# Magellan/IMACS spectroscopy of Grus I: A low metallicity ultra-faint dwarf
galaxy111This paper includes data gathered with the 6.5 meter Magellan
Telescopes located at Las Campanas Observatory, Chile.

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  Joshua D. Simon
Observatories of the Carnegie Institution for Science, 813 Santa Barbara St.,
Pasadena, CA 91101, USA  Anna Frebel Department of Physics and Kavli Institute
for Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Andrew B. Pace McWilliams Center for Cosmology,
Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, 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 Department
of Astronomy and Astrophysics, University of Toronto, 50 St. George Street,
Toronto ON, M5S 3H4, Canada

(Received June, 2022; Revised –; Accepted –)

###### Abstract

We present a chemodynamical study of the Grus I ultra-faint dwarf galaxy (UFD)
from medium-resolution ($R\sim 11,000$) Magellan/IMACS spectra of its
individual member stars. We identify eight confirmed members of Grus I, based
on their low metallicities and coherent radial velocities, and four candidate
members for which only velocities are derived. In contrast to previous work,
we find that Grus I has a very low mean metallicity of
$\langle$[Fe/H]$\rangle=-2.62\pm 0.11$ dex, making it one of the most metal-
poor UFDs. Grus I has a systemic radial velocity of $-143.5\pm 1.2$ km s-1 and
a velocity dispersion of $\sigma_{\text{rv}}=2.5^{+1.3}_{-0.8}$ km s-1 which
results in a dynamical mass of $M_{1/2}\,(r_{h})=8^{+12}_{-4}\times 10^{5}$ M⊙
and a mass-to-light ratio of M/LV = $440^{+650}_{-250}$ M⊙/L⊙. Under the
assumption of dynamical equilibrium, our analysis confirms that Grus I is a
dark-matter-dominated UFD (M/L $>80$ M⊙/L⊙). However, we do not resolve a
metallicity dispersion ($\sigma_{\text{[Fe/H]}}<0.44$ dex). Our results
indicate that Grus I is a fairly typical UFD with parameters that agree with
mass-metallicity and metallicity-luminosity trends for faint galaxies. This
agreement suggests that Grus I has not lost an especially significant amount
of mass from tidal encounters with the Milky Way, in line with its orbital
parameters. Intriguingly, Grus I has among the lowest central density
($\rho_{1/2}\sim 3.5_{-2.1}^{+5.7}\times 10^{7}$ M⊙ kpc-3) of the UFDs that
are not known to be tidally disrupting. Models of the formation and evolution
of UFDs will need to explain the diversity of these central densities, in
addition to any diversity in the outer regions of these relic galaxies.

Galaxies: dwarf— Galaxies: individual (Grus I) — Local Group — stars:
Population II

††journal: ApJ††software: COSMOS reduction pipeline (Dressler et al., 2011;
Oemler et al., 2017) , astropy (Astropy Collaboration et al., 2013, 2018),
emcee (Foreman-Mackey et al., 2013, 2019), galpy (Bovy, 2015)

##  1 Introduction

Over the last two decades, data from large digital sky surveys (e.g., the
Sloan Digital Sky Survey, the Dark Energy Survey, PanSTARRS) have led to an
order-of-magnitude increase in the number of known low surface brightness
stellar systems in the vicinity ($<200$ kpc) of the Milky Way (e.g., Willman
et al., 2005a, b; Zucker et al., 2006; Belokurov et al., 2007; Walsh et al.,
2007; Willman, 2010; Bechtol et al., 2015; Drlica-Wagner et al., 2015; Kim &
Jerjen, 2015; Kim et al., 2015; Koposov et al., 2015a; Laevens et al., 2015a,
b; Drlica-Wagner et al., 2016; Homma et al., 2016, 2018; Mau et al., 2020;
Cerny et al., 2021, 2022). One particularly intriguing class of faint systems,
which were first detected in SDSS data over a decade ago (Willman et al.,
2005a, b), are ultra-faint dwarf galaxies (UFDs). UFDs are the least luminous
($L<10^{5}$ L⊙; Simon 2019), most dark-matter-dominated ($\gtrsim 100$ M⊙/L⊙;
Simon & Geha 2007), and among the oldest ($\sim 13$ Gyr; e.g., Brown et al.
2014) stellar systems. Consequently, they are unique nearby probes of galaxy
formation on the smallest scales (e.g. Rey et al., 2019), early chemical
evolution (e.g. Frebel et al., 2014), and indirect signatures of dark matter
interactions (e.g. Abdallah et al., 2020).

An initial step in characterizing UFDs is to derive their dynamical masses and
metallicities through spectroscopy of member stars. This step is crucial,
because it is often ambiguous upon discovery whether a faint system is a bona-
fide UFD or a globular cluster (GC) (Willman & Strader, 2012). One
distinguishing feature between GCs and UFDs is that GCs are not dark-matter-
dominated (M/L $\lesssim 3$ M⊙/L⊙; McLaughlin & van der Marel 2005) whereas
UFDs are the most dark-matter-dominated known systems ($\gtrsim 100$ M⊙/L⊙;
Simon & Geha 2007). From spectroscopy, one can derive the velocity dispersion
of member stars, which can then be used to derive a dynamical mass (Walker et
al., 2009b; Wolf et al., 2010) and an accompanying mass-to-light ratio for
classification. A metallicity dispersion can also be used to separate GCs from
UFDs, 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). Differences in chemical abundance patterns are also observed (e.g.,
Ji et al., 2019).

Simply identifying a system as a UFD and presenting its general properties
(e.g., dynamical mass, mean metallicity & dispersion) is of scientific
interest. For instance, the number and distribution of the Milky Way’s UFDs
can constrain models of dark matter (e.g. Kim et al., 2018; Nadler et al.,
2021; Mau et al., 2022). Whether or not a UFD lies on the luminosity-mass
relation for dwarf galaxies (Kirby et al., 2013b) can indicate mass loss from
interactions with the Milky Way (e.g., Simon et al., 2017; Li et al., 2018a).
And the kinematics of stars in a UFD can be used to derive a J-factor to
determine the relevance of the system for indirect searches for signatures of
dark matter interactions (e.g., Pace & Strigari, 2019).

In this regard, Grus I is a particularly interesting Milky Way satellite as
its classification has remained somewhat ambiguous. The system was first
discovered in Dark Energy Survey (DES) DR1 data as a metal-poor, faint
($M_{V}=-3.4\pm 0.3$) satellite (Koposov et al., 2015a); although, its
location near a DECam chip-gap in the DES imaging rendered its structural
properties uncertain. Subsequent, wide-field photometric follow-up (Cantu et
al., 2021) derived a half-light radius of $r_{h}=151^{+21}_{-31}$ pc and a
photometric $\langle$[Fe/H]$\rangle=-1.88^{+0.09}_{-0.03}$, suggesting Grus I
to be a UFD due to its large size but with a higher than typical UFD
metallicity. Jerjen et al. (2018) found a lower metallicity of
$\langle$[Fe/H]$\rangle=-2.50^{+0.30}_{-0.30}$ in their photometric study of
Grus I. An initial spectroscopic study of Grus I by Walker et al. (2016) was
unable to resolve a velocity dispersion and derived a mean metallicity of
$\langle$[Fe/H]$\rangle=-1.42^{+0.55}_{-0.42}$ from seven probable member
stars. Such a metallicity, at face value, is abnormally high for a UFD
(typically $\langle$[Fe/H]$\rangle<-2.0$; Simon 2019), but the large
uncertainty on the metallicity precluded a clear classification.

Recent observations have hinted that Grus I is a UFD. The brightest two stars
in Grus I have [Fe/H] $\approx-2.5$ and show deficiencies in neutron-capture
element abundances, which is a distinctive signature of UFD stars (Ji et al.,
2019). A recent study presented in Zoutendijk et al. (2021) supports the
classification of Grus I as a UFD by detecting a large, but uncertain,
velocity dispersion of $10.4^{+9.3}_{-5.1}$ km s-1 using MUSE data ($R\sim
3000$). However, this study does not derive spectroscopic metallicities for
its sample of members, and only selects Grus I member stars through a
kinematic selection. This can artificially inflate the derived velocity
dispersion by making the sample susceptible to contamination from more metal-
rich foreground Milky Way halo stars that have similar kinematics to Grus I. A
detailed and uniform study of Grus I, with a joint metallicity and kinematic
analysis, is therefore needed to conclusively determine its nature.

In this paper, we present a comprehensive study of member stars in Grus I with
new spectroscopy from Magellan/IMACS. We re-observe all likely members that
were presented in Walker et al. (2016) to derive independent velocity and
metallicity measurements, and to search for any binary stars. From our joint
metallicity and velocity analysis, we identify eight member stars and derive a
mean metallicity of $\langle$[Fe/H]$\rangle=-2.62\pm 0.11$ and a velocity
dispersion of $\sigma=2.5^{+1.3}_{-0.8}$ km s-1, confirming that Grus I is a
canonical dark-matter-dominated UFD (M/LV = $440^{+650}_{-250}$ M⊙/L⊙ and M/LV
$>80$ M⊙/L⊙). We then comment on the orbital history and evolution of Grus I,
based on its derived properties and our sample of members.

The paper is organized as follows. In Section 2, we describe our observations;
In Section 3, we outline our methodology in deriving velocities,
metallicities, and identifying members; In Section 4, we derive the dynamical
mass, mean metallicity, and orbit of Grus I, and comment on its evolution; and
in Section 5, we conclude.

##  2 Observations & Data Reduction

Table 1:  Observations Mask | RA (h:m:s) | DEC (d:m:s) | Slit PA | $t_{\text{exp}}$ | Date of Observation | MJD of | Number of | Number of
---|---|---|---|---|---|---|---|---
Name | (J2000) | (J2000) | (deg) | (min) | (MM/DD/YYYY) | ObservationaaFor masks observed over multiple nights, we list the midpoint MJD of observation. | slits | useful spectrabbDefined as having a velocity measurement in Table 2.
Mask 1 | 22:56:40 |  $-50$:10:40 | 90 | 225 | 07/26/2015 | 57229.33 | 28 | 17
Mask 2 | 22:56:36 |  $-50$:08:59 | 214 | 180 | 10/06/2019 | 58762.03 | 72 | 61
Mask 3ccMask 3 was designed to obtain additional velocities for previously confirmed, bright Grus I members in Masks 1 and 2. | 22:56:53 |  $-50$:08:30 | 72 | 30 | 09/14/2021 | 59471.02 | 6 | 3

###  2.1 Summary of Observations

We observed Grus I using the IMACS spectrograph (Dressler et al., 2006) on the
Magellan-Baade Telescope with three separate multi-slit masks in July 2015,
October 2019, and September 2021, respectively (see Table 1 for details). We
operated the spectrograph following previous multi-slit spectroscopic studies
of UFDs using the IMACS instrument (e.g. Simon et al., 2017; Li et al., 2017;
Simon et al., 2020), which we briefly outline here. The observations were
performed using the f/4 camera, which nominally granted a 15$\farcm$4 by
15$\farcm$4 field of view for slit placement. We used a slit size of
0$\farcs$7 and the 1200 $\ell$ mm-1 grating at a tilt angle of 32$\fdg$4,
which granted a resolution of $R\approx 11,000$ and wavelength range of $\sim
7500$ Å to $\sim 9000$ Å. This wavelength range is sufficient to cover the
prominent telluric A-band feature ($\sim 7600$ Å) and the calcium triplet
absorption lines (8498 Å, 8542 Å, 8662 Å). This setup grants a minimum
velocity precision of $\sim 1$ km s-1 (e.g., Simon et al., 2017). We note that
the exact wavelength range varies for each spectrum based on the location of
the slit on the multi-slit mask. However, we placed slits to ensure that at
least the calcium triplet region (8450 Å to 8700 Å) was covered for each star.

Our observing sequence included 2-3 science exposures of 1800 s to 3300 s,
followed by an arc frame for wavelength calibration, and then a quartz frame
for order-tracing and flat-fielding purposes. We note that we used HeNeAr
reference lamps for the wavelength calibration of our observations in 2015,
but switched to KrHeNeAr lamps for all subsequent observations in order to
make use of strong Kr lines between 7600 Å and 7900 Å. The weather was
mediocre ($\sim 1$$\farcs$0 seeing) during the 2015 observations, $\sim
0\farcs 7$ seeing with occasional cirrus for the 2019 observations, and $\sim
0\farcs 6$ seeing with clear skies for the 2021 observations. Table 1 lists
the details of our observations.

We reduced the data following Simon et al. (2017) and Li et al. (2017). The
COSMOS reduction pipeline (Dressler et al., 2011; Oemler et al., 2017) was
used to locate the slits on the CCD array, generate an initial wavelength
solution, and extract 2D spectra. Then, we used a modified version of the
DEEP2 reduction pipeline (Cooper et al., 2012; Newman et al., 2013) that had
been altered by Simon et al. (2017) to refine the IMACS wavelength solution
and extract 1d spectra.

###  2.2 Target Selection

We observed Grus I using three multi-slit masks (see Table 1). Targets for
Mask 1 were selected by overlaying a 12 Gyr, [Fe/H] = $-2.5$ Dartmouth
isochrone (Dotter et al., 2008) at the assumed distance modulus of Grus I
($m-M=20.4$; Koposov et al. 2015a) on a $g,r$ color-magnitude diagram of stars
within 20$\farcm$0 of Grus I. The color-magnitude diagram for this selection
was generated by running a default configuration of Source Extractor (Bertin &
Arnouts, 1996) on DES images of Grus I that were retrieved from the NOAO
public data archive (Flaugher et al., 2015; Morganson et al., 2018). We
identified stars within 0.1 mag of the isochrone as candidate Grus I members
and ultimately selected 28 stars for inclusion on this mask, limited by
constraints arising from slit placement.

Mask 2 was designed using photometry from DES DR1 (Abbott et al., 2018).
Target selection was carried out with a 12.5 Gyr, [Fe/H] = $-2.3$ Dartmouth
isochrone, identifying stars within 0.08 mag of the red giant branch (RGB) and
with Gaia DR2 proper motions consistent with that of Gru I. Eleven RGB
candidates were included on the mask. Mask 3 was designed to obtain an
additional measurement of the two brightest member stars identified from the
previous masks, which each exhibited possible signs of weak radial velocity
variations.

##  3 Analysis

Figure 1: Top left: Color-magnitude diagram of stars observed in this study.
Confirmed non-members of Gru I, as determined by their radial velocities and
metallicities (see Section 3.3) are shown as red crosses. Confirmed members of
Grus I are shown as filled blue circles. Candidate members (those with
velocities consistent with membership, but no metallicity information) are
shown as hollow blue circles. DES J225643.20$-$501130.0, the star with a
radial velocity consistent with Grus I membership but a high metallicity
([Fe/H] $=-0.9\pm 0.38$; see Section 3.3) is indicated by a larger red cross.
A 10 Gyr, [Fe/H] = $-2.2$ MIST isochrone (Dotter, 2016; Choi et al., 2016;
Paxton et al., 2011, 2013, 2015, 2018) is over-plotted at the distance modulus
of Grus I ($m-M$ = 20.48 mag; Cantu et al., 2021) for reference. Top right:
Spatial distribution of stars observed in this study. The dashed ellipse
denotes the Grus I half-light radius presented in Cantu et al. (2021). Bottom
left: Histogram of velocities of the stars in our sample. The Grus I members
clearly cluster between $\sim-150$ km s-1 and $\sim-135$ km s-1. Note that one
star (DES J225643.20$-$501130.0) has a velocity consistent with membership but
is listed as a non-member due to its high metallicity (see paragraph 2 in
Section 3.3). Bottom right: Gaia EDR3 (Gaia Collaboration et al., 2016, 2021)
proper motions of stars in our sample. The members and candidate members of
Grus I cluster at a systemic proper motion of $\mu_{\alpha}\cos\delta=0.07\pm
0.05$ mas yr-1, $\mu_{\delta}=0.25\pm 0.07$ mas yr-1.

###  3.1 Derivation of radial velocities

We derived radial velocities following the methods presented in Simon et al.
(2017) and Li et al. (2017), which we briefly outline here. We performed a
$\chi^{2}$ minimization between our observed spectra and a template IMACS
spectrum of HD122563 from 8450 Å to 8680 Å to measure radial velocities from
the calcium triplet features. The template spectrum of HD 122563 was collected
using the same 0$\farcs$7 slit size and 1200 $\ell$ mm-1 grating as our Grus I
observations. We assumed a velocity of $-26.51$ km s-1 for HD122563 (Chubak et
al., 2012). We derived heliocentric velocity corrections using the astropy
package (Astropy Collaboration et al., 2013, 2018). Random uncertainties on
the radial velocity measurements were derived through Monte Carlo re-sampling:
we added noise to each spectrum based on its signal-to-noise value, re-
measured the radial velocity, and repeated this process 500 times. We took the
standard deviation of the resulting velocity distribution, after clipping
$5\sigma$ outliers, to be the random velocity uncertainty for each star.

We applied a correction to our radial velocities based on the wavelength of
the telluric A-band absorption feature at $\sim 7600$ Å to account for slit
mis-centering effects. We derived this correction by repeating the same steps
as for the radial velocity measurement, but instead performing the $\chi^{2}$
minimization over the wavelength range 7550 Å to 7700 Å with respect to a
template spectrum of the hot, rapidly rotating star HR4781 (Simon et al.,
2017). These corrections were typically $\lesssim 5$ km s-1 and showed a clear
dependence on the location of the slit perpendicular to the dispersion axis of
the CCD mosaic. We thereby modeled these corrections by fitting a line to the
telluric correction as a function of location along this axis of the CCD
mosaic, using only measurements from spectra with S/N $>5$ to ensure a high-
quality sample. We then used this linear model to calculate the telluric
correction for each star, which had the additional benefit of providing a
robust correction for stars that had low S/N or no wavelength coverage of the
A-band region.

We derived a systematic velocity uncertainty of 1.1 km s-1 on our velocity
measurements, based on repeat observations of stars following the methods
presented in e.g., Simon & Geha (2007). Specifically, we divided our raw data
into two subsets, independently reduced each subset, and derived velocities
from the 1D spectra following the above techniques. Then, we found that a
systematic velocity uncertainty of 1.1 km s-1 needed to be added in quadrature
to the random velocity uncertainties for consistency among the velocity
measurement of the same stars (e.g., as in Simon & Geha, 2007; Simon et al.,
2017; Li et al., 2017). We computed final velocity uncertainties by adding in
quadrature the random velocities uncertainties and the systematic velocity
uncertainty. If applicable (i.e., if stars showed no evidence for binarity),
velocity measurements were combined across multiple runs by taking a weighted
average, where the weights were equal to the inverse squared uncertainty of
the velocity measurement.

Our radial velocity measurements are presented in Table 2 and in the lower
left panel of Figure 1. We find 13 stars with radial velocities roughly
consistent with membership to Grus I (between $-$150 km s-1 and $-$130 km
s-1). Of these, nine have metallicity measurements; eight of those have low
metallicities ([Fe/H] $<-2.0$) consistent with UFD membership, and one has a
higher metallicity ([Fe/H] $>-1.0$) that is inconsistent with UFD membership
(see Figure 2, and further discussion in Section 3.3).

Table 2: Velocity measurements for all stars.

ID | MJDaathe midpoint MJD of observation. | RA | DEC |  $g$bbQuoted magnitudes represent the weighted-average dereddened PSF magnitude derived from the DES DR2 catalog (Flaugher et al., 2015; Morganson et al., 2018; Abbott et al., 2021). |  $r$bbQuoted magnitudes represent the weighted-average dereddened PSF magnitude derived from the DES DR2 catalog (Flaugher et al., 2015; Morganson et al., 2018; Abbott et al., 2021). | S/N | $v$ | MEM
---|---|---|---|---|---|---|---|---
|  | (deg) | (deg) | (mag) | (mag) |  | (km s-1) |
DES J225619.85$-$500757.2 | 58762.03 | 344.08273 |  $-$50.13258 | 17.4 | 16.95 | 64.25 | $-4.05\pm 1.11$ | NM
DES J225650.20$-$500814.2 | 58762.03 | 344.20917 |  $-$50.13729 | 21.06 | 20.57 | 4.85 | $-24.18\pm 2.57$ | NM
DES J225625.52$-$500828.1 | 58762.03 | 344.10635 |  $-$50.14116 | 21.9 | 20.5 | 10.77 | $-5.37\pm 1.65$ | NM
DES J225613.76$-$500835.1 | 58762.03 | 344.05735 |  $-$50.14309 | 19.57 | 18.7 | 23.03 | $140.71\pm 1.26$ | NM
DES J225713.21$-$500834.6 | 58762.03 | 344.30507 |  $-$50.14297 | 20.54 | 19.81 | 10.85 | $51.89\pm 1.71$ | NM
DES J225625.24$-$500842.0 | 58762.03 | 344.10519 |  $-$50.14501 | 20.35 | 18.87 | 44.23 | $46.26\pm 1.14$ | NM
DES J225631.22$-$500841.9 | 58762.03 | 344.13012 |  $-$50.14498 | 20.04 | 19.13 | 20.04 | $18.57\pm 1.8$ | NM
DES J225710.06$-$500856.0 | 58762.03 | 344.29192 |  $-$50.1489 | 19.08 | 18.4 | 27.45 | $0.53\pm 1.19$ | NM
DES J225658.06$-$501357.9 | 57229.33 | 344.24192 |  $-$50.23276 | 18.55 | 17.49 | 44.95 | $-140.88\pm 1.11$ | M
$\cdots$ | 58762.03 | 344.24192 |  $-$50.23276 | 18.55 | 17.49 | 53.25 | $-141.59\pm 1.11$ | M
$\cdots$ | 59471.02 | 344.24192 |  $-$50.23276 | 18.55 | 17.49 | 24.79 | $-143.32\pm 1.13$ | M
DES J225643.89$-$500903.0 | 58762.03 | 344.18288 |  $-$50.15085 | 21.43 | 20.93 | 3.5 | $-144.37\pm 7.39$ | CM
DES J225640.97$-$500913.4 | 58762.03 | 344.17074 |  $-$50.15374 | 18.97 | 18.63 | 21.8 | $188.02\pm 1.34$ | NM
DES J225703.50$-$500942.6 | 58762.03 | 344.26461 |  $-$50.16184 | 22.44 | 20.91 | 12.77 | $21.73\pm 1.92$ | NM
DES J225720.93$-$500951.2 | 58762.03 | 344.33724 |  $-$50.16423 | 21.2 | 19.64 | 30.71 | $33.11\pm 1.24$ | NM
DES J225655.34$-$500947.0 | 58762.03 | 344.23059 |  $-$50.16308 | 22.01 | 20.5 | 17.49 | $11.87\pm 1.45$ | NM
DES J225657.50$-$501013.9 | 58762.03 | 344.23959 |  $-$50.17053 | 20.41 | 19.06 | 38.09 | $62.0\pm 1.15$ | NM
DES J225710.72$-$501008.0 | 58762.03 | 344.29467 |  $-$50.16889 | 22.37 | 21.17 | 3.27 | $60.63\pm 7.23$ | NM
DES J225711.61$-$501018.5 | 58762.03 | 344.29838 |  $-$50.17182 | 18.99 | 19.12 | 7.75 | $210.38\pm 6.86$ | NM
DES J225703.66$-$501016.2 | 58762.03 | 344.26527 |  $-$50.17119 | 19.84 | 19.52 | 9.96 | $84.9\pm 1.79$ | NM
DES J225632.36$-$501025.4 | 58762.03 | 344.13486 |  $-$50.17372 | 20.0 | 19.4 | 10.85 | $57.61\pm 1.84$ | NM
DES J225656.51$-$501044.0 | 58762.03 | 344.23547 |  $-$50.1789 | 17.55 | 17.2 | 55.85 | $8.95\pm 1.12$ | NM
DES J225640.78$-$501051.4 | 58762.03 | 344.16992 |  $-$50.18096 | 20.43 | 19.79 | 10.35 | $-142.49\pm 1.46$ | M
$\cdots$ | 59471.02 | 344.16992 |  $-$50.18096 | 20.43 | 19.79 | 5.53 | $-140.68\pm 2.11$ | M
DES J225717.17$-$501105.1 | 58762.03 | 344.32157 |  $-$50.18477 | 19.94 | 19.22 | 12.78 | $79.9\pm 1.91$ | NM
DES J225646.98$-$501226.9 | 58762.03 | 344.19576 |  $-$50.2075 | 21.96 | 20.78 | 4.93 | $12.44\pm 3.69$ | NM
DES J225657.98$-$501252.7 | 58762.03 | 344.24162 |  $-$50.21466 | 19.18 | 18.96 | 15.84 | $279.45\pm 1.6$ | NM
DES J225629.92$-$500433.3 | 57229.33 | 344.12467 |  $-$50.07593 | 19.14 | 18.29 | 33.67 | $-147.39\pm 1.15$ | M
$\cdots$ | 58762.03 | 344.12467 |  $-$50.07593 | 19.14 | 18.29 | 36.66 | $-146.38\pm 1.14$ | M
$\cdots$ | 59471.02 | 344.12467 |  $-$50.07593 | 19.14 | 18.29 | 15.4 | $-144.72\pm 1.26$ | M
DES J225642.47$-$500334.1 | 57229.33 | 344.17699 |  $-$50.05949 | 21.58 | 21.06 | 2.02 | $21.47\pm 10.46$ | NM
DES J225639.47$-$500401.0 | 57229.33 | 344.16449 |  $-$50.06697 | 18.82 | 17.91 | 35.41 | $13.55\pm 1.16$ | NM
DES J225619.67$-$500913.1 | 57229.33 | 344.08198 |  $-$50.15364 | 20.9 | 20.34 | 6.93 | $-146.35\pm 2.39$ | M
$\cdots$ | 58762.03 | 344.08198 |  $-$50.15364 | 20.9 | 20.34 | 6.34 | $-139.67\pm 2.24$ | M
DES J225643.20$-$501130.0 | 57229.33 | 344.18001 |  $-$50.19168 | 21.13 | 20.48 | 3.69 | $-138.53\pm 6.06$ | NM
$\cdots$ | 58762.03 | 344.18001 |  $-$50.19168 | 21.13 | 20.48 | 5.26 | $-138.77\pm 2.31$ | NM
DES J225643.79$-$501332.6 | 57229.33 | 344.18246 |  $-$50.22574 | 21.51 | 20.95 | 2.57 | $-139.07\pm 6.87$ | CM
DES J225637.05$-$501024.8 | 57229.33 | 344.15438 |  $-$50.17357 | 20.46 | 19.81 | 9.29 | $-135.25\pm 2.13$ | M
$\cdots$ | 58762.03 | 344.15438 |  $-$50.17357 | 20.46 | 19.81 | 9.81 | $-143.08\pm 1.58$ | M
DES J225625.69$-$501414.2 | 57229.33 | 344.10707 |  $-$50.23729 | 20.95 | 20.42 | 4.35 | $-144.56\pm 4.0$ | CM
DES J225653.36$-$500924.3 | 57229.33 | 344.22233 |  $-$50.15675 | 19.9 | 19.29 | 13.42 | $-53.12\pm 1.49$ | NM
DES J225657.61$-$500938.5 | 57229.33 | 344.24005 |  $-$50.1607 | 19.21 | 18.43 | 23.37 | $54.94\pm 1.29$ | NM
$\cdots$ | 58762.03 | 344.24005 |  $-$50.1607 | 19.21 | 18.43 | 29.87 | $54.98\pm 1.2$ | NM
DES J225658.78$-$500832.5 | 57229.33 | 344.24495 |  $-$50.14237 | 20.72 | 20.09 | 5.15 | $166.9\pm 2.45$ | NM
DES J225704.98$-$501229.6 | 58762.03 | 344.27078 |  $-$50.20824 | 19.88 | 19.26 | 14.21 | $6.57\pm 1.73$ | NM
DES J225709.08$-$501214.6 | 57229.33 | 344.28784 |  $-$50.20406 | 18.25 | 17.27 | 44.81 | $8.47\pm 1.14$ | NM
DES J225709.39$-$500956.8 | 58762.03 | 344.28915 |  $-$50.1658 | 21.3 | 20.67 | 4.12 | $118.66\pm 2.35$ | NM
DES J225722.15$-$501150.7 | 57229.33 | 344.34232 |  $-$50.19744 | 19.73 | 18.91 | 10.27 | $-29.24\pm 1.7$ | NM
DES J225642.95$-$501741.3 | 57229.33 | 344.17897 |  $-$50.29482 | 21.18 | 20.62 | 3.16 | $-148.87\pm 4.97$ | CM
DES J225643.29$-$500607.3 | 57229.33 | 344.18038 |  $-$50.10203 | 19.74 | 19.07 | 17.25 | $-146.79\pm 1.25$ | M
$\cdots$ | 58762.03 | 344.18038 |  $-$50.10203 | 19.74 | 19.07 | 20.64 | $-146.41\pm 1.24$ | M
DES J225611.70$-$500304.8 | 58762.03 | 344.04878 |  $-$50.05136 | 19.86 | 19.31 | 14.82 | $-85.61\pm 1.35$ | NM
DES J225617.78$-$500309.3 | 58762.03 | 344.0741 |  $-$50.05259 | 20.42 | 19.21 | 20.75 | $116.71\pm 1.38$ | NM
DES J225602.89$-$500353.8 | 58762.03 | 344.01204 |  $-$50.06496 | 20.05 | 18.61 | 57.85 | $-27.75\pm 1.13$ | NM
DES J225618.15$-$500405.3 | 58762.03 | 344.07565 |  $-$50.06815 | 18.94 | 18.66 | 21.47 | $-31.7\pm 1.3$ | NM
DES J225615.03$-$500412.8 | 58762.03 | 344.06263 |  $-$50.07025 | 21.7 | 20.33 | 12.92 | $137.47\pm 1.56$ | NM
DES J225602.84$-$500414.7 | 58762.03 | 344.01186 |  $-$50.07076 | 21.48 | 21.06 | 2.6 | $144.89\pm 5.46$ | NM
DES J225619.00$-$500427.2 | 58762.03 | 344.0792 |  $-$50.07423 | 18.52 | 18.02 | 34.99 | $-22.89\pm 1.15$ | NM
DES J225633.63$-$500426.1 | 58762.03 | 344.14012 |  $-$50.07393 | 21.98 | 20.55 | 12.11 | $-6.86\pm 1.67$ | NM
DES J225626.96$-$500445.3 | 58762.03 | 344.11236 |  $-$50.07927 | 21.77 | 20.68 | 5.73 | $-52.27\pm 4.14$ | NM
DES J225615.78$-$500452.8 | 58762.03 | 344.06578 |  $-$50.08134 | 21.23 | 20.9 | 2.82 | $-48.25\pm 4.49$ | NM
DES J225601.68$-$500459.2 | 58762.03 | 344.00702 |  $-$50.08312 | 22.33 | 20.69 | 15.95 | $-5.16\pm 1.46$ | NM
DES J225603.76$-$500524.5 | 58762.03 | 344.0157 |  $-$50.09014 | 20.94 | 20.31 | 5.53 | $-141.21\pm 1.67$ | M
DES J225624.48$-$500540.8 | 58762.03 | 344.10202 |  $-$50.09468 | 22.19 | 20.61 | 17.33 | $8.0\pm 1.47$ | NM
DES J225638.97$-$500542.4 | 58762.03 | 344.1624 |  $-$50.09511 | 20.02 | 19.43 | 14.25 | $20.45\pm 1.82$ | NM
DES J225644.70$-$500559.7 | 58762.03 | 344.18625 |  $-$50.09993 | 21.95 | 20.63 | 11.68 | $35.89\pm 1.96$ | NM
DES J225608.69$-$500603.8 | 58762.03 | 344.03622 |  $-$50.10107 | 19.66 | 19.19 | 14.54 | $50.85\pm 1.65$ | NM
DES J225628.96$-$500601.9 | 58762.03 | 344.12068 |  $-$50.10054 | 20.97 | 20.0 | 9.75 | $89.51\pm 1.83$ | NM
DES J225613.54$-$500603.5 | 58762.03 | 344.05645 |  $-$50.10099 | 21.05 | 19.92 | 14.86 | $-19.48\pm 1.48$ | NM
DES J225613.72$-$500616.4 | 58762.03 | 344.05718 |  $-$50.10458 | 16.59 | 16.75 | 52.03 | $156.24\pm 1.25$ | NM
DES J225649.23$-$501031.4 | 58762.03 | 344.20513 |  $-$50.17539 | 20.79 | 20.22 | 6.91 | $-142.47\pm 1.83$ | M
DES J225603.42$-$500617.4 | 58762.03 | 344.01426 |  $-$50.10483 | 19.07 | 18.68 | 19.51 | $58.47\pm 1.25$ | NM
DES J225601.57$-$500623.0 | 58762.03 | 344.00655 |  $-$50.1064 | 21.35 | 19.93 | 18.73 | $76.15\pm 1.32$ | NM
DES J225617.16$-$500621.4 | 58762.03 | 344.0715 |  $-$50.10596 | 22.54 | 21.44 | 2.8 | $6.05\pm 9.32$ | NM
DES J225555.38$-$500642.3 | 58762.03 | 343.98078 |  $-$50.11175 | 18.55 | 17.68 | 44.28 | $-70.77\pm 1.14$ | NM
DES J225626.51$-$500651.4 | 58762.03 | 344.11047 |  $-$50.1143 | 19.98 | 18.53 | 51.53 | $11.07\pm 1.12$ | NM
DES J225616.50$-$500651.2 | 58762.03 | 344.06877 |  $-$50.11425 | 21.05 | 20.64 | 3.98 | $142.27\pm 3.55$ | NM
DES J225653.50$-$500716.3 | 58762.03 | 344.22292 |  $-$50.12122 | 21.28 | 20.22 | 8.67 | $27.15\pm 2.49$ | NM
DES J225657.01$-$500740.7 | 58762.03 | 344.23755 |  $-$50.12799 | 18.09 | 17.65 | 43.95 | $-49.15\pm 1.17$ | NM
DES J225644.73$-$500749.0 | 58762.03 | 344.1864 |  $-$50.1303 | 21.99 | 20.7 | 7.64 | $98.16\pm 2.55$ | NM

ccfootnotetext: NM indicates non-members, CM indicates candidate members
(stars with consistent radial velocity, but no derived metallicity), M
indicates members (see Section 3.3).

###  3.2 Derivation of metallicities

We derived metallicities by using the well-established relationship between
the equivalent widths of the calcium triplet absorption lines, the absolute
$V$ magnitude, and the stellar metallicity (Carrera et al., 2013). We measured
equivalent widths of each calcium triplet line by fitting them with a Gaussian
plus Lorentzian profile, following Simon et al. (2017) and Li et al. (2017).
The apparent $V$ magnitude of each star was derived using Equation 5 in
Bechtol et al. (2015) and was converted to an absolute magnitude using a Grus
I distance modulus of $m-M=20.48$ (Cantu et al., 2021).

The random uncertainties in the metallicities were derived following the
procedure in Simon et al. (2020), in which the statistical uncertainty in the
equivalent width from the Gaussian + Lorentzian fit to each line was
propagated to derive a metallicity uncertainty. An additional systematic
uncertainty of 0.32 Å was added in quadrature to the equivalent width
uncertainties (e.g., Simon et al., 2017). The systematic uncertainty in the
final metallicities was assumed to be 0.17 dex, following the stated
uncertainty of the metallicity calibration in Carrera et al. (2013). We took
the final metallicity uncertainty of each star as the quadrature sum of its
random uncertainty and the systematic uncertainty. For stars with spectra over
multiple epochs, we combined metallicity measurements from the individual
spectra by taking the weighted average of the metallicities, where the weights
were the inverse square of the metallicity uncertainties.

We note that the calibration we employ is only valid for red giant branch
stars that are at the distance of Grus I, since the absolute $V$ magnitudes
inputted into the calibration are computed assuming the distance modulus of
Grus I. We see an artifact of this assumption in Figure 2, where a number of
non-members of Grus I (e.g., stars with radial velocities inconsistent with
membership) have spuriously low metallicities. Accordingly, we only report
metallicities in Table 5 for stars that are confirmed members of Grus I
(defined as radial velocities consistent with membership and a low
metallicity; see Section 3.3).

Figure 2: [Fe/H] vs. Radial velocities for stars in this study. The members of
Grus I clearly cluster at low metallicities ([Fe/H] $<-2.0$) and at a
systematic velocity of $\sim-143$ km s-1. Note that one star has a velocity
consistent with membership but a high metallicity ([Fe/H] $-0.9\pm 0.38$ dex),
and is therefore listed as a non-member. There are additional candidate
members in our sample with velocities consistent with membership (see Section
3.3), but are not shown in this plot as the S/N of their spectra is too low
for a metallicity determination.

###  3.3 Identifying members of Grus I

We identify Grus I members based on their clustered radial velocities and the
fact that UFD stars have low metallicities ([Fe/H] $\lesssim-1.5$; Simon
2019). Walker et al. (2016) find that Grus I has a systematic radial velocity
of $-140.5^{+2.4}_{-1.6}$ km s-1. We find a significant over-density of stars
at a similar radial velocity, as shown in the bottom left panel of Figure 1.
We select all stars with radial velocities between $-150$ km s-1 and $-130$ km
s-1 as an initial sample of 13 possible members. There are no stars with
velocities just beyond the threshold of these limits (i.e., no other stars
have velocities $<-100$ km s-1), so it is unlikely that we have excluded any
possible members with this velocity cut. We note that all of the stars with
radial velocities that are consistent with Grus I membership also have Gaia
EDR3 proper motions (Gaia Collaboration et al., 2016, 2021), when available,
consistent with the systematic proper motion of Grus I
($\mu_{\alpha}\cos\delta=0.07\pm 0.05$ mas yr-1,
$\mu_{\delta}=-0.29^{+0.06}_{-0.07}$ mas yr-1; McConnachie & Venn 2020). This
consistency is illustrated in the bottom right panel of Figure 1.

Of the 13 stars with velocities consistent with Grus I membership, 9 have
spectra with sufficient signal-to-noise (S/N $>5$) to derive metallicities
from the calcium triplet absorption features. We find that 8 of these 9 stars
have very low metallicities ([Fe/H] $<-2.0$), consistent with UFD membership
(see Figures 5 and 6 in Simon 2019). Stars at such low metallicities are
unlikely to be foreground Milky Way stars (e.g. Youakim et al., 2020; Chiti et
al., 2021a). One star (DES J225643.20$-$501130.0) has a velocity and proper
motion consistent with membership, but a high metallicity of [Fe/H] = $-0.9\pm
0.38$ which is above the typical metallicity range of UFD stars (no known UFD
star has [Fe/H] $>-1.0$). Based on its high metallicity, we therefore identify
this star as a non-member and exclude it from further analysis, but we note
for completeness that none of the primary conclusions of our paper (e.g.,
orbital properties, Grus I being dark-matter-dominated) would change if we
were to include this star. As noted in Section 3.2, the metallicity
calibration that we employ is only valid for stars at the distance of Grus I.
Accordingly, the metallicities of stars that are likely not members of Grus I
should be disregarded.

We identify the 8 stars with low metallicities ([Fe/H] $<-2.0$) and velocities
consistent with Grus I membership ($-150$ km s-1 to $-130$ km s-1) as
confirmed members (M in Table 2). We report the 4 stars with velocities
consistent with membership, but no metallicity measurements as candidate
members (CM in Table 2). All other stars are identified as non-members. The
analysis in Section 4 is performed using the sample of confirmed members.

###  3.4 Combining our sample with existing literature measurements

There are two published studies of Grus I that report velocity and metallicity
values of individual member stars (Walker et al., 2016; Ji et al., 2019). We
opt to incorporate some of those measurements in our analyses of Grus I to
increase our sensitivity to the velocity dispersion of the system and to aid
in detecting binary stars. In this subsection, we outline how our velocities
and metallicities compare to values presented in those studies, and then
discuss whether/how we incorporate their measurements into our study.

####  3.4.1 Comparison to Walker et al. (2016)

Walker et al. (2016) used the M2FS multi-fiber instrument on the Magellan/Clay
telescope to identify 7 likely members of Grus I ($p_{\text{mem}}>0.5$ in
their Table 1). We re-observed all of those stars (Gru1-003, Grus-004,
Grus1-007, Gru1-023, Gru1-032, Gru1-035, Gru1-038) in this study. We identify
two stars in Walker et al. 2016 (Gru1-022 and Gru1-054) that they do not
classify as likely members to be members with our IMACS data (DES
J225619.67$-$500913.1 and DES J225603.76$-$500524.5, respectively, in Table
2). We find that both stars have IMACS velocities consistent with membership
(between $-143$ km s-1 and $-141$ km s-1) and low metallicities ([Fe/H]
$<-2.5$). They likely missed being classified as members in Walker et al.
(2016) due to their large velocity uncertainties (19.2 km s-1 and 87.9 km s-1,
respectively) in that study. We note that we identify one likely member in
Walker et al. (2016), Gru1-007 (DES J225643.20$-$501130.0), as a non-member
due to its high IMACS metallicity of [Fe/H] = $-0.9\pm 0.38$ (see second
paragraph in Section 3.3). The star also has a relatively high metallicity of
[Fe/H] $=-1.19\pm 0.42$ in Walker et al. (2016) and is marginally redder than
the rest of the Grus I members (as denoted by the larger red cross in the top
left panel of Figure 1).

The most notable discrepancy between our study and Walker et al. (2016) is in
the metallicity measurements. Six stars we classify as confirmed members have
M2FS metallicities in their study (Gru1-003, Gru1-004, Gru1-022, Gru1-032,
Gru1-038, Gru1-054). Our metallicities are, on average, 0.45$\pm 0.14$ dex
lower than their M2FS metallicities. Notably, Gru1-003 (DES
J225637.05$-$501024.8), Gru1-004 (DES J225640.78$-$501051.4), Gru1-022 (DES
J225619.67$-$500913.1), and Gru1-054 (DES J225603.76$-$500524.5) have
discrepancies in their metallicities of over 0.5 dex; although, Gru1-003,
Gru1-022, and Gru1-054 also have highly uncertain M2FS metallicities
($\sigma\geq 0.4$ dex) in Walker et al. (2016). The overall offset between our
metallicities and those in Walker et al. (2016) is largely explained by the
systematic metallicity offset of $+0.32$ dex that Walker et al. (2016) added
to their metallicities to account for discrepancies with solar values. This
offset has been discussed in Chiti et al. (2018) and Ji et al. (2019) as a
cause of discrepancy between M2FS metallicities and those derived from high-
resolution spectroscopy. Accordingly, we adopt our IMACS calcium triplet-based
metallicities in all subsequent analyses.

We find a small, but statistically significant, average velocity offset of
$v_{\text{IMACS}}-v_{\text{M2FS}}=-2.6\pm 0.8$ km s-1 between the IMACS
velocities of the Grus I candidate members and the M2FS velocities presented
in Walker et al. (2016). After accounting for this offset, there are no
$>2\sigma$ velocity outliers between our studies, reflecting agreement between
the M2FS and IMACS velocities. We note that attempting to model this offset as
part of our dynamical modeling (see Section 4.1) returns an offset of
$v_{\text{IMACS}}-v_{\text{M2FS}}=-2.8^{+1.0}_{-0.9}$ km s-1, consistent with
this more direct estimate of the offset.

We opt to combine our velocities with the M2FS velocities in Walker et al.
(2016) to increase the velocity precision of our sample. To account for
possible systematic effects when combining measurements from different
spectrographs, we implement the likelihood function presented in Minor et al.
(2019) in our dynamical analysis in Section 4.1. This likelihood function
simultaneously fits for a velocity offset between samples from different
spectrographs when deriving dynamical parameters. Additionally, we add a
systematic velocity uncertainty of 0.9 km s-1 in quadrature to the velocity
uncertainties presented in Walker et al. (2016), following the analysis of
M2FS velocity uncertainties in Simon et al. (2015). We note that the net
effect of both of these corrections is to decrease the significance of any
detected velocity dispersion, making these conservative choices with respect
to the conclusions of this paper. We present results both with and without
these kinematic adjustments in Section 4.1, but the relevant numbers in Table
4 and elsewhere in the paper reflect the steps that are described in this
paragraph.

####  3.4.2 Comparison to Ji et al. (2019)

Ji et al. (2019) used the MIKE spectrograph on Magellan/Clay to obtain high-
resolution spectra of Gru1-032 (DES J225658.06$-$501357.9) and Gru1-038 (DES
J225629.92$-$500433.3) to derive their detailed abundances. We find excellent
agreement (within 0.1 dex) between our metallicities and their metallicities.
We opt to use our calcium triplet-based metallicities for these stars in the
analysis in this paper to ensure uniformity in how metallicities are derived
across our sample. Moreover, given the agreement between the calcium triplet
metallicities and the MIKE metallicities, opting for one set over the other
does not change any results.

We re-measure the velocities of Gru1-032 (DES J225658.06$-$501357.9) and
Gru1-038 (DES J225629.92$-$500433.3) from the MIKE spectra presented in Ji et
al. (2019), following the steps outlined in Chiti et al. (2022). We derive a
velocity of $v_{\text{MIKE}}=-139.6\pm 1.2$ km s-1 for Gru1-032, and
$v_{\text{MIKE}}=-143.3\pm 1.2$ km s-1 for Gru1-038. These are within $4$ km
s-1 of the IMACS and M2FS velocities. We incorporate these velocity
measurements in our binarity analysis in Section 3.5.

###  3.5 Identifying binary stars in Grus I

We searched for evidence of binarity in our Grus I candidate members by
combining velocity data from this study, Walker et al. (2016), and Ji et al.
(2019). Before performing this analysis, we applied an offset of $-2.6$ km s-1
to the velocities in Walker et al. 2016 (see paragraph 3 in Section 3.4.1). We
also added a systematic velocity uncertainty of 0.9 km s-1 in quadrature to
the uncertainties provided in Walker et al. 2016 (see paragraph 4 in Section
3.4.1). The MIKE velocities from Ji et al. (2019) for Gru1-032 (DES
J225658.06$-$501357.9) and Gru1-038 (DES J225629.92$-$500433.3) were taken as
the values presented in the second paragraph of Section 3.4.2. We note that Ji
et al. (2019) do not report evidence that either Gru1-032 or Gru1-038 are
binaries when comparing their MIKE velocities to M2FS velocities of those
stars in Walker et al. (2016).

We tested for binarity by performing a $\chi^{2}$ test on each star to test
the null hypothesis that its velocity is constant over time. The IMACS
velocities used for this test are provided in Table 2, and the M2FS and MIKE
velocities were included when available. We note that DES
J225649.23$-$501031.4 could not be tested for binarity since it only has a
usable radial velocity measurement from one epoch. The same is effectively
true for DES J225603.76$-$500524.5/Gru1-054, which only has an IMACS velocity
from one epoch and a highly uncertain M2FS velocity. We find strong evidence
($p=0.01$) of binarity for Gru1-003 (DES J225637.05$-$501024.8), and marginal
evidence ($p=0.04$) for Gru1-022 (DES J225619.67$-$500913.1) if one excludes
its uncertain M2FS velocity ($\sigma=$19.2 km s-1). To be conservative, we
exclude velocities from these stars in our dynamical analysis of Grus I in
Section 4.1.

##  4 Discussion

Table 3: Summary of Properties of Grus I

Row | Quantity | Value
---|---|---
(1) | RA (J2000) | $344.166^{+0.007}_{-0.006}$
(2) | Dec (J2000) | $-50.168^{+0.006}_{-0.005}$
(3) | Distance (kpc) | $125^{+6}_{-12}$
(4) |  $m-M$ (mag) | $20.48^{+0.11}_{-0.22}$
(5) |  $r_{\rm 1/2}$ (arcmin) | $4.16^{+0.54}_{-0.74}$
(6) | Ellipticity | $0.44^{+0.08}_{-0.10}$
(7) | Position angle (degrees) | $153^{+8}_{-7}$
(8) | $M_{V,0}$ | $-4.1\pm 0.3$
(9) |  $r_{\rm 1/2}$ (pc) | $151^{+21}_{-31}$
(10) | N${}_{\rm spectroscopic~{}members}$ | 8aaOnly includes stars with a confirmed low metallicity from IMACS spectroscopy.
(11) |  $V_{\rm hel}$ (km s-1) |  $-143.5^{+1.2}_{-1.2}$ km s-1
(12) |  $V_{\rm GSR}$ (km s-1) |  $-189.4^{+1.2}_{-1.2}$ km s-1
(13) |  $\sigma$ (km s-1) |  $2.5^{+1.3}_{-0.8}$ km s-1
(14) | Mass (M⊙) | $8^{+12}_{-4}\times 10^{5}$
(15) | M/LV (M⊙/L⊙) | 440${}^{+650}_{-250}$
(16) | Mean [Fe/H] | $-2.62\pm 0.11$
(17) |  $\mu_{\alpha}\cos{\delta}$ (mas yr-1) |  $0.07\pm 0.05$ mas yr-1
(18) |  $\mu_{\delta}$ (mas yr-1) |  $-0.25\pm 0.07$ mas yr-1
(19) | Orbital pericenter (kpc) | 49${}^{+27}_{-23}$ kpcbbTaken from Pace et al. 2022, which presented Grus I orbital parameters including the effect of the LMC, but with the systemic radial velocity in Walker et al. (2016). Our updated systemic velocity should negligibly affect these values; see Section 4.4 for more discussion.
(20) | Orbital apocenter (kpc) | 205${}^{+58}_{-24}$ kpcbbTaken from Pace et al. 2022, which presented Grus I orbital parameters including the effect of the LMC, but with the systemic radial velocity in Walker et al. (2016). Our updated systemic velocity should negligibly affect these values; see Section 4.4 for more discussion.
(21) |  $\log_{10}{J(0.2\arcdeg)}$ (GeV2 cm-5) | $16.4_{-0.7}^{+0.8}$
(22) |  $\log_{10}{J(0.5\arcdeg)}$ (GeV2 cm-5) | $16.5_{-0.7}^{+0.8}$

Table 4: C

Columns (1) through (9) are from Cantu et al. (2021); Columns (19) and (20)
are from Pace et al. (2022); all other Columns are from this study.

In this Section, we answer four questions about Grus I: (1) What is its
dynamical mass and is it dark-matter-dominated? (2) Does Grus I follow the
mass-metallicity and metallicity-luminosity relations for dwarf galaxies? (3)
What is the viability of using Grus I for searches for dark matter (DM)
interactions? And (4) What is the orbital history of Grus I? We then conclude
by comparing our results to those currently in the literature. In subsequent
analysis, we use the IMACS metallicities and velocities of confirmed Grus I
members (as described in Section 3.3), supplemented by their M2FS velocity
measurements in Walker et al. 2016 (see Section 3.4.1).

Figure 3: Left panels: Corner plot from our Markov Chain Monte Carlo (MCMC)
analysis to determine the systemic radial velocity and velocity dispersion of
Grus I, while jointly fitting for the velocity offset between the M2FS and
IMACS spectrographs (see Section 4.1). We determine a systematic velocity of
$-143.5\pm 1.2$ km s-1 and a velocity dispersion of $2.5^{+1.3}_{-0.8}$ km
s-1, confirming Grus I to be dark matter-dominated ($>80$ M⊙/$L_{\odot}$ from
the 95% confidence interval; see Section 4.1) as is typical of UFDs. Right
panels: Corner plot from our MCMC analysis to determine the mean metallicity
and metallicity dispersion of Grus I. We find that Grus I has a low
$\langle$[Fe/H]$\rangle$ = $-2.62\pm 0.11$, also as is typical of UFDs, and
place an upper limit on the metallicity dispersion of
$\sigma_{\text{[Fe/H]}}<0.44$.

###  4.1 Dynamical mass of Grus I

We derive the dynamical mass within a half-light radius of Grus I using the
estimator presented in Wolf et al. (2010):

$M(r_{1/2})\simeq\left(\frac{\langle\sigma_{\text{los}}^{2}\rangle}{\text{km}^{2}\,\text{s}^{-2}}\right)\,\left(\frac{R_{e}}{\text{pc}}\right)\,M_{\odot}$
(1)

in which $\langle\sigma_{\text{los}}^{2}\rangle$ is the squared line-of-sight
velocity dispersion and $R_{\text{e}}$ is the two-dimensional projected half-
light radius. We adopt $R_{\text{e}}=151^{+21}_{-31}$ pc (Cantu et al., 2021)
in all subsequent calculations.

We derive the velocity dispersion of Grus I using a maximum-likelihood
approach on a joint sample of IMACS and M2FS (Walker et al., 2016) velocity
measurements. We restrict our sample to confirmed members (as described in the
last paragraph of Section 3.3) and stars that do not show evidence of binarity
(see Section 3.5). These restrictions result in a sample of six stars for the
velocity dispersion derivation. Three of these stars (DES J225658.06, DES
J225640.78, and DES J225629.92 in Table 5) have precise M2FS velocities
(uncertainties $<2$ km s-1) in Walker et al. (2016). To self-consistently
incorporate these M2FS velocities with our IMACS velocities when deriving the
velocity dispersion, we implement the likelihood function presented in
equations 2 and 3 of Minor et al. (2019). This likelihood simultaneously fits
for velocity offsets in velocities from different spectrographs when deriving
the systemic velocity and velocity dispersion. We implemented this likelihood
function in emcee (Foreman-Mackey et al., 2013, 2019), and initialized our
sample with 100 walkers with a uniform prior on the velocity offset and
systemic velocity, and a Jeffreys Prior on the velocity dispersion. The
resulting corner plot after 2000 steps is shown in the left panels of Figure
3.

From this MCMC analysis (and as seen in Figure 3), we derive a systemic
velocity of $-143.5\pm 1.2$ km s-1, a velocity dispersion of
$2.5^{+1.3}_{-0.8}$ km s-1, and a velocity offset between measurements from
the M2FS and IMACS spectrographs of $-2.8_{-0.9}^{+1.0}$ km s-1. The 95%
confidence interval (CI) of the velocity dispersion is 1.2 km s-1 to 6.2 km
s-1, demonstrating that we clearly resolve a velocity dispersion at a
$>2\sigma$ level. This dispersion results in a dynamical mass within a half-
light radius of 8${}^{+12}_{-4}\times 10^{5}$ M⊙ (95% CI of 1.7$\times 10^{5}$
M⊙ to 5.2$\times 10^{6}$ M⊙). The corresponding mass-to-light ratio is
440${}^{+650}_{-250}$ M⊙/L⊙ (95% CI of 80 M⊙/L⊙ to 3000 M⊙/L⊙) using the
absolute magnitude of $M_{V}=-4.1\pm 0.3$ reported in Cantu et al. (2021).
This establishes that Grus I is a canonical, dark-matter-dominated UFD.

To ensure this conclusion is robust to how we combined the M2FS and IMACS
velocities, we repeat the above analysis with several modifications and
present the results here. When including the metal-rich star at the systemic
velocity of Grus I in our analysis (DES J225643.20$-$501130.0; see paragraph 2
in Section 3.3), we derive a systemic velocity of $-143.1^{+1.2}_{-1.0}$ km
s-1 and a velocity dispersion of $2.5^{+1.3}_{-0.7}$ km s-1. If we do not add
the systematic velocity uncertainty of 0.9 km s-1 to the M2FS velocities and
repeat the above analysis, we derive a systemic velocity of
$-143.5^{+1.3}_{-1.2}$ km s-1 and a velocity dispersion of $2.7^{+1.3}_{-0.8}$
km s-1. If we choose to combine the M2FS and IMACS velocities by just manually
adding an offset of $-2.6$ km s-1 to the M2FS velocities, taking a weighted
average with the IMACS velocities, and repeating the analysis, we derive a
systematic velocity of $-143.5^{+1.2}_{-1.1}$ km s-1 and a velocity dispersion
of $2.5^{+1.2}_{-0.8}$ km s-1. If we include the two binary candidates (DES
J225637.05$-$501024.8 and DES J225619.67$-$500913.1) using their mean
velocities, we derive a dispersion of $2.3^{+0.9}_{-0.7}$ km s-1; similarly,
if we also include the four candidate members (see Section 3.3), we derive a
velocity dispersion of $2.1^{+0.7}_{-0.6}$ km s-1. Including the MIKE
velocities of DES J225658.06$-$501357.9 and DES J225629.92$-$500433.3 still
results in a significant dispersion of $2.3^{+1.2}_{-0.7}$ km s-1. The only
case that results in the system not being dark-matter-dominated at the
2$\sigma$ level is when only the IMACS velocities of the six confirmed members
are used; this sample results in a dispersion of $2.1^{+1.3}_{-0.9}$ km s-1
and a 95% confidence interval on the mass-to-light ratio from 3 M⊙/L⊙ to 2400
M⊙/L⊙. However, in the latter case, the system again becomes clearly M/LV
dominated when a uniform prior is used instead of Jeffrey’s prior when
deriving the dispersion. Accordingly, in all but one case, none of the Grus I
derived properties are meaningfully sensitive to our choice of how to combine
the M2FS and IMACS datasets. For completeness, we also note that tests with
mock data show that we can recover the correct velocity dispersion of Grus I
with a sample of six stars, with similar uncertainties to what we obtained.

###  4.2 Metallicity properties of Grus I

We derive the mean metallicity and metallicity dispersion of Grus I using the
metallicities of its eight confirmed members (see Table 5). We implement the
exact same MCMC approach and implementation as in Section 4.1, but instead
just use the metallicity-related terms in the likelihood function in equation
4 of Walker et al. (2016) assuming no metallicity gradient. This likelihood
models the metallicity distribution as a Gaussian with a mean metallicity
$\mu_{\text{[Fe/H]}}$ and a metallicity dispersion $\sigma_{\text{[Fe/H]}}$.

We derive that Grus I has a mean metallicity of $\mu_{\text{[Fe/H]}}=-2.62\pm
0.11$ and place a $2\sigma$ upper-limit on the metallicity dispersion of
$\sigma_{\text{[Fe/H]}}<0.45$ (see right panels in Figure 3). The mean
metallicity places Grus I exactly on the mass-metallicity and metallicity-
luminosity relation for UFDs (see Figure 4), affirming its status as a UFD.
The agreement between the location of Grus I on these planes and the
population of UFDs also suggests that Grus I did not experience any unique
effects from e.g., tidal stripping relative to the UFD population. The lack of
a resolved metallicity dispersion in Grus I is most likely due to the small
sample size of members, for it is not uncommon for UFDs to show metallicity
dispersions below our upper limit of 0.45 dex (see Supplemental Table 1 in
Simon 2019).

For completeness, we note that including the metal-rich star at the systemic
velocity of Grus I (DES J225643.20$-$501130.0; see paragraph 2 in Section 3.3)
returns a mean metallicity of $-2.46^{+0.21}_{-0.19}$ dex and, unsurprisingly,
a resolved metallicity dispersion of $0.53^{+0.25}_{-0.19}$ dex. Consequently,
even if we were to assume that DES J225643.20$-$501130.0 were a member, Grus I
would still have an overall low metallicity in line with other UFDs (see
Figure 4). The hypothetically resolved metallicity dispersion would also only
strengthen the conclusion that Grus I is a UFD. High-resolution spectroscopic
follow-up of DES J225643.20$-$501130.0 is not easily obtainable due to its
faintness ($g\sim 19.5$), but would remove any ambiguity in the star’s
association with Grus I by allowing neutron-capture element abundances to be
derived (e.g., Ji et al., 2019).

Figure 4: Top: UFD dynamical masses as a function of UFD mean metallicity (see
Appendix A for a full list of references). The Grus I properties derived in
Walker et al. (2016) are shown in green. The properties derived in this study
are shown in red. Our derived metallicity and dynamical mass (see Table 4)
place Gru I in the expected mass-metallicity regime for UFDs. Bottom: Same as
above, but for the metallicity-luminosity relation. Our results place Grus I
exactly on the UFD trend.

###  4.3 J-factor calculations for Grus I

We compute the astrophysical component of the dark matter annihilation flux
(J-factor) and decay flux (D-factor) following Pace & Strigari (2019).
Briefly, this involves comparing the observed velocity distribution to a
theoretical velocity dispersion from solutions of the spherical Jeans
equations (e.g., Geringer-Sameth et al., 2015; Bonnivard et al., 2015). In the
Jeans modeling, we assume a NFW dark matter profile, a Plummer distribution
for the stellar component, and that the stellar anisotropy is constant with
radius. For more details see Pace & Strigari (2019).

From the combined IMACS and M2FS data set, we compute integrated J-factors of
$\log_{10}{J}=16.2_{-0.7}^{+0.8},~{}16.4_{-0.7}^{+0.8},~{}16.5_{-0.7}^{+0.8}$
within solid angles of $0.1\arcdeg,~{}0.2\arcdeg,~{}0.5\arcdeg$ in logarithmic
units of GeV2 cm-5 and compute integrated D-factors of $\log_{10}{D}=16.3\pm
0.4,~{}16.7\pm 0.4,~{}17.2\pm 0.5$ within solid angles of
$0.1\arcdeg,~{}0.2\arcdeg,~{}0.5\arcdeg$ in logarithmic units of GeV cm-2. The
J-factor scales as $J\propto\sigma^{4}/r_{1/2}d^{2}$ and the low velocity
dispersion and large size lead to a small dark matter flux from Grus I (Pace &
Strigari, 2019). Due to the low dark matter density of Grus I, the J-factor is
quite small compared to other UFDs at similar distances and has one of the
lowest J-factors (second to Crater II Caldwell et al., 2017a). For reference,
the largest J-factors are $\log_{10}{J}\sim 19$ for Segue 1 and Reticulum II
(Pace & Strigari, 2019). If Grus I were at its orbital pericenter ($\sim
50~{}{\rm kpc}$) the J-factor would increase by a factor of $\sim 7$ but Grus
I would still remain as one of the lowest J-factors for MW satellites. Grus I
will likely only be useful in stacked analysis for searches for dark matter
annihilation.

###  4.4 Orbital history & central density of Grus I

We initially follow the steps described in Section 4.4 of Simon et al. (2020)
to model the orbit of Grus I. We first derive a systemic proper motion for
Grus I of $\mu_{\alpha}\cos{\delta}=0.07\pm 0.05$ mas yr-1 and
$\mu_{\delta}=-0.25\pm 0.07$ mas yr-1 by taking the inverse-variance weighted
average of the Gaia EDR3 proper motions (Gaia Collaboration et al., 2016,
2021) of its eight confirmed members. This systemic proper motion agrees
exactly with the result from the mixture model approach in Pace et al. (2022)
and is consistent with the Grus I proper motion of
$\mu_{\alpha}\cos{\delta}=0.07\pm 0.05$ mas yr-1 and $\mu_{\delta}=-0.27\pm
0.07$ mas yr-1 reported in Battaglia et al. (2022). This systemic proper
motion, coupled with the radial velocity, distance, R.A., and Decl. in Table 4
provides 6D phase space information from which to calculate the orbit of Grus
I given a Galactic potential.

As a first pass, we initialized orbit instances in the galpy package (Bovy,
2015) for Grus I in a MWPotential2014 potential which had been modified to
increase the halo mass to $1.6\times 10^{12}\,M_{\odot}$ following e.g.,
Carlin & Sand (2018). We note that this potential does not include the effect
of the Large Magellanic Cloud (LMC), and so the orbital parameters in this
paragraph are shown for comparison purposes only and should not supplant those
in e.g., Pace et al. 2022 (see discussion in next paragraph). We generate
10000 instances of these orbits, sampling from the distance, proper motion,
and velocity measurements in Table 4 as Gaussian distributions, and integrate
forwards and backwards for 2 Gyr. We derive a pericenter of 20${}^{+13}_{-10}$
kpc, and find that Grus I will pass its pericenter in $\sim 400$ Myr.
Additionally, we find that Grus I has not had a close encounter (within
$\sim$10 kpc) with the LMC, suggesting that it is not an LMC satellite. This
is in agreement with previous studies (e.g., Kallivayalil et al., 2018;
Battaglia et al., 2022), and our pericenter is consistent with the non-LMC
Grus I pericenter in Pace et al. (2022) of $28^{+16}_{-13}$ kpc. This suggests
that our updated Grus I radial velocity relative to Walker et al. (2016)
should not have a significant effect on the Grus I orbital parameters.

Pace et al. (2022) re-derive the orbital parameters of Grus I while accounting
for the gravitational effects of the LMC. Given their inclusion of the LMC,
the parameters in that study should supersede the parameters presented in the
previous paragraph. We note that their assumed systemic Grus I radial velocity
($-140.5\pm 2.0$ km s-1 from Walker et al. 2016) and proper motions
($\mu_{\alpha}\,\cos\delta=0.07\pm 0.05$ mas yr-1 and $\mu_{\delta}=-0.25\pm
0.07$ mas yr-1) are comparable to what is presented Table 4. Indeed, the only
parameter that is marginally different is the systemic velocity of Grus I (by
3 km s-1). The effect of this difference will be negligible compared to
uncertainties arising from the proper motion of the system, meaning the orbit
results in Pace et al. (2022) from including the LMC should be comparable to
what one would derive when assuming the Grus I parameters in this study. Pace
et al. (2022) find that the Grus I orbit pericenter increases to
$49^{+27}_{-23}$ kpc (see Figure 4 in Pace et al. 2022) when including the
effect of the LMC, and that Grus I is still likely unassociated with the LMC.

Intriguingly, the derived central density of Grus I from the Jeans modeling in
Section 4.3 is $\rho_{1/2}\sim 3.5_{-2.1}^{+5.7}\times 10^{7}$ M⊙ kpc-3, among
the lowest of UFDs that show no signs of tidal disruption (see Figure 5 in
Pace et al. 2022). Given the large pericenter of the orbit of Grus I when
including the influence of the LMC, its density is unlikely to be
significantly further suppressed on a short timescale by future tidal
encounters with the Milky Way. As increasing samples of UFDs are discovered
and characterized with upcoming surveys (e.g., LSST), models of the formation
and evolution of UFDs will need to explain this diversity of inner densities
independently of mass loss scenarios from interactions with the Milky Way
(e.g., Ji et al. 2021).

###  4.5 Comparison to previous studies

We derive metallicity and kinematic properties of Grus I that are more precise
than those currently in the literature, largely due to our addition of a
comprehensive sample of IMACS velocities and metallicities. In particular, we
resolve a velocity dispersion ($\sigma=2.5^{+1.3}_{-0.8}$ km s-1), find that
Grus I is a dark-matter-dominated system ($M_{1/2}\,(r_{h})=8^{+12}_{-4}\times
10^{5}$ M⊙ and M/L${}_{V}=440^{+650}_{-250}$ M⊙/L⊙), and that Grus I has a
mean metallicity ($\langle$[Fe/H]$\rangle=-2.62\pm 0.11$ dex) that is among
the lowest of known UFDs (see Figure 4).

Our derived quantities are also generally consistent with the existing upper
limits and quantities in the literature. Walker et al. (2016) derive a
systemic radial velocity of $-140.5^{+2.4}_{-1.6}$ km s-1, a dispersion of
$\sigma_{v_{\text{los}}}<9.8$ km s-1 and a dynamical mass of
$M_{1/2}\,(r_{h})<2.5\times 10^{6}$ M⊙, which are consistent with our
quantities. Their Grus I mean metallicity
($\langle$[Fe/H]$\rangle=-1.42^{+0.55}_{-0.42}$) is just consistent at the
2$\sigma$ level with our derived metallicity if one also accounts for the
+0.32 dex offset that was applied to M2FS metallicities (see discussion in
paragraph 2 of Section 3.4.1). Zoutendijk et al. (2021) derive a systemic
velocity of $-139.2^{+6.1}_{-5.2}$ km s-1, a velocity dispersion of
$10.4^{+9.3}_{-5.1}$ km s-1, and a mass and mass-to-light ratio of
$M_{1/2}\,(r_{1/2})=1.1^{+2.1}_{-0.8}\times 10^{6}\,$
M${}_{\odot}-1.7^{+2.9}_{-1.2}\times 10^{6}$ M⊙ and $7.4^{+60.2}_{-6.3}\times
10^{3}$ M⊙ L${}_{\odot}^{-1}-3.2^{+33.9}_{-2.7}\times 10^{4}$ M⊙
L${}_{\odot}^{-1}$, respectively. These dispersion, mass, and mass-to-light
values are systematically higher than our derived quantities, but still
consistent within 2$\sigma$. We highlight that our larger sample of members
than the previous M2FS study, and our precise IMACS spectroscopic metallicity
values allow us to cleanly separate Grus I members from the foreground. This
leads to more robust constraints on the dynamical properties of the system,
through less uncertain kinematic parameters. We thus conclusively show that
Grus I is a canonical low-metallicity, dark-matter-dominated UFD.

##  5 Conclusion

We present a comprehensive study of the metallicity and kinematic properties
of Grus I, confirming it to be a very metal-poor
($\langle$[Fe/H]$\rangle=-2.62\pm 0.11$ dex), dark-matter-dominated
(M/L${}_{V}=440^{+650}_{-250}$ M⊙/L⊙) UFD. We combine existing M2FS
spectroscopic measurements of Grus I members in the literature (Walker et al.,
2016) with comprehensive IMACS spectroscopic follow-up of known and newly
discovered members. With our updated sample of eight confirmed Grus I members,
we significantly revise downward the existing spectroscopic metallicity of
Grus I ($\langle$[Fe/H]$\rangle=-1.42^{+0.55}_{-0.42}$; Walker et al. 2016)
and consequently find that Grus I is one of the lowest metallicity UFDs. We
also resolve a velocity dispersion of $\sigma=2.5^{+1.3}_{-0.8}$ km s-1,
consistent with the existing upper limit of $\sigma_{v_{\text{los}}}<9.8$ km
s-1 from Walker et al. (2016) and below the previously reported dispersion of
$10.4^{+9.3}_{-5.1}$ km s-1 in Zoutendijk et al. (2021). Our analysis
corroborates existing hints in the literature from e.g., neutron-capture
element abundances (Ji et al., 2019) that Grus I is a UFD.

We note that our additional IMACS observations robustly constrain the
properties of Grus I in two ways. First, the velocity baseline of our IMACS
observations extends from 2015 to 2021 and all of the candidate members in
Walker et al. (2016) were re-observed. This dataset, when coupled with
velocities from Walker et al. (2016) and MIKE observations in Ji et al.
(2019), allows us to test nearly every Grus I member for binarity (see Section
3.5). We identified two Grus I members as possible binaries and excluded them
from subsequent dynamical analysis to avoid biases. Second, our IMACS
metallicities are more precise than the bulk of existing Grus I metallicities
(see Section 3.4.1), which allows for a more accurate determination of the
metallicity properties of Grus I and also a cleaner separation of members from
the foreground. From our revised analyses, it is clear that Grus I is not an
anomalous UFD. We find no evidence of significant mass loss through tidal
interactions, and our metallicity measurements place the galaxy on the UFD
mass-metallicity and mass-luminosity relations (see Figure 4). Table 4 lists
the full properties of Grus I.

We perform an orbital analysis of Grus I in a simple Milky Way potential, and
find that Grus I is unlikely to be associated with the LMC. As described in
Pace et al. (2022), the Grus I orbital properties are notably affected by the
including gravitational effect of the LMC by e.g., shifting its pericenter to
$\sim 50$ kpc. However, those updated parameters still show no evidence that
Grus I is tidally disrupting or associated with the LMC (Pace et al., 2022).

Interestingly, the central density of Grus I ($\rho_{1/2}\sim
3.5_{-2.1}^{+5.7}\times 10^{7}$ M⊙ kpc-3) is among the lowest of UFDs that are
not known to be tidally disrupting (see Figure 5 in Pace et al. 2022). Only
Grus II has a lower density and Columba I has an upper limit that is a factor
of three larger; however, a number of classical dwarf galaxies (e.g., Ant 2,
Crater 2, Fornax) have lower densities. Despite its low density, it is
unlikely that Grus I is disrupting given its orbit and agreement with UFD
scaling relations (see Section 4.2). Much as models of UFD evolution attempt
to explain the diversity in the outskirts of these systems (e.g., Chiti et
al., 2021b; Tarumi et al., 2021), explaining the variations of their
properties in general (e.g., inner densities) will also be key to
understanding the evolution of these relic galaxies. Future surveys (e.g.,
LSST) have the potential to discover large samples of faint systems in the
Milky Way and the Local Group (e.g., Mutlu-Pakdil et al. 2021) to assess the
full range of their properties.

Table 5:  IMACS Metallicities of confirmed Grus I members ID | RA | DEC |  $g$aaQuoted magnitudes represent the weighted-average dereddened PSF magnitude derived from the DES DR2 catalog (Flaugher et al., 2015; Morganson et al., 2018; Abbott et al., 2021). |  $r$aaQuoted magnitudes represent the weighted-average dereddened PSF magnitude derived from the DES DR2 catalog (Flaugher et al., 2015; Morganson et al., 2018; Abbott et al., 2021). | [Fe/H] | MEM
---|---|---|---|---|---|---
| (deg) | (deg) | (mag) | (mag) |  |
DES J225658.06$-$501357.9 | 344.24192 |  $-$50.23276 | 18.55 | 17.49 | $-2.66\pm 0.19$ | M
DES J225640.78$-$501051.4 | 344.16992 |  $-$50.18096 | 20.43 | 19.79 | $-2.09\pm 0.29$ | M
DES J225629.92$-$500433.3 | 344.12467 |  $-$50.07593 | 19.14 | 18.29 | $-2.45\pm 0.21$ | M
DES J225619.67$-$500913.1 | 344.08198 |  $-$50.15364 | 20.90 | 20.34 | $-2.79\pm 0.28$ | M
DES J225637.05$-$501024.8 | 344.15438 |  $-$50.17357 | 20.46 | 19.81 | $-2.59\pm 0.27$ | M
DES J225643.29$-$500607.3 | 344.18038 |  $-$50.10203 | 19.74 | 19.07 | $-2.90\pm 0.22$ | M
DES J225603.76$-$500524.5 | 344.0157 |  $-$50.09014 | 20.94 | 20.31 | $-2.70\pm 0.43$ | M
DES J225649.23$-$501031.4 | 344.20513 |  $-$50.17539 | 20.79 | 20.22 | $-2.92\pm 0.48$ | M

A.C. is supported by a Brinson Prize Fellowship at the University of
Chicago/KICP. J.D.S is supported in part by the National Science Foundation
under grant AST-1714873. A.F. acknowledges support from NSF grant AST-1716251.
A.B.P. is supported by NSF grant AST-1813881. T.S.L acknowledges financial
support from Natural Sciences and Engineering Research Council of Canada
(NSERC) through grant RGPIN-2022-04794. This work has made use of data from
the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This project used public
archival data from the Dark Energy Survey (DES). 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 FacilitiesCouncil 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
Energéticas, 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. This research has made use of NASA’s Astrophysics Data System
Bibliographic Services (Wenger et al., 2000).

##  Appendix A References for dwarf galaxy data in Figure 4

Here we list the references for the masses, metallicities, and luminosities of
the dwarf galaxies plotted in Figure 4: Majewski et al. (2003); Battaglia et
al. (2006); Simon & Geha (2007); Bellazzini et al. (2008); de Jong et al.
(2008); Mateo et al. (2008); Okamoto et al. (2008); Koch et al. (2009); Walker
et al. (2009a); Walker et al. (2009b); Simon et al. (2011); Willman et al.
(2011); Fabrizio et al. (2012); Kirby et al. (2013a); Kirby et al. (2013b);
Frebel et al. (2014); Bechtol et al. (2015); Drlica-Wagner et al. (2015);
Koposov et al. (2015b); Kim et al. (2015); Kirby et al. (2015); Simon et al.
(2015); Crnojević et al. (2016); Ji et al. (2016); Kim et al. (2016);
Torrealba et al. (2016a); Torrealba et al. (2016b); Collins et al. (2017);
Caldwell et al. (2017b); Kirby et al. (2017); Li et al. (2017); Mucciarelli et
al. (2017); Simon et al. (2017); Spencer et al. (2017); Chiti et al. (2018);
Koposov et al. (2018); Longeard et al. (2018); Li et al. (2018b); Muñoz et al.
(2018); Mutlu-Pakdil et al. (2018); Torrealba et al. (2018); Simon (2019);
Simon et al. (2020); Jenkins et al. (2021); Longeard et al. (2021); Chiti et
al. (2022); Cerny et al. (2022);.

##  Appendix B Compilation of velocity measurements of Grus I members

In Table 6, we compile all velocity measurements of confirmed Grus I members
in this work with their velocity measurements in Walker et al. (2016). Note
that a zero-point offset of $-2.6$ km s-1 has been applied to the velocities
in Walker et al. (2016) to account for an offset between M2FS and IMACS
velocities (see Section 3.4.1).

Table 6: Compilation of velocity measurements for confirmed Grus I members Name |  MJDaaDefined as the MJD at the midpoint of observation. For velocities reported in Walker et al. (2016), we list the MJD derived from Table 1 in that study. | R.A. (deg) | DEC (deg) | Instrument | $v_{\text{helio}}$ | $v_{\text{err}}$ | Ref.
---|---|---|---|---|---|---|---
|  | (J2000) | (J2000) |  |  (km s-1) |  (km s-1) |
DES J225658.06$-$501357.9 | 57222.3 | 344.24192 |  $-$50.23276 | M2FS |  $-141.0$bbOffset of $-2.6$ km s-1 has been applied to account for a zero-point offset between M2FS and IMACS velocities (see paragraph 3 in Section 3.4.1). | $0.4$ |  Gru1-032 in Walker et al. (2016)
$\cdots$ | 57229.3 | 344.24192 |  $-$50.23276 | IMACS | $-140.88$ | 1.11 | This work
$\cdots$ | 58762.0 | 344.24192 |  $-$50.23276 | IMACS | $-141.59$ | 1.11 | This work
$\cdots$ | 59471.0 | 344.24192 |  $-$50.23276 | IMACS | $-143.32$ | 1.13 | This work
DES J225640.78$-$501051.4 | 57222.3 | 344.16992 |  $-$50.18096 | M2FS |  $-142.0$bbOffset of $-2.6$ km s-1 has been applied to account for a zero-point offset between M2FS and IMACS velocities (see paragraph 3 in Section 3.4.1). | 1.4 |  Gru1-004 in Walker et al. (2016)
$\cdots$ | 58762.0 | 344.16992 |  $-$50.18096 | IMACS | $-142.49$ | 1.46 | This work
$\cdots$ | 59471.0 | 344.16992 |  $-$50.18096 | IMACS | $-140.68$ | 2.11 | This work
DES J225629.92$-$500433.3 | 57222.3 | 344.12467 |  $-$50.07593 | M2FS |  $-146.9$bbOffset of $-2.6$ km s-1 has been applied to account for a zero-point offset between M2FS and IMACS velocities (see paragraph 3 in Section 3.4.1). | 0.8 |  Gru1-038 in Walker et al. (2016)
$\cdots$ | 57229.3 | 344.12467 |  $-$50.07593 | IMACS | $-147.39$ | 1.15 | This work
$\cdots$ | 58762.0 | 344.12467 |  $-$50.07593 | IMACS | $-146.38$ | 1.14 | This work
$\cdots$ | 59471.0 | 344.12467 |  $-$50.07593 | IMACS | $-144.72$ | 1.26 | This work
DES J225619.67$-$500913.1 | 57222.3 | 344.08198 |  $-$50.15364 | M2FS | $-143.8$ | 19.2 |  Gru1-022 in Walker et al. (2016)
$\cdots$ | 57229.3 | 344.08198 |  $-$50.15364 | IMACS | $-146.35$ | 2.39 | This work
$\cdots$ | 58762.0 | 344.08198 |  $-$50.15364 | IMACS | $-139.67$ | 2.24 | This work
DES J225637.05$-$501024.8 | 57222.3 | 344.15438 |  $-$50.17357 | M2FS | $-140.2$ | 3.9 |  Gru1-003 in Walker et al. (2016)
$\cdots$ | 57229.3 | 344.15438 |  $-$50.17357 | IMACS | $-135.25$ | 2.13 | This work
$\cdots$ | 58762.0 | 344.15438 |  $-$50.17357 | IMACS | $-143.08$ | 1.58 | This work
DES J225643.29$-$500607.3 | 57229.3 | 344.18038 |  $-$50.10203 | IMACS | $-146.79$ | 1.25 | This work
$\cdots$ | 58762.0 | 344.18038 |  $-$50.10203 | IMACS | $-146.41$ | 1.24 | This work
DES J225603.76$-$500524.5 | 57222.3 | 344.01570 |  $-$50.09014 | M2FS | $-128.0$ | 87.9 |  Gru1-054 in Walker et al. (2016)
$\cdots$ | 58762.03 | 344.0157 |  $-$50.09014 | IMACS | $-141.21$ | 1.67 | This work
DES J225649.23$-$501031.4 | 58762.0 | 344.20513 |  $-$50.17539 | IMACS | $-142.47$ | 1.83 | This work

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