high-resolution surveys such as APOGEE and Gaia shows offsets within $1-2$ km
s-1, while the SoS dataset (dominated by low-resolution LAMOST and SDSS
spectra) shows a systematic offset of $\sim$ 2.5 km s-1. We are investigating
the cause of this offset, which is likely associated with the DESI wavelength
calibration and adjustments using skylines.

Figure 9: The comparison of radial velocities measured in the DESI SV program
in bright conditions to those from other surveys. Colored curves show
comparisons to SDSS DR14, APOGEE DR17, LAMOST DR7, and Gaia DR3, while the
black curve shows the comparison to the homogenized SoS dataset (Tsantaki et
al., 2021).

####  7.4.2 Radial velocity accuracy

Figure 10 shows the median radial velocity error reported by the RVS pipeline
for SV spectra, as a function of stellar color and magnitude. The SV data
provide a representative sampling of the color and magnitude range, and hence
velocity accuracy, expected for the main survey.

Figure 10: The typical radial velocity uncertainty in bright observing
conditions for total exposure times below 1000s. Each bin of the color-
magnitude diagram shows the radial velocity uncertainty reported by the RVS
pipeline. The lines indicate the radial velocity errors of 0.5, 1, and 3
$\mathrm{km\,s^{-1}}$.

To validate the radial velocity errors, we analyze the pairwise velocity
differences from several tiles that were observed multiple times in SV. Figure
11 shows the distribution of pairwise velocity differences as a function of
the combined velocity uncertainty. We also show the robust estimate of the
standard deviation of pair-wise differences obtained using the 16th and 84th
percentiles in bins of velocity uncertainty. The red curve is the expected
behavior if the radial velocity errors have an additional systematic component
of $\sim 0.9\,\mathrm{km\,s^{-1}}$. This extra systematic error component is
likely due to the wavelength calibration. Adding this systematic error in
quadrature to the radial velocity errors reported by our pipeline, we see that
the distribution of pairwise radial velocity errors normalized by the total
uncertainty is very close to a normal distribution (see Figure 12).

Figure 11: The accuracy of radial velocity errors from individual DESI
exposures. Black points show the robust standard deviation estimate (from the
16th and 84th percentiles) for pairwise radial velocity measurements as a
function of their combined formal uncertainties
$\sqrt{\sigma_{1}^{2}+\sigma_{2}^{2}}$. If the radial velocity errors reported
by the pipeline are accurate, the black points should lie on a one-to-one
line. The red line shows the model curve after a $0.9\,\mathrm{km\,s^{-1}}$
systematic error has been added in quadrature to the reported errors. Figure
12: The distribution of pairwise radial velocity differences normalized by the
radial velocity errors with a $0.9\mathrm{\,km\,s^{-1}}$ systematic error
added. The red curve shows a Gaussian distribution with zero mean and unit
variance.

####  7.4.3 [Fe/H] abundances

To assess the accuracy of iron abundances, we compare the measurements from
the SV data with measurements of the same targets in APOGEE DR17, LAMOST DR7
LRS and SDSS DR14 SSPP. A histogram of the differences is shown in Figure 13.
The overlap of DESI with APOGEE, LAMOST, and SDSS comprises $\sim$ 400, 16,000
and 10,000 stars, respectively. The top panel of the figure shows the
comparison of $\mathrm{[Fe/H]}$ measurements from the RVS pipeline, while the
bottom panel shows the comparison to the FERRE abundances. This comparison
shows that the [Fe/H] calibration of both the RVS and SP pipelines is within
$0.1$—$0.2$ dex of that of other surveys. Some scatter in the metallicity
residuals can be attributed to the SDSS, LAMOST, APOGEE, and DESI measurement
errors.

To separate the effects of random errors in the DESI [Fe/H] measurements from
systematic errors and errors in external catalogs, we also characterize [Fe/H]
precision in bins of color and magnitude using repeated observations of the SV
fields. Figure 14 shows the distribution of pairwise [Fe/H] residuals for
$\sim$ 3 million pairs of measurements, using observations with exposure times
between 150 and 1000s. The [Fe/H] accuracy is estimated from the 16th to 84th
percentile range of the distribution. The figure shows that, as expected, the
[Fe/H] precision is a strong function of magnitude, with values around 0.05 at
$r=16$, worsening to $0.2$–$0.4$ at $r=19$. For blue stars, $0.2<r<0.4$, the
precision is noticeably worse than that for redder stars at the same
magnitude. This is likely due to the impact of bright observing conditions,
which degrade the signal most strongly in the blue arm of the instrument, and
to the decreasing number of detectable absorption lines for hotter stars.

Figure 13: Comparison of abundances determined by the RVS (top panel) and SP
(bottom panel) pipelines against data from other surveys. Dark blue curves
show the residuals of DESI [Fe/H] measurements to the SDSS DR14 measurements,
light blue curves show the comparison to LAMOST DR7 LRS measurements, and
green curves show the comparison to APOGEE DR17 [Fe/H] measurements. In the
legend we provide the 16th/50th/84th percentiles of the [Fe/H] residuals for
each survey.

####  7.4.4 Stellar atmospheric parameters

We do not provide here a detailed comparison between our measurements of $\log
g$ and $T_{\mathrm{eff}}$ and those from other surveys, but they show good
agreement. The typical deviation (corresponding to the 16th/84th percentile
range) of $T_{\mathrm{eff}}$ with respect to APOGEE and LAMOST is
$-100\lesssim\delta T_{\rm eff}\lesssim 250$ K, with a median offset of
approximately 100 K. The RVS pipeline gives a broader range of
$T_{\mathrm{eff}}$ offsets than the SP pipeline. The $\log g$ differences
between DESI and other surveys are $-0.1\lesssim\delta\log g\lesssim 0.5$ with
a median offset of 0.2 dex and are similar between the RVS and SP pipelines.

###  7.5 Abundances of star clusters and dwarf galaxies

To validate the abundance measurements from the survey, specifically their
accuracy, we also look at DESI observations of several globular clusters and
OCs as well as dwarf galaxies for which there is a good external measurement
of [Fe/H]. Fig. 15 shows the distribution of measured abundances for several
objects from Table 4 that were observed during SV. For this figure we do not
attempt to identify carefully likely members of each object, only selecting
stars that have proper-motion within $1\,\mathrm{mas\,yr^{-1}}$ and radial
velocity within 10-15$\mathrm{\,km\,s^{-1}}$ of the parent object. The plot
provides a broad overview of the [Fe/H] accuracy of DESI. The expectation is
that cluster members should show narrow distributions centered on their true
[Fe/H] values, while dwarf galaxy members are expected to show some [Fe/H]
spread. The observed [Fe/H] spreads on the figure are also expected to be
affected by random [Fe/H] errors that are magnitude- and colour-dependent, as
discussed in Section 7.4.3. We focus here on the [Fe/H] offsets. We clearly
see that for several systems, like M13 and M5, DESI measurements (from both
the RVS and SP pipelines) are systematically shifted from the literature
values. If we compare the median DESI metallicity for each system to other
measurements from the literature, we see that the average offset
$\mathrm{[Fe/H]_{\mathrm{DESI}}}-\mathrm{[Fe/H]_{\mathrm{external}}}$ is
$-0.13$ dex for RVS and $-0.14$ dex for SP. The range spanned by the [Fe/H]
offsets is $-0.27$ dex (M5) to 0.06 dex (M53) for the RVS pipeline, and
$-0.32$ (M13) to 0.1 dex (NGC 2419) for the SP pipeline.

Figure 14: The estimates of [Fe/H] random errors from the RVS pipeline as a
function of color and magnitude. In each color–magnitude bin we show the
typical random error estimated from the 16th–84th percentile range of the
pairwise [Fe/H] differences between repeated measurements of the same stars.
Figure 15: Comparison of DESI [Fe/H] measurements by the MWS RVS and SP
pipelines of stars in star clusters and a dwarf galaxy to literature
measurements from Carretta et al. (2009), Kirby et al. (2011), and D’Orazi et
al. (2020). Each panel shows a sample of stars observed as part of the DESI
SV1 program (Table 4). We only use stars with proper-motions and radial
velocities matching the expected proper-motion (within
$1\,\mathrm{mas\,yr^{-1}}$) and radial velocity (within
$10$-$15\mathrm{\,km\,s^{-1}}$ of the corresponding object). We only include
measurements from spectra with $S/N>6$ in at least one of the arms. The curves
show kernel density estimates with an Epanechnikov kernel, assuming a
bandwidth of 0.3 dex, a conservative estimate of the precision of the DESI
metallicity measurements. Orange lines show literature values of the
metallicities. For Draco we also show the 1$\sigma$ metallicity scatter in the
system. The number of stars used for the analysis is provided in the legend of
each panel.

####  7.5.1 Quality of the fits

Fig. 16 shows five typical spectra for MWS main sample targets and the
corresponding fits from the RVS pipeline. The S/N is representative of what is
expected for the survey at the corresponding magnitudes. The agreement between
the data and the model is very good even at high S/N. We also note that, since
the RVS model includes a polynomial multiplicative correction to the spectrum
(see Eq. 3), the agreement between the model and the data directly probes the
accuracy of the flux calibration. Fig. 17 summarizes the quality of the
spectral fits by showing the typical $\chi^{2}$ per degree of freedom (DOF)
for the RVS pipeline (left) and the SP pipeline (right), as a function of the
color and magnitude of the star. In both cases we see that $\chi^{2}$ has a
strong dependence on magnitude and color. For the RVS fits, the chi-squares
are close to unity for faint stars, as expected if the errors are treated
correctly. For the SP fits, the chi-squares seem to be slightly below unity
for faint stars. However, both pipelines show strong increases in
$\chi^{2}/\mathrm{DOF}$ to $\sim 3$–$10$ at bright magnitudes and for stars
with $g-r\sim 2$. This is primarily due to the limitations of the stellar
atmospheric grids used, leading to template mismatches that are apparent at
high S/N and for cool stars with many absorption lines and molecular bands.

Figure 16: DESI spectra of several stars spanning the typical range of color
and magnitude observed in the MWS main sample. The data are shown in black.
The spikes in variance at $\sim 5800$Å and $\sim 7500$Å correspond to regions
of overlap between spectrograph arms. In orange we overplot the best-fit
models from the RVS pipeline. The gray band, $4300-4450$Å, indicates
wavelengths affected by a dichroic defect, which we mask in our fits (see Guy
et al., 2022). Figure 17: The median logarithm of $\chi^{2}$ per DOF for
spectral fits with the RVS and SP pipelines, as a function of target color and
magnitude. Figure 18: DESI spectrum (gray) of the white dwarf GD 362,
revealing the metal pollution of the otherwise pristine helium and hydrogen
atmosphere. A model fit is shown in red with prominent metal features labeled.

###  7.6 White dwarf SV results: remnant planetary systems

DESI has already identified several hundred planetary systems around white
dwarfs via the metal pollution of their atmospheres. A dedicated study of
these planetary systems is beyond the scope of this paper. Here we showcase
the potential of this statistical sample using one of the most polluted white
dwarfs so far observed by DESI, GD 362 (Gianninas et al., 2004; Zuckerman et
al., 2007; Xu et al., 2013). GD 362 is extreme in both its pollution from
planetary material (a total of 17 elements have been previously identified in
the white dwarf’s atmosphere; Zuckerman et al. 2007; Xu et al. 2013), as well
as its fairly sizable hydrogen content in an otherwise helium-dominated
atmosphere (which can be indicative of water accretion Jura & Xu, 2010; Klein
et al., 2010; Gentile Fusillo et al., 2017).

The DESI spectrum of GD 362 obtained on 2021 June 21 is shown in Fig. 18,
revealing strong absorption lines from many metals, including Ca, Mg, and Fe.
To analyze the DESI spectrum of GD 362, we compute a grid of white dwarf model
spectra using the code of Koester (2010) and by sampling the parameter space
in $T_{\mathrm{eff}}$, $\log g$ and number abundances $\log[\mathrm{H/He}]$
and $\log[\mathrm{Z/He}]$ around the values determined by Xu et al. (2013). We
fix the metal-to-metal ratios $\log\mathrm{[Z/Ca]}$ to those of Xu et al.
(2013). Using that grid, we find $\mbox{$T_{\mathrm{eff}}$}=10,500$ K, $\log
g=8.00$, $\log$[H/He] = $-1.75$, and $\log\mathrm{[Ca/He]}=-6.84$ as the best-
fit parameters. The parameters differ somewhat from those of Zuckerman et al.
(2007) and Xu et al. (2013) ($\mbox{$T_{\mathrm{eff}}$}=10,540$ K, $\log
g=8.24$, $\log$[H/He] = $-1.14$, and $\log\mathrm{[Ca/He]}=-6.24$), which is
unsurprising as these authors based their analysis on deep Keck High
Resolution Echelle Spectrometer data of this star. However, incorporating the
Gaia photometry and astrometry in our analysis (Section 6.3) will offset the
lower S/N of the DESI spectrum. DESI will identify $\simeq 1000$ debris-
polluted white dwarfs, allowing the first large-scale statistical analysis of
the characteristics of these planetary systems as a function of host star mass
and age. The mws-wd sample will also include many heavily polluted white
dwarfs and probe the extreme parameter spaces of remnant planetary systems.

###  7.7 MWS Targets in SV3 Fields

Figure 19: Fraction of all MWS main sample targets (main-blue, main-red and
main-broad) observed in the SV3 region close to the north ecliptic pole,
$(l,b)\approx(92\,\deg,30\,\deg)$, in $15^{\prime}\times 15^{\prime}$ pixels.
Circles at $24^{\prime}$ and $87^{\prime}$ indicate the region of $\gtrsim
90\%$ completeness discussed in the text (the outer circle is slightly smaller
than the nominal size of a DESI tile).

The 20 SV3 regions (green circles in Fig. 8) each comprise 26-28 slightly
dithered DESI pointings with an area of overlap equivalent to a single DESI
tile. Compared to the four-pass MWS main survey, this dense coverage pattern
provides much higher completeness on all target classes. Several of these
regions overlap the Sagittarius stream, but the majority do not fall on known
Milky Way halo structures.

For a typical SV3 region, nine observations were taken under standard bright-
sky conditions comparable to those expected for MWS and BGS, 13 under dark
conditions (in which the DESI cosmological surveys will operate), and five
under extremely bright conditions (in which the main DESI survey will switch
to the backup stellar program). Fibers on the bright SV3 tiles were allocated
to targets from the BGS and MWS SV selections, with BGS having higher priority
(this is roughly the same way in which fibers will be allocated in the main
survey, although the BGS target density was higher in SV3). Fibers were also
assigned to flux standard stars and secondary program stellar targets on the
dark SV3 tiles.

Fig. 19 shows the completeness of MWS main survey targets (main-blue, main-red
and main-broad) from bright-time SV3 observations in a typical SV3 region
(this example is near the north ecliptic pole, $b\sim 30\,\deg$). The
completeness is $\gtrsim 90\%$ in the annulus $24^{\prime}<r<87^{\prime}$. The
dither pattern results in slightly lower ($\lesssim 80\%$) completeness near
the center (slightly extended to the northeast) and at the edge of each
region.

This high completeness allows us to characterize the parent sample from which
the MWS targets are drawn in these regions, using the measurements made by the
RVS and SP pipelines (Section 6). In the following comparisons, we use all
stars from SV3 that would be selected in one of the three main survey
categories (main-blue, main-red, main-broad). We consider only stars with a
successful RVS pipeline velocity measurement (RVS_WARN = 0) and $S/N\gtrsim 2$
in all three spectrograph arms. These data quality cuts remove $\sim 1\%$ of
all MWS main survey targets in the SV3 dataset. We refer to this subset of SV3
targets as the MWS SV3 sample.

Figure 20: $\mathrm{[Fe/H]}$ distributions for all the stars in the SV3
dataset that belong to any of the three MWS main survey target categories. The
gray lines show the sum of the three distributions. The bin width is 0.2 dex.
Solid and dotted lines show results from our RVS and SP pipelines,
respectively.

Fig. 20 shows the MDF of the MWS SV3 sample in each of the three main survey
target categories. As expected, the distribution peaks at
$\mathrm{[Fe/H]}\approx-0.5$, with the main-blue selection (which samples
metal-poor turnoff stars in the thick disk and halo) dominating at lower
metallicity and the main-broad selection (mostly nearby metal-rich disk stars)
dominating at higher metallicity. The main-red selection has a similar
distribution to main-broad below $\mathrm{[Fe/H]}\approx-0.5$ and notably
fewer stars around solar metallicity. An offset of $\lesssim 0.2$ dex is
apparent between the RVS and SP pipelines for main-red and main-broad targets,
but not for main-blue targets (see Sec. 7.4.3).

Figure 21: Comparison of the metallicity distribution of MWS main survey
targets in the SV3 dataset, measured by the RV pipeline (black; as in Fig.
20), to data from APOGEE, SEGUE, and LAMOST.

Fig. 21 compares the combined MDF of all MWS main survey targets in the SV3
sample (as shown in Fig. 20) to data from APOGEE (Majewski et al., 2017),
SEGUE (Yanny et al., 2009a; Rockosi et al., 2022) and LAMOST (Cui et al.,
2012), restricted to the same range of high Galactic latitudes and imposing
basic quality cuts for each survey171717APOGEE: SDSS DR17, plotting
$\mathrm{FE\\_H}$ with $\mathtt{STARFLAG}=0$ and $0<\mathtt{M\\_H\\_ERR}<0.2$.
SEGUE: SDSS DR17, plotting $\mathtt{FEH\\_ADOP}$ with
$\mathtt{ZWARNING}=0|16$, $\mathtt{SNR}>10$, $\mathtt{ELODIERVFINALERR}>0$,
and $\mathtt{FEH\\_ADOP}>-5$. LAMOST: DR7 v2, plotting $\mathtt{fe\\_h}$ with
$\mathtt{snrr}>10$, $0<\mathtt{feh\\_err}<0.5$, and $\mathtt{rv\\_err}>0$..
This comparison illustrates the much broader scope of the MWS target selection
compared to these previous surveys (similar considerations motivated the
design of the medium-resolution H3 survey; Conroy et al., 2019). The main-blue
targets in our SV3 data have a similar distribution to the sample from SEGUE,
which selected for the metal-poor halo. The main-red and main-broad samples
have distributions similar to the data from LAMOST and APOGEE, both of which
comprise intrinsically brighter stars and include subsets with selection
functions tuned to recovering halo giants.

Figure 22: Surface gravity distributions for all stars in the SV3 dataset that
would be selected in any of the three MWS main survey target categories. Solid
lines show results from the RVS pipeline and dotted lines results from the SP
pipeline. Figure 23: $\mathrm{[Fe/H]}$ distributions for main-blue, main-red
and main-broad targets in the SV3 dataset, divided into "giant" ($\log g\leq
3$; solid) and "dwarf" ($\log g>3$; dashed) subsets (as shown in Fig. 22,
there are very few main-broad giants in the dataset).

Fig. 22 shows the $\log g$ distributions of main survey targets in the SV3
data. As expected, the main-broad sample is dominated by dwarf stars. The
main-red sample was selected to reduce the contamination of foreground dwarfs
and recover a higher proportion of giants. Fig. 22 shows that, although main-
red contains a large number of dwarf contaminants (a necessary consequence of
the mild astrometric selection required to avoid strong kinematic bias) there
is also a clear second peak at low $\log g$ values, which is absent in main-
broad. The main-blue sample contains a large number of giants and subgiants;
as shown in Fig. 6, in the MWS magnitude range main-blue probes the metal-poor
main-sequence turnoff, subgiant branch, and horizontal branch at distances
$20<r<60$ kpc. The $\log g$ distributions from the RVS and SP pipelines
broadly agree, the most notable exception being a slightly higher number of
main-blue and main-broad stars with $\log g<4$ in the SP results.

Figure 24: Color–magnitude diagrams for giants ($\log g<3.5$) in the SV3
fields, separated into bins of $\mathrm{[Fe/H]}$ (panels; range shown in each
panel). We overplot MIST isochrones (corresponding to the central
$\mathrm{[Fe/H]}$ of each bin) at 15, 30, 60, 90, and 180 kpc (line styles, as
shown in the leftmost panel). Larger points indicate the small number of
giants in main-broad. The vertical line shows the separation in color between
the main-blue and main-red selections. Figure 25: Comparison of our RVS
pipeline measurements of surface gravity from the SV3 dataset (thick lines) to
the predictions of our modified (broken-power-law halo) Galaxia model (thin
colored lines) selected in the same regions. From left to right, the panels
show the main-blue, main-red and main-broad selections. Individual structural
components in Galaxia are shown by dotted (disk), dotted-dashed (thick disk),
and dashed gray lines (halo, with our fiducial broken-power-law density
profile; see text).

Fig. 23 shows separate metallicity distributions for dwarfs and giants. main-
blue giants (median $\mathrm{[Fe/H]}\approx-1.5$) are clearly sampling the
metal-poor halo. main-red giants are notably more metal-rich
($\mathrm{[Fe/H]}\approx-0.9$), with a distribution similar to that of main-
blue dwarfs. The main-red selection is weighted toward the lower RGB out to
$\sim 30$ kpc (at larger distances the density of giants falls rapidly), and
is therefore likely to be dominated by the relatively metal-rich Gaia
Enceladus feature (Belokurov et al., 2018; Helmi et al., 2018; Naidu et al.,
2020). The main-red and main-broad dwarf samples have median
$\mathrm{[Fe/H]}\approx-0.4$ and $-0.3$ respectively, consistent with the
expectation that they are dominated by the outer thin and thick disks. The
main-blue dwarf sample is biased toward the metal-poor tail of those
populations.

Fig. 24 provides another perspective on the same data, showing color–magnitude
diagrams for giants in different ranges of metallicity. The isochrones in this
figure (from the MIST library; Paxton et al. 2011, 2013, 2015; Choi et al.
2016; Dotter 2016) illustrate the types of stars entering the selection
function at different distances. A metal-rich structure is clearly visible in
the main-red sample at 30-50 kpc.

The figures above demonstrate that the MWS main target selection function will
yield a representative survey of distant Galactic structures at high latitude.
Comparison to predicted distributions for the same fields by the Galaxia model
(Sharma et al., 2011) supports this conclusion. The metallicity and velocity
distributions for the SV3 data have shapes and amplitudes in broad agreement
with the default Galaxia model. Our fiducial broken-power-law halo variant
(see section 4.2) improves this agreement by reducing the counts of distant
red giants in the main-red sample. Some discrepancy in detail between Galaxia
and the SV3 data is expected: the MWS selection is sensitive to stars from the
Gaia Enceladus progenitor and the Sagittarius stream (which are not included
in the Galaxia model) and to the slope of the smooth stellar halo density
profile.

Finally, Fig. 25 compares the $\log g$ distributions of the SV3 data and our
Galaxia mock catalog with a broken-power-law halo (convolved with a fiducial
Gaussian error $\sigma_{\log g}=0.2$). Galaxia predicts substantially more
high-proper-motion giants in the main-broad selection than we see in the data.
These are associated with the thin and thick disks. The counts of giants in
the main-red sample are in reasonable agreement at $\log g\approx 2$ but are
overpredicted by Galaxia at both higher $\log\,g$ (an excess of thick disk
giants) and lower $\log\,g$ (an excess of halo giants). The latter difference
is sensitive to the outer slope of the density profile.

##  8 Summary

We have presented the scientific motivation and final target selection
criteria for DESI MWS, which will obtain radial velocities, stellar
parameters, and chemical abundances for approximately seven million stars over
contiguous footprints in the north and south Galactic caps totaling $\sim
14,000\mathrm{deg^{2}}$. The overarching goal of MWS is to provide new
constraints on the assembly history of the Milky Way and the distribution of
dark matter through measurements of chemical composition and radial velocity.
The main MWS sample focuses on stars in the outer thick disk and stellar halo.
It is essentially magnitude-limited for colors $g-r<0.7$ (the halo and thick
disk turnoff; main-blue) and has only a weak astrometric selection applied to
redder stars to favor the targeting of distant giants (main-red). These two
samples will have $\simeq 30\%$ spectroscopic completeness. Red stars failing
the astrometric selection (main-broad) will still be observed, with
spectroscopic completeness $\simeq 19\%$. This straightforward and inclusive
selection function will greatly simplify the forward modeling of the survey.
It will also favor serendipitous discoveries; essentially every $16<r<19$ star
in the DESI footprint has a finite probability of being observed by MWS.
Combined with Gaia, the main MWS sample will be an excellent resource for
mapping structures and substructures in the thick disk and accreted halo,
probing distances from 1 to $\gtrsim 100$ kpc with multiple overlapping tracer
populations. MWS will also provide highly complete samples of white dwarfs,
faint M-dwarfs, BHBs, and RR Lyrae variables. These samples will address the
star formation history of the Milky Way disk, provide additional probes of the
Galactic structure and serve as a resource for a wide range of stellar and
planetary physics. MWS will be supplemented by a backup observing program
targeting brighter stars and several more specific secondary science programs,
which will be described in a separate publication.

The first DESI data release (DESI collaboration et al., 2023) will include
approximately 500,000 stellar spectra from the MWS SV program, introduced in
Sec. 7. We have used these data to show that, with our current analysis
pipelines, DESI can measure stellar radial velocities to an accuracy $\simeq
1\,\mathrm{km\,s^{-1}}$ and [Fe/H] to $\sim 0.2\,\mathrm{dex}$, for
representative main-sequence turnoff and giant branch halo tracers in our main
sample, given observing conditions comparable to those used for MWS targets in
the full bright-time MWS. This velocity precision meets the requirements of
the scientific program described in Section 3. It is sufficient to distinguish
kinematic substructures (for example, tidal streams and shells) from the bulk
stellar halo, to explore large-scale velocity perturbations associated with
the LMC, and to characterize the internal velocity dispersion of features as
dynamically cold as the tidal streams of globular clusters.

We have quantified systematic offsets in our measurements with respect to
previous spectroscopic surveys and between our two main analysis pipelines.
The discrepancies are most significant in the parameters and abundances
measured for very cool stars. The results in Section 7.4.3 give us confidence
that [Fe/H] uncertainties from DESI are, at least, comparable to those from
other surveys at similar resolution, such as SDSS SEGUE. The random [Fe/H]
uncertainties span a range of 0.05 dex for our brightest targets to 0.4 dex
for the faintest. When comparing to external high-resolution measurement of
clusters and dwarf galaxies, we see a typical systematic offset of $\sim 0.15$
dex in the DESI measurements. However, this varies from system to system,
likely indicating systematic errors that are a function of temperature,
$\mathrm{[Fe/H]}$ or $\mathrm{[\alpha/Fe]}$. We plan to investigate and where
possible correct these deficiencies in preparation for the first DESI data
release.

The radial velocity, metallicity, and surface gravity distributions we obtain
from the highly complete and higher-S/N SV3 minisurvey over $\approx
100\,\mathrm{deg}^{2}$ are broadly consistent with predictions from the
Galaxia Milky Way model (Sharma et al., 2011). The agreement in giant counts
is greatly improved if we assume a steeper decline in the density of halo
stars at Galactocentric distances $\gtrsim 25$ kpc, relative to Galaxia’s
original "unbroken"-power-law halo density profile. A mock realization of the
full MWS survey based on this modified Galaxia model predicts $\simeq 1$
million MWS targets beyond 15 kpc, $\sim 100,000$ beyond 30 kpc and $\sim
1000$ beyond 100 kpc, of which we will be able to observe $\approx 30\%$. We
therefore expect spectrophotometric distance estimates based on MWS data to
provide strong constraints on the outer density profile of the stellar halo.

MWS is one of several active or near-future large-scale Galactic spectroscopy
projects, including H3 (a smaller medium-resolution stellar survey with
similar goals to MWS; Conroy et al., 2019), 4MOST (in the southern hemisphere;
de Jong et al., 2019) and WEAVE (in the northern hemisphere; Dalton et al.,
2012). The 4MOST and WEAVE spectrographs have a high-resolution mode ($R\sim
20,000$) in addition to an $R\sim 5000$ mode capable of surveys comparable in
scope to MWS. These surveys complement one another. MWS is particularly well
suited to a large-scale mapping of the outer thick disk, the Gaia Enceladus
debris, the Sagittarius stream, and other northern-sky overdensities. The MWS
data should greatly improve our understanding of how these features contribute
to the overall stellar halo density, metallicity, and velocity dispersion
profiles, and provide a robust foundation for detailed comparisons with
theoretical models.

We thank the reviewer, Matthias Steinmetz, for his thorough reading of our
manuscript and constructive suggestions. A.P.C. and N.K. are supported by a
Taiwan Ministry of Education (MoE) Yushan Fellowship awarded to A.P.C., and by
Taiwan National Science and Technology Council (NSTC) grant
109-2112-M-007-011-MY3. This work used high-performance computing facilities
operated by the Center for Informatics and Computation in Astronomy (CICA) at
National Tsing Hua University. This equipment was funded by MoE, NSTC, and
National Tsing Hua University. C.A.P. acknowledges financial support from the
Spanish Ministry of Science and Innovation (MICINN) projects AYA2017-86389-P
and PID2020-117493GB-I00. C.J.M. acknowledges financial support from Imperial
College London through an Imperial College Research Fellowship grant. M.V. and
L.B.e.S. acknowledge support from NASA-ATP award 80NSSC20K0509. The work of
A.D. and J.N. is supported by NOIRLab, which is managed by the Association of
Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation. T.S.L. acknowledges financial support
from the Natural Sciences and Engineering Research Council of Canada (NSERC)
through grant RGPIN-2022-04794. B.T.G. was supported by grant ST/T000406/1
from the Science and Technology Facilities Council (STFC). This project has
received funding from the European Research Council under the European Union’s
Horizon 2020 research and innovation program (grant agreement No. 101020057).
This research made use of computing time available on the high-performance
computing systems at the Instituto de Astrofisica de Canarias. The authors
thankfully acknowledge the technical expertise and assistance provided by the
Spanish Supercomputing Network (Red Espanola de Supercomputacion), as well as
the computer resources used: the LaPalma Supercomputer and the Diva cluster,
both located at the Instituto de Astrofisica de Canarias.

This research is supported by the Director, Office of Science, Office of High
Energy Physics of the U.S. Department of Energy (DOE) under contract No.
DE–AC02–05CH11231, and by the National Energy Research Scientific Computing
Center, a DOE Office of Science User Facility under the same contract.
Additional support for DESI is provided by the U.S. National Science
Foundation, Division of Astronomical Sciences, under contract No. AST-0950945
to the NSF’s National Optical-infrared Astronomy Research Laboratory; the
Science and Technology Facilities Council of the United Kingdom; the Gordon
and Betty Moore Foundation; the Heising-Simons Foundation; the French
Alternative Energies and Atomic Energy Commission (CEA); the National Council
of Science and Technology of Mexico (CONACYT); MICINN; and the DESI Member
Institutions: https://www.desi.lbl.gov/collaborating-institutions.

The DESI Legacy Imaging Surveys consist of three individual and complementary
projects: the Dark Energy Camera Legacy Survey (DECaLS), the Beijing–Arizona
Sky Survey (BASS), and the Mayall $z$-band Legacy Survey (MzLS). DECaLS, BASS,
and MzLS include data obtained, respectively, at the Blanco telescope, Cerro
Tololo Inter-American Observatory, NSF’s NOIRLab; at the Bok telescope,
Steward Observatory, University of Arizona; and at the Mayall telescope, Kitt
Peak National Observatory, NOIRLab. NOIRLab is operated by the Association of
Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation. Pipeline processing and analyses of the
data were supported by NOIRLab and the Lawrence Berkeley National Laboratory
(LBNL). The Legacy Surveys also use data products from the Near-Earth Object
Wide-field Infrared Survey Explorer (NEOWISE), a project of the Jet Propulsion
Laboratory/California Institute of Technology, funded by the National
Aeronautics and Space Administration. The Legacy Surveys were supported by the
Director, Office of Science, Office of High Energy Physics of the U.S. DOE;
the National Energy Research Scientific Computing Center, a DOE Office of
Science User Facility; the U.S. National Science Foundation, Division of
Astronomical Sciences; the National Astronomical Observatories of China,
Chinese Academy of Sciences, and the Chinese National Natural Science
Foundation. LBNL is managed by the regents of the University of California
under contract to the U.S. DOE. The complete acknowledgments can be found at
https://www.legacysurvey.org/.

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.

Funding for SDSS-IV has been provided by the Alfred P. Sloan Foundation, the
U.S. DOE of Science, and the participating institutions. SDSS-IV acknowledges
support and resources from the Center for High Performance Computing at the
University of Utah. The SDSS website is www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS Collaboration including the Brazilian
Participation Group, the Carnegie Institution for Science, Carnegie Mellon
University, the Center for Astrophysics $|$ Harvard & Smithsonian, the Chilean
Participation Group, the French Participation Group, Instituto de Astrofísica
de Canarias, the Johns Hopkins University, the Kavli Institute for the Physics
and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean
Participation Group, LBNL, Leibniz Institut für Astrophysik Potsdam (AIP),
Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für
Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik
(MPE), the National Astronomical Observatories of China, New Mexico State
University, New York University, University of Notre Dame, Observatário
Nacional / MCTI, the Ohio State University, Pennsylvania State University,
Shanghai Astronomical Observatory, the United Kingdom Participation Group,
Universidad Nacional Autónoma de México, University of Arizona, University of
Colorado Boulder, University of Oxford, University of Portsmouth, University
of Utah, University of Virginia, University of Washington, University of
Wisconsin, Vanderbilt University, and Yale University.

The Guoshoujing Telescope (the Large Sky Area Multi-object Fiber Spectroscopic
Telescope LAMOST) is a National Major Scientific Project built by the Chinese
Academy of Sciences. Funding for the project has been provided by the National
Development and Reform Commission. LAMOST is operated and managed by the
National Astronomical Observatories, Chinese Academy of Sciences.

For the purpose of open access, the authors have applied a Creative Commons
attribution (CC BY) license to any author-accepted manuscript version arising
from this submission.

The authors are honored to be permitted to conduct scientific research on
Iolkam Du’ag (Kitt Peak), a mountain with particular significance to the
Tohono O’odham Nation.

For more information, visit desi.lbl.gov

## References

  * Abadi et al. (2006) Abadi, M. G., Navarro, J. F., & Steinmetz, M. 2006, MNRAS, 365, 747, doi: 10.1111/j.1365-2966.2005.09789.x
  * Abareshi et al. (2022) Abareshi, B., Aguilar, J., Ahlen, S., et al. 2022, AJ, 164, 207
  * Aguado et al. (2017) Aguado, D. S., Allende Prieto, C., González Hernández, J. I., Rebolo, R., & Caffau, E. 2017, A&A, 604, A9, doi: 10.1051/0004-6361/201731320
  * Allende Prieto et al. (2006) Allende Prieto, C., Beers, T. C., Wilhelm, R., et al. 2006, ApJ, 636, 804, doi: 10.1086/498131
  * Allende Prieto et al. (2018) Allende Prieto, C., Koesterke, L., Hubeny, I., et al. 2018, A&A, 618, A25, doi: 10.1051/0004-6361/201732484
  * Allende Prieto et al. (2015) Allende Prieto, C., Fernández-Alvar, E., Aguado, D. S., et al. 2015, A&A, 579, A98, doi: 10.1051/0004-6361/201525904
  * Allende Prieto et al. (2020) Allende Prieto, C., Cooper, A. P., Dey, A., et al. 2020, Research Notes of the AAS, 4, 188, doi: 10.3847/2515-5172/abc1dc
  * Amorisco (2017) Amorisco, N. C. 2017, MNRAS, 464, 2882
  * Anguiano et al. (2017) Anguiano, B., Rebassa-Mansergas, A., García-Berro, E., et al. 2017, MNRAS, 469, 2102, doi: 10.1093/mnras/stx796
  * Angus et al. (2020) Angus, R., Beane, A., Price-Whelan, A. M., et al. 2020, AJ, 160, 90, doi: 10.3847/1538-3881/ab91b2
  * Antoja et al. (2020) Antoja, T., Ramos, P., Mateu, C., et al. 2020, A&A, 635, L3, doi: 10.1051/0004-6361/201937145
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * 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
  * Aumer et al. (2016) Aumer, M., Binney, J., & Schönrich, R. 2016, MNRAS, 462, 1697, doi: 10.1093/mnras/stw1639
  * Bailey et al. (2022) Bailey, S. J., et al. 2022, in prep.
  * Barnes (2007) Barnes, S. A. 2007, ApJ, 669, 1167, doi: 10.1086/519295
  * Bastian & Lardo (2018) Bastian, N., & Lardo, C. 2018, ARA&A, 56, 83, doi: 10.1146/annurev-astro-081817-051839
  * Beers & Christlieb (2005) Beers, T. C., & Christlieb, N. 2005, ARA&A, 43, 531, doi: 10.1146/annurev.astro.42.053102.134057
  * Bell et al. (2008) Bell, E. F., Zucker, D. B., Belokurov, V., et al. 2008, ApJ, 680, 295, doi: 10.1086/588032
  * Belokurov et al. (2018) Belokurov, V., Erkal, D., Evans, N. W., Koposov, S. E., & Deason, A. J. 2018, MNRAS, 478, 611, doi: 10.1093/mnras/sty982
  * Belokurov & Kravtsov (2022) Belokurov, V., & Kravtsov, A. 2022, MNRAS, 514, 689, doi: 10.1093/mnras/stac1267
  * Belokurov et al. (2020) Belokurov, V., Sanders, J. L., Fattahi, A., et al. 2020, MNRAS, 494, 3880, doi: 10.1093/mnras/staa876
  * Beraldo e Silva et al. (2020) Beraldo e Silva, L., Debattista, V. P., Khachaturyants, T., & Nidever, D. 2020, MNRAS, 492, 4716, doi: 10.1093/mnras/staa065
  * Beraldo e Silva et al. (2021) Beraldo e Silva, L., Debattista, V. P., Nidever, D., Amarante, J. A. S., & Garver, B. 2021, MNRAS, 502, 260, doi: 10.1093/mnras/staa3966
  * Bergeron et al. (1992) Bergeron, P., Wesemael, F., & Fontaine, G. 1992, ApJ, 387, 288, doi: 10.1086/171080
  * Besla et al. (2007) Besla, G., Kallivayalil, N., Hernquist, L., et al. 2007, ApJ, 668, 949, doi: 10.1086/521385
  * Besla et al. (2010) —. 2010, ApJ, 721, L97, doi: 10.1088/2041-8205/721/2/L97
  * Bird et al. (2013) Bird, J. C., Kazantzidis, S., Weinberg, D. H., et al. 2013, ApJ, 773, 43, doi: 10.1088/0004-637X/773/1/43
  * Bird et al. (2019) Bird, S. A., Xue, X.-X., Liu, C., et al. 2019, AJ, 157, 104, doi: 10.3847/1538-3881/aafd2e
  * Bland-Hawthorn & Gerhard (2016) Bland-Hawthorn, J., & Gerhard, O. 2016, ARA&A, 54, 529, doi: 10.1146/annurev-astro-081915-023441
  * Bland-Hawthorn et al. (2015) Bland-Hawthorn, J., Sutherland, R., & Webster, D. 2015, ApJ, 807, 154, doi: 10.1088/0004-637X/807/2/154
  * Blanton et al. (2017) Blanton, M. R., Bershady, M. A., Abolfathi, B., et al. 2017, AJ, 154, 28, doi: 10.3847/1538-3881/aa7567
  * Boeche et al. (2011) Boeche, C., Siebert, A., Williams, M., et al. 2011, AJ, 142, 193, doi: 10.1088/0004-6256/142/6/193
  * Bonaca & Hogg (2018) Bonaca, A., & Hogg, D. W. 2018, ApJ, 867, 101, doi: 10.3847/1538-4357/aae4da
  * Bonaca et al. (2019) Bonaca, A., Hogg, D. W., Price-Whelan, A. M., & Conroy, C. 2019, ApJ, 880, 38, doi: 10.3847/1538-4357/ab2873
  * Bose et al. (2016) Bose, S., Hellwing, W. A., Frenk, C. S., et al. 2016, MNRAS, 455, 318, doi: 10.1093/mnras/stv2294
  * Bournaud et al. (2009) Bournaud, F., Elmegreen, B. G., & Martig, M. 2009, ApJL, 707, L1, doi: 10.1088/0004-637X/707/1/L1
  * Bovy (2014) Bovy, J. 2014, ApJ, 795, 95, doi: 10.1088/0004-637X/795/1/95
  * Bovy (2016) —. 2016, Physical Review Letters, 116, 121301, doi: 10.1103/PhysRevLett.116.121301
  * Bovy et al. (2017) Bovy, J., Erkal, D., & Sanders, J. L. 2017, MNRAS, 466, 628, doi: 10.1093/mnras/stw3067
  * Bowden et al. (2015) Bowden, A., Belokurov, V., & Evans, N. W. 2015, MNRAS, 449, 1391, doi: 10.1093/mnras/stv285
  * Buder et al. (2021) Buder, S., Sharma, S., Kos, J., et al. 2021, MNRAS, 506, 150, doi: 10.1093/mnras/stab1242
  * Bullock & Johnston (2005) Bullock, J. S., & Johnston, K. V. 2005, ApJ, 635, 931, doi: 10.1086/497422
  * Callingham et al. (2019) Callingham, T. M., Cautun, M., Deason, A. J., et al. 2019, MNRAS, 484, 5453, doi: 10.1093/mnras/stz365
  * Cantat-Gaudin & Anders (2020) Cantat-Gaudin, T., & Anders, F. 2020, A&A, 633, A99, doi: 10.1051/0004-6361/201936691
  * Carlberg (2012) Carlberg, R. G. 2012, ApJ, 748, 20, doi: 10.1088/0004-637X/748/1/20
  * Carlberg (2013) —. 2013, ApJ, 775, 90, doi: 10.1088/0004-637X/775/2/90
  * Carlberg (2018) —. 2018, ApJ, 861, 69, doi: 10.3847/1538-4357/aac88a
  * Carlberg & Grillmair (2021) Carlberg, R. G., & Grillmair, C. J. 2021, ApJ, 922, 104
  * 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
  * Chaussidon et al. (2022) Chaussidon, E., Yèche, C., Palanque-Delabrouille, N., et al. 2022, arXiv e-prints, arXiv:2208.08511.  https://arxiv.org/abs/2208.08511
  * 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
  * Choi et al. (2016) Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102
  * Church et al. (2019) Church, B. V., Mocz, P., & Ostriker, J. P. 2019, MNRAS, 485, 2861, doi: 10.1093/mnras/stz534
  * Ciucă et al. (2021) Ciucă, I., Kawata, D., Miglio, A., Davies, G. R., & Grand, R. J. J. 2021, MNRAS, 503, 2814, doi: 10.1093/mnras/stab639
  * Clarke et al. (2019) Clarke, A. J., Debattista, V. P., Nidever, D. L., et al. 2019, MNRAS, 484, 3476, doi: 10.1093/mnras/stz104
  * Clementini et al. (2019) Clementini, G., Ripepi, V., Molinaro, R., et al. 2019, A&A, 622, A60, doi: 10.1051/0004-6361/201833374
  * Conroy et al. (2021) Conroy, C., Naidu, R. P., Garavito-Camargo, N., et al. 2021, Nature, 592, 534, doi: 10.1038/s41586-021-03385-7
  * Conroy et al. (2019) Conroy, C., Bonaca, A., Cargile, P., et al. 2019, ApJ, 883, 107, doi: 10.3847/1538-4357/ab38b8
  * Cooper et al. (2015) Cooper, A. P., Parry, O. H., Lowing, B., Cole, S., & Frenk, C. 2015, MNRAS, 454, 3185, doi: 10.1093/mnras/stv2057
  * Cooper et al. (2010) Cooper, A. P., Cole, S., Frenk, C. S., et al. 2010, MNRAS, 406, 744, doi: 10.1111/j.1365-2966.2010.16740.x
  * Cropper et al. (2018) Cropper, M., Katz, D., Sartoretti, P., et al. 2018, A&A, 616, A5, doi: 10.1051/0004-6361/201832763
  * Cui et al. (2012) Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, Research in Astronomy and Astrophysics, 12, 1197, doi: 10.1088/1674-4527/12/9/003
  * Cummings et al. (2018) Cummings, J. D., Kalirai, J. S., Tremblay, P.-E., Ramirez-Ruiz, E., & Choi, J. 2018, ApJ, 866, 21, doi: 10.3847/1538-4357/aadfd6
  * Cunningham et al. (2019) Cunningham, E. C., Deason, A. J., Sanderson, R. E., et al. 2019, ApJ, 879, 120, doi: 10.3847/1538-4357/ab24cd
  * Dalton et al. (2012) Dalton, G., Trager, S. C., Abrams, D. C., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8446, Ground-based and Airborne Instrumentation for Astronomy IV, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 84460P, doi: 10.1117/12.925950
  * Daou et al. (1990) Daou, D., Wesemael, F., Bergeron, P., Fontaine, G., & Holberg, J. B. 1990, ApJ, 364, 242, doi: 10.1086/169407
  * Dawson et al. (2013) Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2013, AJ, 145, 10, doi: 10.1088/0004-6256/145/1/10
  * de Jong et al. (2019) de Jong, R. S., Agertz, O., Berbel, A. A., et al. 2019, The Messenger, 175, 3, doi: 10.18727/0722-6691/5117
  * de Salas et al. (2019) de Salas, P. F., Malhan, K., Freese, K., Hattori, K., & Valluri, M. 2019, Journal of Cosmology and Astro-Particle Physics, 2019, 037, doi: 10.1088/1475-7516/2019/10/037
  * De Silva et al. (2015) De Silva, G. M., Freeman, K. C., Bland-Hawthorn, J., et al. 2015, MNRAS, 449, 2604, doi: 10.1093/mnras/stv327
  * Deason et al. (2011) Deason, A. J., Belokurov, V., & Evans, N. W. 2011, MNRAS, 416, 2903, doi: 10.1111/j.1365-2966.2011.19237.x
  * Deason et al. (2013) Deason, A. J., Belokurov, V., Evans, N. W., & Johnston, K. V. 2013, ApJ, 763, 113, doi: 10.1088/0004-637X/763/2/113
  * Deason et al. (2018) Deason, A. J., Belokurov, V., Koposov, S. E., & Lancaster, L. 2018, ApJ, 862, L1, doi: 10.3847/2041-8213/aad0ee
  * Deason et al. (2014) Deason, A. J., Belokurov, V., Koposov, S. E., & Rockosi, C. M. 2014, ApJ, 787, 30
  * Deason et al. (2015) Deason, A. J., Belokurov, V., & Weisz, D. R. 2015, MNRAS, 448, L77, doi: 10.1093/mnrasl/slv001
  * Deason et al. (2021) Deason, A. J., Erkal, D., Belokurov, V., et al. 2021, MNRAS, 501, 5964, doi: 10.1093/mnras/staa3984
  * Debattista et al. (2008) Debattista, V. P., Moore, B., Quinn, T., et al. 2008, ApJ, 681, 1076, doi: 10.1086/587977
  * DESI Collaboration et al. (2016a) DESI Collaboration, Aghamousa, A., Aguilar, J., et al. 2016a, ArXiv e-prints.  https://arxiv.org/abs/1611.00036
  * DESI Collaboration et al. (2016b) —. 2016b, ArXiv e-prints.  https://arxiv.org/abs/1611.00037
  * DESI Collaboration et al. (2023) DESI Collaboration, et al. 2023, in prep.
  * DESI collaboration et al. (2023) DESI collaboration et al. 2023, in prep.
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168
  * Dey et al. (2022) Dey, A., Najita, J. R., Koposov, S. E., et al. 2022, arXiv e-prints, arXiv:2208.11683
  * Djorgovski & Sosin (1989) Djorgovski, S., & Sosin, C. 1989, ApJL, 341, L13, doi: 10.1086/185446
  * Dobbie et al. (2006) Dobbie, P. D., Napiwotzki, R., Burleigh, M. R., et al. 2006, MNRAS, 369, 383, doi: 10.1111/j.1365-2966.2006.10311.x
  * D’Orazi et al. (2020) D’Orazi, V., Oliva, E., Bragaglia, A., et al. 2020, A&A, 633, A38, doi: 10.1051/0004-6361/201936651
  * Dotter (2016) Dotter, A. 2016, ApJS, 222, 8
  * Drimmel & Spergel (2001) Drimmel, R., & Spergel, D. N. 2001, ApJ, 556, 181, doi: 10.1086/321556
  * Eisenstein et al. (2006) Eisenstein, D. J., Liebert, J., Harris, H. C., et al. 2006, ApJS, 167, 40, doi: 10.1086/507110
  * Eisenstein et al. (2011) Eisenstein, D. J., Weinberg, D. H., Agol, E., et al. 2011, AJ, 142, 72, doi: 10.1088/0004-6256/142/3/72
  * Erkal & Belokurov (2015a) Erkal, D., & Belokurov, V. 2015a, MNRAS, 450, 1136, doi: 10.1093/mnras/stv655
  * Erkal & Belokurov (2015b) —. 2015b, MNRAS, 454, 3542, doi: 10.1093/mnras/stv2122
  * Erkal et al. (2016) Erkal, D., Belokurov, V., Bovy, J., & Sanders, J. L. 2016, Monthly Notices of the Royal Astronomical Society, 463, 102, doi: 10.1093/mnras/stw1957
  * Erkal et al. (2018) Erkal, D., Li, T. S., Koposov, S. E., et al. 2018, MNRAS, 481, 3148, doi: 10.1093/mnras/sty2518
  * Erkal et al. (2019) Erkal, D., Belokurov, V., Laporte, C. F. P., et al. 2019, MNRAS, 487, 2685, doi: 10.1093/mnras/stz1371
  * Errani et al. (2015) Errani, R., Penarrubia, J., & Tormen, G. 2015, MNRAS, 449, L46, doi: 10.1093/mnrasl/slv012
  * Farihi et al. (2009) Farihi, J., Jura, M., & Zuckerman, B. 2009, ApJ, 694, 805, doi: 10.1088/0004-637X/694/2/805
  * Fellhauer et al. (2006) Fellhauer, M., Belokurov, V., Evans, N. W., et al. 2006, ApJ, 651, 167, doi: 10.1086/507128
  * Fernández-Alvar et al. (2015) Fernández-Alvar, E., Allende Prieto, C., Schlesinger, K. J., et al. 2015, A&A, 577, A81, doi: 10.1051/0004-6361/201425455
  * Font et al. (2020) Font, A. S., McCarthy, I. G., Poole-Mckenzie, R., et al. 2020, MNRAS, 498, 1765, doi: 10.1093/mnras/staa2463
  * Frebel et al. (2015) Frebel, A., Chiti, A., Ji, A. P., Jacobson, H. R., & Placco, V. M. 2015, ApJ, 810, L27, doi: 10.1088/2041-8205/810/2/L27
  * Freeman & Bland-Hawthorn (2002) Freeman, K., & Bland-Hawthorn, J. 2002, ARA&A, 40, 487, doi: 10.1146/annurev.astro.40.060401.093840
  * Gaia Collaboration et al. (2021a) Gaia Collaboration, Smart, R. L., Sarro, L. M., et al. 2021a, å, 649, A6, doi: 10.1051/0004-6361/202039498
  * Gaia Collaboration et al. (2021b) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021b, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Gänsicke et al. (2012) Gänsicke, B. T., Koester, D., Farihi, J., et al. 2012, MNRAS, 424, 333, doi: 10.1111/j.1365-2966.2012.21201.x
  * Garavito-Camargo et al. (2019) Garavito-Camargo, N., Besla, G., Laporte, C. F. P., et al. 2019, arXiv e-prints.  https://arxiv.org/abs/1902.05089
  * García-Berro et al. (2010) García-Berro, E., Torres, S., Althaus, L. G., et al. 2010, Nature, 465, 194, doi: 10.1038/nature09045
  * García Pérez et al. (2016) García Pérez, A. E., Allende Prieto, C., Holtzman, J. A., et al. 2016, AJ, 151, 144, doi: 10.3847/0004-6256/151/6/144
  * Gentile Fusillo et al. (2017) Gentile Fusillo, N. P., Gänsicke, B. T., Farihi, J., et al. 2017, MNRAS, 468, 971, doi: 10.1093/mnras/stx468
  * Gentile Fusillo et al. (2015) Gentile Fusillo, N. P., Gänsicke, B. T., & Greiss, S. 2015, MNRAS, 448, 2260, doi: 10.1093/mnras/stv120
  * Gentile Fusillo et al. (2019) Gentile Fusillo, N. P., Tremblay, P.-E., Gänsicke, B. T., et al. 2019, MNRAS, 482, 4570, doi: 10.1093/mnras/sty3016
  * Giammichele et al. (2012) Giammichele, N., Bergeron, P., & Dufour, P. 2012, ApJS, 199, 29, doi: 10.1088/0067-0049/199/2/29
  * Gianninas et al. (2004) Gianninas, A., Dufour, P., & Bergeron, P. 2004, ApJ, 617, L57, doi: 10.1086/427080
  * Gibbons et al. (2014) Gibbons, S. L. J., Belokurov, V., & Evans, N. W. 2014, MNRAS, 445, 3788, doi: 10.1093/mnras/stu1986
  * Gilmore et al. (2012a) Gilmore, G., Randich, S., Asplund, M., et al. 2012a, The Messenger, 147, 25
  * Gilmore et al. (2012b) —. 2012b, The Messenger, 147, 25
  * Gizis et al. (2000) Gizis, J. E., Monet, D. G., Reid, I. N., et al. 2000, AJ, 120, 1085, doi: 10.1086/301456
  * Gomez et al. (2015) Gomez, F. A., Besla, G., Carpintero, D. D., et al. 2015, ApJ, 802, 128, doi: 10.1088/0004-637X/802/2/128
  * Grand et al. (2016) Grand, R. J. J., Springel, V., Gómez, F. A., et al. 2016, MNRAS, 459, 199, doi: 10.1093/mnras/stw601
  * Grillmair & Carlin (2016) Grillmair, C. J., & Carlin, J. L. 2016, in Astrophysics and Space Science Library, Vol. 420, Tidal Streams in the Local Group and Beyond, ed. H. J. Newberg & J. L. Carlin, 87, doi: 10.1007/978-3-319-19336-6_4
  * Guan (2006) Guan, X. 2006, Phys. Rev. A, 74, 023413, doi: 10.1103/PhysRevA.74.023413
  * Guidry et al. (2021) Guidry, J. A., Vanderbosch, Z. P., Hermes, J. J., et al. 2021, ApJ, 912, 125, doi: 10.3847/1538-4357/abee68
  * Guy et al. (2022) Guy, J., Bailey, S., Kremin, A., et al. 2022, arXiv e-prints, arXiv:2209.14482, doi: 10.48550/arXiv.2209.14482
  * Hahn et al. (2022) Hahn, C., Wilson, M. J., Ruiz-Macias, O., et al. 2022, arXiv e-prints, arXiv:2208.08512.  https://arxiv.org/abs/2208.08512
  * Han et al. (2022) Han, J. J., Naidu, R. P., Conroy, C., et al. 2022, arXiv e-prints, arXiv:2202.07662.  https://arxiv.org/abs/2202.07662
  * Hansen et al. (2007) Hansen, B. M. S., Anderson, J., Brewer, J., et al. 2007, ApJ, 671, 380, doi: 10.1086/522567
  * Harris et al. (2020) Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
  * Hasselquist et al. (2019) Hasselquist, S., Carlin, J. L., Holtzman, J. A., et al. 2019, The Astrophysical Journal, 872, 58, doi: 10.3847/1538-4357/aafdac
  * Hattori et al. (2020) Hattori, K., Valluri, M., & Vasiliev, E. 2020, arXiv e-prints, arXiv:2012.03908.  https://arxiv.org/abs/2012.03908
  * Helmi (2004) Helmi, A. 2004, ApJ, 610, L97, doi: 10.1086/423340
  * Helmi (2020) —. 2020, ARA&A, 58, 205, doi: 10.1146/annurev-astro-032620-021917
  * Helmi et al. (2018) Helmi, A., Babusiaux, C., Koppelman, H. H., et al. 2018, Nature, 563, 85, doi: 10.1038/s41586-018-0625-x
  * Henry et al. (1994) Henry, T. J., Kirkpatrick, J. D., & Simons, D. A. 1994, AJ, 108, 1437
  * Henry et al. (2018) Henry, T. J., Jao, W.-C., Winters, J. G., et al. 2018, AJ, 155, 265, doi: 10.3847/1538-3881/aac262
  * Hermes et al. (2017) Hermes, J. J., Gänsicke, B. T., Kawaler, S. D., et al. 2017, ApJS, 232, 23, doi: 10.3847/1538-4365/aa8bb5
  * Hogg et al. (2019) Hogg, D. W., Eilers, A.-C., & Rix, H.-W. 2019, AJ, 158, 147, doi: 10.3847/1538-3881/ab398c
  * Holl et al. (2018) Holl, B., Audard, M., Nienartowicz, K., et al. 2018, A&A, 618, A30, doi: 10.1051/0004-6361/201832892
  * Hollands et al. (2018) Hollands, M. A., Gänsicke, B. T., & Koester, D. 2018, MNRAS, 477, 93, doi: 10.1093/mnras/sty592
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
  * Husser et al. (2013) Husser, T. O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6, doi: 10.1051/0004-6361/201219058
  * Ibata et al. (2019) Ibata, R. A., Malhan, K., & Martin, N. F. 2019, ApJ, 872, 152, doi: 10.3847/1538-4357/ab0080
  * Iben et al. (1997) Iben, Icko, J., Ritossa, C., & García-Berro, E. 1997, ApJ, 489, 772, doi: 10.1086/304822
  * Iorio & Belokurov (2019) Iorio, G., & Belokurov, V. 2019, MNRAS, 482, 3868
  * Iorio & Belokurov (2021) —. 2021, MNRAS, 502, 5686, doi: 10.1093/mnras/stab005
  * Ishigaki et al. (2014) Ishigaki, M. N., Tominaga, N., Kobayashi, C., & Nomoto, K. 2014, ApJ, 792, L32, doi: 10.1088/2041-8205/792/2/L32
  * Jing & Suto (2000) Jing, Y. P., & Suto, Y. 2000, ApJ, 529, L69, doi: 10.1086/312463
  * Johnston et al. (2005) Johnston, K. V., Law, D. R., & Majewski, S. R. 2005, ApJ, 619, 800, doi: 10.1086/426777
  * Johnston et al. (1999) Johnston, K. V., Zhao, H., Spergel, D. N., & Hernquist, L. 1999, ApJ, 512, L109, doi: 10.1086/311876
  * Jönsson et al. (2020) Jönsson, H., Holtzman, J. A., Allende Prieto, C., et al. 2020, AJ, 160, 120, doi: 10.3847/1538-3881/aba592
  * Jura & Xu (2010) Jura, M., & Xu, S. 2010, AJ, 140, 1129, doi: 10.1088/0004-6256/140/5/1129
  * Kafle et al. (2018) Kafle, P. R., Sharma, S., Robotham, A. S. G., Elahi, P. J., & Driver, S. P. 2018, MNRAS, 475, 4434, doi: 10.1093/mnras/sty118
  * Kalirai et al. (2014) Kalirai, J. S., Marigo, P., & Tremblay, P.-E. 2014, ApJ, 782, 17, doi: 10.1088/0004-637X/782/1/17
  * Katz et al. (2022) Katz, D., Sartoretti, P., Guerrier, A., et al. 2022, arXiv e-prints, arXiv:2206.05902.  https://arxiv.org/abs/2206.05902
  * Kazantzidis et al. (2004) Kazantzidis, S., Kravtsov, A. V., Zentner, A. R., et al. 2004, ApJ, 611, L73, doi: 10.1086/423992
  * Kiman et al. (2019) Kiman, R., Schmidt, S. J., Angus, R., et al. 2019, AJ, 157, 231, doi: 10.3847/1538-3881/ab1753
  * Kirby et al. (2011) Kirby, E. N., Lanfranchi, G. A., Simon, J. D., Cohen, J. G., & Guhathakurta, P. 2011, ApJ, 727, 78, doi: 10.1088/0004-637X/727/2/78
  * Kirby et al. (2008) Kirby, E. N., Simon, J. D., Geha, M., Guhathakurta, P., & Frebel, A. 2008, ApJ, 685, L43, doi: 10.1086/592432
  * Kirkby et al. (2022) Kirkby, D., et al. 2022, in prep.
  * Kirkpatrick et al. (2019) Kirkpatrick, J. D., Martin, E. C., Smart, R. L., et al. 2019, ApJS, 240, 19, doi: 10.3847/1538-4365/aaf6af
  * Klein et al. (2010) Klein, B., Jura, M., Koester, D., Zuckerman, B., & Melis, C. 2010, ApJ, 709, 950, doi: 10.1088/0004-637X/709/2/950
  * Kleinman et al. (2013) Kleinman, S. J., Kepler, S. O., Koester, D., et al. 2013, ApJS, 204, 5, doi: 10.1088/0067-0049/204/1/5
  * Koester (2010) Koester, D. 2010, Memorie della Societa Astronomica Italiana, 81, 921
  * Koester et al. (2014) Koester, D., Gänsicke, B. T., & Farihi, J. 2014, A&A, 566, A34, doi: 10.1051/0004-6361/201423691
  * Koposov (2019) Koposov, S. E. 2019, RVSpecFit: Radial velocity and stellar atmospheric parameter fitting.  http://ascl.net/1907.013
  * Koposov et al. (2010) Koposov, S. E., Rix, H.-W., & Hogg, D. W. 2010, ApJ, 712, 260, doi: 10.1088/0004-637X/712/1/260
  * Koposov et al. (2011) Koposov, S. E., Gilmore, G., Walker, M. G., et al. 2011, ApJ, 736, 146, doi: 10.1088/0004-637X/736/2/146
  * Koposov et al. (2019) Koposov, S. E., Belokurov, V., Li, T. S., et al. 2019, MNRAS, 485, 4726, doi: 10.1093/mnras/stz457
  * Kota et al. (2022) Kota, T., Kirkpatrick, J. D., Caselden, D., et al. 2022, AJ, 163, 116, doi: 10.3847/1538-3881/ac4713
  * Kowalski (2006) Kowalski, P. M. 2006, ApJ, 641, 488, doi: 10.1086/500358
  * Kunz et al. (2002) Kunz, R., Fey, M., Jaeger, M., et al. 2002, ApJ, 567, 643, doi: 10.1086/338384
  * Küpper et al. (2015) Küpper, A. H. W., Balbinot, E., Bonaca, A., et al. 2015, ApJ, 803, 80, doi: 10.1088/0004-637X/803/2/80
  * Kurucz (1979) Kurucz, R. L. 1979, ApJS, 40, 1, doi: 10.1086/190589
  * Kurucz (1993) —. 1993, VizieR Online Data Catalog, VI/39
  * Kuzma et al. (2016) Kuzma, P. B., Da Costa, G. S., Mackey, A. D., & Roderick, T. A. 2016, MNRAS, 461, 3639, doi: 10.1093/mnras/stw1561
  * Lancaster et al. (2019) Lancaster, L., Koposov, S. E., Belokurov, V., Evans, N. W., & Deason, A. J. 2019, MNRAS, 486, 378, doi: 10.1093/mnras/stz853
  * Laporte et al. (2021) Laporte, C. F. P., Koposov, S. E., & Belokurov, V. 2021, MNRAS, doi: 10.1093/mnrasl/slab109
  * Law & Majewski (2010) Law, D. R., & Majewski, S. R. 2010, ApJ, 714, 229, doi: 10.1088/0004-637X/714/1/229
  * Leon et al. (2000) Leon, S., Meylan, G., & Combes, F. 2000, A&A, 359, 907
  * Li et al. (2019) Li, T. S., Koposov, S. E., Zucker, D. B., et al. 2019, MNRAS, 490, 3508, doi: 10.1093/mnras/stz2731
  * Li et al. (2021) Li, T. S., Koposov, S. E., Erkal, D., et al. 2021, ApJ, 911, 149, doi: 10.3847/1538-4357/abeb18
  * 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
  * Li et al. (2020) Li, Z.-Z., Qian, Y.-Z., Han, J., et al. 2020, ApJ, 894, 10, doi: 10.3847/1538-4357/ab84f0
  * Liebert et al. (2005) Liebert, J., Bergeron, P., & Holberg, J. B. 2005, ApJS, 156, 47
  * Loebman et al. (2018) Loebman, S. R., Valluri, M., Hattori, K., et al. 2018, ApJ, 853, 196, doi: 10.3847/1538-4357/aaa0d6
  * López-Corredoira et al. (2002) López-Corredoira, M., Cabrera-Lavers, A., Garzón, F., & Hammersley, P. L. 2002, A&A, 394, 883, doi: 10.1051/0004-6361:20021175
  * Luo et al. (2015) Luo, A. L., Zhao, Y.-H., Zhao, G., et al. 2015, Research in Astronomy and Astrophysics, 15, 1095, doi: 10.1088/1674-4527/15/8/002
  * Mackereth et al. (2017) Mackereth, J. T., Bovy, J., Schiavon, R. P., et al. 2017, MNRAS, 471, 3057, doi: 10.1093/mnras/stx1774
  * Mackereth et al. (2019) Mackereth, J. T., Bovy, J., Leung, H. W., et al. 2019, MNRAS, 489, 176, doi: 10.1093/mnras/stz1521
  * Majewski et al. (2017) Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784d
  * Malhan & Ibata (2019) Malhan, K., & Ibata, R. A. 2019, MNRAS, 486, 2995, doi: 10.1093/mnras/stz1035
  * Malhan et al. (2021) Malhan, K., Valluri, M., & Freese, K. 2021, MNRAS, 501, 179, doi: 10.1093/mnras/staa3597
  * Mamajek & Hillenbrand (2008) Mamajek, E. E., & Hillenbrand, L. A. 2008, ApJ, 687, 1264, doi: 10.1086/591785
  * Maraston (1998) Maraston, C. 1998, MNRAS, 300, 872, doi: 10.1046/j.1365-8711.1998.01947.x
  * Martell & Grebel (2010) Martell, S. L., & Grebel, E. K. 2010, A&A, 519, A14, doi: 10.1051/0004-6361/201014135
  * Martell et al. (2011) Martell, S. L., Smolinski, J. P., Beers, T. C., & Grebel, E. K. 2011, A&A, 534, A136, doi: 10.1051/0004-6361/201117644
  * Martig et al. (2014) Martig, M., Minchev, I., & Flynn, C. 2014, MNRAS, 443, 2452, doi: 10.1093/mnras/stu1322
  * Martig et al. (2016) Martig, M., Fouesneau, M., Rix, H.-W., et al. 2016, MNRAS, 456, 3655, doi: 10.1093/mnras/stv2830
  * Masseron & Gilmore (2015) Masseron, T., & Gilmore, G. 2015, MNRAS, 453, 1855, doi: 10.1093/mnras/stv1731
  * Mateu (2017) Mateu, C. 2017, galstreams: Milky Way streams footprint library and toolkit, Astrophysics Source Code Library, record ascl:1711.010.  http://ascl.net/1711.010
  * Mateu (2022) —. 2022, arXiv e-prints, arXiv:2204.10326.  https://arxiv.org/abs/2204.10326
  * Mateu et al. (2018) Mateu, C., Read, J. I., & Kawata, D. 2018, MNRAS, 474, 4112, doi: 10.1093/mnras/stx2937
  * McConnachie (2012) McConnachie, A. W. 2012, AJ, 144, 4
  * Meisner et al. (2017) Meisner, A. M., Lang, D., & Schlegel, D. J. 2017, ArXiv e-prints.  https://arxiv.org/abs/1705.06746
  * Meisner et al. (2021) Meisner, A. M., Schneider, A. C., Burgasser, A. J., et al. 2021, ApJ, 915, 120, doi: 10.3847/1538-4357/ac013c
  * Mészáros et al. (2012) Mészáros, S., Allende Prieto, C., Edvardsson, B., et al. 2012, AJ, 144, 120, doi: 10.1088/0004-6256/144/4/120
  * Miller et al. (2022) Miller, T., et al. 2022, in prep.
  * Minchev et al. (2015) Minchev, I., Martig, M., Streich, D., et al. 2015, ApJ, 804, L9, doi: 10.1088/2041-8205/804/1/L9
  * Momany et al. (2006) Momany, Y., Zaggia, S., Gilmore, G., et al. 2006, A&A, 451, 515, doi: 10.1051/0004-6361:20054081
  * Montalbán et al. (2021) Montalbán, J., Mackereth, J. T., Miglio, A., et al. 2021, NatAs, 5, 640, doi: 10.1038/s41550-021-01347-7
  * Moore (1996) Moore, B. 1996, ApJ, 461, L13, doi: 10.1086/309998
  * Myers et al. (2023) Myers, A. D., Moustakas, J., Bailey, S., et al. 2023, AJ, 165, 50, doi: 10.3847/1538-3881/aca5f9
  * 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
  * Naidu et al. (2020) Naidu, R. P., Conroy, C., Bonaca, A., et al. 2020, ApJ, 901, 48, doi: 10.3847/1538-4357/abaef4
  * Nelder & Mead (1965) Nelder, J. A., & Mead, R. 1965, Computer Journal, 7, 308
  * Ness et al. (2016) Ness, M., Hogg, D. W., Rix, H. W., et al. 2016, ApJ, 823, 114, doi: 10.3847/0004-637X/823/2/114
  * Newton et al. (2016) Newton, E. R., Irwin, J., Charbonneau, D., et al. 2016, ApJ, 821, 93, doi: 10.3847/0004-637X/821/2/93
  * Nidever et al. (2021) Nidever, D. L., Dey, A., Fasbender, K., et al. 2021, AJ, 161, 192, doi: 10.3847/1538-3881/abd6e1
  * Nordlander et al. (2019) Nordlander, T., Bessell, M. S., Da Costa, G. S., et al. 2019, MNRAS, 488, L109, doi: 10.1093/mnrasl/slz109
  * Nordström et al. (2004) Nordström, B., Mayor, M., Andersen, J., et al. 2004, A&A, 418, 989, doi: 10.1051/0004-6361:20035959
  * Oswalt et al. (1996) Oswalt, T. D., Smith, J. A., Wood, M. A., & Hintzen, P. 1996, Nature, 382, 692, doi: 10.1038/382692a0
  * Pauli et al. (2003) Pauli, E., Napiwotzki, R., Altmann, M., et al. 2003, A&A, 400, 877, doi: 10.1051/0004-6361:20030012
  * Pauli et al. (2006) Pauli, E., Napiwotzki, R., Heber, U., Altmann, M., & Odenkirchen, M. 2006, A&A, 447, 173, doi: 10.1051/0004-6361:20052730
  * Paxton et al. (2011) Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3
  * Paxton et al. (2013) Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4
  * Paxton et al. (2015) Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15
  * Peñarrubia et al. (2017) Peñarrubia, J., Varri, A. L., Breen, P. G., Ferguson, A. M. N., & Sánchez-Janssen, R. 2017, MNRAS, 471, L31, doi: 10.1093/mnrasl/slx094
  * Peter et al. (2013) Peter, A. H. G., Rocha, M., Bullock, J. S., & Kaplinghat, M. 2013, MNRAS, 430, 105, doi: 10.1093/mnras/sts535
  * Petersen & Peñarrubia (2020) Petersen, M. S., & Peñarrubia, J. 2020, MNRAS, 494, L11, doi: 10.1093/mnrasl/slaa029
  * Pizzolato et al. (2003) Pizzolato, N., Maggio, A., Micela, G., Sciortino, S., & Ventura, P. 2003, A&A, 397, 147, doi: 10.1051/0004-6361:20021560
  * Prada et al. (2019) Prada, J., Forero-Romero, J. E., Grand, R. J. J., Pakmor, R., & Springel, V. 2019, MNRAS, 490, 4877, doi: 10.1093/mnras/stz2873
  * Price-Whelan & Bonaca (2018a) Price-Whelan, A. M., & Bonaca, A. 2018a, ApJ, 863, L20, doi: 10.3847/2041-8213/aad7b5
  * Price-Whelan & Bonaca (2018b) —. 2018b, ApJ, 863, L20, doi: 10.3847/2041-8213/aad7b5
  * Price-Whelan et al. (2019) Price-Whelan, A. M., Mateu, C., Iorio, G., et al. 2019, AJ, 158, 223, doi: 10.3847/1538-3881/ab4cef
  * Raichoor et al. (2020) Raichoor, A., Eisenstein, D. J., Karim, T., et al. 2020, Research Notes of the American Astronomical Society, 4, 180, doi: 10.3847/2515-5172/abc078
  * Raichoor et al. (2022a) Raichoor, A., et al. 2022a, in prep.
  * Raichoor et al. (2022b) Raichoor, A., Moustakas, J., Newman, J. A., et al. 2022b, arXiv e-prints, arXiv:2208.08513.  https://arxiv.org/abs/2208.08513
  * Ramos et al. (2020) Ramos, P., Mateu, C., Antoja, T., et al. 2020, A&A, 638, A104, doi: 10.1051/0004-6361/202037819
  * Rebassa-Mansergas et al. (2016) Rebassa-Mansergas, A., Anguiano, B., García-Berro, E., et al. 2016, MNRAS, 463, 1137, doi: 10.1093/mnras/stw2021
  * Recio-Blanco et al. (2022) Recio-Blanco, A., de Laverny, P., Palicio, P. A., et al. 2022, arXiv e-prints, arXiv:2206.05541.  https://arxiv.org/abs/2206.05541
  * Rehemtulla et al. (2022) Rehemtulla, N., Valluri, M., & Vasiliev, E. 2022, MNRAS, 511, 5536, doi: 10.1093/mnras/stac400
  * Rockosi et al. (2022) Rockosi, C. M., Lee, Y. S., Morrison, H. L., et al. 2022, ApJS, 259, 60, doi: 10.3847/1538-4365/ac5323
  * Ruiz-Macias et al. (2020) Ruiz-Macias, O., Zarrouk, P., Cole, S., et al. 2020, Research Notes of the American Astronomical Society, 4, 187, doi: 10.3847/2515-5172/abc25a
  * Sanders & Binney (2013) Sanders, J. L., & Binney, J. 2013, MNRAS, 433, 1826, doi: 10.1093/mnras/stt816
  * Sanders & Das (2018) Sanders, J. L., & Das, P. 2018, MNRAS, 481, 4093, doi: 10.1093/mnras/sty2490
  * Sandford et al. (2020) Sandford, N. R., Weisz, D. R., & Ting, Y.-S. 2020, ApJS, 249, 24, doi: 10.3847/1538-4365/ab9cb0
  * Schlafly et al. (2022) Schlafly, E. F., et al. 2022, in prep.
  * Schlegel et al. (2022) Schlegel, D. J., et al. 2022, in prep.
  * Schmeja et al. (2014) Schmeja, S., Kharchenko, N. V., Piskunov, A. E., et al. 2014, A&A, 568, A51, doi: 10.1051/0004-6361/201322720
  * Schmidt et al. (2007) Schmidt, S. J., Cruz, K. L., Bongiorno, B. J., Liebert, J., & Reid, I. N. 2007, AJ, 133, 2258, doi: 10.1086/512158
  * Schörck et al. (2009) Schörck, T., Christlieb, N., Cohen, J. G., et al. 2009, A&A, 507, 817, doi: 10.1051/0004-6361/200810925
  * Sesar et al. (2011) Sesar, B., Jurić, M., & Ivezić, Ž. 2011, ApJ, 731, 4, doi: 10.1088/0004-637X/731/1/4
  * Sestito et al. (2020) Sestito, F., Martin, N. F., Starkenburg, E., et al. 2020, MNRAS, 497, L7, doi: 10.1093/mnrasl/slaa022
  * Sestito et al. (2021) Sestito, F., Buck, T., Starkenburg, E., et al. 2021, MNRAS, 500, 3750, doi: 10.1093/mnras/staa3479
  * Sharma et al. (2011) Sharma, S., Bland-Hawthorn, J., Johnston, K. V., & Binney, J. 2011, ApJ, 730, 3, doi: 10.1088/0004-637X/730/1/3
  * Shetrone et al. (2019) Shetrone, M., Tayar, J., Johnson, J. A., et al. 2019, ApJ, 872, 137, doi: 10.3847/1538-4357/aaff66
  * Shipp et al. (2020a) Shipp, N., Price-Whelan, A., Tavangar, K., Mateu, C., & Drlica-Wagner, A. 2020a, arXiv e-prints, arXiv:2006.12501.  https://arxiv.org/abs/2006.12501
  * Shipp et al. (2020b) Shipp, N., Price-Whelan, A. M., Tavangar, K., Mateu, C., & Drlica-Wagner, A. 2020b, AJ, 160, 244, doi: 10.3847/1538-3881/abbd3a
  * Siegal-Gaskins & Valluri (2008) Siegal-Gaskins, J. M., & Valluri, M. 2008, ApJ, 681, 40, doi: 10.1086/587450
  * Silber et al. (2023) Silber, J. H., Fagrelius, P., Fanning, K., et al. 2023, AJ, 165, 9
  * Simon & Geha (2007) Simon, J. D., & Geha, M. 2007, ApJ, 670, 313, doi: 10.1086/521816
  * Skumanich (1972) Skumanich, A. 1972, ApJ, 171, 565, doi: 10.1086/151310
  * Sollima (2020) Sollima, A. 2020, MNRAS, 495, 2222, doi: 10.1093/mnras/staa1209
  * Souto et al. (2019) Souto, D., Allende Prieto, C., Cunha, K., et al. 2019, ApJ, 874, 97, doi: 10.3847/1538-4357/ab0b43
  * Starkenburg et al. (2017) Starkenburg, E., Martin, N., Youakim, K., et al. 2017, MNRAS, 471, 2587, doi: 10.1093/mnras/stx1068
  * Stauffer et al. (2018) Stauffer, J., Rebull, L. M., Cody, A. M., et al. 2018, AJ, 156, 275, doi: 10.3847/1538-3881/aae9ec
  * Steinmetz (2003) Steinmetz, M. 2003, in Astronomical Society of the Pacific Conference Series, Vol. 298, GAIA Spectroscopy: Science and Technology, ed. U. Munari, 381–+
  * Steinmetz et al. (2020a) Steinmetz, M., Matijevič, G., Enke, H., et al. 2020a, AJ, 160, 82, doi: 10.3847/1538-3881/ab9ab9
  * Steinmetz et al. (2020b) Steinmetz, M., Guiglion, G., McMillan, P. J., et al. 2020b, AJ, 160, 83, doi: 10.3847/1538-3881/ab9ab8
  * Szentgyorgyi et al. (2011) Szentgyorgyi, A., Furesz, G., Cheimets, P., et al. 2011, PASP, 123, 1188, doi: 10.1086/662209
  * Ting & Rix (2019) Ting, Y.-S., & Rix, H.-W. 2019, ApJ, 878, 21, doi: 10.3847/1538-4357/ab1ea5
  * Ting et al. (2017) Ting, Y.-S., Rix, H.-W., Conroy, C., Ho, A. Y. Q., & Lin, J. 2017, ApJ, 849, L9, doi: 10.3847/2041-8213/aa921c
  * Toonen et al. (2017) Toonen, S., Hollands, M., Gänsicke, B. T., & Boekholt, T. 2017, A&A, 602, A16, doi: 10.1051/0004-6361/201629978
  * Tremblay et al. (2011) Tremblay, P. E., Bergeron, P., & Gianninas, A. 2011, ApJ, 730, 128, doi: 10.1088/0004-637X/730/2/128
  * Tremblay et al. (2014) Tremblay, P.-E., Kalirai, J. S., Soderblom, D. R., Cignoni, M., & Cummings, J. 2014, ApJ, 791, 92, doi: 10.1088/0004-637X/791/2/92
  * Tremblay et al. (2017) Tremblay, P.-E., Gentile-Fusillo, N., Raddi, R., et al. 2017, MNRAS, 465, 2849, doi: 10.1093/mnras/stw2854
  * Tsantaki et al. (2021) Tsantaki, M., Pancino, E., Marrese, P., et al. 2021, arXiv e-prints, arXiv:2110.09316.  https://arxiv.org/abs/2110.09316
  * Vanderburg et al. (2020) Vanderburg, A., Rappaport, S. A., Xu, S., et al. 2020, Nature, 585, 363, doi: 10.1038/s41586-020-2713-y
  * Vargya et al. (2021) Vargya, D., Sanderson, R., Sameie, O., et al. 2021, arXiv e-prints, arXiv:2104.14069.  https://arxiv.org/abs/2104.14069
  * Vasiliev et al. (2021) Vasiliev, E., Belokurov, V., & Erkal, D. 2021, MNRAS, 501, 2279, doi: 10.1093/mnras/staa3673
  * Velazquez & White (1999) Velazquez, H., & White, S. D. M. 1999, MNRAS, 304, 254, doi: 10.1046/j.1365-8711.1999.02354.x
  * Vincenzo et al. (2021) Vincenzo, F., Weinberg, D. H., Montalbán, J., et al. 2021, arXiv e-prints, arXiv:2106.03912.  https://arxiv.org/abs/2106.03912
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
  * Walker et al. (1996) Walker, I. R., Mihos, J. C., & Hernquist, L. 1996, ApJ, 460, 121, doi: 10.1086/176956
  * Wang et al. (2017) Wang, M.-Y., Fattahi, A., Cooper, A. P., et al. 2017, MNRAS, 468, 4887
  * Wang et al. (2020) Wang, W., Han, J., Cautun, M., Li, Z., & Ishigaki, M. N. 2020, Science China Physics, Mechanics, and Astronomy, 63, 109801, doi: 10.1007/s11433-019-1541-6
  * Wegg et al. (2019) Wegg, C., Gerhard, O., & Bieth, M. 2019, MNRAS, 485, 3296, doi: 10.1093/mnras/stz572
  * Wegg & Phinney (2012) Wegg, C., & Phinney, E. S. 2012, MNRAS, 426, 427, doi: 10.1111/j.1365-2966.2012.21394.x
  * WFIRST Astrometry Working Group et al. (2019) WFIRST Astrometry Working Group, Sanderson, R. E., Bellini, A., et al. 2019, Journal of Astronomical Telescopes, Instruments, and Systems, 5, 044005, doi: 10.1117/1.JATIS.5.4.044005
  * Williams et al. (2009) Williams, K. A., Bolte, M., & Koester, D. 2009, ApJ, 693, 355, doi: 10.1088/0004-637X/693/1/355
  * Winget et al. (1987) Winget, D. E., Hansen, C. J., Liebert, J., et al. 1987, ApJ, 315, L77
  * Xiang & Rix (2022) Xiang, M., & Rix, H.-W. 2022, Natur, 603, 599, doi: 10.1038/s41586-022-04496-5
  * Xiang et al. (2021) Xiang, M., Rix, H.-W., Ting, Y.-S., et al. 2021, ApJS, 253, 22, doi: 10.3847/1538-4365/abd6ba
  * Xiang et al. (2019) Xiang, M., Ting, Y.-S., Rix, H.-W., et al. 2019, ApJS, 245, 34, doi: 10.3847/1538-4365/ab5364
  * Xiang et al. (2020) Xiang, M.-S., Rix, H.-W., Ting, Y.-S., et al. 2020, ApJ, 898, 28, doi: 10.3847/1538-4357/ab99a5
  * Xu et al. (2013) Xu, S., Jura, M., Klein, B., Koester, D., & Zuckerman, B. 2013, ApJ, 766, 132, doi: 10.1088/0004-637X/766/2/132
  * Yanny et al. (2009a) Yanny, B., Rockosi, C., Newberg, H. J., et al. 2009a, AJ, 137, 4377, doi: 10.1088/0004-6256/137/5/4377
  * Yanny et al. (2009b) —. 2009b, AJ, 137, 4377, doi: 10.1088/0004-6256/137/5/4377
  * Yèche et al. (2020) Yèche, C., Palanque-Delabrouille, N., Claveau, C.-A., et al. 2020, Research Notes of the American Astronomical Society, 4, 179, doi: 10.3847/2515-5172/abc01a
  * York et al. (2000) York, D. G., Adelman, J., Anderson, John E., J., et al. 2000, AJ, 120, 1579, doi: 10.1086/301513
  * Zasowski et al. (2013) Zasowski, G., Johnson, J. A., Frinchaboy, P. M., et al. 2013, AJ, 146, 81, doi: 10.1088/0004-6256/146/4/81
  * Zavala & Frenk (2019) Zavala, J., & Frenk, C. S. 2019, Galaxies, 7, 81
  * Zemp et al. (2012) Zemp, M., Gnedin, O. Y., Gnedin, N. Y., & Kravtsov, A. V. 2012, ApJ, 748, 54, doi: 10.1088/0004-637X/748/1/54
  * Zhou et al. (2020) Zhou, R., Newman, J. A., Dawson, K. S., et al. 2020, Research Notes of the American Astronomical Society, 4, 181, doi: 10.3847/2515-5172/abc0f4
  * Zhou et al. (2023) Zhou, R., Dey, B., Newman, J. A., et al. 2023, AJ, 165, 58, doi: 10.3847/1538-3881/aca5fb
  * Zorotovic et al. (2010) Zorotovic, M., Schreiber, M. R., Gänsicke, B. T., & Nebot Gómez-Morán, A. 2010, A&A, 520, A86, doi: 10.1051/0004-6361/200913658
  * Zou et al. (2017) Zou, H., Zhou, X., Fan, X., et al. 2017, PASP, 129, 064101, doi: 10.1088/1538-3873/aa65ba
  * Zuckerman et al. (2007) Zuckerman, B., Koester, D., Melis, C., Hansen, B. M., & Jura, M. 2007, ApJ, 671, 872, doi: 10.1086/522223