less
clear if MW tidal disruption is at play (see e.g., Section 5.6 of Jensen et
al., 2024, for a detailed discussion) even if it has a close pericenter of
$\sim 20$ kpc (Pace et al., 2022). In particular, the intersection of many
stellar streams with the Seg1 field makes a conclusive statement difficult.
Our discovery of a few brighter ($g<20.2$) candidate stars beyond $9r_{h}$ is
suggestive, but not conclusive, evidence of tidal features, and spectroscopic
follow-up of these stars will be important to confirm any association and
interpret the nature of this system. Boo2 has a pericenter of $\sim 36$ kpc,
and other orbital parameters do not show evidence of it being especially prone
to tidally disruption (Pace et al., 2022).

Another plausible mechanism to displace stars to large distances relies on
processes during the formation of UFDs, such as early galaxy mergers and
stellar feedback, which may kinematically heat the system and form an extended
stellar halo (Deason et al., 2014). For example, the extended stellar profiles
of some UFDs (e.g., Tucana II; Chiti et al. 2021) have been discussed as a
potential result of the merging of two primordial galaxies at $z\gtrsim 2$
(Deason et al., 2014; Tarumi et al., 2021), or early supernova feedback driven
by a bursty star formation history (Wheeler et al., 2019; Pan & Kravtsov,
2023). This is also related to claims that higher-mass dwarf spheroidals have
cored DM profiles due to bursty star formation or supernova outflows (e.g.,
Pontzen & Governato, 2012; Amorisco et al., 2014; Read et al., 2016; Orkney et
al., 2021).

While we cannot claim a clear mechanism for the formation of the stellar
outskirts of UFDs from this study alone, spectroscopic follow up of candidate
members is one observational avenue to further investigate distinguish between
potential formation processes (e.g., to investigate velocity gradients and
chemical differences between the central/outer populations; Chiti et al. 2023;
Waller et al. 2023). We provide a list of candidate members in Tables 3, 4,
and 5 to help guide such work, and also indicate stars that have already been
observed by ongoing but unpublished work from the S5 Collaboration. In
particular, we highlight that spectroscopic follow-up of brighter distant
candidates of Boo2 or Seg1 may pin down the evolutionary nature of this
system, given that their orbital parameters suggest that they may not be
especially prone to disruption (e.g., Pace et al. 2022). If the distant stars
do reflect tidal perturbations, then it may suggest that larger numbers of
UFDs have potentially been tidally perturbed and lost a significant fraction
of their DM halo mass due to interactions with the MW (e.g., Peñarrubia et
al., 2008).

##  6 Conclusions

In this paper, we show that DECam $u$-band photometry, which covers the
prominent Ca ii K metal absorption line, can be used to compute photometric
metallicities and effectively select candidate member stars at large radial
distances for three MW UFDs: Boo1, Boo2, and Seg1. We combine multi-band
photometry information from DELVE (Drlica-Wagner et al., 2022), proper motion
information from _Gaia_ (Gaia Collaboration et al., 2022), and photometric
metallicities from DECam to select candidate member stars. We present the
spatial distribution of candidate member stars for all three systems. Two of
the systems potentially show signs of tidal disruption, but further
spectroscopy follow-up is necessary to confirm this. We assess the purity and
completeness of our sample, and use purity as a measure to guide future
spectroscopic follow-ups of the new candidate member stars we found. Our main
findings can be summarized as follows:

  1. 1.

The DECam photometry can be used to efficiently distinguish between candidate
member and non-member stars and to compute photometric metallicities (Figure
4, 5). Our photometric metallicities generally agree spectroscopic
metallicities from Jenkins et al. (2021) for Boo1 member stars and from Frebel
et al. (2014) for Seg1 member stars.

  2. 2.

The spatial distribution of Boo1 shows a prominent elongation along the
direction of the proper motion of the sytem, indicating that Boo1 is possibly
undergoing tidal disruption by the MW (Figures 7 and 8). This corroborates
previous wide-field spectroscopic studies of the system (e.g., Longeard et
al., 2022)

  3. 3.

The spatial distribution of Boo2 shows that there are several candidate member
stars in the north-east direction of the system consistent with the proper
motion of the system, but three of them turn out to be outliers in CMD and may
thus be unlikely to be members. (Figures 7 and 12). The remaining candidates
could be targets for future spectroscopic follow-up.

  4. 4.

Seg1 is contaminated by the stellar streams 300S and Sagittarius, so we add an
additional metallicity cut of [Fe/H] $<-2$ to lessen substructure
contamination. The spatial distribution of Seg1 also suggests a hint of tidal
disruption feature (Figure 7, 13), but spectroscopic follow-up is needed of
identified candidate members.

  5. 5.

We present tables of identified member stars and candidate members to aid
future spectroscopic studies, in addition to providing a literature
compilation of members. We note that several candidates already have
spectroscopy from the Southern Stellar Stream Spectroscopic Survey ($S^{5}$
collaboration, in prep), and this information is also indicated in the tables.

##  7 acknowledgments

This work is supported by the Quad Undergraduate Research program at the
University of Chicago, and the Department of Astronomy and Astrophysics at the
University of Chicago. We thank Sergey Koposov for providing his code for
proper motion reflex corrections. The Proposal ID for the DECam observations
is 2021A-0272.

A.C. is supported by a Brinson Prize Fellowship at the University of
Chicago/KICP. A.D.W acknowledges support from NSF grants AST-2006340,
AST-2108168, and AST-2307126. A.P.J. acknowledges support from NSF grant
AST-2307599. G.L. acknowledges FAPESP (procs. 2021/10429-0 and 2022/07301-5).

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.

The DECam Local Volume Exploration Survey (DELVE; NOAO Proposal ID 2019A-0305,
PI: Drlica-Wagner) is partially supported by Fermilab LDRD project L2019-011,
the NASA Fermi Guest Investigator Program Cycle 9 No. 91201, and NSF
AST-2307126.

This project used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana–Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, the Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho
de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Científico e Tecnológico and the Ministério da Ciência,
Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the
Collaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne National Laboratory, the University
of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Enérgeticas, Medioambientales y Tecnológicas–Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH)
Zürich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the
Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig-Maximilians Universität München and the associated Excellence
Cluster Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, the Ohio State University, the
OzDES Membership Consortium, the University of Pennsylvania, the University of
Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the
University of Sussex, and Texas A&M University.

Based in part on observations at Cerro Tololo Inter-American Observatory,
National Optical Astronomy Observatory, which is operated by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation.

Database access and other data services are hosted by the Astro Data Lab at
the Community Science and Data Center (CSDC) of the National Science
Foundation’s National Optical Infrared Astronomy Research Laboratory, operated
by the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation.

The software packages NUMPY (van der Walt et al., 2011), SCIPY (Jones et al.,
2001), Astropy (Astropy Collaboration et al., 2018), MATPLOTLIB (Hunter,
2007), and GITHUB were invaluable in conducting the analyses presented in this
paper. We also used the Starlink Tables Infrastructure Library Tool Set
(STILTS)333http://www.starlink.ac.uk/stilts/ (Taylor, 2006) extensively.
Additionally, this research relied heavily on the Astrophysics Data Service
(ADS) and the preprint repository arXiv.

Table 3: Boo1 member star catalog

_Gaia_ source ID | RA | DEC | $u0$ | $g0$ | $i0$ | PMRA | PMDEC |  [Fe/H]phot | Purity |  MEM_FLAG1 |  S5_obs2 |  Ref.3 | CMD_outlier_flag
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  |  |  |  mas yr-1 |  mas yr-1 |  |  |  |  |  |
1231095269513901568 | 210.02998 | 15.2386 | $20.90\pm 0.035$ | 20.17 | 19.50 | 0.302 | $-0.442$ | $-2.44\pm 0.41$ | 0.88 | 0 | 1 | a | 0
1230887118218565504 | 210.0679 | 14.9441 | $20.52\pm 0.035$ | $19.75$ | $18.98$ | 0.149 | $-0.334$ | $-3.01\pm 0.71$ | 0.97 | 0 | 1 | a | 0
1231090596588925056 | 209.7151 | 15.1449 | $21.41\pm 0.035$ | $20.67$ | $19.99$ | 0.517 | $-0.766$ | $-2.31\pm 0.32$ | 0.00 | 1 | 1 | a | 0
1230874954871117824 | 210.1153 | 14.7380 | $21.26\pm 0.035$ | $20.47$ | $19.78$ | 0.171 | $-0.505$ | $-2.03\pm 0.26$ | 0.78 | 1 | 1 | a | 0

(A full version of this table is in a machine readable format online)(A full
version of this table is in a machine readable format online)footnotemark:

11footnotetext: The MEM_FLAG numbers are illustrated in Section 4.1.3.

22footnotetext: S5_obs: S5_obs $=1$ means this star was observed in S5, and
S5_obs $=0$ means it was not observed in S5.

33footnotetext: a.Longeard et al. (2022); b.Jenkins et al. (2021)

Table 4: Boo2 member stars catalog

_Gaia_ source ID | RA | DEC | $u0$ | $g0$ | $i0$ | PMRA | PMDEC |  [Fe/H]phot | Purity | MEM_FLAG | S5_obs |  Ref.1 | CMD_outlier_flag
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  |  |  |  mas yr-1 |  mas yr-1 |  |  |  |  |  |
3727837759579718272 | 209.4061 | 12.8635 | $18.84\pm 0.035$ | $18.15$ | $17.48$ | $-1.67$ | 0.526 | $-3.61\pm 0.75$ | 1. | 0 | 0 | b | 1
3727825076541007232 | 209.4323 | 12.7905 | $20.95\pm 0.035$ | $20.21$ | $19.54$ | $-1.569$ | 0.370 | $-2.26\pm 0.31$ | 0.99 | 0 | 0 | b | 0
3728628853900665856 | 208.4935 | 12.9786 | $20.66\pm 0.035$ | $19.96$ | $19.32$ | $-2.076$ | 0.268 | $-2.25\pm 0.33$ | 0.65 | 2 | 0 | ... | 0
3727823118035927936 | 209.5725 | 12.8035 | $21.40\pm 0.035$ | $20.71$ | $20.10$ | $-1.787$ | $-1.205$ | $-2.50\pm 0.75$ | 0.69 | 3 | 1 | ... | 0
1230683227532109056 | 209.2676 | 13.7516 | $21.37\pm 0.035$ | $20.75$ | $20.19$ | $-0.596$ | 0.685 | $-2.5\pm 0.75$ | 0.00 | 3 | 0 | ... | 0

(A full version of this table is in a machine readable format online)(A full
version of this table is in a machine readable format online)footnotemark:

11footnotetext: a.Koch et al. (2009); b.Bruce et al. (2023); c.Ji et al.
(2016)

Table 5: Seg1 member stars catalog

_Gaia_ source ID | RA | DEC | $u0$ | $g0$ | $i0$ | PMRA | PMDEC |  [Fe/H]phot | Purity | MEM_FLAG | S5_obs |  Ref.1 | CMD_outlier_flag
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  |  |  |  mas yr-1 |  mas yr-1 |  |  |  |  |  |
621943184658438784 | 151.7180 | 16.0433 | $19.35\pm 0.035$ | $18.74$ | $18.10$ | $-2.017$ | $-1.662$ | $-4.\pm 0.75$ | 0.99 | 0 | 1 | a,b | 0
621924492960734464 | 151.7603 | 15.8487 | $19.13\pm 0.035$ | $18.36$ | $17.66$ | $-1.898$ | $-1.698$ | $-2.28\pm 0.29$ | 0.99 | 0 | 1 | a,b | 0
621925901710013952 | 151.8407 | 15.9068 | $20.97\pm 0.035$ | $20.50$ | $20.18$ | $-2.333$ | $-1.339$ | $-2.68\pm 0.75$ | 0. | 1 | 0 | a | 0
622634296435669376 | 150.7791 | 16.0090 | $20.65\pm 0.035$ | $20.04$ | $19.47$ | $-1.609$ | $1.352$ | $-2.50\pm 0.75$ | 0.86 | 2 | 0 | ... | 0
621819764477687296 | 151.4164 | 15.5965 | $20.59\pm 0.035$ | $20.01$ | $19.54$ | $-2.483$ | $-0.394$ | $-2.07\pm 0.54$ | 0.91 | 2 | 0 | ... | 0
622820771030434816 | 151.2795 | 16.9198 | $21.33\pm 0.035$ | $20.81$ | $20.42$ | $-1.155$ | $0.165$ | $-2.11\pm 0.79$ | 0. | 3 | 0 | ... | 0
622790908122977920 | 151.1391 | 16.7076 | $21.32\pm 0.035$ | $20.81$ | $20.43$ | $-4.231$ | $-0.581$ | $-2.17\pm 0.88$ | 0. | 3 | 0 | ... | 0

(A full version of this table is in a machine readable format online)(A full
version of this table is in a machine readable format online)footnotemark:

11footnotetext: a.Simon et al. (2011); b.Frebel et al. (2014); c.Norris et al.
(2010)

## References

  * Abbott et al. (2018) Abbott, T. M. C., Abdalla, F. B., Allam, S., et al. 2018, ApJS, 239, 18, doi: 10.3847/1538-4365/aae9f0
  * Abbott et al. (2021) Abbott, T. M. C., Adamów, M., Aguena, M., et al. 2021, ApJS, 255, 20, doi: 10.3847/1538-4365/ac00b3
  * Abdallah et al. (2020) Abdallah, H., Adam, R., Aharonian, F., et al. 2020, Phys. Rev. D, 102, 062001, doi: 10.1103/PhysRevD.102.062001
  * Ahumada et al. (2020) Ahumada, R., Prieto, C. A., Almeida, A., et al. 2020, ApJS, 249, 3, doi: 10.3847/1538-4365/ab929e10.48550/arXiv.1912.02905
  * Alvarez & Plez (1998) Alvarez, R., & Plez, B. 1998, A&A, 330, 1109, doi: 10.48550/arXiv.astro-ph/9710157
  * Amorisco et al. (2014) Amorisco, N. C., Zavala, J., & de Boer, T. J. L. 2014, ApJ, 782, L39, doi: 10.1088/2041-8205/782/2/L39
  * Anthony-Twarog et al. (1991) Anthony-Twarog, B. J., Laird, J. B., Payne, D., & Twarog, B. A. 1991, AJ, 101, 1902, doi: 10.1086/115815
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Belokurov et al. (2006a) Belokurov, V., Zucker, D. B., Evans, N. W., et al. 2006a, ApJ, 647, L111, doi: 10.1086/507324
  * Belokurov et al. (2006b) \---. 2006b, ApJ, 642, L137, doi: 10.1086/504797
  * Belokurov et al. (2007) \---. 2007, ApJ, 654, 897, doi: 10.1086/509718
  * Bernstein et al. (2017) Bernstein, G. M., Abbott, T. M. C., Desai, S., et al. 2017, PASP, 129, 114502, doi: 10.1088/1538-3873/aa858e
  * Bertin (2006) Bertin, E. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 112
  * Bertin (2011) Bertin, E. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 442, Astronomical Data Analysis Software and Systems XX, ed. I. N. Evans, A. Accomazzi, D. J. Mink, & A. H. Rots, 435
  * Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164
  * Brown et al. (2014) Brown, T. M., Tumlinson, J., Geha, M., et al. 2014, ApJ, 796, 91, doi: 10.1088/0004-637X/796/2/91
  * Bruce et al. (2023) Bruce, J., Li, T. S., Pace, A. B., et al. 2023, ApJ, 950, 167, doi: 10.3847/1538-4357/acc943
  * Calore et al. (2018) Calore, F., Serpico, P. D., & Zaldivar, B. 2018, J. Cosmology Astropart. Phys, 2018, 029, doi: 10.1088/1475-7516/2018/10/029
  * Carretta et al. (2009) Carretta, E., Bragaglia, A., Gratton, R., D’Orazi, V., & Lucatello, S. 2009, A&A, 508, 695, doi: 10.1051/0004-6361/200913003
  * Chiti et al. (2020) Chiti, A., Frebel, A., Jerjen, H., Kim, D., & Norris, J. E. 2020, ApJ, 891, 8, doi: 10.3847/1538-4357/ab6d72
  * Chiti et al. (2021) Chiti, A., Frebel, A., Simon, J. D., et al. 2021, Nature Astronomy, 5, 392, doi: 10.1038/s41550-020-01285-w
  * Chiti et al. (2023) Chiti, A., Frebel, A., Ji, A. P., et al. 2023, AJ, 165, 55, doi: 10.3847/1538-3881/aca416
  * Cole et al. (2000) Cole, S., Lacey, C. G., Baugh, C. M., & Frenk, C. S. 2000, MNRAS, 319, 168, doi: 10.1046/j.1365-8711.2000.03879.x
  * Czekaj et al. (2014) Czekaj, M. A., Robin, A. C., Figueras, F., Luri, X., & Haywood, M. 2014, A&A, 564, A102, doi: 10.1051/0004-6361/201322139
  * Dall’Ora et al. (2006) Dall’Ora, M., Clementini, G., Kinemuchi, K., et al. 2006, ApJ, 653, L109, doi: 10.1086/510665
  * Deason et al. (2014) Deason, A., Wetzel, A., & Garrison-Kimmel, S. 2014, ApJ, 794, 115, doi: 10.1088/0004-637X/794/2/115
  * Dotter et al. (2008) Dotter, A., Chaboyer, B., Jevremović, D., et al. 2008, ApJS, 178, 89, doi: 10.1086/589654
  * Drlica-Wagner et al. (2015) Drlica-Wagner, A., Bechtol, K., Rykoff, E. S., et al. 2015, ApJ, 813, 109, doi: 10.1088/0004-637X/813/2/109
  * Drlica-Wagner et al. (2022) Drlica-Wagner, A., Ferguson, P. S., Adamów, M., et al. 2022, ApJS, 261, 38, doi: 10.3847/1538-4365/ac78eb
  * Filion & Wyse (2021) Filion, C., & Wyse, R. F. G. 2021, ApJ, 923, 218, doi: 10.3847/1538-4357/ac2df1
  * Flaugher et al. (2015) Flaugher, B., Diehl, H. T., Honscheid, K., et al. 2015, AJ, 150, 150, doi: 10.1088/0004-6256/150/5/150
  * Frebel et al. (2014) Frebel, A., Simon, J. D., & Kirby, E. N. 2014, ApJ, 786, 74, doi: 10.1088/0004-637X/786/1/74
  * Fu et al. (2018) Fu, S. W., Simon, J. D., Shetrone, M., et al. 2018, ApJ, 866, 42, doi: 10.3847/1538-4357/aad9f9
  * Fu et al. (2023) Fu, S. W., Weisz, D. R., Starkenburg, E., et al. 2023, arXiv e-prints, arXiv:2306.06260, doi: 10.48550/arXiv.2306.06260
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2022, arXiv e-prints, arXiv:2208.00211, doi: 10.48550/arXiv.2208.00211
  * Garling et al. (2018) Garling, C., Willman, B., Sand, D. J., et al. 2018, ApJ, 852, 44, doi: 10.3847/1538-4357/aa9bf1
  * Geha et al. (2009) Geha, M., Willman, B., Simon, J. D., et al. 2009, ApJ, 692, 1464, doi: 10.1088/0004-637X/692/2/1464
  * Hartley et al. (2022) Hartley, W. G., Choi, A., Amon, A., et al. 2022, MNRAS, 509, 3547, doi: 10.1093/mnras/stab3055
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Jenkins et al. (2021) Jenkins, S. A., Li, T. S., Pace, A. B., et al. 2021, ApJ, 920, 92, doi: 10.3847/1538-4357/ac1353
  * Jensen et al. (2024) Jensen, J., Hayes, C. R., Sestito, F., et al. 2024, MNRAS, 527, 4209, doi: 10.1093/mnras/stad3322
  * Ji et al. (2016) Ji, A. P., Frebel, A., Simon, J. D., & Geha, M. 2016, ApJ, 817, 41, doi: 10.3847/0004-637X/817/1/41
  * Jones et al. (2001) Jones, E., Oliphant, T., & Peterson, P. 2001, SciPy: Open Source Scientific Tools for Python.  http://www.scipy.org
  * Keller et al. (2007) Keller, S. C., Schmidt, B. P., Bessell, M. S., et al. 2007, PASA, 24, 1, doi: 10.1071/AS07001
  * Kim et al. (2018) Kim, S. Y., Peter, A. H. G., & Hargis, J. R. 2018, Phys. Rev. Lett., 121, 211302, doi: 10.1103/PhysRevLett.121.211302
  * Koch et al. (2009) Koch, A., Wilkinson, M. I., Kleyna, J. T., et al. 2009, ApJ, 690, 453, doi: 10.1088/0004-637X/690/1/453
  * Koposov et al. (2015) Koposov, S. E., Belokurov, V., Torrealba, G., & Evans, N. W. 2015, ApJ, 805, 130, doi: 10.1088/0004-637X/805/2/130
  * Li et al. (2018) Li, T. S., Simon, J. D., Kuehn, K., et al. 2018, ApJ, 866, 22, doi: 10.3847/1538-4357/aadf91
  * Li et al. (2022) Li, T. S., Ji, A. P., Pace, A. B., et al. 2022, ApJ, 928, 30, doi: 10.3847/1538-4357/ac46d3
  * Limberg et al. (2023) Limberg, G., Queiroz, A. B. A., Perottoni, H. D., et al. 2023, ApJ, 946, 66, doi: 10.3847/1538-4357/acb694
  * Longeard et al. (2021) Longeard, N., Martin, N., Ibata, R. A., et al. 2021, MNRAS, 503, 2754, doi: 10.1093/mnras/stab604
  * Longeard et al. (2022) Longeard, N., Jablonka, P., Arentsen, A., et al. 2022, MNRAS, 516, 2348, doi: 10.1093/mnras/stac1827
  * Longeard et al. (2023) Longeard, N., Jablonka, P., Battaglia, G., et al. 2023, arXiv e-prints, arXiv:2304.13046, doi: 10.48550/arXiv.2304.13046
  * Malhan et al. (2022) Malhan, K., Valluri, M., Freese, K., & Ibata, R. A. 2022, ApJ, 941, L38, doi: 10.3847/2041-8213/aca6e5
  * Martin et al. (2007) Martin, N. F., Ibata, R. A., Chapman, S. C., Irwin, M., & Lewis, G. F. 2007, MNRAS, 380, 281, doi: 10.1111/j.1365-2966.2007.12055.x
  * Martínez-Vázquez et al. (2021) Martínez-Vázquez, C. E., Cerny, W., Vivas, A. K., et al. 2021, AJ, 162, 253, doi: 10.3847/1538-3881/ac2368
  * Mau et al. (2022) Mau, S., Nadler, E. O., Wechsler, R. H., et al. 2022, ApJ, 932, 128, doi: 10.3847/1538-4357/ac6e65
  * McConnachie (2012) McConnachie, A. W. 2012, AJ, 144, 4, doi: 10.1088/0004-6256/144/1/4
  * McConnachie & Venn (2020) McConnachie, A. W., & Venn, K. A. 2020, Research Notes of the American Astronomical Society, 4, 229, doi: 10.3847/2515-5172/abd18b
  * Morganson et al. (2018) Morganson, E., Gruendl, R. A., Menanteau, F., et al. 2018, PASP, 130, 074501, doi: 10.1088/1538-3873/aab4ef
  * Muñoz et al. (2018) Muñoz, R. R., Côté, P., Santana, F. A., et al. 2018, ApJ, 860, 66, doi: 10.3847/1538-4357/aac16b
  * Munshi et al. (2019) Munshi, F., Brooks, A. M., Christensen, C., et al. 2019, ApJ, 874, 40, doi: 10.3847/1538-4357/ab0085
  * Mutlu-Pakdil et al. (2019) Mutlu-Pakdil, B., Sand, D. J., Walker, M. G., et al. 2019, ApJ, 885, 53, doi: 10.3847/1538-4357/ab45ec
  * Nadler et al. (2021) Nadler, E. O., Drlica-Wagner, A., Bechtol, K., et al. 2021, Phys. Rev. Lett., 126, 091101, doi: 10.1103/PhysRevLett.126.091101
  * Norris et al. (2008) Norris, J. E., Gilmore, G., Wyse, R. F. G., et al. 2008, ApJ, 689, L113, doi: 10.1086/595962
  * Norris et al. (2010) Norris, J. E., Gilmore, G., Wyse, R. F. G., Yong, D., & Frebel, A. 2010, ApJ, 722, L104, doi: 10.1088/2041-8205/722/1/L104
  * Orkney et al. (2021) Orkney, M. D. A., Read, J. I., Rey, M. P., et al. 2021, MNRAS, 504, 3509, doi: 10.1093/mnras/stab1066
  * Ou et al. (2024) Ou, X., Chiti, A., Shipp, N., et al. 2024, arXiv e-prints, arXiv:2403.00921, doi: 10.48550/arXiv.2403.00921
  * Pace et al. (2022) Pace, A. B., Erkal, D., & Li, T. S. 2022, ApJ, 940, 136, doi: 10.3847/1538-4357/ac997b
  * Pace & Li (2019) Pace, A. B., & Li, T. S. 2019, ApJ, 875, 77, doi: 10.3847/1538-4357/ab0aee
  * Pan & Kravtsov (2023) Pan, Y., & Kravtsov, A. 2023, arXiv e-prints, arXiv:2310.08636, doi: 10.48550/arXiv.2310.08636
  * Peñarrubia et al. (2008) Peñarrubia, J., Navarro, J. F., & McConnachie, A. W. 2008, ApJ, 673, 226, doi: 10.1086/523686
  * Plez (2012) Plez, B. 2012, Turbospectrum: Code for spectral synthesis, Astrophysics Source Code Library, record ascl:1205.004.  http://ascl.net/1205.004
  * Pontzen & Governato (2012) Pontzen, A., & Governato, F. 2012, MNRAS, 421, 3464, doi: 10.1111/j.1365-2966.2012.20571.x
  * Read et al. (2016) Read, J. I., Agertz, O., & Collins, M. L. M. 2016, MNRAS, 459, 2573, doi: 10.1093/mnras/stw713
  * Rimoldini et al. (2023) Rimoldini, L., Holl, B., Gavras, P., et al. 2023, A&A, 674, A14, doi: 10.1051/0004-6361/202245591
  * Robin et al. (2003) Robin, A. C., Reylé, C., Derrière, S., & Picaud, S. 2003, A&A, 409, 523, doi: 10.1051/0004-6361:20031117
  * Roderick et al. (2016) Roderick, T. A., Mackey, A. D., Jerjen, H., & Da Costa, G. S. 2016, MNRAS, 461, 3702, doi: 10.1093/mnras/stw1541
  * Schlegel et al. (1998) Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525, doi: 10.1086/305772
  * Simon (2019) Simon, J. D. 2019, ARA&A, 57, 375, doi: 10.1146/annurev-astro-091918-104453
  * Simon & Geha (2007) Simon, J. D., & Geha, M. 2007, ApJ, 670, 313, doi: 10.1086/521816
  * Simon et al. (2011) Simon, J. D., Geha, M., Minor, Q. E., et al. 2011, ApJ, 733, 46, doi: 10.1088/0004-637X/733/1/46
  * Simon et al. (2017) Simon, J. D., Li, T. S., Drlica-Wagner, A., et al. 2017, ApJ, 838, 11, doi: 10.3847/1538-4357/aa5be7
  * Slater et al. (2020) Slater, C. T., Ivezić, Ž., & Lupton, R. H. 2020, AJ, 159, 65, doi: 10.3847/1538-3881/ab6166
  * Starkenburg et al. (2017) Starkenburg, E., Martin, N., Youakim, K., et al. 2017, MNRAS, 471, 2587, doi: 10.1093/mnras/stx1068
  * Strutz (2010) Strutz, T. 2010, Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond)
  * Tarumi et al. (2021) Tarumi, Y., Yoshida, N., & Frebel, A. 2021, ApJ, 914, L10, doi: 10.3847/2041-8213/ac024e
  * Tau et al. (2024) Tau, E. A., Vivas, A. K., & Martínez-Vázquez, C. E. 2024, AJ, 167, 57, doi: 10.3847/1538-3881/ad1509
  * Taylor (2006) Taylor, M. B. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 666
  * Usman et al. (2024) Usman, S. A., Ji, A. P., Li, T. S., et al. 2024, MNRAS, doi: 10.1093/mnras/stae185
  * van der Walt et al. (2011) van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Science and Engineering, 13, 22, doi: 10.1109/MCSE.2011.37
  * Vivas et al. (2020) Vivas, A. K., Martínez-Vázquez, C., & Walker, A. R. 2020, ApJS, 247, 35, doi: 10.3847/1538-4365/ab67c0
  * Walker et al. (2009) Walker, M. G., Mateo, M., Olszewski, E. W., et al. 2009, ApJ, 704, 1274, doi: 10.1088/0004-637X/704/2/1274
  * Waller et al. (2023) Waller, F., Venn, K. A., Sestito, F., et al. 2023, MNRAS, 519, 1349, doi: 10.1093/mnras/stac3563
  * Walsh et al. (2008) Walsh, S. M., Willman, B., Sand, D., et al. 2008, ApJ, 688, 245, doi: 10.1086/592076
  * Wheeler et al. (2019) Wheeler, C., Hopkins, P. F., Pace, A. B., et al. 2019, MNRAS, 490, 4447, doi: 10.1093/mnras/stz2887
  * White & Frenk (1991) White, S. D. M., & Frenk, C. S. 1991, ApJ, 379, 52, doi: 10.1086/170483
  * Willman & Strader (2012) Willman, B., & Strader, J. 2012, AJ, 144, 76, doi: 10.1088/0004-6256/144/3/76
  * Willman et al. (2005a) Willman, B., Blanton, M. R., West, A. A., et al. 2005a, AJ, 129, 2692, doi: 10.1086/430214
  * Willman et al. (2005b) Willman, B., Dalcanton, J. J., Martinez-Delgado, D., et al. 2005b, ApJ, 626, L85, doi: 10.1086/431760
  * Wolf et al. (2010) Wolf, J., Martinez, G. D., Bullock, J. S., et al. 2010, MNRAS, 406, 1220, doi: 10.1111/j.1365-2966.2010.16753.x