# Overview of the DESI Milky Way Survey

Andrew P. Cooper Institute of Astronomy and Department of Physics, National
Tsing Hua University, 101 Kuang-Fu Rd. Sec. 2, Hsinchu 30013, Taiwan  Center
for Informatics and Computation in Astronomy, NTHU, 101 Kuang-Fu Rd. Sec. 2,
Hsinchu 30013, Taiwan  Physics Division, National Center for Theoretical
Sciences, Taipei 10617, Taiwan<EMAIL_ADDRESS>Sergey E. Koposov
Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford
Hill, Edinburgh EH9 3HJ, UK  Institute of Astronomy, University of Cambridge,
Madingley Rd., Cambridge CB3 0HA, UK  Carlos Allende Prieto Instituto de
Astrofísica de Canarias, C/ Vía Láctea s/n, E-38205 La Laguna, Tenerife, Spain
Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna,Tenerife, Spain
Christopher J. Manser Imperial College London, South Kensington Campus, London
SW7 2AZ, UK  Namitha Kizhuprakkat  Institute of Astronomy and Department of
Physics, National Tsing Hua University, 101 Kuang-Fu Rd. Sec. 2, Hsinchu
30013, Taiwan  Center for Informatics and Computation in Astronomy, NTHU, 101
Kuang-Fu Rd. Sec. 2, Hsinchu 30013, Taiwan  Adam D. Myers  Department of
Physics & Astronomy, University of Wyoming, 1000 E. University, Dept. 3905,
Laramie, WY 82071, USA  Arjun Dey  NSF’s NOIRLab, 950 N. Cherry Ave., Tucson,
AZ 85719, USA  Boris T. Gänsicke Department of Physics, University of Warwick,
Gibbet Hill Rd., Coventry, CV4 7AL, UK  Ting S. Li Department of Astronomy &
Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada  Constance
Rockosi Department of Astronomy and Astrophysics, University of California,
Santa Cruz, 1156 High St., Santa Cruz, CA 95065, USA  University of California
Observatories, 1156 High St., Sana Cruz, CA 95065, USA  Monica Valluri
Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
Joan Najita  NSF’s NOIRLab, 950 N. Cherry Ave., Tucson, AZ 85719, USA  Alis
Deason  Institute for Computational Cosmology, Department of Physics, Durham
University, South Rd., Durham DH1 3LE, UK  Anand Raichoor Lawrence Berkeley
National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720, USA  Mei-Yu Wang
Pittsburgh Supercomputing Center, Carnegie Mellon University, Pittsburgh, PA
15213, USA  Yuan-Sen Ting  Research School of Astronomy & Astrophysics,
Australian National University, Cotter Rd., Weston, ACT 2611, Australia
School of Computing, Australian National University, Acton, ACT 2601,
Australia  Bokyoung Kim Institute for Astronomy, University of Edinburgh,
Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK  Andreia Carrillo
Institute for Computational Cosmology, Department of Physics, Durham
University, South Rd., Durham DH1 3LE, UK  Wenting Wang  Department of
Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University,
Shanghai 200240, China  Leandro Beraldo e Silva  Department of Astronomy,
University of Michigan, Ann Arbor, MI 48109, USA  Jiwon Jesse Han Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138,
USA  Jiani Ding  Department of Astronomy and Astrophysics, University of
California, Santa Cruz, 1156 High St., Santa Cruz, CA 95065, USA  University
of California Observatories, 1156 High St., Sana Cruz, CA 95065, USA  Miguel
Sánchez-Conde  Instituto de Física Teórica (IFT) UAM/CSIC, Universidad
Autónoma de Madrid, Cantoblanco, E-28049, Madrid, Spain  Jessica N. Aguilar
Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720,
USA  Steven Ahlen Physics Dept., Boston University, 590 Commonwealth Ave.,
Boston, MA 02215, USA  Stephen Bailey Lawrence Berkeley National Laboratory, 1
Cyclotron Rd., Berkeley, CA 94720, USA  Vasily Belokurov  Institute of
Astronomy, University of Cambridge, Madingley Rd., Cambridge CB3 0HA, UK
Center for Computational Astrophysics, Flatiron Institute, 162 5th Ave., New
York, NY 10010, USA  David Brooks  Department of Physics & Astronomy,
University College London, Gower St., London, WC1E 6BT, UK  Katia Cunha
Steward Observatory, University of Arizona, 933 N, Cherry Ave, Tucson, AZ
85721, USA  Kyle Dawson  Department of Physics and Astronomy, The University
of Utah, 115 South 1400 East, Salt Lake City, UT 84112, USA  Axel de la
Macorra  Instituto de Física, Universidad Nacional Autónoma de México, Cd. de
México C.P. 04510, México  Peter Doel  Department of Physics & Astronomy,
University College London, Gower St., London, WC1E 6BT, UK  Daniel J.
Eisenstein  Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden St.,
Cambridge, MA 02138, USA  Parker Fagrelius  NSF’s NOIRLab, 950 N. Cherry Ave.,
Tucson, AZ 85719, USA  Kevin Fanning  Department of Physics, The Ohio State
University, 191 West Woodruff Ave., Columbus, OH 43210, USA  Center for
Cosmology and AstroParticle Physics, The Ohio State University, 191 West
Woodruff Ave., Columbus, OH 43210, USA  Andreu Font-Ribera  Institut de Física
d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology,
Campus UAB, 08193 Bellaterra Barcelona, Spain  Jaime E. Forero-Romero
Departamento de Física, Universidad de los Andes, Cra. 1 No. 18A-10, Edificio
Ip, CP 111711, Bogotá, Colombia  Enrique Gaztañaga  Institut d’Estudis
Espacials de Catalunya (IEEC), 08034 Barcelona, Spain  Institute of Space
Sciences, ICE-CSIC, Campus UAB, Carrer de Can Magrans s/n, 08913 Bellaterra,
Barcelona, Spain  Satya Gontcho A Gontcho Lawrence Berkeley National
Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720, USA  Department of Physics
and Astronomy, University of Rochester, 500 Joseph C. Wilson Boulevard,
Rochester, NY 14627, USA  Julien Guy  Lawrence Berkeley National Laboratory, 1
Cyclotron Rd., Berkeley, CA 94720, USA  Klaus Honscheid  Center for Cosmology
and AstroParticle Physics, The Ohio State University, 191 West Woodruff Ave.,
Columbus, OH 43210, USA  Department of Physics, The Ohio State University, 191
West Woodruff Ave., Columbus, OH 43210, USA  Robert Kehoe  Department of
Physics, Southern Methodist University, 3215 Daniel Ave., Dallas, TX 75275,
USA  Theodore Kisner Lawrence Berkeley National Laboratory, 1 Cyclotron Rd.,
Berkeley, CA 94720, USA  Anthony Kremin Lawrence Berkeley National Laboratory,
1 Cyclotron Rd., Berkeley, CA 94720, USA  Martin Landriau Lawrence Berkeley
National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720, USA  Michael E. Levi
Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720,
USA  Paul Martini Center for Cosmology and AstroParticle Physics, The Ohio
State University, 191 West Woodruff Ave., Columbus, OH 43210, USA  Department
of Astronomy, The Ohio State University, 4055 McPherson Laboratory, 140 W 18th
Ave., Columbus, OH 43210, USA  Aaron M. Meisner NSF’s NOIRLab, 950 N. Cherry
Ave., Tucson, AZ 85719, USA  Ramon Miquel  Institució Catalana de Recerca i
Estudis Avançats, Passeig de Lluís Companys, 23, 08010 Barcelona, Spain
Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science
and Technology, Campus UAB, 08193 Bellaterra Barcelona, Spain  John Moustakas
Department of Physics and Astronomy, Siena College, 515 Loudon Rd.,
Loudonville, NY 12211, USA  Jundan Nie National Astronomical Observatories,
Chinese Academy of Sciences, A20 Datun Rd., Chaoyang District, Beijing,
100101, P.R. China  Nathalie Palanque-Delabrouille Lawrence Berkeley National
Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720, USA  IRFU, CEA, Université
Paris-Saclay, F-91191 Gif-sur-Yvette, France  Will J. Percival Waterloo Centre
for Astrophysics, University of Waterloo, 200 University Ave W, Waterloo, ON
N2L 3G1, Canada  Department of Physics and Astronomy, University of Waterloo,
200 University Ave W, Waterloo, ON N2L 3G1, Canada  Perimeter Institute for
Theoretical Physics, 31 Caroline St. North, Waterloo, ON N2L 2Y5, Canada
Claire Poppett  Lawrence Berkeley National Laboratory, 1 Cyclotron Rd.,
Berkeley, CA 94720, USA  Space Sciences Laboratory, University of California,
Berkeley, 7 Gauss Way, Berkeley, CA 94720, USA  University of California,
Berkeley, 110 Sproul Hall #5800 Berkeley, CA 94720, USA  Francisco Prada
Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, s/n,
E-18008 Granada, Spain  Nabeel Rehemtulla Department of Astronomy, University
of Michigan, Ann Arbor, MI 48109, USA  Edward Schlafly Lawrence Livermore
National Laboratory, P.O. Box 808 L-211, Livermore, CA 94551, USA  David
Schlegel  Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA
94720, USA  Michael Schubnell  Department of Physics, University of Michigan,
Ann Arbor, MI 48109, USA  Ray M. Sharples  Centre for Advanced
Instrumentation, Department of Physics, Durham University, South Rd., Durham
DH1 3LE, UK  Institute for Computational Cosmology, Department of Physics,
Durham University, South Rd., Durham DH1 3LE, UK  Gregory Tarlé Department of
Physics, University of Michigan, Ann Arbor, MI 48109, USA  Risa H. Wechsler
Kavli Institute for Particle Astrophysics and Cosmology, Stanford University,
Menlo Park, CA 94305, USA  Physics Department, Stanford University, Stanford,
CA 93405, USA  SLAC National Accelerator Laboratory, Menlo Park, CA 94305, USA
David H. Weinberg Department of Astronomy, The Ohio State University, 4055
McPherson Laboratory, 140 W 18th Ave., Columbus, OH 43210, USA  Center for
Cosmology and AstroParticle Physics, The Ohio State University, 191 West
Woodruff Ave., Columbus, OH 43210, USA  Zhimin Zhou National Astronomical
Observatories, Chinese Academy of Sciences, A20 Datun Rd., Chaoyang District,
Beijing, 100101, P.R. China  Hu Zou National Astronomical Observatories,
Chinese Academy of Sciences, A20 Datun Rd., Chaoyang District, Beijing,
100101, P.R. China

(Received 2022 September 8; Revised 2022 December 20; Accepted 2023 January
16)

###### Abstract

We describe the Milky Way Survey (MWS) that will be undertaken with the Dark
Energy Spectroscopic Instrument (DESI) on the Mayall 4m telescope at the Kitt
Peak National Observatory. Over the next 5 yr DESI MWS will observe
approximately seven million stars at Galactic latitudes $|b|>20^{\circ}$, with
an inclusive target selection scheme focused on the thick disk and stellar
halo. MWS will also include several high-completeness samples of rare stellar
types, including white dwarfs, low-mass stars within 100 pc of the Sun, and
horizontal branch stars. We summarize the potential of DESI to advance
understanding of Galactic structure and stellar evolution. We introduce the
final definitions of the main MWS target classes and estimate the number of
stars in each class that will be observed. We describe our pipelines for
deriving radial velocities, atmospheric parameters, and chemical abundances.
We use $\simeq 500,000$ spectra of unique stellar targets from the DESI Survey
Validation program (SV) to demonstrate that our pipelines can measure radial
velocities to $\simeq 1\,\mathrm{km\,s^{-1}}$ and $\mathrm{[Fe/H]}$ accurate
to $\simeq 0.2$ dex for typical stars in our main sample. We find the stellar
parameter distributions from $\approx 100\,\mathrm{deg}^{2}$ of SV
observations with $\gtrsim 90$% completeness on our main sample are in good
agreement with expectations from mock catalogs and previous surveys.

Galaxy: abundances – Galaxy: kinematics and dynamics – Galaxy: stellar content
– Galaxy: structure – stars: general – surveys

††software: NumPy (Harris et al., 2020), SciPy (Virtanen et al., 2020),
Astropy (Astropy Collaboration et al., 2013, 2018), Matplotlib (Hunter, 2007),
PyGaia (A. Brown; Gaia Project Scientist Support Team and the Gaia DPAC;
https://github.com/agabrown/PyGaia), galstreams (Mateu, 2017).††facilities:
Mayall (Mosaic3), Bok (90Prime), Blanco (DECam), WISE, Gaia.

##  1 Introduction

Figure 1: The DESI MWS footprint. Gray lines indicate the approximate Galactic
latitude limit of the survey, $b\pm 20\arcdeg$. The density of MWS targets is
shown in gray scale. Colored symbols indicate known Milky Way satellites
(stars) and globular clusters (triangles). Points and tracks (colors given in
the legend) show the four most prominent streams, as reported in the
galstreams compilation (Mateu, 2017): Sgr, represented by the Law & Majewski
(2010) model; Palomar 5 (Price-Whelan et al., 2019); GD 1 (Price-Whelan &
Bonaca, 2018a) and Orphan (Koposov et al., 2019). We also show the approximate
extent of the Hercules–Aquila cloud as reported in galstreams (based on
Grillmair & Carlin, 2016). Many other less prominent streams and stellar
overdensities are known in the MWS footprint (see, e.g. Mateu, 2022).

The Dark Energy Spectroscopic Instrument (DESI) is currently the premier
multiobject spectrograph for wide-field surveys (DESI Collaboration et al.,
2016a; Abareshi et al., 2022). DESI deploys 5000 fibers over a $3^{\circ}.2$
diameter field of view at the prime focus of the Mayall 4m telescope at Kitt
Peak National Observatory (DESI Collaboration et al., 2016b; Silber et al.,
2023; Miller et al., 2022). The fibers feed 10 identical three-arm
spectrographs, each spanning 3600-9824Å at an FWHM resolution of about 1.8Å.
Each fiber can be positioned individually by a robotic actuator within a
radius of $1^{\prime}.48$, with a small overlap between the patrol regions of
adjacent fibers. The total time to slew the telescope, read out the
spectrograph, and reconfigure the focal plane between successive survey
exposures can be $\lesssim 2$ minutes (Abareshi et al., 2022). This allows
large areas of sky to be surveyed very rapidly at a density of $\sim 600$
targets per square degree.

Although DESI is optimized for galaxy redshift surveys, it is also well suited
to observing large numbers of Milky Way stars over wide areas at low spectral
resolution. DESI will therefore carry out a Milky Way Survey (MWS) alongside
its primary 5-year cosmological program (DESI Collaboration et al., 2016a).
MWS will operate during bright-sky conditions (when high-redshift galaxy
observations are inefficient) and will share the DESI focal plane with a low-
redshift Bright Galaxy Survey (BGS; Hahn et al., 2022). Although BGS galaxies
will be prioritized for fiber assignment, there is often no BGS target in the
patrol region of a DESI fiber. This provides an excellent opportunity to
obtain large numbers of stellar spectra, which MWS is designed to exploit.

The primary MWS program will observe approximately seven million stars to a
limiting magnitude of $r=19$ across the full DESI bright-time program
footprint. As shown in Fig. 1, this footprint covers most of the northern
Galactic cap region and a significant fraction of the southern cap. It
includes many known substructures in the Milky Way stellar halo, such as the
Sagittarius, Orphan, and GD 1 streams; the Hercules–Aquila and Virgo
overdensities; and many dwarf satellite galaxies and globular clusters. MWS
will provide radial velocities, stellar parameters, and metallicities for an
order of magnitude more stars than found in existing samples with similar
resolution from the SEGUE and LAMOST surveys, in the same range of magnitudes
($r>16$) and Galactic latitudes (see Section 2).

The MWS selection function is designed to be inclusive, minimally biased, and
amenable to forward modeling. The main MWS sample will focus on large-scale
spatial and kinematic structures up to 150 kpc from the Sun, using three
target categories, main-blue, main-red and main-broad, which in combination
cover the full color–magnitude space within $16<r<19$ (see Section 4.2). main-
blue randomly samples all point sources in this magnitude range with blue
optical colors ($g-r<0.7$). It will be dominated by metal-poor main-sequence
turnoff stars in the thick disk and inner halo, and will also contain more
distant horizontal branch stars. We expect these targets to have a
spectroscopic completeness of $\approx 30\%$ and to comprise 56% of the main
MWS sample. main-red ($\approx 30\%$ complete, 12% of the main sample) applies
Gaia proper-motion and parallax criteria to sources with redder colours
($g-r>0.7$) to boost the probability of observing distant halo giants. Sources
with $g-r>0.7$ that do not meet those astrometric criteria, mostly redder
main-sequence stars in the thin disk, are targeted at lower priority in the
main-broad category ($\approx 20\%$ complete, 32% of the main sample). Based
on survey forecasts (see Section 5), we expect to observe $\approx 6.6$
million unique targets in the MWS main sample (90% of all MWS spectra). These
data will constrain the star formation history and chemical and dynamical
evolution of the Galactic thick disk and stellar halo, and allow us to
identify the low-contrast remnants of ancient dwarf galaxy accretion events.
Radial velocities from MWS combined with Gaia astrometry will constrain the
three-dimensional distribution of dark matter in the Galaxy.

As part of the primary MWS, the generously selected main sample will be
supplemented by several much smaller but highly complete samples of rare
stellar types with very low density on the sky. MWS will target a near-
complete sample of white dwarfs to the Gaia magnitude limit in order to obtain
an independent measurement of the star formation history of the disk and halo
populations. It will also collect a highly complete sample of stars in the
Gaia catalog within 100 pc, to investigate the fundamental properties of low-
mass stars and measure the stellar initial mass function. Blue horizontal
branch stars (BHBs) and RR Lyrae variables will be prioritized for their use
as tracers of the distant metal-poor halo. In addition to these primary
samples, the DESI surveys will allocate a small number of fibers to
specialized secondary science programs, some of which will focus on stars. The
survey will also operate a backup program for poor observing conditions, which
we expect to yield spectra for several million stars brighter than those in
the primary MWS sample. The secondary and backup programs will be described in
separate publications; here we provide only brief summaries of their relevance
to the goals of MWS.

This paper presents the context (Section 2) and scientific motivation of MWS
(Section 3), the target selection scheme (Section 4), and the survey strategy
(Section 5), including forecasts for the final size of each primary sample. In
Section 6 we describe the core components of our spectroscopic analysis
pipeline. From 2019 November to 2021 May, DESI carried out a survey validation
(SV) campaign consisting of three subprograms (SV1, SV2, and SV3). The SV1 and
SV3 datasets each contain spectra for $\sim 200,000$ unique stars, covering a
superset of the MWS selection function. These observations will be the basis
for the first DESI MWS data release. They include observations of calibration
fields, such as open and globular clusters, and an $\approx 100$ square degree
high-completeness minisurvey representative of the northern Galactic cap. We
give an overview of these datasets in Section 7 and use them to demonstrate
that our survey design and analysis pipeline meet the requirements set by the
ambitious science goals of MWS. We summarize in Section 8.

Machine-readable tables of the data shown in the figures of this paper are
available at https://doi.org/10.5281/zenodo.7013864. The complete sets of
targets selected for the main MWS and the DESI SV programs are available at
https://data.desi.lbl.gov/public/ets/target/ as described by Myers et al.
(2023).

##  2 DESI MWS in context

Table 1: Summary of completed and ongoing stellar spectroscopic surveys with $\gtrsim 10^{5}$ targets, discussed in Section 2. Columns give the number of targets (either in the latest data release or forecast) and the approximate magnitude range, spectral resolution $R$, and wavelength coverage. The rightmost columns give the most recent data release (except where noted, $N_{\mathrm{star}}$ is the number of unique stars that release) and reference for each survey. For LAMOST, we count the number of unique Gaia source IDs with spectral class STAR and separate the low resolution survey into two rows, respectively for stars in the MWS magnitude range and brighter stars. The table is divided into low-resolution and medium/high resolution surveys. Survey |  $N_{\mathrm{star}}$/$10^{6}$ | Mag. Range | $R$ |  $\lambda$ (Å) | Release | Reference
---|---|---|---|---|---|---
DESI MWS | 7.2a | $16<r<{\color[rgb]{0,0,0}20}$ | 2500–5000 | 3600–9900 | – | –
SEGUE I | 0.2 | $16<r<20$ | 1850–2200 | 3800–9200 | DR17 | Yanny et al. (2009a)
SEGUE II | 0.1 | $16<r<20$ | 1850–2200 | 3800–9200 | DR17 | Rockosi et al. (2022)
LAMOST LRS | 1.8b |  $16<G<18$c | $\approx 1800$ | 3700–9000 | DR8 | Luo et al. (2015)
| 5.0d | $10<G<16$ | $\approx 1800$ | 3700–9000 | DR8 | Luo et al. (2015)
LAMOST MRS | 1.1 | $10<G<15$ | $\approx 7500$ | 4900–6800 | DR8 | Luo et al. (2015)
RAVE | 0.5 | $9<I<12$ | 7500 | 8410–8795 | DR6 | Steinmetz et al. (2020a)
Gaia RVS | 33e | $G<14$ | 11,500 | 8450–8720 | DR3 | Katz et al. (2022)
Gaia-ESO | 0.1 | $17<r<18$ | 20,000 | 3700–9500 | DR5 | Gilmore et al. (2012a)
GALAH | 0.6 | $9<V<14$ | 20,000–50,000 | 4718–7890d | DR3 | Buder et al. (2021)
APOGEE | 0.7 | $10<G<17$ | 22,500 | 15,140–16,960 | DR17 | Majewski et al. (2017)
H3 | 0.3f | $15<r<18$ | 32,000 | 5150–5300 | – | Conroy et al. (2019)
Notes: aForecast. b1.2M at $|b|>20$, of which 0.6M have stellar parameters.
c69,233 with $G>18$. d2.9M at $|b|>20$, of which
2.3M have stellar parameters; e5.6M have stellar parameters (Recio-Blanco et
al., 2022). fFour bands of width 200Å.

DESI is the first on-sky instrument among a new generation of multiobject
survey spectrographs with a 4m aperture, high fiber density over a wide field
of view, and rapid fiber positioning. These advances allow a new approach to
large-scale stellar spectroscopy, which seeks to minimize selection biases and
to provide uniformly high spectroscopic completeness over a large fraction of
the sky. As we describe below, even subject to operational constraints imposed
by the DESI cosmological programs, MWS expects to assemble an effectively
flux-limited sample of $\simeq 7$ million stellar spectra to a magnitude limit
$r\lesssim 19$ over 5 yr. In comparison to existing surveys, DESI MWS will
provide a much higher density of faint stars to search for substructures and
to probe the kinematics and chemistry of the outer thin disk, thick disk,
tidal streams, and diffuse stellar halo.

Table 1 lists the parameters of other recent spectroscopic surveys of
$>10^{5}$ stars with spectral resolution comparable to or greater than that of
DESI. The closest existing counterparts to DESI MWS in scientific scope and
spectral resolution ($R\equiv\lambda/\mathrm{FWHM}\simeq 2000$) are the Sloan
Digital Sky Survey (SDSS) optical surveys (York et al., 2000; Eisenstein et
al., 2011; Blanton et al., 2017) and the LAMOST survey (Cui et al., 2012).

The primary SDSS low-resolution stellar surveys were SEGUE-1 (Yanny et al.,
2009a) and SEGUE-2 (Rockosi et al., 2022), which together observed $\simeq
300,000$ stars. Stars were also observed as calibration targets and
serendipitously by other SDSS programs, including $\sim 380,000$ stars by the
BOSS/eBOSS cosmological surveys (Dawson et al., 2013). The SEGUE surveys each
covered $\lesssim 1500$ $\mathrm{deg}^{2}$ in total, with individual fields
distributed over the SDSS imaging footprint. The SEGUE-2 target selection
focused on the distant stellar halo, with similar scientific goals to MWS. The
most significant differences of MWS from SEGUE its are contiguous sky
coverage, much larger number of spectra and broader, simpler selection
function.

LAMOST (Cui et al., 2012; Luo et al., 2015) is an ongoing survey covering
17,000 $\mathrm{deg}^{2}$ in the northern hemisphere
($0^{\circ}<\delta<60^{\circ}$) including the Galactic anticenter. To date,
LAMOST has obtained more than 11 million $R\approx 1800$ stellar spectra in
its LRS, primarily for stars brighter than $r\sim 18$. The most recent public
data release (DR8 v2) contains $10.3$ million LRS stellar spectra. Stellar
parameters have been derived for $6.7$ million of these, corresponding to
$\approx 4.8$ million unique sources in the Gaia catalog. LAMOST also includes
a medium-resolution survey ($\approx 1.1$M stars in LAMOST DR8). In comparison
to LAMOST, MWS will provide many more spectra for fainter stars in the outer
thick disk and stellar halo. Of the 4.8 million unique stars with stellar
parameters in LAMOST LRS (DR8), only $\approx 580,000$ are at Galactic
latitudes $|b|>20^{\circ}$ and fainter than Gaia $G=16$.

High-resolution Milky Way surveys, such as Gaia-ESO (Gilmore et al., 2012b),
GALAH (De Silva et al., 2015), RAVE (Steinmetz et al., 2020a), APOGEE
(Zasowski et al., 2013; Majewski et al., 2017), and the ongoing H3 survey
(Conroy et al., 2019), have collected spectra for substantial samples of
bright stars ($\lesssim 1$ million) with $R\simeq 20,000$-$50,000$. APOGEE has
observed $\approx 400,000$ stars at $|b|>20^{\circ}$, of which $\sim 95\%$ are
brighter than $G=17$. Although APOGEE observations have concentrated on the
Galactic bulge and disk, a number of fields have been observed in the halo.
Some of these fields targeted have known halo substructures, including the
Sagittarius stream (e.g. Hasselquist et al., 2019), and include target
selections that overlap in distance with MWS. The brightest MWS targets
observed with the APOGEE halo dataset will be useful for calibrating MWS
parameter and abundance measurements.

The H3 survey is using MMT Hectochelle (Szentgyorgyi et al., 2011) to observe
$300,000$ high resolution optical spectra ($R=32,000$) in the northern
hemisphere sky at $|b|>20^{\circ}$ and $\delta>-20^{\circ}$, sparsely sampling
$15,000$ $\mathrm{deg}^{2}$. H3 targets a magnitude range similar to that of
MWS, and has similar science goals focused on the stellar halo. Like the MWS
selection function, the H3 selection function is close to magnitude-limited,
with a weak parallax selection, and priority given to sparsely distributed
halo giant candidates, BHBs, and RR Lyrae variables. In many respects H3
therefore provides a complementary (slightly shallower) high-resolution
counterpart to MWS.

Radial velocity surveys with intermediate resolution, such as RAVE (Steinmetz,
2003), have also focused on brighter targets than those in MWS. By far the
largest of these is the Gaia Radial Velocity Spectrometer survey (RVS)
(Cropper et al., 2018). Both RAVE and Gaia RVS use a narrow spectral window
around the Ca ii triplet ($8400\lesssim\lambda\lesssim 8800$Å). Despite this
limited wavelength coverage, multiple individual abundances have been
recovered for the majority of the 0.5 million $R\approx 7,500$ RAVE spectra,
including [Fe/H], to an accuracy of $\approx 0.2$ dex (Boeche et al., 2011;
Steinmetz et al., 2020b). Recio-Blanco et al. (2022), using an extension of
the same core pipeline, report abundances for $\sim 5$ million Gaia RVS
spectra with $G<14$. MWS will provide both radial velocities and chemical
abundance information, based on measurements over a wider range of
wavelengths, for a significant fraction of much fainter stars, including many
with Gaia astrometric measurements but no useful Gaia RVS data.

It has previously been shown that multiple elemental abundances can be
extracted from low-resolution spectra (e.g. Fernández-Alvar et al., 2015; Ting
et al., 2017; Xiang et al., 2019). These approaches can be further developed
with DESI, which, compared to SDSS and LAMOST, has better sensitivity at
$\lambda\lesssim 4000$Å and slightly higher resolution. Precise
spectrophotometric distances can also be estimated based on spectra at the
resolution of DESI, to better than $10\%$ at signal-to-noise ratios (S/N)
$>50$ (Hogg et al., 2019; Xiang et al., 2021) and 20% at S/N $>20$.
Furthermore, DESI’s broad optical wavelength range will provide useful
information about stellar ages for red giants inferred through mass estimates
from C and N abundances (Masseron & Gilmore, 2015; Martig et al., 2016; Ness
et al., 2016; Sanders & Das, 2018; Shetrone et al., 2019).

##  3 Science Goals of DESI MWS

DESI MWS will assemble an extremely large sample of radial velocities and
chemical abundances, predominantly for distant stars at high Galactic
latitude. In this section we review how these data, combined with
spectrophotometric distance estimates and Gaia astrometry, will advance
understanding of the dark and luminous structure of the Milky Way, the history
of stellar mass growth through tidal stripping, in situ star formation, and
stellar (and planetary) astrophysics.

###  3.1 Probing the Dark Matter and Accretion History of the Milky Way

Dark matter constitutes approximately 86% of the gravitating mass in the
present-day universe. Galaxies form in dark matter potential wells. While the
large-scale distribution of galaxies traces the dark matter distribution on
cosmological scales, the internal kinematics of galaxies provides a uniquely
powerful laboratory in which to study the small-scale structure of dark
matter.

Galaxies build their stellar halos through mergers with satellite galaxies,
which may be accompanied by their own globular cluster systems. As dwarf
galaxies are tidally disrupted, their stars and globular clusters are pulled
out into thin tidal streams. Mergers with lower mass ratios may also generate
or enhance a galactic thick disk component. Because dynamical times in the
outer halo are long assuming approximate global dynamical equilibrium, the
kinematics of halo stars and globular clusters probe the mass distribution and
dynamics of the dark matter halo (for recent reviews, see Bland-Hawthorn &
Gerhard, 2016; Wang et al., 2020, and references therein). The merger history
of the Milky Way is preserved in the clustering of stellar debris from past
accretion events, and correlations between halo stars in phase space and in
abundance space encode the assembly history of the Galaxy (see, e.g. Helmi,
2020).

####  3.1.1 The Shape and Mass of the Dark Matter Halo

Characterizing the dark matter halo of the Milky Way is crucial for
understanding our Galaxy in its cosmological context. This requires accurate
constraints on its total mass ($M_{\mathrm{vir}}$) within the virial radius
($r_{\mathrm{vir}}$), the form of the radial mass density profile, and its
three-dimensional shape (spherical, axisymmetric, or triaxial).

$\Lambda$CDM cosmological simulations predict that the smooth components of
stellar halos have power-law or broken-power-law stellar density profiles
(e.g. Cooper et al., 2010; Deason et al., 2013; Amorisco, 2017; Font et al.,
2020) and predominantly radially anisotropic velocity dispersion profiles
(Bullock & Johnston, 2005; Abadi et al., 2006; Loebman et al., 2018). Current
observations are in broad agreement with these predictions; namely, the Milky
Way stellar halo has a “broken” density profile (Deason et al., 2011; Sesar et
al., 2011), and the orbits of halo stars, at least in the inner $\sim 30-50$
kpc, are highly eccentric (Deason et al., 2018; Bird et al., 2019; Cunningham
et al., 2019; Iorio & Belokurov, 2019, 2021; Lancaster et al., 2019; Hattori
et al., 2020).

Dark matter halos are believed to depart significantly from spherical
symmetry. Cosmological simulations assuming collisionless dark matter produce
halos that are triaxial and have almost constant shape at all radii (Jing &
Suto, 2000). Simulations that include baryons produce halos that are oblate-
axisymmetric within the inner one-third of the virial radius, but become
triaxial or prolate at larger radii (Kazantzidis et al., 2004; Debattista et
al., 2008; Zemp et al., 2012; Prada et al., 2019). Cosmological simulations
with warm dark matter (sterile neutrinos, Bose et al., 2016) and self-
interacting dark matter (Peter et al., 2013; Vargya et al., 2021) also predict
triaxial dark matter halos, albeit with small but quantifiable differences in
the variation of shape with radius.

Estimates of the shape of the Milky Way’s dark matter halo from halo field
stars, based on samples within $\approx 30$ kpc, imply a nearly spherical
inner halo (Wegg et al., 2019; Hattori et al., 2020). Recent attempts to probe
the mass and shape of the dark matter halo have been greatly advanced by all-
sky Gaia proper-motion measurements for individual stars to $G\sim 20$ and
averaged proper-motions for more distant satellites and globular clusters
(e.g. Callingham et al., 2019; Li et al., 2020; Deason et al., 2021). Studies
combining Gaia proper motions and radial velocities from the H3 survey suggest
that the dark matter halo of the Milky Way may be triaxial or tilted relative
to the Milky Way disk (Han et al., 2022), although self-consistent modeling is
required to confirm this. More generally, the total virial mass, inner density
slope, concentration parameter, and local dark matter density of the halo
remain uncertain (Callingham et al., 2019) and depend quite strongly on the
assumed properties of the baryonic components (de Salas et al., 2019).

Despite evidence that the Milky Way experienced a significant merger event
(the “Gaia Sausage/Enceladus” (GSE); see Section 3.1.3) approximately $8-11$
Gyr ago and is currently interacting with the Large Magellanic Cloud (LMC; see
below), most estimates of the global mass distribution of dark matter in the
Galaxy assume that it is in dynamical equilibrium. In many contexts, this
assumption is justified; tests with mock data from cosmological simulations of
Milky Way analogs including those with ongoing interactions (e.g. Kafle et
al., 2018; Hattori et al., 2020; Rehemtulla et al., 2022) show that both the
mass and average flattening of the halo can be estimated with 15-25% accuracy
using datasets that cover large areas of the sky and extend to large distances
from the Galactic center.

DESI MWS survey will greatly improve our understanding of the mass and shape
of the dark matter halo by significantly increasing the samples of halo
tracers ($\sim 1$ million turnoff and subgiant branch stars between 10 and 30
kpc and $\sim 10,000$ giant stars in the halo beyond 30 kpc; see below) with
precise radial velocities (velocity errors $\sigma_{v_{los}}\sim
1-20\,\mathrm{km\,s^{-1}}$) and spectrophotometric distances. MWS will also
obtain spectra for half of all Gaia-detected RR Lyrae variables with
brightness $14<G<19$ in the survey footprint and increase the sample of known
BHBs with radial velocities by a factor of $\approx 3$ (see sections 4.4.2 and
4.4.4). Radial velocities, in conjunction with better proper-motion
measurements from future Gaia data releases and proper motions from the Roman
Observatory’s High Latitude Survey (WFIRST Astrometry Working Group et al.,
2019), will enable us to more fully characterize the dark matter halo of the
Milky Way, significantly reducing the current factor of $\sim 2$ uncertainties
on the cumulative mass of the Milky Way within $\sim 100$ kpc.

##### Mapping the interaction with the LMC.

It has become clear in the past 15 yr that the Milky Way can no longer be
modeled to high accuracy as an isolated galaxy. There is considerable evidence
that the ongoing gravitational interaction with the LMC may have distorted the
halo and displaced the stellar component of the Galaxy away from the center of
the dark matter potential. Hubble Space Telescope proper-motion measurements
of the LMC have been used to show that the LMC is on its first infall and has
only recently passed its pericenter (Besla et al., 2007). Furthermore, the LMC
is much more massive than previously believed, $\sim 2\times
10^{11}\,\mathrm{M_{\odot}}$ (Besla et al., 2010), massive enough to cause a
significant reflex motion of $\sim 40-60\,\mathrm{km\,s^{-1}}$ of the Milky
Way disk (Gomez et al., 2015).

The dynamical response of the Galactic stellar and dark matter halo to the LMC
has two primary components. First, a classical dynamical friction wake is
produced behind the LMC in the Galactic southern hemisphere as it orbits the
Milky Way, accompanied by a density enhancement in the Galactic northern
hemisphere referred to as the “collective response.” Second, the fact that
both the LMC and the Milky Way orbit their common barycenter results in a
“reflex velocity” of the stellar halo relative to the Milky Way disk. This was
predicted to appear as a dipole in the velocity distribution of halo stars
(Garavito-Camargo et al., 2019) and has been detected (Petersen & Peñarrubia,
2020). More recently, Conroy et al. (2021) have used star counts from Gaia to
measure the stellar overdensity due to the dynamical friction wake and
collective response. Both of these overdensities have been observed in nearly
the same locations predicted by $N$-body simulations. Although the wake is in
the Galactic southern hemisphere and outside the DESI footprint, the
“collective response” in the Galactic north lies partially within the
footprint of the main survey and will also be covered by the DESI Backup
Program. A velocity accuracy for DESI MWS of $1-20\mathrm{km\,s^{-1}}$ will be
sufficient to yield constraints on the predicted dark matter wake and large-
scale motions in the stellar halo associated with the ongoing gravitational
interaction between the Milky Way and the LMC.

####  3.1.2 Small-scale Substructure in the Dark Matter Halo

The distribution of dark matter on small scales, including the subhalo mass
function and the central density profiles of dwarf galaxies, is an extremely
important probe of the nature of dark matter (e.g. Zavala & Frenk, 2019). MWS
can constrain these properties in the Milky Way and Local Group through
observations of tidal streams and dwarf galaxies.

##### Tidal Streams.

Kinematically cold structures like stellar tidal streams are ideal for probing
small-scale substructures in the Milky Way’s dark matter halo. Interactions
between cold streams and dark matter subhalos can produce stream gaps,
overdensities and characteristic off-stream structures (“S-shaped” kinks and
“spurs”) (Siegal-Gaskins & Valluri, 2008; Carlberg, 2013; Erkal & Belokurov,
2015a), as well as perturbations to the line-of-sight velocities and proper
motions of stars near the gaps (Erkal & Belokurov, 2015b). The velocities of
stars near gaps in cold, thin globular cluster streams (such as the gaps, kink
and spur observed in GD 1, or the ATLAS and Aliqa Uma streams; e.g. Price-
Whelan & Bonaca 2018b; Li et al. 2021) will constrain the clumpiness of the
dark matter distribution encountered by the stream (e.g. Carlberg, 2012; Erkal
et al., 2016; Bovy et al., 2017; Bonaca et al., 2019). In addition, it has
been recently shown from simulations that secular tidal evolution of accreted
globular cluster streams can be used to probe the density profiles of the
parent dwarf galaxies from which the clusters were accreted by the Milky Way
(Malhan et al., 2021). Such secular tidal evolution produces broader “cocoon”
components around thin streams (Carlberg, 2018) and increases the velocity
dispersion over large swaths of the stream (Malhan et al., 2021). DESI spectra
will provide the stellar chemical abundances that are crucial for determining
stream membership and will enable discrimination between localized
perturbations from subhalos and secular tidal evolution. Furthermore, the
chemical abundance and radial velocity gradients along dwarf galaxy streams
will constrain the rate of stellar mass loss, providing further clues to their
dark matter distributions (Errani et al., 2015).

Many known tidal streams are covered by the MWS footprint and target selection
criteria (e.g., Sagittarius, GD 1, Palomar 5 and the Orphan stream), including
43 of the 73 streams and other halo substructures in the galstreams
catalog111https://github.com/cmateu/galstreams, revision 35b71b1. (Mateu,
2017; Mateu et al., 2018) and tens of more recently discovered Gaia streams
(e.g. Ibata et al., 2019; Mateu, 2022). For each of these, we expect MWS to
identify on the order of $\sim 10$-$100$ member stars per stream. For example,
based on the selection criteria and fiber assignment forecasts described
below, we expect to obtain spectra for $\sim 600$ candidate members of the GD
1 stream (satisfying a broad cut in position and proper motion), of which
$\sim 10-30$% may be true members. This number may be even greater for the
Sagittarius stream: we expect to obtain spectra for $\sim 6,600$ of the $\sim
33,600$ candidate stream members identified by Antoja et al. (2020) in our
footprint with magnitudes $15<G<20$, and a further $\sim 1,800$ Sagittarius RR
Lyrae from the catalog of Ramos et al. (2020) in the same magnitude range. For
comparison, Vasiliev et al. (2021) find that 4,465 stars in their catalog of
55,192 probable Sagittarius members have existing radial velocities. We expect
to observe $\approx 2,800$ of the 5,600 Vasiliev et al. candidate members in
the MWS footprint, of which 306 have existing radial velocities. Of course,
MWS may also observe members of Sagittarius, GD 1 and other streams that are
not identified in existing catalogs. MWS radial velocities, chemical
abundances, and spectrophotometric distances for candidate stream members, in
conjunction with Gaia proper motions, will enable us to better assess
membership and chemical homogeneity (or the opposite) within streams, and to
search for yet unknown phase-space substructures.

Since tidal streams approximately trace the orbits of their progenitors, they
have been widely used for measuring the shape of the Milky Way’s dark matter
halo (Johnston et al., 1999, 2005; Helmi, 2004; Fellhauer et al., 2006;
Koposov et al., 2010; Law & Majewski, 2010; Sanders & Binney, 2013; Bovy,
2014, 2016; Gibbons et al., 2014; Bowden et al., 2015; Küpper et al., 2015;
Malhan & Ibata, 2019; Vasiliev et al., 2021). A high-precision model of the
Sagittarius stream (Vasiliev et al., 2021) has been derived from Gaia proper
motions (Antoja et al., 2020), following the realization that the LMC gives
rise to a significant reflex motion of the Milky Way’s center of mass (Gomez
et al., 2015). This nonequilibrium model implies a radially varying and time-
dependent shape for the Milky Way halo. However, even this model relies on a
limited sample of stars with radial velocities. MWS will provide 6-dimensional
kinematic information from multiple stellar streams, which can be jointly used
to constrain the Milky Way’s dark halo density profile to even greater
precision (Bonaca & Hogg, 2018). Furthermore, some of these streams can be
used to probe the mass of the LMC at large radii. Erkal et al. (2018) first
argued that the LMC could induce a substantial proper motion perpendicular to
the track of the stream on the sky, and this offset could be used to measure
the mass of the LMC. Such a misalignment of proper motions with the stream
track has been found in the Orphan–Chenab stream (Koposov et al., 2019) and
used to constrain the LMC and Milky Way potential simultaneously (Erkal et
al., 2019). A similar analysis has been carried out for the Sagittarius stream
(Vasiliev et al., 2021). Recently, Shipp et al. (2020b) extended this approach
to five stellar streams with proper motions measured by Gaia EDR3 and radial
velocities measured by the Southern Stellar Stream Spectroscopic Survey
($S^{5}$; Li et al., 2019, 2022). Using this 6-dimensional kinematic
information for an ensemble of streams, they found a mass of the LMC ranging
within $\sim 1.4-1.9\times 10^{11}\,\mathrm{M_{\odot}}$.

##### Satellite dwarf galaxies.

The satellite galaxies of the Milky Way provide an additional testing ground
for the nature of dark matter on small scales (Simon & Geha, 2007; Nadler et
al., 2021). The particle physics governing dark matter may have observable
effects on the luminosity function of satellite galaxies, the density profiles
of their dark matter halos (cusps versus cores), and the production of
energetic Standard Model particles through annihilation or decay. Satellites
also provide a window into the formation of the oldest and least massive
galaxies, inaccessible to direct observation (Kirby et al., 2008; Bland-
Hawthorn et al., 2015). Many open questions remain concerning the structure,
stellar populations, and star formation histories of these galaxies, answers
to which would shed light on their past interactions with the Milky Way and
complement surveys of the diffuse stellar halo.

Although significant resources have been invested to discover and characterize
dwarf galaxies, very few spectroscopic observations have been taken in their
outskirts, mainly due to the limited field of view of existing spectroscopic
facilities. Recent work suggests at least some of these galaxies may be
surrounded by significant low surface brightness structure, which simulations
suggest may occur even for galaxies that are not presently losing significant
mass through tidal stripping (e.g. Wang et al., 2017). For example, Chiti et
al. (2020) used deep SkyMapper UV photometry to find candidate members of the
ultrafaint dwarf galaxy Tucana II out to 7 half-light radii. Spectroscopic
follow-up is now required to confirm their association, and more generally to
address the prevalence and properties of similar features in other satellite
galaxies.

The DESI MWS footprint includes 31 known dwarf spheroidal and ultrafaint dwarf
galaxies (according to McConnachie 2012, see Figure 1). Sixteen of these have
distance modulus smaller than $20$ and hence, potentially, red giant branch
(RGB) stars within the MWS main survey selection. The primary MWS target
selection categories will therefore provide a sparse but extremely wide-field
sampling of potential members in the outskirts of these galaxies, most of
which have half-light radii well within the $3^{\circ}.1$ field-of-view of
DESI. In addition, a DESI secondary program will allocate fibers at higher
priority to potential members (selected in a broad window of proper-motion and
color–magnitude space) around dwarf galaxies in the DESI footprint, in both
the bright- and dark-time DESI surveys. The confirmation of distant members
will enable the study of large-scale metallicity gradients and tidal effects.

####  3.1.3 The Assembly History of the Milky Way Halo

The accretion and star formation histories of the Milky Way are encoded in its
stellar populations. The Milky Way was formed through the accumulation of
stars, gas, and dark matter through mergers, which continues to the present.
The stellar halo and thick disk still retain kinematic signatures of this
process, which MWS seeks to recover through measurements of line-of-sight
velocity, metallicity, and $\alpha$-abundance, in combination with Gaia proper
motions. DESI also has the potential to measure individual elemental
abundances including C, Mg, Ca, and Fe abundances. These measurements will
enable the identification of fossil remnants of the assembly process in a
multidimensional phase space, including the relating of tidally-stripped halo
stars to their parent objects (i.e., dwarf galaxies and globular clusters).

Our view of the stellar halo has changed dramatically since the first data
releases of the Gaia mission. It is now understood that the inner halo (within
20–30 kpc) is dominated by one massive dwarf progenitor, namely the GSE
(Belokurov et al., 2018; Helmi et al., 2018). This major event in the Milky
Way’s assembly history was predicted from the observed halo star counts by
Deason et al. (2013), who argued that the “break" in the stellar halo density
profile (at 20–30 kpc) signifies the apocenter of a massive accretion event.
Our view of the (inner) halo is thus intricately linked with the properties of
the GSE event. The large increase in stellar halo tracers provided by DESI in
the inner region of the halo dominated by the GSE will be essential to
quantifying the details of this accretion event and the properties of the
progenitor dwarf galaxy. For example, the two-dimensional phase space of
Galactocentric distance and radial velocity can be used to identify shells
(overdensities around common orbital apocenters) linked to the GSE. These in
turn can be used to constrain the orbit and accretion time of the progenitor,
while the metallicity distribution function (MDF) and chemical abundances can
be used to infer its stellar mass and star formation history.

The DESI footprint covers many well-known Milky Way globular clusters. Finding
and characterizing tidal features around globular clusters is crucial to
understanding their orbits and mass-loss histories. Estimates of the fraction
of mass contributed to the Milky Way stellar halo by disrupted globular
clusters range from 50% (Martell & Grebel, 2010; Martell et al., 2011) to
negligible (e.g. Deason et al., 2015). Significant mass loss ($\geq 90\%$)
from globular clusters has been invoked to explain the presence of multiple
stellar populations within them (see, e.g., Bastian & Lardo, 2018, and
references therein); however, such extreme mass loss requires globular
clusters to be born with very much larger effective radii than currently
observed.

Several imaging studies, especially those carried out in combination with Gaia
proper motions, have led to the discovery of tidal tails associated with a few
globular clusters (e.g., Shipp et al., 2020a; Sollima, 2020). At the same
time, the lack of convincing signs of tails around other Milky Way GCs (e.g.,
Leon et al., 2000; Kuzma et al., 2016) has led to speculation that they may be
embedded in their own dark matter halos (e.g. Peñarrubia et al., 2017;
Carlberg & Grillmair, 2021) which prevents stars from escaping at the expected
rate (Moore, 1996). However, it is likely that the extremely low surface
brightness of these features limits the discovery potential of imaging alone.
DESI’s spectroscopic observations can complement these results by identifying
stripped stars through kinematic and chemical tagging. This will allow a
better characterization of the tidal features themselves and the frequency
with which they occur around globular clusters.

More generally, DESI MWS radial velocities and stellar abundances, in
conjunction with Gaia proper motions, will enable us to determine what
fraction of the halo is made up of merger or tidally stripped remnants, and
whether there exists a smooth, isotropic component that is chemically and
dynamically old. As demonstrated by Belokurov & Kravtsov (2022) using APOGEE
abundances, such data can also constrain the properties, and hence the origin,
of an ‘in situ’ stellar halo component. Distinguishing between the wide range
of processes that produce in situ stellar halos in cosmological simulations
(including early chaotic gas accretion and disk collapse, dynamical heating,
and star formation in cooling instabilities or accreted gas; see, e.g. Cooper
et al., 2015) would be a significant advance in the understanding of early
galaxy formation as a whole, and would address a major source of uncertainty
in the galactic archaeology of the Milky Way and other galaxies.

####  3.1.4 The Formation History of the Milky Way Thick Disk

The disk of the Milky Way, visible from any dark site, is the feature that
defines its morphology. The disk is made up of at least two components of
different thickness, and there is evidence that the outer disk may show warps
and flares (Djorgovski & Sosin, 1989; Drimmel & Spergel, 2001; López-
Corredoira et al., 2002; Mackereth et al., 2017). Past studies of stars in the
Milky Way disk have focused on the inner disk (R $\lesssim$ 13 kpc) and
generally been restricted to the thin (and young) disk component (e.g. Martig
et al., 2014; Aumer et al., 2016; Mackereth et al., 2019; Ting & Rix, 2019).
DESI MWS will focus primarily on the thick disk.

The thick disk of the Milky Way is believed to be an ancient structure that
has been dynamically heated over time. Several scenarios have been proposed
for its origin: secular evolution due to scattering with giant molecular
clouds (e.g. Aumer et al., 2016; Ting & Rix, 2019) or dark matter
substructures (Church et al., 2019), in situ formation from cooling of a thick
and turbulent interstellar medium (so called “upside-down growth”; Bird et
al., 2013; Grand et al., 2016), heating of a protodisk by a massive merger
(e.g. Walker et al., 1996; Velazquez & White, 1999), and early scattering by
massive clumps (Bournaud et al., 2009; Clarke et al., 2019; Beraldo e Silva et
al., 2020). A combination of dynamical and chemical data on thick disk stars
is required to distinguish between these various scenarios. In particular, the
long dynamical times, especially in the outer disk, result in a persistent
memory of past perturbations, either secular or external, which have created
lasting Galactic warps and flares (Momany et al., 2006; Minchev et al., 2015;
Laporte et al., 2021).

DESI MWS will yield chemodynamical measurements of $\sim 4$ million thick disk
stars. The DESI spectral resolution is sufficient to determine the abundance
of C, Mg, Ca and Fe to an internal statistical precision of $\approx 0.1-0.2$
dex for the majority of stars, and of additional elements (e.g. Al, Si, Cr)
for a subset with higher S/N (see Ting et al., 2017; Xiang et al., 2019, 2020;
Sandford et al., 2020). Chemical and age estimates (derivable, for giant
stars, using C and N features; Masseron & Gilmore, 2015; Martig et al., 2016;
Ness et al., 2016; Sanders & Das, 2018; Ting & Rix, 2019; Vincenzo et al.,
2021) as a function of the scale height and orbital properties will help
constrain the origin of the thick disk and the relative ages of the main disk
components (e.g. Belokurov et al., 2020; Beraldo e Silva et al., 2021; Ciucă
et al., 2021; Montalbán et al., 2021; Xiang & Rix, 2022). MWS will also study
open clusters (OCs) in the thick and thin disks. Although most OCs are at
below $|b|<20$, several fall within the MWS footprint, including M67 and M44.
These well-studied clusters can be used to calibrate abundance measurements
and assess systematic differences with other surveys. DESI spectra can, in
principle, be used to explore chemical abundance inhomogeneities in these
clusters, probing the diffusion of heavy elements in stellar atmospheres (e.g.
Souto et al., 2019) and perhaps constraining cluster formation timescales. The
broad sky coverage of MWS will enable searches for former cluster members as
they disperse through the Galaxy, and potentially contribute to the discovery
and characterization of old OCs at high latitude (e.g. Schmeja et al., 2014;
Cantat-Gaudin & Anders, 2020).

####  3.1.5 Primordial Stars in the Milky Way

Primordial Milky Way stars are expected to form with extremely low metal
abundance (perhaps zero). Stars that form after the pristine interstellar
medium has been metal-enriched by the first supernova are predicted to reflect
exotic abundance ratios and can inform models of yields from the first
generation of supernovae. For example, dramatically high carbon-to-iron ratios
have been found and are interpreted to be the result of fallback of the
innermost layers of supernova progenitors (Ishigaki et al., 2014; Nordlander
et al., 2019).

Studies of the MDF show that only 1 in 10,000 halo stars has a metallicity
$\mathrm{[Fe/H]}<-4$ (Beers & Christlieb, 2005; Starkenburg et al., 2017).
This, together with the decrease in metallicity in the outer halo, makes large
and distant samples a necessity in order to search efficiently for the first-
generation low-mass stars that have survived. Surprisingly, a significant
fraction of the stars with the lowest iron abundances have their orbits in the
Galactic plane (Sestito et al., 2020, 2021).

Most of the extremely metal-poor stars known have been identified from deep
surveys of the Galactic halo, such as the Hamburg/ESO Survey (Schörck et al.,
2009) and SDSS (Yanny et al., 2009a; Rockosi et al., 2022). Although
metallicity precision is likely to be poor at $\mathrm{[Fe/H]}<-4$ for spectra
at the resolution of DESI, such stars can, at least, be identified efficiently
for follow-up observations (e.g. Allende Prieto et al., 2015; Frebel et al.,
2015). Given the large sample size of MWS and its focus on faint stars at high
latitude, we expect to uncover over 100 new stars with $\mathrm{[Fe/H]}<-4$,
which would triple the number of currently known stars in this regime. We also
hope to identify new stars with iron abundances $\mathrm{[Fe/H]}<-7$,
comparable to the current lowest known measurements (Nordlander et al., 2019).
The statistics of the parameters and chemical abundances of these stars will
shed light on the first generation of stars, and their supernovae (Ishigaki et
al., 2014; Nordlander et al., 2019).

###  3.2 The DESI White Dwarf Survey

White dwarfs are the final stage of evolution for stars with masses $\lesssim
8-10\,\mathrm{M_{\odot}}$ (Iben et al., 1997; Dobbie et al., 2006), a destiny
that the majority of A/F-type stars in the Milky Way have already reached. As
such, white dwarfs play a central role across a variety of areas in
astrophysics. These dense stellar remnants are chemically stratified with
atmospheric compositions dominated by hydrogen and/or helium (e.g., Eisenstein
et al. 2006; Giammichele et al. 2012), although $\simeq$ 20% of white dwarfs
display spectroscopic peculiarities (see Figure 2 for examples). Spectroscopy
spanning the full optical range is therefore critically important for the
study of white dwarfs.

Homogeneous samples of white dwarfs with accurate physical parameters are
essential for constraining and calibrating stellar evolution theory (Williams
et al., 2009; Cummings et al., 2018), internal rotation profiles and loss of
angular momentum (Hermes et al., 2017), and fundamental nuclear reaction rates
(Kunz et al., 2002), with important implications for stellar population
synthesis and galaxy evolution theory (Maraston, 1998; Kalirai et al., 2014).
Because of their well-constrained cooling ages, white dwarfs provide an
insight into the age of the Galactic disk (Winget et al., 1987; Oswalt et al.,
1996), OCs (García-Berro et al., 2010), and globular clusters (Hansen et al.,
2007), and can even trace variations in the Galactic star-formation rate
(Tremblay et al., 2014). White dwarfs also indirectly allow the investigation
of other areas of astrophysics, such as main-sequence stars in binaries with
white dwarfs (Zorotovic et al., 2010; Rebassa-Mansergas et al., 2016; Toonen
et al., 2017), planetary systems (Zuckerman et al., 2007; Farihi et al., 2009;
Gänsicke et al., 2012; Koester et al., 2014; Hollands et al., 2018; Vanderburg
et al., 2020; Guidry et al., 2021), and extreme physics (Guan, 2006; Kowalski,
2006).

Figure 2: Various types of white dwarf systems observed by DESI. Most white
dwarfs have atmospheres dominated by hydrogen or helium, and their spectra
contain only Balmer (DA) or He I (DB) lines. As the white dwarfs cool, they
eventually cease to produce these lines, resulting in featureless spectra
(DC). However, $\simeq 20\%$ of white dwarfs exhibit spectroscopic
peculiarities. Accretion of planetary material results in photospheric
contamination by metals (DAZ, DBZ, and DZ). The presence of carbon in the
atmospheres of white dwarfs can indicate the dredge up of material from the
white dwarf core, or, in higher-mass white dwarfs, is an indication of a
merger, possibly descending from R Corona Borealis stars (DQ). Up to 10% show
magnetic fields (up to $10^{9}\,\mathrm{MG}$) via Zeeman splitting across all
atmospheric compositions (e.g. DAH), and serve as laboratories for atomic
physics under extreme conditions. Finally, white dwarf binaries span a wide
range of evolutionary channels. One common type of white dwarf binary is a
cataclysmic variable (CV), where a main-sequence companion accretes onto a
white dwarf via an accretion disk that can be identified from double-peaked
line profiles.

Gentile Fusillo et al. (2019) assembled the first unbiased all-sky magnitude-
limited ($G\simeq 20$) sample of $\simeq 260,000$ white dwarf candidates using
Gaia DR2. While the Gaia data are sufficient to identify white dwarfs with
high confidence, follow-up spectroscopy is required (Figure 2) to determine
their physical properties and derive fundamental properties that are necessary
to address the science areas outlined above.

The DESI white dwarf survey will target $\simeq$70,000 white dwarfs largely
from the Gentile Fusillo et al. (2019) sample, and will roughly double the
number of white dwarfs with high-quality spectroscopy in the northern
hemisphere (Kleinman et al., 2013; Gentile Fusillo et al., 2015). This will be
the first large and homogeneous spectroscopic sample that is not subject to
complex selection effects, and is therefore ideally suited for detailed
statistical analyses of white dwarfs in the context of galactic, stellar, and
planetary structures and evolution. The large sample size will also result in
the identification of rare white dwarf species, tracing the extremes of
parameter space of short-lived phases in their evolution. The combination of
accurate Gaia parallaxes and photometry with spectroscopic mass determinations
will result in an extremely stringent test of the mass–radius relation of
white dwarfs (Tremblay et al., 2017). The DESI spectroscopy will also provide
radial velocity measurements, which will complement the Gaia proper-motions
and produce the first large sample of white dwarfs with full 3D kinematics.
With this sample, the thin disk, thick disk, and halo populations can be
distinguished (Pauli et al., 2003, 2006; Anguiano et al., 2017), with an
expected $\simeq 1\%$ of halo white dwarfs. Furthermore, the kinematics will
provide constraints on the age–velocity dispersion relation, and insight into
the mass distribution of white dwarfs that formed via binary mergers (Wegg &
Phinney, 2012).

###  3.3 The DESI Nearby Star Survey

Prior to Gaia, our knowledge of the solar neighborhood was extremely limited:
the RECONS survey (Henry et al., 1994, 2018) provided only a nearly complete
view of the stellar population within 10 pc, comprising $\simeq 300$ stellar
systems, of which about a third are binaries or higher multiples. Thanks to
Gaia, the inventory of nearby stars has considerably increased, and is now
$\simeq 90$% complete for stars down to the hydrogen burning limit,
$M_{G}\simeq 15$, within 100 pc (Gaia Collaboration et al., 2021a).

MWS will include a highly complete spectroscopic census of stars within 100 pc
of the Sun. As described below, these stars will be selected in the DESI
footprint based on Gaia parallaxes, in the magnitude range $16\leq G\leq 20$
mag (i.e. below the faint limit of the Gaia RVS spectrograph). This sample
will be heavily dominated by M-dwarfs, which represent the bulk of the
Galactic stellar mass. Much of the current framework for the star formation
history of the Milky Way disk and the low-mass end of the stellar initial mass
function is based on smaller and brighter analogs of this sample (Freeman &
Bland-Hawthorn, 2002; Nordström et al., 2004; Henry et al., 2018). The MWS 100
pc sample will provide the most complete census of the kinematics, chemical
evolution, and initial mass function in the extended solar neighborhood to
date. DESI will cover two major indicators of stellar activity, H$\alpha$
emission and the Ca II H and K doublet, and the 100 pc MWS sample will provide
detailed constraints on the fraction of active M-dwarfs; on empirical
relations between magnetic activity, rotation rate (which can be determined
from, e.g., Zwicky Transient Facility light curves), and age (Skumanich, 1972;
Pizzolato et al., 2003; Barnes, 2007; Mamajek & Hillenbrand, 2008); and on the
role of multiplicity in magnetic activity (notably for older stars; (Newton et
al., 2016; Stauffer et al., 2018). Correlations between kinematics (i.e.
tangential velocity, velocity dispersion, or vertical action) and stellar
activity (Gizis et al., 2000; Schmidt et al., 2007; Kiman et al., 2019; Angus
et al., 2020) can also be explored with this sample.

Our knowledge of the coldest (late T and Y type) brown dwarfs ($350\lesssim
T_{\rm eff}\lesssim 500$ K) is similarly restricted to this volume
(Kirkpatrick et al., 2019; Kota et al., 2022). In addition to the Gaia 100 pc
sample, a DESI secondary program will target fast-moving high-proper-motion
identified using combinations of multi-epoch data from SDSS, the NOIRLab
Source Catalog (Nidever et al., 2021), and the Wide-field Infrared Survey
Explorer (WISE) data (e.g., Meisner et al., 2021). These data will sample the
faint end of the brown dwarf luminosity function, and provide better
constraints on the low-mass end of the initial mass function.

###  3.4 Survey requirements

The scientific goals above impose common requirements on the sample of stars
to be observed, and on the performance of DESI and its pipelines, particularly
on the accuracy of key measurements (stellar parameters, radial velocities,
and abundances) on the final dataset. The rest of this paper presents the
design of the survey and our first evaluation of our pipeline against those
requirements.

In the next section, we describe our target selection procedure and forecast
the size and content of the full sample. We determine the completeness of each
target class by applying the DESI fiber assignment algorithm, accounting for
the prioritization of targets from BGS. For the bulk of our targets the
completeness is $\approx 30$ per cent averaged over the footprint. Using a
simple mock catalog based on an empirical model of the Galactic structure, we
demonstrate that our target selection recovers tracers with sufficient density
and distance coverage to address the core dark matter and stellar halo
structure science goals. In future work, we will apply our target selection to
mock catalogs derived from ab initio cosmological simulations, to better
understand the effects of halo-to-halo variation and substructures.

We then introduce our analysis pipelines and use data from early DESI
observations to demonstrate that we can recover radial velocities and
$\mathrm{[Fe/H]}$ to the necessary precision of $1\,\mathrm{km\,s^{-1}}$ and
$\approx 0.2$ dex respectively. We identify systematic offsets with respect to
other surveys and literature $\mathrm{[Fe/H]}$ measurements for globular
clusters and dwarf galaxies. We also demonstrate that metal pollution
signatures of planetary systems can be identified in DESI spectra of white
dwarfs.

We identify priorities for development of the current pipelines, which we
expect to include $\mathrm{[\alpha/Fe]}$ measurements, more robust fitting of
very cool stars, and potential improvements to radial velocity accuracy below
$1\,\mathrm{km\,s^{-1}}$. These improvements will be addressed in future
publications, along with more detailed studies of the white dwarf and nearby
samples, spectrophotometric distance estimates, and the recovery of individual
element abundances.

##  4 Selecting Milky Way Targets for DESI

This section describes the selection criteria for MWS targets. This
description updates the summary given in Allende Prieto et al. (2020) and
corresponds to the final design of MWS at the start of the main survey in 2021
May. We refer the reader to Myers et al. (2023) for further details of the
DESI target selection process, the desitarget software, and associated data
products.

###  4.1 Overview of MWS target categories

##### Primary targets.

The MWS main sample is designed to address the dark matter halo, stellar halo,
and thick disk science cases described in sections 3.1.1, 3.1.3 and 3.1.4. It
comprises the bulk of the stellar targets that will be observed by DESI MWS,
split into three categories222These names refer to the mws_mask (and in some
cases scnd_mask and desi_mask) bitmask fields described in Myers et al.
(2023). They are used in the DESI data products to identify categories of
targets selected according to specific criteria., main-blue, main-red and
main-broad. The union of these categories is essentially a magnitude-limited
selection and therefore well suited to characterizing stellar halo
substructures associated with disrupted Milky Way satellites and globular
clusters (section 3.1.2) and to the serendipitous discovery of rare types of
stars (such as extremely metal poor stars; section 3.1.5).

The main sample selection function is deliberately generous. Any starlike
source in the survey footprint with magnitude $16<r<19$ has a finite
probability of being observed in one of the three MWS main target categories
(excluding only sources that are masked or have poor data quality in the input
imaging). As we describe in detail below, main-blue (defined by the simple
color criterion $g-r<0.7$) will provide a highly complete sample of metal-poor
main-sequence, turnoff, and bluer subgiant stars, with distances in the range
5 – 30 kpc and no kinematic selection bias. This will be a dense, high-
fidelity dataset with which to study the thick disk and inner halo over the
likely extent of the GSE debris, as well as Sagittarius and many other known
streams.

We assign redder stars ($g-r>0.7$) in the same $16<r<19$ magnitude range to
the main-red category if Gaia astrometry indicates they are more likely to be
distant halo giants, and to the main-broad category otherwise. We give main-
red targets the same fiber assignment priority as main-blue targets. We give
main-broad targets lower priority in order to select more main-red giant
candidates to probe the kinematics and substructure of the outer stellar halo,
particularly to provide dynamical constraints on the dark matter halo mass
over a large fraction of the virial radius. Of course, not all stars in main-
red will be distant giants. The astrometric selection criteria are "mild"; as
described in more detail below, they accept relatively high contamination from
nearby red main-sequence stars as a trade-off to minimize kinematic bias.
Based on the current DESI bright-time observing plan, focal plane state, and
fiber assignment strategy, we expect main-red spectra to account for $\approx
12\%$ of the main sample and to have a completeness of $\approx 32\%$ (similar
to that of main-blue). The fraction of true distant halo stars in main-red
will be sensitive to the form of the stellar halo density profile at large
distances; below, we present a fiducial model of the halo density which
predicts $\sim 5,000$–$10,000$ main-red giants beyond 50 kpc and $\sim 1,000$
beyond 100 kpc. Although main-broad targets will have lower spectroscopic
completeness than main-red $(\sim 19\%)$, those spectra will still account for
$\approx 32\%$ of the main MWS sample. They will serve both as a constraint on
forward models of the MWS dataset and as an important scientific sample in
their own right, providing radial velocities for thin disk stars without Gaia
RVS spectra, as well as more detailed abundance measurements.

In addition to the main sample, MWS includes several high-priority samples of
targets with high scientific value and low surface density ($\lesssim 10$ per
square degree), comprising white dwarfs (mws-wd, section 3.2), faint nearby
stars (mws-nearby, section 3.3), RR Lyrae variables (mws-rrlyr), and
horizontal branch stars (mws-bhb). These target categories are given higher
fiber assignment priority than the main sample to ensure high completeness, as
discussed in Section 5. Two further categories, faint-blue and faint-red,
target fainter stars in the same color ranges as the main-blue and main-red
samples, at lower priority and hence much lower completeness.

F-type stars in a similar magnitude range to the main MWS sample will be
targeted as flux standards across all bright- and dark-time DESI
programs333White dwarfs were also targeted as standards in the DESI SV
programs, and consequently received a larger number of repeat and dark-time
observations than they would have as MWS targets alone. White dwarfs are not
currently being targeted as standards in the main DESI survey program.. The
algorithm for selecting flux standards is more complex than that for the main-
blue sample, of which they are essentially a subset (flux standards can be
slightly brighter than the flux limit of the main sample). Their targeting and
prioritization is independent of MWS; survey, hence they may also be observed
as part of the MWS main sample or as one of the high-priority MWS samples.
Main MWS targets will be observed only once by design; they will only be
reobserved if no unobserved MWS targets or targets from any other program are
available to a fiber. However, stars may be observed as flux standards
multiple times in both bright and dark conditions.

We refer to the MWS main, high priority and faint samples collectively as the
primary MWS target categories. All these targets are selected within the
bright-time program footprint, shown in Fig. 1. The following subsections give
the specific target selection criteria for each category. Most criteria are
based on optical photometry from Data Release 9 of the DESI Legacy Imaging
Survey (LS DR9; Zou et al., 2017; Dey et al., 2019; Schlegel et al., 2022),
which also includes infra-red photometry derived from WISE data (Meisner et
al., 2017), and is matched to photometry from Gaia DR2 and astrometric
measurements from Gaia EDR3 (Gaia Collaboration et al., 2021b).

Table 2 lists the number of targets per category in the bright-time footprint
(categories are not mutually exclusive). Approximately 30.5 million unique LS
sources meet the primary sample selection criteria. Section 5 describes the
relative prioritization among the categories and the resulting fiber
assignment efficiencies over four passes of the footprint, which are also
listed in Table 2. The complete survey will contain $\simeq 7.2$ million
spectra of unique stars from the primary MWS categories, of which $\simeq 6.5$
million are from the three main sample categories.

##### Secondary targets.

As noted in Section 1, the DESI survey also defines a number of secondary
science programs, each of which corresponds to one or more secondary target
classes444These are distinguished in the DESI data products by a nonzero entry
in the SCND_TARGET column corresponding to one or more fields in the scnd_mask
bitmask; see Myers et al. (2023).. The secondary programs will use spare
fibers or dedicated observations of specific areas (not necessarily within the
main survey footprint) to complement the goals of the primary dark- and
bright-time DESI surveys. Several secondary programs are complementary to MWS,
including observations of fainter BHBs and white dwarf binary candidates using
dark time, higher prioritization for proper-motion and color outliers, surveys
of M31 and M33 (Dey et al., 2022), and high-completeness observations of
selected Milky Way dwarf satellites and globular clusters. These secondary
programs will be described separately. The targets for these secondary
programs may overlap with primary MWS targets. Myers et al. (2023) provide a
more detailed explanation of the primary and secondary target categories, how
they can be identified in DESI target catalogs, and the implications of
targets being selected by multiple programs.

##### Backup targets.

Finally, in poor weather conditions and bright skies (including twilight), the
DESI backup program will target stars brighter than those in the MWS main
sample. The backup program will cover a larger footprint, extending to lower
Galactic latitude ($|b|\gtrsim 7^{\circ}$). Backup targets will be prioritized
in three categories by magnitude and color, to favor stars for which high S/N
can be achieved in poor conditions, with two additional categories to favor
brighter halo giants555In the DESI data products, backup program targets can
be identified using the MWS target column (MWS_TARGET) and associated bitmask
(mws_mask), but the backup program is in most respects treated separately from
the other DESI surveys (DESI Collaboration et al., 2023; Myers et al., 2023)..
This sample will be suited to detailed chemodynamical modeling of the Galactic
disk and nearby stellar halo. The total number of spectra obtained by the
backup program will depend on observing conditions. Extrapolating from the
first months of the main survey, we expect the backup program will obtain at
least five million additional stellar spectra. A full description of the
backup program will be given in a separate publication.

###  4.2 Main sample selection

Table 2: Summary of main MWS target classes. From left to right, columns give the name of the class in the mws_mask bitmask, the total number of DR9 targets in the class available to a DESI fiber and the total number and fraction of fibers assigned to those targets in a fiducial 4-pass survey (with the footprint and focal plane state defined in March 2022; see text). Targets may be counted in more than one class; the final row gives the total number of unique targets. Class | $N_{\mathrm{footprint}}$ | $N_{\mathrm{fiber}}$ | $\%_{\mathrm{4\,pass}}$
---|---|---|---
main-red | 2,589,211 | 805,794 | 31
main-blue | 11,450,969 | 3,693,518 | 32
main-broad | 10,783,830 | 2,077,222 | 19
mws-wd | 66,811 | 66,365 | 99
mws-nearby | 33,788 | 20,892 | 62
mws-rrlyr | 17,303 | 8981 | 52
mws-bhb | 32,353 | 17,706 | 55
faint-red | 960,134 | 71,771 | 7
faint-blue | 4,606,314 | 486,568 | 11
Total (unique) | 30,470,033 | 7,197,722 | 24

The MWS main sample is selected from the LS DR9 source catalog combined with
astrometric measurements from Gaia EDR3. It is divided into three
subcategories: main-blue, main-red and main-broad. All three categories share
the following definition of a MWS main sample stellar target based on fields
in the LS DR9 catalog666https://www.legacysurvey.org/dr9/description:

  * •

$16<r<19$

  * •

$r_{\mathrm{obs}}<20$

  * •

type = PSF

  * •

gaia_astrometric_excess_noise $<3$

  * •

gaia_duplicated_source = False

  * •

brick_primary = True

  * •

nobs_{g,r} $>0$

  * •

{g,r}_flux $>0$

  * •

fracmasked_{g,r} $<0.5$

The observed $r$-band magnitude is obtained from the LS flux in nanomaggies as
$r_{\mathrm{obs}}=22.5-2.5\log_{10}$ r_flux. The extinction-corrected
magnitude is computed as $r=r_{\mathrm{obs}}+2.5\log_{10}$ mws_transmission_r.
We do not put any requirements on the availability or quality of data in the
LS $z$ band.

The main-blue subsample is further defined by the color criterion

  * •

$g-r<0.7$

with $g$ defined in the same way as $r$ above. main-blue is therefore an
approximately magnitude-limited selection, comprised mainly of main-sequence
turnoff stars and bluer subgiants. Stars redward of the $g-r=0.7$ cut include
redder main-sequence stars, subgiants, and giants. To improve the sampling of
the more distant galaxy, higher priority is given to main-red targets, which
have astrometric cuts designed to reduce nearby main-sequence contaminants.
However, Gaia astrometry becomes less precise near the faint limit of MWS, so
the lower priority main-broad target category loosens these astrometric cuts.
More specifically, the main-red subsample is defined by the following
additional criteria:

  * •

$g-r\geq 0.7$

  * •

astrometric_params_solved $\geq 31$

  * •

Gaia parallax $\pi<3\sigma_{\pi}+0.3\;\mathrm{mas}$

  * •

Gaia proper-motion $|\mu|<5\sqrt{f_{r}/f_{19}}\;\mathrm{mas/yr}$
$\left(f_{x}=10^{(22.5-x)/2.5}\right)$

The main-broad sample comprises stars with color $g-r\geq 0.7$ that satisfy
the same magnitude and data quality requirements as the other two categories,
but do not satisfy one or more of the astrometric criteria that define main-
red (stars that do not have well-measured astrometric parameters in the Gaia
catalog are therefore included in main-broad).

The parallax cut applied to main-red with respect to main-broad aims to remove
nearby red contaminants in order to recover a larger sample of distant halo
giants. However, because Gaia parallax accuracy is not good enough at the
faint limit of the survey, $r=19$, we also apply a proper-motion cut to reject
stars with high tangential velocities that are more likely to be nearby
contaminants. The proper-motion cut is made to be a function of the $r$-band
magnitude, corresponding to $5\,\mathrm{mas\,yr^{-1}}$ at $r=19$ and $\sim
20\,\mathrm{mas\,yr^{-1}}$ at $r=16$. This corresponds to different limits on
tangential velocity, depending on the absolute magnitude of the target. For
example, for a 10 Gyr old stellar population with $\mathrm{[Fe/H]}<-0.5$, the
faintest stars on the giant branch with $g-r>0.7$ will have $M_{r}\lesssim 1$,
thus the proper-motion cut will select all stars with tangential velocities
below $950\,\mathrm{km\,s^{-1}}$. For stars with fainter $M_{r}$, for example
the subgiant branch stars of a 10 Gyr old stellar population with
$\mathrm{[Fe/H]=0}$ that have $M_{r}\sim 3.5$, the tangential velocity cut
will correspond to $\sim 300\,\mathrm{km\,s^{-1}}$.

The lower probability of observing stars with high tangential velocities in
the main-red sample at distances $\lesssim 20$ kpc does not compromise the
science goals of MWS. As shown below, the MWS sample at these distances is
overwhelmingly dominated by main-blue targets, which have no astrometric
selection bias. It reduces the chance of discovering extremely high-velocity
red stars around the base of the giant branch at these intermediate distances,
but not to zero, because such objects are still targeted in the main-broad
selection.

Finally, the faint-blue and faint-red samples extend the main-blue and main-
red classes, respectively, to the fainter magnitude range $19<r<20$. The
selection criteria are otherwise identical to those for the corresponding main
classes, except for a slightly fainter limit on the observed $r$-band
magnitude, $r_{\mathrm{obs}}<20.1$. These faint categories are intended as
targets of last resort and are given the lowest fiber assignment priority of
any unobserved target777We treat faint-blue and faint-red targets as part of
our primary sample, but for technical reasons, they are implemented in the
DESI target selection software as secondary program targets (and hence are
identifiable in the data products using scnd_mask and SCND_TARGET rather than
mws_mask and MWS_TARGET). See Myers et al. (2023). Although faint-blue and
faint-red will be much lower completeness and lower S/N samples, they will
provide opportunities for serendipitous discovery and may boost the detection
significance of faint substructures.

###  4.3 Main sample targets in the Galaxia model

Figure 3: Top panels: Density of MWS main sample targets at high Galactic
latitude ($b>70\,\deg$) in the space of $g-r$ color and proper-motion, in our
broken-power-law halo Galaxia mock catalog (left) and the real MWS target
catalog (right). The vertical line marks the color separation between the
main-blue and main-red/main-broad samples. The horizontal lines show the
separation in proper-motion between main-red and main-broad at $r=16$ (upper
dotted line) and $r=19$ (lower dashed line). The main-sequence turnoff and
giant branch of the globular cluster M15 are visible as density peaks at
$\log_{10}\,|\mu|/\mathrm{mas\,yr^{-1}}\sim 0.4$. Bottom panels: The
contribution of thick disk (left) and halo stars (right) to the density
distribution in the Galaxia mock catalog.

Fig. 3 shows the color and proper-motion distribution of main-blue, main-red
and main-broad targets888Note that stars with low proper-motion can also be
assigned to main-broad if they have low parallax, or if their proper-motion or
parallax is not measured by Gaia. at high Galactic latitude ($b>70\arcdeg$).
We compare these distributions to a mock catalog derived from the Galaxia
Milky Way model (Sharma et al., 2011), which describes the phase-space
distribution of stellar populations in the Milky Way’s thin disk, thick disk,
and halo. The parameters of the default Galaxia model were calibrated to
surveys of relatively bright and nearby stars. More recent studies have
improved our knowledge of these parameters, particularly for the stellar halo.
The original Galaxia model uses a power-law density profile with a logarithmic
slope of $-2.44$, which is inconsistent with recent evidence that the stellar
halo density breaks to a much steeper slope at a distance of $\sim 25$ kpc
(e.g. Bell et al., 2008; Deason et al., 2013, 2014). To make more accurate
predictions for MWS, we modify the Galaxia model such that the logarithmic
slope of the stellar halo density profile999For these simple estimates of
target counts, we only modify the Galaxia density profile. This is a
simplification. If the break is associated with the characteristic apocenter
of debris from a single progenitor that dominates the inner halo, the velocity
(and hence proper-motion) distribution in the model should also be adjusted.
changes from $-2.5$ to $-4$ at a Galactocentric distance of 25 kpc. To turn
the output of Galaxia into a mock MWS survey, we convert magnitudes from
Galaxia to the LS photometric system via the PS1 color terms given on the LS
website, and assign proper-motion and parallax errors using
PyGaia101010https://github.com/agabrown/PyGaia. We then apply exactly the same
footprint and target selection functions (except for the LS data quality
flags) to obtain mock main-blue, main-red and main-broad samples.

The upper panels of Fig. 3 show two broad peaks in both the MWS target catalog
(top right) and our Galaxia mock catalog (top left). These correspond to the
metal-poor halo (bluer and low proper-motion, mostly in the main-blue sample)
and the thin disk (redder and high proper-motion, mostly in the main-broad
sample). In the distribution of real main-blue targets, two smaller,
concentrated peaks visible at $\log_{10}|\mu/\mathrm{mas\,yr^{-1}}|\sim 0.4$
correspond to the main-sequence and giant branch of the globular cluster M15.
In the Galaxia mock, the lower-density sequence that bridges the disk and halo
regions of the diagram corresponds to the thick disk, as shown in the lower
left panel, where we isolate the thick disk stars in Galaxia. The lower right
panel shows only the halo stars in Galaxia, demonstrating that the three
distinct sequences visible in main-blue correspond to the halo main-sequence,
the metal-poor thick disk main sequence and the halo giant branch (from blue
to red).

Figure 4: The color and proper-motion distribution of all MWS main sample
targets, as shown in the top right panel of Fig. 3, here for the full MWS
footprint (left). The middle and right panels show the separation of targets
into main-blue/main-red (separated by $g-r=0.7$, vertical dashed line) and
main-broad (separated according to the parallax and magnitude-dependent
proper-motion criteria described in the text; the proper-motion cuts at the
bright and faint limits of the sample are shown by horizontal lines).

Fig. 4 illustrates the magnitude-dependent proper-motion cut that divides the
$g-r>0.7$ sample into main-red and main-broad (this figure includes all
targets in the survey footprint, not just those at high latitude). Thick disk
stars are included in main-red at $r=16$ but almost completely relegated to
main-broad at the faint limit of $r=19$.

Figure 5: Number of MWS main sample target stars beyond a given heliocentric
distance in our broken power-law variant of the Galaxia model (see text), for
stars selected in the MWS footprint according to the main-blue, main-red and
main-broad criteria. In the left panel, mock MWS targets are separated by
Galaxia structural component (thin disk, thick disk and halo), and in the
right panel they are separated by MWS target category. Profiles for the
original single-power-law halo model (Sharma et al., 2011) are shown by dotted
lines of the same color.

Fig. 5 shows the distribution of heliocentric distances in our mock catalog.
The mock main-blue targets are dominated by thick disk stars between 1 and 10
kpc. main-blue contains a further $\sim\leavevmode\nobreak\ 500,000$ stars
between 10 and 20 kpc, which corresponds to the transition between the thick
disk and halo in Galaxia. In this distance range the mock MWS sample is
dominated by the metal-poor turnoff and subgiant branch. Beyond 20 kpc the
mock sample is dominated by the stellar halo. For comparison, the dotted lines
in Fig. 5 show the number of distant giants predicted by the original Galaxia
model (Sharma et al., 2011), which has a much shallower density profile in the
outer stellar halo. Our fiducial model predicts MWS will target $\sim 1,000$
giants beyond 100 kpc, whereas the original Galaxia model predicts $\sim
10,000$. The right-hand panel of Fig. 5 shows that most of the difference is
in the main-red and main-broad samples (which include all but the most metal
poor giants at large distances).

Finally, Fig. 6 illustrates how halo stars of different types enter the MWS
selection function at different distances. For example, the figure shows that,
in this MWS mock survey, halo turnoff and subgiant branch stars dominate the
sample up to $\sim 10$ kpc. The mock survey targets $\sim 100,000$ horizontal
branch stars between 10 and 50 kpc at a volume density of 1 to 10 per
$\mathrm{kpc}^{-3}$, and comparable numbers of RGB and red clump stars in the
same region. These are target densities; they can be converted to densities of
observed spectra with reference to the fiber assignment simulations described
in Sec. 5. Those simulations show that, in a 5 yr survey sharing the DESI
focal plane with BGS, we expect to observe $\sim 30\%$ of the main-blue and
main-red targets (e.g. $\sim 300$ of the $\sim 1000$ giants beyond 80 kpc).

Figure 6: The heliocentric distances of MWS main sample stellar halo targets
in our Galaxia model variant with a broken-power-law stellar halo density
profile. The top panel shows the number of MWS targets beyond a given
heliocentric distance. The bottom panel shows the volume density of targets at
a given distance. Colors correspond to the eight regions of the
$T_{\mathrm{eff}}-\log g$ diagram (inset). Dotted lines correspond to main-
sequence and turnoff stars, solid lines to subgiants and giants, and dashed
lines to horizontal branch stars. The solid black lines correspond to the
whole sample.

###  4.4 High-priority Sample Selections

####  4.4.1 mws-wd

We select white dwarfs using a set of $BP-RP$ color and $G$-band absolute
magnitude criteria based on Gentile Fusillo et al. (2019) that identify the
white dwarf cooling sequence in the Gaia photometric catalog alone. This
selection is applied to the LS catalog using the properties of cross-matched
Gaia EDR3 sources; the LS photometry is not used in this selection.
Photometric measurements are taken from Gaia DR2 and astrometric measurements
from EDR3.

  * •

$G_{\mathrm{abs}}>5$

  * •

$BP-RP<1.7$

  * •

$G_{\mathrm{abs}}>5.93+5.047(BP-RP)$

  * •

$G_{\mathrm{abs}}>6(BP-RP)^{3}-21.77(BP-RP)^{2}+27.91(BP-RP)+0.897$

These criteria are applied to a sample defined by extinction-corrected Gaia
$G$ flux (gaia_phot_g_mean_mag in the LS catalog) at high latitude, with mild
parallax and proper-motion cuts to select against nearby luminous blue stars
(early-type main-sequence stars, horizontal branch stars, and subdwarfs) as
well as QSOs:

  * •

$G<20.0$

  * •

$|b|>20$ degrees

  * •

$\pi/\sigma_{\pi}>1\;\mathrm{mas}$

  * •

astrometric_params_solved $\geq 31$

  * •

$|\mu|>2\;\mathrm{mas/yr}$

We impose the following photometric quality cut, because failing this
criterion results in poor astrometry:

  * •

phot_bp_rp_excess_factor $<1.7+0.06(BP-RP)^{2}$

However, we retain objects that have reliable parallaxes and significant
proper-motions that meet either of the following criteria:

  * •

astrometric_sigma5d_max $<1.5$

  * •

(astrometric_excess_noise $<1$) & ($\pi/\sigma_{\pi}>4$) &
($|\mu|>10\;\mathrm{mas/yr}$)

####  4.4.2 mws-rrlyr

We target Gaia DR2 sources with magnitudes $14<G<19$ that are classified as RR
Lyrae by the general variability classifier and the Special Object Studies
classifier (Holl et al., 2018; Clementini et al., 2019), comprising all
objects from the table vari_rrylrae and any sources from the table
vari_classifier_result for which best_class_name includes "RR". For technical
reasons, mws-rrlyr targets are associated with the secondary target bitmask in
the DESI data products, rather than the MWS bitmask (see Myers et al., 2023).

####  4.4.3 mws-nearby

To address the goals described in Section 3.3, we select dwarf stars within
$100$ pc of the Sun based only on apparent Gaia magnitude and parallax,
allowing for moderate parallax uncertainties:

  * •

$16<G<20$

  * •

$\pi+\sigma_{\pi}>10\;\mathrm{mas}$

  * •

astrometric_params_solved $\geq 31$

No extinction correction is necessary to select stars at these distances. This
sample corresponds to fewer than 10 targets per square degree. As described
below, to ensure high completeness, mws-nearby targets are prioritized over
all other MWS targets except mws-wd and mws-rrlyr.

####  4.4.4 mws-bhb

We select BHBs starting from the basic definition of main sample stars given
at the start of this section (common to main-blue and main-red), with the
following additional criteria:

  * •

$G>10$

  * •

$\pi\leq 0.1+3\sigma_{\pi}\;\mathrm{mas}$

  * •

$-0.35\leq g-r\leq-0.02$

  * •

$-0.05\leq X_{\mathrm{BHB}}\leq 0.05$

  * •

$r-2.3(g-r)-W1_{\mathrm{faint}}<-1.5$

These criteria exclude nearby stars and select around the BHB locus in a
combined LS and WISE color space, defined by

$\displaystyle X_{\mathrm{BHB}}$ $\displaystyle=$
$\displaystyle(g-z)-[1.07163(g-r)^{5}-1.42272(g-r)^{4}$
$\displaystyle+\,0.69476(g-r)^{3}-0.12911(g-r)^{2}$
$\displaystyle+\,0.66993(g-r)-0.11368]$ (1)

and

$W1_{\mathrm{faint}}=22.5-2.5\log_{10}(W1-3\sigma_{W1}),$ (2)

where $W1$ and $\sigma_{W1}$ are the WISE $3.4\mathrm{\mu m}$ flux and its
error, respectively.

###  4.5 Flux standards

Stellar flux standards for all DESI dark and bright programs are selected as
point sources having blue colors consistent with F-type stars around the
metal-poor main-sequence turnoff:

  * •

$16<G<18$

  * •

$0<g-r<0.35$

  * •

$r-z<0.2$

Stars in the magnitude range $18<G<19$ that meet the same color criteria are
also considered for use as standards, at lower priority. Myers et al. (2023)
describe the full set of criteria for selecting flux standards for DESI,
including additional requirements on photometric quality in the LS. Since
approximately 100 flux standards are assigned at higher priority than all
other targets on every configuration of the DESI focal plane, this subset of
the main-blue sample will be observed at a higher sampling rate and have a
higher fraction of stars with repeat observations. These stars ($6000\lesssim
T_{\mathrm{eff}}\lesssim 7000$K dwarfs) will have distances up to $\lesssim
20$ kpc, with most in the range $5\lesssim d\lesssim 10$ kpc (see Fig. 6).
Flux standards can be identified in the DESI data products using the
DESI_TARGET bitmask (see Myers et al., 2023).

##  5 Observing Strategy

###  5.1 The DESI bright-time program

The DESI bright-time program comprises both MWS and BGS. The observing
strategy and fiber assignment strategy for the bright-time program are
primarily designed to meet the goals of BGS. BGS galaxies are prioritized over
all MWS targets when assigning fibers, with the exception of mws-wd targets
($\sim 1$ per square degree). The higher priority of BGS galaxies is therefore
the main limitation on the fraction of MWS targets that will be allocated a
DESI fiber. We describe the relative prioritization of the different MWS
target categories in the next subsection.

The bright-time program defines 5675 tiles to cover a footprint of more than
14,000 $\mathrm{deg}^{2}$ (a minimum coverage of $9000$ $\mathrm{deg}^{2}$ is
a design requirement of BGS; see Hahn et al., 2022). Each tile corresponds to
a single configuration of DESI fibers. The tiles are organized into four
passes of $\sim 1400$ tiles each. Tiles within a pass do not overlap. Tiles on
different passes are offset such that all points on the sky will be covered by
three tiles on average. A detailed description of the tiling strategy is given
in Raichoor et al. (2022a).

On successive passes covering a particular area of the sky, fibers are
preferentially assigned to unobserved targets. In general, a fiber will only
be assigned to reobserve an MWS target if no unobserved target is
available111111mws-bhb targets are an exception. They will be observed for a
second time at a priority only slightly lower than that at their first
observation, to obtain higher S/N.. All bright-time tiles will be observed to
an effective exposure time of $T_{\mathrm{eff}}=180\,\mathrm{s}$, defined as
the time required to achieve the same S/N that would be obtained for a typical
BGS emission line galaxy in an exposure of $180$s under nominal dark
conditions (Hahn et al., 2022). Actual exposure times are scaled on the fly,
based on real-time measurements of sky brightness, seeing, and transparency;
the airmass; and the Milky Way dust attenuation of the tile (Kirkby et al.,
2022; Schlafly et al., 2022). The decision to observe dark, bright, or backup
program tiles is also made according a real-time measure of survey speed, the
rate at which S/N increases for a fiducial target under the prevailing
observing conditions (Schlafly et al., 2022). The total open-shutter time on
each tile may be split over several exposures, possibly on different nights,
until $T_{\mathrm{eff}}$ (computed from the spectra themselves) is reached
(Guy et al., 2022). In section 7 we show examples of co-added MWS spectra with
$T_{\mathrm{eff}}\simeq 180$s.

###  5.2 Target density and fiber assignment

The density of MWS targets varies significantly across the bright-time
footprint, which ranges from the edge of the Galactic plane ($|b|\simeq
20^{\circ}$) to the Galactic poles. This is illustrated in Fig. 7, which shows
the range of surface densities of main-red, main-blue, and main-broad targets
across the survey footprint. The median density of main-red (main-blue, main-
broad) targets is $\gtrsim 150$ (500, 600) per square degree.

Figure 7: Fraction of survey footprint having less than a given surface
density of targets in the three main MWS target categories individually (solid
lines) and in total (dashed line).

For comparison, the average density of DESI fibers on a single tile (i.e. one
pass of the survey) is at most $\simeq 667$ per square degree (if all
positioners are operational). However, not all fibers will be available for
allocation to MWS targets. A fiber will be preferentially assigned to a BGS
target in its patrol region. Moreover, on each tile, DESI allocates 50 fiber
positioners to flux standards and 40-65 fibers to blank sky locations, per
spectrograph petal, which leaves at most 4500 fibers available for science
targets. This will be reduced further by nonoperational fiber positioners, the
number of which will vary over the course of the survey and is $\sim$15% as of
2021 December (Silber et al., 2023).

Operational positioners are allocated to targets in a predetermined priority
order, based on target category. Each category is assigned an integer base
priority that establishes the ordering of classes in fiber assignment. Fiber
collisions between targets of the same category (and between classes with the
same base priority, such as main-blue and main-red) are resolved by a
continuous subpriority value, randomly assigned to each target at the start of
the survey (see Myers et al., 2023). Further details of the DESI fiber
assignment algorithms are given in Raichoor et al. (2022a).

The highest-priority target category in the bright-time program overall is
mws-wd, followed by all BGS target categories, and then by all other MWS
categories. The order of all MWS categories from highest to lowest priority is
therefore mws-wd, mws-rrlyr, mws-nearby, mws-bhb, main-blue and main-red (at
equal priority), main-broad and finally faint-blue and faint-red (at equal
priority). This scheme prioritizes the most scientifically valuable but
sparsely distributed targets above the bulk of the main MWS sample.

Table 2 gives estimates of the number of targets in each MWS category that
will be allocated to a fiber over the course of the survey. These estimates
are made by running the DESI fiber assignment algorithm on all bright-time
program tiles, assuming the state of the focal plane current in 2022 March.
The estimates further assume that all tiles will be observed to their planned
effective exposure time, $T_{\mathrm{eff}}$. Over the entire footprint, we
expect to assign a fiber to approximately 30% of main-blue and main-red
targets, falling to 19% for the lower-priority main-broad sample. The higher
priority mws-wd, mws-nearby, mws-rrlyr and mws-bhb samples have
correspondingly higher completeness (99%, 62%, 52% and 55% respectively).
Completeness increases as target density falls toward the Galactic poles, such
that $\sim 40\%$ of the footprint has $\sim 50\%$ completeness for main-blue
and main-red.

BGS targets have a mean density of $\sim 1,400$ per square degree with tile-
to-tile fluctuations corresponding to the large-scale structure in the low-
redshift galaxy distribution. Since DESI can deploy at most $\sim 600$ fibers
per square degree (after accounting for standards and sky fibers), more MWS
targets will be observed in the later passes of the survey, when the density
of remaining unobserved BGS targets is lower. Approximately 35% of the MWS
sample will be observed on the fourth pass, alongside the final 15% of BGS
targets. Approximately 11% of the MWS targets will be observed more than once;
for the majority of these no other target is available to a fiber. The tile-
to-tile fluctuations in BGS density give rise to corresponding fluctuations in
the MWS completeness of $\approx\pm 5\%$ at high latitude. The clustering
pattern of the extragalactic large-scale structure will therefore be imprinted
on the apparent clustering of observed MWS targets.

##  6 The DESI MWS Data Pipeline

A massive software development effort has been carried out to ensure that the
main data products from DESI, such as extracted flux-calibrated spectra and
galaxy redshifts, are of the highest possible quality and processed on a daily
basis from the beginning of the survey. The main DESI pipeline uses the
Redrock spectral fitting code to determine redshifts (Bailey et al., 2022).
Redrock classifies spectra into broad categories (galaxy, star, white dwarf,
quasar, etc.) but is not optimized for stellar radial velocity measurement at
the accuracy required for MWS science. MWS has therefore developed additional
software to extract information from stellar spectra, which we refer to
collectively as the MWS pipeline.

There are three main components to the MWS pipeline, which we refer to as RVS,
SP, and WD. The RVS component derives stellar radial velocities and
atmospheric parameters. The SP component deals with the determination of
stellar atmospheric parameters and complements the RVS branch by providing a
way for inferring abundances for individual elements through the definition of
spectral windows. The WD component is focused on determining parameters for
white dwarf stars. Each of these components is based on improvements to
existing tools for the analysis of stellar spectra.

###  6.1 RVS

The RVS pipeline determines the radial velocities of all stellar objects and
finds the best stellar atmospheric parameters. The pipeline algorithms are
based on ideas first presented in Koposov et al. (2011), where stellar
spectra, without flux calibration, are fit by stellar templates multiplied by
a polynomial continuum. The code has been expanded to perform interpolation
across templates for the Gaia-ESO project (Gilmore et al., 2012a). A python
implementation of these algorithms, RVSpecfit, is publicly available (Koposov,
2019)121212https://github.com/segasai/rvspecfit, including a version specific
to DESI (which we describe here) and variants for other surveys, such as S5 Li
et al. (2019) and the WHT Extended Aperture Velocity Explorer survey (WEAVE;
Dalton et al., 2012).

We briefly summarize the algorithm. A stellar spectrum ${\bf S}$ evaluated at
pixels with wavelengths $\lambda_{k}$ is modeled as

$M(\lambda_{k}|{\bf\alpha},v,\phi)=\sum_{i}\alpha_{i}P_{i}(\lambda_{k})T\left(\lambda_{k}\sqrt{\frac{1-v/c}{1+v/c}}|\phi\right)$
(3)

where $T(\lambda|\phi)$ is the interpolated stellar template from the library
convolved to the resolution of the observed spectrum. $P_{i}(\lambda)$ denotes
basis functions, such as polynomials $\lambda^{i}$, Chebyshev polynomials, or
radial basis functions (RBFs), which take care of modifying the continuum
shape. The vector ${\bf\alpha}$ is a vector of linear coefficients, $v$ is the
radial velocity, and $\phi$ is the vector of stellar atmospheric parameters,
abundances, and potentially stellar rotations $V{\sin i}$. As shown in Koposov
et al. (2011) the vector of linear coefficients, $\alpha$, can be determined
through simple linear algebra operations. This allows us to compute the log-
likelihood for each spectrum given only the stellar atmospheric parameters and
radial velocities, $\log P({\bf S}|\phi,v)$. In the case of DESI, the total
log-likelihood function is the sum of the log-likelihoods for each of the
three arms of the spectrograph.

The RVS pipeline optimizes the log-likelihood combined across the three arms
simultaneously through Nelder–Mead optimization (Nelder & Mead, 1965). Since
the likelihood surface is extremely complex in the radial velocity dimension,
we need to provide a reasonable initial guess. This is obtained from cross-
correlation of the continuum normalized spectrum with a 0.5% subset of
continuum-normalized templates from the PHOENIX grid. We continuum-normalize
both the observed spectra and the model templates by a spline-based continuum
with a regular grid of knots in wavelength separated by
$1000\,\mathrm{km\,s^{-1}}$. The cross-correlation uses the uncertainties and
is computed as $({\bf S}/{\bf E}^{2}\circledast{\bf T})^{2}/(1/{\bf
E}^{2}\circledast{\bf T}^{2})$, where T is the template vector, S is the
spectrum, E is the uncertainty vector, and $\circledast$ is a convolution
operator that is computed using a fast Fourier transform. The cross-
correlation functions from the three arms of the instrument are added
together. The best cross-correlation velocity and the stellar template
parameters are then used as a starting point for the likelihood optimization.

Both the initial cross-correlation step and the nonlinear optimization steps
are conducted in the radial velocity interval of $\pm
1500\,\mathrm{km\,s^{-1}}$.

The interpolated stellar templates are constructed from the PHOENIX grid of
models in a two-step process. First, global RBF interpolation is used to
interpolate the original grid from Husser et al. (2013) onto a regular grid
without holes, using steps of 0.2 in $\mathrm{[Fe/H]}$, 0.25 in
$\mathrm{[\alpha/Fe]}$ and the original grid points in $\log g$ and
$T_{\mathrm{eff}}$. This grid is then convolved to the average resolution of
DESI in the $B$, $R$ and $Z$ arms. The resulting templates are then
interpolated using multilinear interpolation.

Type of Star | Models | Bands Fit | Parameters | Reference
---|---|---|---|---
Cool and very cool ($2,300<T_{\rm eff}<5,100$ K) | Phoenix | $R,Z$ |  $T_{\rm eff},\log g$, [Fe/H], [$\alpha$/Fe] | Husser et al. (2013)
Cool and warm ($3,500<T_{\rm eff}<30,000$K) | Kurucz | $B,R,Z$ |  $T_{\rm eff},\log g$, [Fe/H], [$\alpha$/Fe], $\xi$ | Allende Prieto et al. (2018)
White dwarf | Koester | $B,R,Z$ | $T_{\rm eff},\log g$ | Koester (2010)
Table 3: Summary of the families of grids of model spectra employed in the SP
branch of the DESI-MWS pipeline.

We note that, because we are fitting the product of the template model and a
polynomial or RBF continuum modifier, at this stage we are not using large-
scale flux calibration information in the spectra. Currently we use 10 basis
functions in each arm for the continuum modification. This approach may be
refined in the future.

The RVS pipeline quantifies the uncertainty in the parameters of each fit
through an estimate of the Hessian matrix at the minimum. However, the
uncertainty in radial velocity is estimated somewhat differently, by
evaluating the log-likelihood from the best-fit template $P({\bf
S}|v,\phi_{0})$ on a finely spaced grid of radial velocities and computing the
standard deviation of the radial velocity (which is equivalent to assuming a
uniform prior on the radial velocity and computing the standard deviation over
the posterior).

The RVS outputs are the best-fit stellar atmospheric parameters [Fe/H], $\log
g$, $\mathrm{[\alpha/Fe]}$; the best-fit radial velocity; the stellar rotation
$V\sin i$; and their uncertainties. We also return the best-fit chi-square
values per arm $\chi^{2}_{min,B}$, $\chi^{2}_{min,R}$ and $\chi^{2}_{min,Z}$
and the combined $\chi^{2}$. To facilitate the identification of sources that
are not well fit by stellar templates, such as galaxies, quasars, or unknown
types of objects, we also compute the $\chi^{2}$ values for a continuum-only
model, i.e. a template $T(\lambda)=1$ in Eq. 3, providing $\chi^{2}_{cont,B}$,
$\chi^{2}_{cont,R}$ and $\chi^{2}_{cont,Z}$. The rationale for computing these
chi-squares is that they give a reference value for the goodness of fit, with
respect to which we can assess the stellar fits.

The outputs of the pipeline are also used to populate the 64 bit warning
bitmask RVS_WARN, as follows. If the difference in $\chi^{2}$ of a stellar
model with respect to the continuum model is small,
$(\chi^{2}_{min,B}+\chi^{2}_{min,R}+\chi^{2}_{min,Z})-(\chi^{2}_{cont,B}+\chi^{2}_{cont,R}+\chi^{2}_{cont,Z})<50$,
the first bit of RVS_WARN is set to 1. If the radial velocity is within
$5\,\mathrm{km\,s^{-1}}$ of the edges of the interval of radial velocities
considered, $[-1500,1500]\mathrm{\,\mathrm{km\,s^{-1}}}$, the second bit of
RVS_WARN is set to 1. If the radial velocity error is larger than
$100\,\mathrm{\,\mathrm{km\,s^{-1}}}$ the third bit of RVS_WARN is set to 1. A
good spectrum without any of those issues has $\mathtt{RVS\\_WARN}=0$.

The RVS pipeline, by default, does not require either targeting information or
Redrock results. However when processing the main survey data, if Redrock
outputs are available we use the classification from Redrock to avoid fitting
spectra of quasars and galaxies. Thus we only process through RVSpecfit the
spectra that either are classified as type STAR by Redrock or have been
targeted as either a Milky Way target, a stellar secondary target, or a
spectrophotometric standard.

###  6.2 SP

The SP pipeline is based on FERRE131313https://github.com/callendeprieto/ferre
(Allende Prieto et al., 2006), a FORTRAN code that fits numerical models to
data by optimization and interpolation of a precomputed model grid. FERRE has
been used in the analysis of SDSS optical spectra (Yanny et al., 2009b;
Rockosi et al., 2022), and SDSS/APOGEE near-IR high-resolution spectra
(Majewski et al., 2017), and in other surveys such as Gaia-ESO (Gilmore et
al., 2012a).

A new python software package,
piferre141414https://github.com/callendeprieto/piferre, has been written
specifically to handle DESI MWS data. This package reads the reduced spectra,
corrects for the radial velocity (measured by the MWS RVS pipeline or the
primary DESI pipeline), resamples the spectra, and prepares submission scripts
for batch processing, taking advantage of FERRE’s OpenMP parallelism. The
piferre package manages the independent processing of DESI tiles, exposures,
and petals; collects the results. and creates the final data products.

Only the spectra that have been successfully fitted by the RVS pipeline are
processed by the SP pipeline. The input data are the observed spectra and
associated inverse covariance arrays.

We set up FERRE to work with grids of model spectra having between two and
five parameters: mostly, effective temperature $T_{\rm eff}$, surface gravity
$\log g$ and metallicity $\mathrm{[Fe/H]}$, and, in some instances,
microturbulence $\xi$ and [$\alpha$/Fe] as well. We adopt several sources for
the template models, including the same PHOENIX models Husser et al. (2013) of
the RVS pipeline (Section 6.1) for very cool stars ($2300<T_{\rm eff}<5100$
K), Kurucz ATLAS9 models (Kurucz, 1979, 1993) for warmer stars ($3500<T_{\rm
eff}<30,000$ K) (Mészáros et al., 2012; Allende Prieto et al., 2018) and
models for DA and DB white dwarfs (Koester, 2010). Table 3 describes the
parameter range, steps, and origin of the models we use to analyze DESI
commissioning and SV data. In some cases there are multiple grids for each
family: one for PHOENIX models, five for the Kurucz models, and four for the
Koester models.

FERRE derives all the atmospheric parameters simultaneously and provides error
covariance matrices for every spectrum by inverting the Hessian matrix. As in
the case of the RVS code, the optimization is based on the Nelder-Mead
algorithm (Nelder & Mead, 1965). As expected for a purely spectroscopic
analysis, there are significant correlations between the uncertainties in
$T_{\mathrm{eff}}$ and $\log g$, and especially between $T_{\mathrm{eff}}$ and
[Fe/H].

We analyze the continuum-normalized spectra, after dividing the data by a
running mean with a width of 500 spectral bins (equivalent to 250 Å). This is
similar to the normalization approach described by Aguado et al. (2017), which
ignores the continuum information and focuses on the absorption lines. The
entire spectral range is fitted for all models, except for the lowest-
temperature stars in the Phoenix models, for which the blue ($B$) spectrograph
arm is ignored because including it leads to significant systematic errors.
All the spectra are evaluated against all the model libraries in Table 3. The
solution with the smallest value of the reduced chi-square is kept and the
others are discarded. The results comprise the parameter estimates, the error
covariance matrix, and the best-fitting model, which can be directly compared
with the continuum-normalized observation. We also store a version of the best
model without continuum normalization, which may be used for flux calibration.
A success flag is set for fits with $\chi^{2}<1.5$ and median S/N $>5$.

The SP pipeline performs a number of iterations holding the atmospheric
parameters fixed, except for [Fe/H] or [$\alpha$/Fe], to infer the abundances
of several elements by evaluating the $\chi^{2}$ in regions of the spectrum
dominated by transitions associated with those elements. This procedure
resembles the methodology followed in APOGEE (García Pérez et al., 2016;
Jönsson et al., 2020), and requires a careful definition of the windows to be
used for each element. These are created by assigning weights $W_{\lambda}$
($X$) proportional to the derivative of the flux ($F$) with respect to the
abundance of the element of interest ($X$), subtracting possible contributions
from the rest of the elements,

$W_{\lambda}(X)=\frac{\partial F_{\lambda}}{\partial X}-\sum_{Y\neq
X}\frac{\partial F_{\lambda}}{\partial Y},$ (4)

where the derivatives are computed using a solar model atmosphere. The weights
are set to zero when Eq. 4 gives a value smaller than a predetermined
threshold.

###  6.3 WD

In addition to the white dwarf fitting performed by the SP branch of the
pipeline described above, we fit DA white dwarfs with a bespoke code using
models provided by Koester (2010), which span $6\,000\,\textrm{K}\leq
T_{\textrm{eff}}\leq 100\,000\,\textrm{K}$ and $4.00\leq\log g\leq 9.75$. The
fitting procedure employed is similar to that outlined in detail in Liebert et
al. (2005). We first continuum-normalize the flux of the observed and
convolved model spectra around the Balmer lines, H$\beta$ to H8, which are all
contained within the blue arm of the DESI spectrograph (see Table 5.5 of DESI
Collaboration et al. 2016b). This fitting procedure allows us to use white
dwarfs as an independent test of the absolute flux calibration of DESI
obtained from F- and A-type stars across the blue, red, and NIR spectrograph
arms, because the best-fit white dwarf models are based solely on fits to the
blue arm spectra.

After the continuum normalization, we determine the best-fitting models from
our grid. As the equivalent width (EW) of the Balmer lines go through a
maximum at approximately $T_{\textrm{eff}}\simeq 12\,000\,\textrm{K}$
(dependent on $\log g$, Daou et al. 1990; Bergeron et al. 1992), we determine
two solutions, one hotter and one cooler than this $T_{\textrm{eff}}$. We use
both initial best-fit grid solutions as our first estimates for a $\chi^{2}$
minimization between the observed and linearly interpolated model grid
spectra. The degeneracy between the two solutions can be broken either with
the continuum flux of the flux-calibrated DESI spectrum, or through use of
Gaia photometry and parallaxes. The current WD pipeline uses the DESI
continuum flux, but as this can be affected by flux calibration (e.g. Tremblay
et al. 2011), we plan to incorporate the Gaia photometry and parallaxes in a
future code development. We also plan to extend this code to DB and DBA white
dwarf model fitting, using data from both the blue and red arms of the DESI
spectrograph.

Figure 8: SV fields discussed in the text. Orange and green circles indicate
fields with large numbers of stellar targets in the SV1 and SV3 programs,
respectively, which were selected specifically for the validation of the MWS
main survey and prioritized stellar targets. Black circles correspond to the
SV2 program, which will be presented separately. Gray circles show SV fields
not associated with the stellar SV program. Purple points and tracks show the
extent of the Sagittarius, GD 1 and Orphan streams as reported by the
galstreams compilation; references are given in Fig. 1. Gray lines indicate
the approximate Galactic latitude limit of the survey, $|b|\pm 20\arcdeg$.

##  7 SV

The DESI SV campaign (SV; DESI Collaboration et al., 2023) included
observations dedicated to MWS. These were split into two major subprograms,
SV1 and SV3. Fig. 8 shows all the DESI SV fields and highlights those
associated with MWS. The MWS target selection for SV was previously described
in Allende Prieto et al. (2020); other DESI SV programs were introduced in
Raichoor et al. (2020), Zhou et al. (2020), Yèche et al. (2020), and Ruiz-
Macias et al. (2020). The results of these other programs and the final target
selections for the DESI cosmological surveys are given in companion papers by
DESI Collaboration et al. (2023), Raichoor et al. (2022b), Zhou et al. (2023),
Chaussidon et al. (2022) and Hahn et al. (2022).

The following subsections summarize the MWS SV observations. We then use these
data to test our analysis pipelines (introduced in Section 6) and to evaluate
our survey selection function. These tests reflect the current state of our
pipelines, which we will continue to develop ahead of the first MWS data
release. The quantity and quality of the DESI SV spectra also allow us to
address a number of interesting scientific questions, including the detection
of extended features around star clusters and satellite galaxies, the
structure of the GD 1 stream, the discovery of rare sources, and the
characterization of radial velocity variability in our sample. We will present
these scientific results from the MWS SV program in separate publications.

###  7.1 SV target selection

In all the SV3 fields and all but a few of the SV1 fields, targets were
selected using a simpler version of the scheme described in Section 4 (see
also Allende Prieto et al., 2020). This selection was magnitude-limited
between $r=16$ and $r=19$ and did not include the astrometric criteria we use
to separate main-red and main-broad targets in the main survey. The mws-wd and
mws-nearby samples were selected as in Sections 4.4.1 and 4.4.3, except that
the astrometric criteria were applied to the Gaia DR2 catalog rather than to
EDR3.

For the SV, stars in the range $19<r<20$ were also included at lower priority.
A subset of MWS SV1 tiles included additional sets of high-priority targets
specific to the region observed (for example, likely members of satellite
galaxies and star clusters selected using Gaia astrometry, or stars observed
by previous surveys).

###  7.2 SV1 MWS Data Set

In SV1, the 14 regions listed in Table 4 were observed to significantly
greater depth than the main survey151515These fields are different from those
observed in the SV1 ‘BGS+MWS’ program, which prioritized a larger set of BGS
targets and filled spare fibers with MWS targets. For more details of the SV1
program see DESI Collaboration et al. (2023).. In most cases, these
observations consisted of a single fiber configuration (tile) for which
multiple exposures were accumulated under different observing conditions. The
completeness of MWS targets in these regions is therefore somewhat higher than
that for the main survey (because, in SV1, all fibers were allocated to stars)
but lower than that for the SV3 fields (because the same targets were observed
on all exposures regardless of their accumulated S/N). We use these high-S/N
and multi-epoch spectra to validate our analysis pipelines.

Most MWS SV1 regions (orange circles in Fig. 8) correspond to known features
in the Milky Way halo, including the GD 1 stream, several globular clusters,
and the satellite dwarf galaxies Draco, Sextans, and UMa II. Other tiles were
placed on blank regions. Since the angular sizes of most of the star clusters
and dwarf galaxies are much smaller than the DESI field of view, much of the
area on those tiles is also effectively blank. Additional tiles were placed on
the UMa II satellite galaxy and the globular clusters M53 and NGC 5053 with
customized target selections favoring likely members of those systems. SV1
included many other observations dedicated to testing the DESI cosmological
surveys (gray circles in Fig. 8), which yielded a small number of additional
stars.

The RVS and SP pipelines are run on the co-added spectra of 45,738 unique SV1
targets, of which 38,051 were targeted by the MWS SV1 program, mostly in the
MWS SV1 fields but also with spare fibers in the BGS SV1 program. Many of
these MWS targets are observed more than once. Among the MWS targets, 1209
($\sim 3\%$) cannot be fit reliably by RVS.

The remaining 7687 SV1 spectra comprise brighter flux standards and
serendipitous (potentially) stellar contaminants to the galaxy and QSO
selections of other DESI SV programs161616Particularly along the Sagittarius
stream, which was targeted under dark conditions in SV1 to quantify
contamination of the QSO target selection.. We attempt to fit all targets
classified as stars by the Redrock pipeline even if they would not be selected
in the main MWS survey, although many of these are faint extragalactic sources
and therefore have a higher failure rate in our fitting.

Region Name | R.A. [∘] | Decl. [∘] | Objective |  $T_{\mathrm{eff}}$ (s) | $N_{\mathrm{exp}}$ | Target Selection
---|---|---|---|---|---|---
NGC 2419 | 114.54 | 39.38 | Globular cluster | 1424 | 14 | Standard
GD 1 Low Latitude A | 128.50 | 0.80 | Tidal stream | 1034 | 23 | Standard
UMa II | 132.87 | 63.73 | Dwarf galaxy | 1071 | 10 | Standard
UMa II (extra) | 132.87 | 63.73 | Dwarf galaxy | 85 | 2 | Customized
Sextans | 153.26 | -1.11 | Dwarf galaxy | 250 | 3 | Standard
Orphan | 159.08 | 7.50 | Tidal stream | 1118 | 5 | Standard
GD 1 High Latitude A | 163.74 | 47.86 | Tidal stream | 1536 | 18 | Standard
GD 1 High Latitude B | 173.55 | 52.86 | Tidal stream | 2038 | 14 | Standard
NGP | 192.86 | 27.13 | Blank sky | 914 | 21 | Standard
BOSS 7456 | 198.04 | 0.00 | Blank sky/calibration | 1647 | 12 | Customized
M53+N5053 | 199.10 | 18.30 | Globular cluster | 1829 | 16 | Standard
M53+N5053 (deep) | 198.30 | 17.50 | Globular cluster | 6178 | 8 | Customized
M5 | 229.64 | 2.58 | Globular cluster | 2698 | 17 | Standard
M13 | 250.42 | 36.96 | Globular cluster | 2787 | 16 | Standard
M92 | 259.28 | 43.64 | Globular cluster | 3446 | 14 | Standard
Draco | 260.07 | 58.42 | Dwarf galaxy | 2258 | 16 | Standard
Table 4: Summary of dedicated MWS observations in SV1. From left to right,
columns give the name and central coordinates of the field, the objective of
the observation (in most cases the main feature of interest), the total
effective exposure time calculated according to the bright-time metric (see
text), the number of exposures taken in SV1, and the target selections used
for those configurations (standard refers to the MWS SV1 target selection
criteria described in the text, customized to cases in which one or more
additional high-priority target categories were added to the standard
selection).

###  7.3 SV3 MWS Data Set

In SV3 (also referred to as the One-percent Survey in other DESI
publications), 20 regions with the area of a single DESI field were observed
using multiple tiles dithered in a rosette pattern around a common center,
each with total coverage comparable to a single DESI tile. Details of these
regions and the corresponding DESI observations are given in DESI
Collaboration et al. (2023). The total area covered is
$100\,\mathrm{deg}^{2}$, mostly distributed over Galactic latitudes $25<b<65$
degrees, with two tiles covering the north Galactic pole.

Unlike the case of the SV1 observations, multiple exposures of each SV3 tile
were accumulated up to an effective exposure time only 20% greater than that
to be used for each main survey tile, with fibers on subsequent tiles in the
dither pattern being reallocated to unobserved targets. Fibers were assigned
to BGS and MWS targets on the same focal plane in the same priority order that
will be used in the main survey, but with the broader target selection
criteria used in SV1 (see below). This strategy mimics the full DESI survey,
but with $\sim 6$ bright-time passes on each region rather than 4 (the other
tiles in each region were observed with the dark-time and backup program
target selections). The result is a highly complete sampling of each region,
typically yielding spectra for $\gtrsim 90\%$ of MWS targets (see Section
7.7). Fig. 8 shows that, in contrast to the SV1 fields, most of the SV3 fields
do not overlap significant Milky Way substructures (most are cosmological deep
fields). However, four are close to the midline of the Sagittarius stream and
a further four are in its outskirts. Three more regions lie close to the GD 1
stream.

The MWS SV3 dataset contains 213,414 spectra taken under bright conditions,
almost all of which ($99.6\%$) are for MWS main survey targets. Of these, 982
($\approx 0.5\%$) are not fit successfully by the RVS pipeline. Visual
inspection suggests the majority of these failures are for QSOs. Other classes
of targets for which the current version of the RVS pipeline fails or produces
unreliable results include white dwarfs (which we fit separately) and cool
M-dwarfs, which we discuss further in Sec. 7.5.1.

###  7.4 Validating the pipelines

####  7.4.1 Radial velocities

We validate the radial velocities from the RVS pipeline by comparing them to
radial velocities from other large surveys. Figure 9 shows the distribution of
radial velocity residuals for the stellar sources observed during the SV
program in bright observing conditions. The different curves show comparisons
to different individual surveys, while the black curve shows a comparison to
the Survey of Surveys (SoS) dataset (Tsantaki et al., 2021), a homogenized set
of radial velocities from various surveys. We remark that the comparison to