# DESI luminous red galaxy samples for cross-correlations

Rongpu Zhou  Simone Ferraro  Martin White  Joseph DeRose  Noah Sailer  Jessica
Aguilar  Steven Ahlen  Stephen Bailey  David Brooks  Todd Claybaugh  Kyle
Dawson  Axel de la Macorra  Biprateep Dey  Peter Doel  Andreu Font-Ribera
Jaime E. Forero-Romero  Satya Gontcho A Gontcho  Julien Guy  Anthony Kremin
Andrew Lambert  Laurent Le Guillou  Michael Levi  Christophe Magneville  Marc
Manera  Aaron Meisner  Ramon Miquel  John Moustakas  Adam D. Myers  Jeffrey A.
Newman  Jundan Nie  Will Percival  Mehdi Rezaie  Graziano Rossi  Eusebio
Sanchez  David Schlegel  Michael Schubnell  Hee-Jong Seo  Gregory Tarlé
Zhimin Zhou

###### Abstract

We present two galaxy samples, selected from DESI Legacy Imaging Surveys (LS)
DR9, with approximately 20,000 square degrees of coverage and spectroscopic
redshift distributions designed for cross-correlations such as with CMB
lensing, galaxy lensing, and the Sunyaev-Zel’dovich effect. The first sample
is identical to the DESI Luminous Red Galaxy (LRG) sample, and the second
sample is an extended LRG sample with 2-3 times the DESI LRG density. We
present the improved photometric redshifts, tomographic binning and their
spectroscopic redshift distributions and imaging systematics weights, and
magnification bias coefficients. The catalogs and related data products will
be made publicly available. The cosmological constraints using this sample and
Planck lensing maps are presented in a companion paper. We also make public
the new set of general-purpose photometric redshifts trained using DESI
spectroscopic redshifts, which are used in this work, for all galaxies in LS
DR9.

##  1 Introduction

This decade will witness a dramatic increase in data available from large-
scale structure (LSS) and cosmic microwave background (CMB) surveys, with
measurements from the Dark Energy Survey (DES) [2], the Dark Energy
Spectroscopic Instrument (DESI) [3, 4], the Legacy Survey of Space and Time
(LSST) on the Vera Rubin Observatory [5], Euclid [6], the Atacama Cosmology
Telescope (ACT) [7], the South Pole Telescope (SPT) [8] the Simons Observatory
(SO) [9], and others. Each of these new facilities will enable transformative
science, but with major leaps in capabilities occurring simultaneously with
many probes, their combination could be even more powerful. One of the most
exciting scientific opportunities afforded by these surveys is the ability to
cross-correlate the data sets that are overlapping on the sky. The promise of
cross-correlations is that they enable new science as well as increase the
robustness of the core science being pursued by each project. Moreover, by
breaking degeneracies between astrophysical and cosmological parameters, the
overall statistical power can be greatly enhanced. The cross-correlation with
samples in different redshift bins (tomography) can allow us to study the
redshift dependence of the signal in question, and recover the time-evolution
of various quantities.

In this paper, we define and characterize the photometric sample of DESI
Luminous Red Galaxies [10] (henceforth “Main LRGs”) and a higher–density
extended LRG sample (henceforth “Extended LRGs”). We also present and publicly
release a new set of general-purpose photo-$z$’s that uses DESI spectroscopic
redshifts for training. We use the photo-$z$’s of the LRG samples to define
four tomographic bins spanning the redshift range $0.4\lesssim z\lesssim 1.1$.
We also provide spectroscopic redshift distributions using DESI spectroscopic
data and imaging systematics weights for each redshift bin, and we calculate
the effect of lensing magnification on the galaxy surface densities. The high
reliability of the redshift distributions (thanks to the very high
spectroscopic success rate), the small fraction of contaminants (see table 1)
and the high spatial uniformity make these samples very well suited to cross-
correlations.

In particular, (an earlier version of) this Main LRG sample has been recently
used in the tomographic analysis of Planck CMB lensing [1], for which this
work serves as a companion paper; see appendix A for a discussion of the
difference between this earlier sample and the updated LRG sample presented in
this work. In [1], the authors used the galaxy auto-correlation, together with
its cross-correlation with Planck CBM lensing to provide a ${\sim}\,4\%$
constraint on the amplitude of structure at low redshift with negligible
uncertainties on the redshift distribution of galaxies, since it is directly
measured from DESI spectroscopy. This follows previous work using previous
releases of the same imaging data [11, 12, 13].

Other future applications include the cross-correlation with maps of the
thermal or kinematic Sunyaev-Zel’dovich effect (tSZ and kSZ respectively),
galaxy or CMB lensing measurements from current and future experiments, as
well as maps of the Cosmic Infrared Background (CIB).

The remainder of the paper is organized as follows: in section 2 we describe
the imaging data used to extract our sample. In section 3, we discuss the
selection of the sample. In section 4 we explore the impact and mitigation of
imaging systematics, while in section 5 we measure the number count slope
necessary to model magnification bias. We characterize the angular clustering
of the samples and present forecasts for a few cross-correlation scenarios in
section 6. We describe the data products in section 7, and we conclude in
section 8. Appendix A describes the difference between the Main LRG sample
presented in this work and an earlier version used in [1]. Appendix B contains
a more detailed description of the new photometric redshifts. Appendix C
describes how we model the change in fiber-flux (which is used in the sample
selections) for a magnified galaxy.

##  2 Data

###  2.1 DESI imaging data

The parent imaging is the DESI Legacy Imaging Surveys Data Release 9, which is
a combination of optical and mid-infrared imaging used for DESI target
selection. The data covers three optical bands ($g$, $r$, $z$), with four
additional mid-IR bands ($W1-W4$) provided by the Wide-field Infrared Survey
Explorer (WISE; [14]). Three individual surveys, using three telescopes,
provide the optical imaging data: at the Cerro Tololo Inter-American
Observatory is the Dark Energy Camera Legacy Survey (DECaLS; [15]) using the
Blanco telescope, providing imaging in the South Galactic Cap (SGC) and the
North Galactic Cap (NGC) at DEC<32.375∘, and at the Kitt Peak National
Observatory are the Beijing–Arizona Sky Survey (BASS; [16, 15]) using the Bok
Telescope and the Mayall $z$-band Legacy Survey (MzLS; [15]) using the Mayall
Telescope, providing imaging in the NGC at DEC>32.375∘. The DESI imaging also
includes non-DECaLS observations from the DECam instrument, mainly from the
Dark Energy Survey (DES; [2]). Hereafter, we denote the region with DECam
imaging (i.e., DECaLS and DES) as Southern imaging (or simply South) and the
region covered by BASS+MzLS as Northern imaging (or simply North). These terms
should not be confused with the NGC and SGC. There are small differences in
the photometry between North and South, and we implement slightly different
galaxy selection cuts and train the photo-$z$ algorithms separately in the two
regions to account for these differences. Within the Southern imaging, the DES
region is deeper than the DECaLS region, but we do not distinguish them in
photo-$z$ estimation or sample selection because the effects of the different
depths on the galaxy samples is relatively small and because the DECaLS/DES
boundary is not well defined. We will discuss the differences in the different
imaging regions in section 4.

Images are processed and calibrated through the National Optical Astronomy
Observatory (NOAO) Community Pipeline, then fed into The Tractor [17], which
uses forward-modeling to perform source extraction and produce probabilistic
inference of source properties. Our analysis is based on Data Release 9 (DR9)
of the DESI Legacy Imaging Surveys [15], which is used for DESI target
selection and contains 1,969,942,678 unique objects and covers 19,721 deg2 in
all three optical bands jointly. The BASS+MzLS imaging covers 5,064 deg2 of
the NGC with Declination$>32.375^{\circ}$, whereas DECam imaging covers the
rest of the DR9 footprint. After applying the masks and footprint trimming
described in section 3.3, the total area is roughly 16,700 deg2, with
BASS+MzLS (North), DECaLS and DES covering 4,200, 4,700 and 7,800 deg2,
respectively.

Table 1 lists the key information about the imaging coverage and the LRG
samples.

Imaging coverage (with 1+ observations in $grz$ bands) | 19700 deg2
---|---
Imaging coverage after applying masks and footprint trimming | 16700 deg2
DESI spectroscopic coverage | 14800 deg2
Surface density of Main LRGs | 600 deg-2
Surface density of Extended LRGs | 1669 deg-2
Comoving number density of Main LRGs | $5\times 10^{-4}\ h^{3}\mathrm{Mpc}^{-3}$
Comoving number density of Extended LRGs | $\leq 1.5\times 10^{-3}\ h^{3}\mathrm{Mpc}^{-3}$
Stellar contamination in Main LRGs | 0.3%
Stellar contamination in Extended LRGs | 0.3%
Redshift failure rate of Main LRGs (in Main Survey) | 1.0%
Redshift failure rate of Extended LRGs (in Survey Validation) | 0.9%
Table 1:  Key facts about the LRG samples. The second row is the “clean”
footprint with the following cuts (see section 3.3 for details): “clean” in
the veto mask, 2+ observations in $grz$ bands, E(B-V)<0.15, and stellar
density less than 2500 deg-2; the surface densities in rows 4 and 5 are based
on this area. “Stellar contamination” is the fraction of photometric LRGs
(that are “clean” in the veto mask) that are classified as stars based on the
DESI spectroscopic data. The last two columns list the fraction of
spectroscopic LRGs that are rejected by redshift quality cuts (see section
2.2), and they are based on Main Survey data for the Main LRGs and Survey
Validation data for the Extended LRGs.

####  2.1.1 Zero point correction at $\mathrm{Dec}<-29.25^{\circ}$

Ref. [18] showed that in LS DR9 the photometric zero point has systematic
offsets of up to 19 mmag at $\mathrm{Dec}<-29.25^{\circ}$ (where the
calibration is based on internal calibration whereas Pan-STARRS [19] is used
at $\mathrm{Dec}>-29.25^{\circ}$) in $r$ and $z$ bands. This offset is large
enough to affect the density of the LRG samples. We correct for these
systematic zero point offsets by artificially modifying the fluxes (and
inverse variances) of the objects for all objects at
$\mathrm{Dec}<-29.25^{\circ}$. We model the smooth-varying offsets by fitting
a monopole and dipole to the offset map from [18] at
$\mathrm{Dec}<-29.25^{\circ}$ using the healpy [20] fit_dipole routine.

Specifically, the corrected magnitude for an object is
$m_{\mathrm{corr}}=m_{\mathrm{original}}-\Delta m$, and the magnitude offset
is $\Delta m=a+\textbf{v}\cdot\textbf{b}$, where $a$ and b are the best-fit
parameters,
$\textbf{v}=(\cos\delta\cos\alpha,\cos\delta\sin\alpha,\sin\delta)$, and
$\alpha$ and $\delta$ are the right ascension and declination, respectively.
For the $r$ band, $a=-0.0054387$,
$\textbf{b}=(0.0025345,-0.0036355,0.010219)$; for the $z$ band, $a=0.0144506$,
$\textbf{b}=(0.0000641,-0.013588,0.0039126)$; the resulting $\Delta m$ is in
units of magnitude.

After obtaining the corrected photometric catalogs, we recompute the
photo-$z$’s and rerun the LRG selection and photo-$z$ tomographic cuts for
every object at $\mathrm{Dec}<-29.25^{\circ}$. We find that the zero point
correction brings the surface densities consistent with the rest of the DES
region. The changes in the surface density at $\mathrm{Dec}<-29.25^{\circ}$
compared to the original DR9 photometry are: -5.6%, 0.5%, 2.9%, 9.4% in bins
1-4 of the Main LRG subsamples, and -6.4%, -0.1%, 1.0%, 7.3% in bins 1-4 of
the Extended LRG subsamples (the tomographic subsamples are described in
section 3.4). The zero point correction also produces coherent changes in the
photo-$z$ by as much as 0.01, and the exact change varies with redshift and
location.

The LRG sample in [1] was not corrected for the zero point offsets at
$\mathrm{Dec}<-29.25^{\circ}$ (as we were not aware of this issue when it was
published). We compare the angular power spectra of the sample in [1] and the
updated sample in appendix A.

###  2.2 Spectroscopic redshifts

We use spectroscopic data from the DESI Survey Validation [21] (henceforth
“SV1”) and the first year of DESI Main Survey (henceforth “Y1”) to accurately
characterize the redshift distributions and stellar contaminations.
Specifically, we use the data reduction (the version internally named “iron”)
that will be published with the DESI Y1 Data Release. We also use the publicly
available DESI redshifts in the photo-$z$ training, specifically the tile-
based redshifts from the DESI Early Data Release [22].

A detailed characterization of the spectroscopic performance of the DESI LRGs
is presented in [10]. Here we briefly summarize the redshift performance with
some numbers updated for the Y1 data. To remove incorrect redshifts, we apply
the following quality cuts similar to those in [10]: $\Delta\chi^{2}>15$,
$z_{\mathrm{redrock}}<1.45$, and ZWARN=0. The fraction of objects that fail
the quality cuts (“redshift failures”) is 1.0% of the observed Main LRG
targets, and the Extended LRGs (which have longer exposure times from SV1)
have a similar failure rate. We estimate that less than 0.2% of the objects
that pass the quality cuts are catastrophic redshift failures (which we define
as deviating by more than 1000 km/s from the true redshift) based on deep
observations from SV1. Only 0.3% of the photometric LRGs are spectroscopically
classified as stars. The failure rate for each redshift subsample is listed in
tables 2 and 3. The note that the aforementioned redshift failure rates and
stellar contamination rates are estimates for the “clean” sample with the veto
masks (described in section 3.3) applied, and the rates are much higher for
the masked objects.

The LRGs that are rejected by the redshift quality cuts are predominantly
fainter objects, and therefore they are more likely to be at higher redshifts.
To get unbiased redshift distributions, each galaxy is assigned a weight equal
to the inverse of the predicted success rate. The success rate is predicted
using the $z$-band fiber-magnitude and the effective exposure time; see
section 4.4 of [10] for details. For computing the redshift distributions, we
also exclude 40 fibers that either have much higher than normal redshift
failure rates or have anomalous redshift distributions; these issues are
mostly caused by defects in the DESI spectrograph CCDs.

###  2.3 Photometric redshifts

Figure 1: Left panel: photo-$z$ vs spec-$z$ for 1.9 million galaxies in the
Main LRG sample observed in DESI Y1. Right panel: same as the left panel but
for 12k galaxies in the Extended LRG sample in DESI SV1. Both panels are based
on photo-$z$’s from the Southern imaging. The photo-$z$ scatter is slightly
larger in the (slightly shallower) Northern imaging.

We provide a new set of photometric redshifts for all objects in LS DR9. While
publicly available photo-$z$’s based on the method and training data described
in [23] are already released as part of LS DR9, we compute this new set of
photo-$z$’s to include improvements in the photo-$z$ algorithm and to take
advantage of the newly available spectroscopic training data from the DESI
survey.

Here we summarize the main changes from the previously released DR9
photo-$z$’s. We provide a more complete description of the photo-$z$ algorithm
in Appendix B. The first major change is that we have added DESI spectroscopic
redshifts into the random forest training dataset. This spectroscopic sample
includes galaxies from the Bright Galaxy Survey (BGS), Luminous Red Galaxies,
Emission Line Galaxies (ELGs) and quasars observed during DESI Survey
Validation (SV1) and the 1% Survey (SV3). We also added SDSS DR16 quasars in
the training data. This additional training data improves the overall
photo-$z$ accuracy, especially in the North where training data was lacking,
and reduces the bias at higher redshifts caused by the lack of spec-$z$’s
coverage in that redshift-color-magnitude space. Some of the new training data
(e.g., ELGs) does not significantly affect photo-$z$ performance of LRGs, but
they improve the photo-$z$’s for other galaxy/quasar populations, and they are
thus beneficial for this general-purpose photo-$z$ catalog. The second major
change is that the photo-$z$’s are computed with 10-fold cross-validation, so
that the photo-$z$ errors no longer depend on whether or not the object is in
the spectroscopic training set. This change is less relevant for the
tomographic analysis, but is important for analyses that utilize individual
photo-$z$’s (e.g., galaxy-galaxy lensing).

We use DESI spectroscopic redshifts to assess the photo-$z$ performance of the
Main and Extended LRG samples (described in section 3). Figure 1 shows the
spec-$z$ vs photo-$z$ for the Southern imaging. For the Main sample, the
overall photo-$z$ error, quantified by the normalized median absolute
deviation $\sigma_{\mathrm{NMAD}}\equiv 1.48\times\mathrm{median}(|\Delta
z|/(1+z_{\mathrm{spec}}))$ where $\Delta
z=z_{\mathrm{phot}}-z_{\mathrm{spec}}$, is 0.024 (0.026) in South (North), and
the outlier fraction, defined as having $|\Delta
z|>0.1\times(1+z_{\mathrm{spec}})$, is 1.8% (2.0%) in South (North). For the
Extended sample, the photo-$z$ error is 0.027 (0.031) in South (North) and the
outlier fraction is 2.1% (3.2%).

This new set of photo-$z$’s for all objects in DR9 is publicly available and
described in section 7. An earlier version of the photo-$z$’s was used for
tomographic binning in [1], and we describe the differences in appendix A.

##  3 Galaxy selection

In this section, we present the two galaxy samples. The first sample is the
DESI Main LRG sample, and the second sample is a higher-density galaxy sample
based on the extended LRG selection in DESI Survey Validation. We also
describe the tomographic binning based on photometric redshifts, and
characterize the redshift distributions using DESI spectroscopic redshifts.

###  3.1 Main LRG sample

Figure 2: Left panel: the redshift distributions of the full DESI LRG Main
sample (in gray) and the four subsamples, derived directly from 2.3 million
DESI spectroscopic redshifts. Right panel: same as the left panel but for the
Extended LRG sample, based on 22k DESI spectroscopic redshifts. In both
panels, units of the y-axis are the number of galaxies per square degree
within the redshift bin with width $dz=0.02$.

Figure 3: Same as figure 2 but showing the comoving number densities as a
function of redshift.

The Main LRG sample is identical to the DESI Main Survey LRG target sample
described in [10]. Here we briefly summarize the selection. The sample is
selected with optical photometry in $g$, $r$ and $z$ bands and infrared
photometry in WISE $W1$. A luminosity cut in $r-W1$ vs $W1$ produces a roughly
constant comoving density of $5\times 10^{-4}\ h^{3}\mathrm{Mpc}^{-3}$ up to
$z=0.8$ and the faint limit in $z$-band fiber-magnitude produces a tail in the
$N(z)$ that extends beyond $z=1.0$. A stellar rejection cut in $z-W1$ vs $r-z$
ensures very low (0.3%) stellar contamination. And color cuts in $g-W1$ and
$r-W1$ removes galaxies at $z<{\sim}\,0.4$.

The selection cuts for the Main LRG sample in the South:

$\displaystyle z_{\mathrm{fiber}}<21.60$ (3.1a) $\displaystyle
z-W1>0.8\times(r-z)-0.6$ (3.1b) $\displaystyle(g-W1>2.9)\ \mathrm{OR}\
(r-W1>1.8)$ (3.1c) $\displaystyle\begin{split}&((r-W1>1.8\times(W1-17.14))\
\mathrm{AND}\\\ &(r-W1>W1-16.33))\ \mathrm{OR}\ (r-W1>3.3)\end{split}$ (3.1d)

and in the North:

$\displaystyle z_{\mathrm{fiber}}<21.61$ (3.2a) $\displaystyle
z-W1>0.8\times(r-z)-0.6$ (3.2b) $\displaystyle(g-W1>2.97)\ \mathrm{OR}\
(r-W1>1.8)$ (3.2c) $\displaystyle\begin{split}&((r-W1>1.83\times(W1-17.13))\
\mathrm{AND}\\\ &(r-W1>W1-16.31))\ \mathrm{OR}\ (r-W1>3.4)\end{split}$ (3.2d)

where $g$, $r$, $z$, $W1$ are extinction-corrected magnitudes and
$z_{\mathrm{fiber}}$ is the $z$-band fiber-magnitude that corresponds to the
flux within an aperture of diameter 1.5 arcsec (the size of the DESI fiber).

After applying the veto masks (see section 3.3), only 0.3% of the photometric
LRGs are stars. Stars are uncorrelated with extragalactic datasets and are
therefore expected to give a negligible contribution to the cross-correlations
(see for example section 7.1 of [24] for a detailed discussion of this). Such
a low stellar contamination fraction is also expected to give a negligible
contribution to the galaxy auto-correlation, except possibly on the very
largest scales. Since we’ll mostly be working on scales that are not expected
to be affected by this, we leave a full analysis of the effect of stellar
contamination to future work.

We obtain the redshift distribution and comoving density of the Main LRG
sample using the 2.3 million spectroscopic redshifts from the DESI Y1 data,
and they are shown in figures 2 and 3. The sample can be used as a single
sample as just described, or in conjunction with the photometric redshifts
provided. For tomographic analyses, we provide four subsamples selected with
photometric redshifts, but whose redshift distributions have been measured
with DESI spectroscopic redshifts. Their redshift distributions are thus known
with very high precision and hence these are particularly well-suited to
cross-correlation analyses. The tomographic subsamples are described in
section 3.4.

###  3.2 Extended LRG sample

In addition to the DESI LRG sample, we created an “Extended LRG sample” with
higher densities, useful for measurements that are limited by shot noise.
While DESI will not observe the majority of the Extended LRGs, it has already
obtained spectra for a large number of Extended LRGs from DESI SV1 which are
sufficient for characterizing their redshift distributions.

The requirement of available spectra constrains the selection of the Extended
LRG sample to within the DESI SV1 LRG selection. As described in appendix A of
[10], the SV1 LRGs are selected with two sets of selection cuts, the “optical”
selection and the “IR” selection (with a lower-density version of the SV1 IR
selection ultimately being adopted as the Main LRG selection). The Extended
LRG sample is a subset of the SV1 IR sample, with small offsets in the
selection cuts compared to the SV1 IR selection to account for the differences
in photometry between North and South. We use the same stellar-rejection cut
as in the Main LRG selection (instead of the more relaxed version used in SV1
selections). And we only use fiber-magnitude for the faint limit (instead of
also using the total magnitude in SV1 selections). The selection cuts for the
Extended LRG sample in the South are:

$\displaystyle z_{\mathrm{fiber}}<21.96$ (3.3a) $\displaystyle
z-W1>0.8\times(r-z)-0.6$ (3.3b) $\displaystyle r-W1>1.0$ (3.3c)
$\displaystyle(r-W1>1.8\times(W1-17.48))\ \mathrm{OR}\ (r-W1>3.1)$ (3.3d)

and in the North:

$\displaystyle z_{\mathrm{fiber}}<22.0$ (3.4a) $\displaystyle
z-W1>0.8\times(r-z)-0.6$ (3.4b) $\displaystyle r-W1>1.03$ (3.4c)
$\displaystyle(r-W1>1.8\times(W1-17.44))\ \mathrm{OR}\ (r-W1>3.2)$ (3.4d)

The SV1 data includes 34 DESI dark-time tiles covering roughly 230 deg2 (130
deg2 in the South and 100 deg2 in the North), with roughly 6% fiber-assignment
completeness. We use 22k spectroscopic redshifts of the Extended LRGs from the
DESI SV1 data to obtain their redshift distribution and comoving density, and
they are shown in figures 2 and 3. The $N(z)$ is noisier than that of the Main
LRGs due to the smaller area and smaller number of spectroscopic redshifts
available.

###  3.3 Masks and imaging quality cuts

The DESI LRG selection already implements some minimum masking using mask bits
in DR9111https://www.legacysurvey.org/dr9/bitmasks/#maskbits: the BRIGHT,
GALAXY and CLUSTER masks. A significant fraction of contaminants, mostly stars
(especially at lower galactic latitudes), remain after the minimum masking.
Therefore, in addition to these minimal target masks, we recommend applying
the “veto” masks described in [10] (see section 2.4 of that reference) that
remove additional contaminated areas around bright stars as well as areas
affected by imaging artifacts and unrelated astrophysical foregrounds (large
galaxies, planetary nebulae, etc.).

Optionally, one could apply the additional imaging quality cuts that were used
in [1]: 1) Require two or more exposures in the $g$, $r$ and $z$ bands. 2)
Require $E(B-V)<0.15$ (using the $E(B-V)$ map from [25]). 3) Apply a cut on
stellar density: using the stellar density map provide by [26] (which is based
on Gaia stars with $12\leq G<17$) and degraded to a HEALPix resolution of
nside=64, and requiring the stellar density in each pixel to be less than 2500
per deg2.

For the requirement of $2+$ exposures, instead of using the “NOBS” values in
the DR9 tractor catalogs, we use the “PIXEL_NOBS” values extracted from brick-
level images (which are also used for randoms). This is because the tractor
‘NOBS” values do not exactly match the “NOBS” values in the
randoms222https://www.legacysurvey.org/dr9/issues/#nobs-differs-between-the-
tractor-catalogs-and-random-catalogs, whereas the “PIXEL_NOBS” values exactly
match the survey geometry of the randoms.

###  3.4 Tomographic bins

Bin | North selection | South selection | $\bar{n}_{\theta}$ | $\bar{z}$ | $\Delta z$ | $f_{\mathrm{star}}$ | $f_{\mathrm{fail}}$
---|---|---|---|---|---|---|---
1 | $0.400\leq z_{\mathrm{phot}}<0.545$ | $0.400\leq z_{\mathrm{phot}}<0.540$ | 81.9 | 0.470 | 0.063 | 0.2% | 0.3%
2 | $0.545\leq z_{\mathrm{phot}}<0.719$ | $0.540\leq z_{\mathrm{phot}}<0.713$ | 148.1 | 0.628 | 0.074 | 0.1% | 0.7%
3 | $0.719\leq z_{\mathrm{phot}}<0.851$ | $0.713\leq z_{\mathrm{phot}}<0.860$ | 162.4 | 0.791 | 0.078 | 0.2% | 1.0%
4 | $0.851\leq z_{\mathrm{phot}}<1.024$ | $0.860\leq z_{\mathrm{phot}}<1.020$ | 148.3 | 0.924 | 0.096 | 0.4% | 1.3%
Table 2: Key facts about the Main LRG subsamples. Here $z_{\mathrm{phot}}$ is
the Z_PHOT_MEDIAN value from the photo-$z$ catalog, $\bar{n}_{\theta}$ is the
surface density in deg-2, $\bar{z}$ is the mean redshift, $\Delta z$ is the
standard deviation in $z$, $f_{\mathrm{star}}$ is the star fraction and
$f_{\mathrm{fail}}$ is the redshift failure rate. The values of $\bar{z}$,
$\Delta z$, $f_{\mathrm{star}}$ and $f_{\mathrm{fail}}$ are derived from the
DESI Y1 data.

For some applications, e.g. the cross-correlation with CMB lensing, it is more
useful to have subsamples of galaxies in tomographic bins with well-
characterized redshift distributions, rather than individual galaxies with
photometric redshifts. Here we divide each LRG sample into 4 bins using
photometric redshifts, specifically, using the Z_PHOT_MEDIAN value from the
photo-$z$ catalog. The photo-$z$ cuts and summary statistics of each subsample
are listed in tables 2 and 3. We excluded objects at the tails of the
$z_{\mathrm{phot}}$ distribution from the subsamples to achieve more compact
redshift distributions for subsamples 1 and 4. We measure the redshift
distributions of the subsamples using spectroscopic redshifts from DESI. For
tomographic analyses, the spectroscopic $N(z)$ should be preferred over the
use of individual photometric redshifts. Density maps of the Main and Extended
LRG subsamples are shown in figures 4 and 5.

Bin | North selection | South selection | $\bar{n}_{\theta}$ | $\bar{z}$ | $\Delta z$ | $f_{\mathrm{star}}$ | $f_{\mathrm{fail}}$
---|---|---|---|---|---|---|---
1 | $0.400\leq z_{\mathrm{phot}}<0.545$ | $0.400\leq z_{\mathrm{phot}}<0.540$ | 185.5 | 0.467 | 0.065 | 0.3% | 0.1%
2 | $0.545\leq z_{\mathrm{phot}}<0.719$ | $0.540\leq z_{\mathrm{phot}}<0.713$ | 311.0 | 0.633 | 0.077 | 0.2% | 0.3%
3 | $0.719\leq z_{\mathrm{phot}}<0.854$ | $0.713\leq z_{\mathrm{phot}}<0.860$ | 422.6 | 0.794 | 0.086 | 0.2% | 0.7%
4 | $0.854\leq z_{\mathrm{phot}}<1.010$ | $0.860\leq z_{\mathrm{phot}}<1.000$ | 438.4 | 0.929 | 0.102 | 0.4% | 0.9%
Table 3: As table 2 but for the extended LRG subsamples. The values of
$\bar{z}$, $\Delta z$, $f_{\mathrm{star}}$ and $f_{\mathrm{fail}}$ are derived
from the DESI SV1 data.

Figure 4: Density maps of the Main LRG subsamples (after applying the veto
masks and requiring 2+ observations in $grz$ bands) with HEALPix NSIDE=128.
Note that additional cuts on the footprint described in section 3.3 (that
remove areas with high Galactic extinction and high stellar density) are not
applied here, nor are the imaging weights in section 4 applied.

Figure 5: As figure 4, but for the Extended LRG subsamples.

##  4 Imaging and foreground systematics

Here we study the impact of imaging and foreground systematics, such as
variations in depth, seeing and Galactic extinction $E(B-V)$, on the density
and redshift distribution of the binned LRG subsamples.

Figures 6 and 7 show the density trends with imaging/foreground systematics
for the 4th redshift bin of the Main and Extended samples, respectively. The
4th redshift bin is shown here because it is the faintest subsample and has
some of the largest density trends. To mitigate the imaging systematics, we
provide weights based on linear regression fits of the systematics properties
as described in section 3.1 of [10]. The imaging weights are based on the
assumption that the variations in the galaxy number densities due to imaging
variations are effectively the result of random downsampling of the galaxy
sample, and the multiplicative weights correct for the downsampling factor.
The systematics properties used in the linear regression are seeing and depth
in three optical bands and $E(B-V)$. The “galaxy depth” values in the LS DR9
catalogs do not account for Galactic extinction which effectively reduces the
imaging depth for extragalactic sources, and to account for this effect we add
an $E(B-V)$ term to the depth value. While the WISE $W1$ magnitude is used in
the LRG selection, we do not include the $W1$ depth as an input for the linear
regression because 1) we do not see a significant density trend with $W1$
depth and 2) there is a discrepancy in the value of the $W1$ depth between the
tractor catalog and the randoms that prevent us from using the randoms to
assign weights.

The density trends after applying the linear regression weights are shown as
the dashed lines in figures 6 and 7. Figure 8 shows the weights maps (i.e.,
the average weight of objects within each pixel) for the Main LRGs. Some
prominent features in the weight maps include variations in Galactic
extinction $E(B-V)$, e.g., in the North Polar Spur (at $\mathrm{RA}\sim
150^{\circ},\mathrm{Dec}\sim 70^{\circ}$), and depth and seeing variations,
e.g., the exposure tiling patterns and the overall offsets in the deeper DES
region and across the North/South boundary.

It is known that the $E(B-V)$ map from [25] is correlated with large-scale
structures due to contamination from the cosmic infrared background (e.g., see
[27]), and the inclusion of $E(B-V)$ in the linear regression variables might
remove actual LSS clustering signal. Therefore we also provide a separate set
of weights that do not use $E(B-V)$ in the linear regression fits. We show the
weight maps without $E(B-V)$ in figure 9. For the angular power spectrum and
correlation function calculations in section 6, we use the weights that use
$E(B-V)$. For the Main LRGs, the changes in $C_{\ell}$ from using the
$E(B-V)$-free weights are mainly at large angular scales, and they are
relatively small (only reaching 1% for the lowest-redshift subsample, and only
in the lowest $\ell$ bin). The lowest-redshift subsample is most sensitive to
$E(B-V)$ because it is most affected by the $g-W1$ and $r-W1$ cuts, which are
sensitive to $E(B-V)$, in the Main LRG selection that removes $z<0.4$
galaxies.

Figure 6: Density trends with imaging/foreground systematics properties for
the 4th redshift bin of the Main sample (based on HEALPix maps with
NSIDE=256). The solid lines are
$N_{\mathrm{gal}}/\overline{N}_{\mathrm{gal}}-1$, where $N_{\mathrm{gal}}$ is
the average density within each bin in the systematics property, and
$\overline{N}_{\mathrm{gal}}$ is the average number density over the full
final footprint. The dashed lines are after applying the linear weights. The
histograms show the normalized number of HEALPix pixels in each systematics
bin for each region. The $E(B-V)$ term in the depth values is added to account
for Galactic extinction. Note that while the trends with Gaia stellar density
and $W1$ depth are shown here, they are not used as inputs for the weights
(see section 4).

Figure 7: As figure 6 but for the same (4th) redshift bin of the Extended
sample.

Figure 8: Maps of the imaging systematics weights for the Main LRG subsamples
that include $E(B-V)$ in the linear regression variables, shown in HEALPix
resolution of NSIDE=128.

Figure 9: As figure 8 but without $E(B-V)$ as input for the imaging
systematics weights.

Figure 10: Maps of the mean spectroscopic redshift for the Main LRG subsamples
with HEALPix NSIDE=16, based on redshifts from the DESI Y1 data.

Figure 11: Similar to figure 10 but showing the width of the redshift bin,
i.e., the normalized median absolute deviation of the spectroscopic redshifts
in each HEALPix pixel (with NSIDE=16) for the Main LRG subsamples.

Besides the variation in surface density, imaging systematics could also cause
spatial variations in the redshift distribution. The DESI Y1 data allows us to
directly assess such variations in the Main LRG subsamples. We show maps of
the mean spectroscopic redshift in each HEALPix pixel (with NSIDE=16) for each
subsamples using Y1 data in figure 10, and maps of the “width” (measured by
the normalized median absolute deviation) of the redshift bins in figure 11.
Both sets of maps are almost entirely dominated by noise. To interpret the
results, we compare the DESI LRG subsamples with 25 sets of Abacus mock LRG
catalogs [28] (also see [29]) based on the AbacusSummit simulation [30, 31]
with the same footprint as the Y1 data. The mock LRG subsamples are created by
randomly sub-sampling the mock catalogs to reproduce the redshift
distributions of the DESI LRG subsamples. We find that the DESI LRG subsamples
have $1\%-14\%$ larger RMS in the per-pixel mean redshift than the mock
realization with the largest RMS. For the RMS scatter in the per-pixel
redshift bin width, they agree within $4\%$. The larger per-pixel mean
redshift scatter in the LRG subsamples may be partly due to a mismatch between
the mocks and the LRGs (e.g., it is known that the mocks have $\sim 5\%$ lower
bias than the LRG sample; see [29]), or it may be be an indication of the
effects of imaging systematics on the redshift distributions (e.g., the
redshift distribution for some of the redshift bins are visibly different in
each imaging regions in figures 2 and 12).

As is apparent in figures 6-9, the three imaging regions –– BASS+MzLS in the
North and DECaLS and DES in the South –– have very different depth and seeing,
and these differences have a noticeable impact on the LRG densities. The
Northern imaging, which is based on imaging from the Bok and Mayall
telescopes, has similar data quality compared to DECaLS in the $z$ band, but
the $g$ and $r$ bands are 0.4 mag shallower and have significantly worse
seeing. The LRG selection cuts and the photo-$z$ cuts in the North are
adjusted to account for the instrument and depth differences, but it is not
possible to completely homogenize the galaxy samples across the North/South
boundary. The DES region is deeper than DECaLS, on average by 0.5 mag in $g$
and $z$ bands and 0.85 mag in $r$ band. The deeper DES imaging results in
slightly different sample properties (e.g., surface density), especially for
the two highest-redshift bins in which the LRGs are fainter and more sensitive
to depth variations. Table 4 lists the average surface density, mean redshift
and scatter separately in each of the three regions, and figure 12 shows the
redshift distributions of the Main LRG samples in the DECaLS and DES regions
separately.

We note that due to the differences in depth and seeing, the physical
properties (such as mass distribution, bias etc) of the samples in the
different regions are slightly different: we believe this is because shallower
regions will have more scatter of fainter/lower mass galaxies into the
selection boundary. While variations in number density can be corrected with
the systematic weights as described in this section, changes in physical
properties cannot. Depending on the application and on the required accuracy,
one may want to treat the galaxies in the DES region as a different sample and
fit bias parameters independently. For some applications, measuring the
correct mean bias is sufficient and the split is not necessary. A full study
of the differences is beyond the scope of this paper, but at fixed cosmology
and using the same scale cuts as [1], the best-fit linear bias parameters in
the DES region compared to the rest can differ by up to333We find strong
evidence for a difference in clustering power for bin 4, and mild evidence for
bins 2 and 3, while bin 1 is consistent with having the same clustering within
the measurement error. $\sim$ 0.7, 2, 3, 5% in the four photometric bins. At
the same time, table 4 and figure 12 show that there some differences in
$\bar{z}$, which are at the 0.001 level for the first two bins, but are $\sim
0.003$ and $\sim 0.007$ for bins 3 and 4 respectively. Depending on the
analysis being performed, this difference can have non-negligible impact on
the clustering (especially when considering the full redshift distribution on
the two footprints, rather than just $\bar{z}$) and may need to be taken into
account. In summary, the highest redshift bins show statistically significant
differences in the value of the bias and $\bar{z}$ and therefore the sample in
the DES region and in other regions should be considered as different samples
with different redshift distributions and independent bias parameters and shot
noise for many applications. Clustering differences between BASS+MzLS in the
North and DECaLS in the South appear negligible444however we have not
performed full cosmological fits. Nonetheless, they are much smaller than the
difference between the DES footprint and the remaining area., so depending on
the application and the accuracy required, they may be treated as a single
sample.

Bin |  | $\bar{n}_{\theta}$ |  |  | $\bar{z}$ |  |  | $\Delta z$ |  |
---|---|---|---|---|---|---|---|---|---|---
| North | DECaLS | DES | North | DECaLS | DES | North | DECaLS | DES |
1 | 83.3 | 80.9 | 82.4 | 0.470 | 0.470 | 0.469 | 0.064 | 0.063 | 0.064 |
2 | 149.3 | 147.5 | 147.9 | 0.630 | 0.627 | 0.626 | 0.075 | 0.073 | 0.072 |
3 | 163.7 | 164.7 | 157.4 | 0.791 | 0.791 | 0.794 | 0.079 | 0.078 | 0.077 |
4 | 150.2 | 151.0 | 142.3 | 0.922 | 0.925 | 0.932 | 0.099 | 0.094 | 0.092 |
Table 4: Main LRG statistics similar to table 2 but separately listing the
values for the three imaging regions: North (BASS+MzLS), DECaLS and DES.

Figure 12: As the left panel of figure 2 but showing the Main LRG redshift
distributions for the DECaLS and DES regions separately. They are based on
1.67 million and 0.204 million DESI redshifts in the DECaLS and DES regions,
respectively.

##  5 Number count slope and magnification bias

In addition to the “intrinsic” clustering of galaxies that arises from their
tracing of the cosmic web, the observed galaxy number count is also modulated
by a lensing magnification term, which correlates the observed number count
with matter along the line of sight. Knowing the size of the magnification
bias, parameterized by the “number count slope” defined below, is necessary
for interpreting both the galaxy auto-correlation and its cross-correlation
with other tracers (see for example [24] for its importance in recent
analyses). For the purpose of estimating magnification bias, we measure the
response of the number density of galaxies in each redshift bin to lensing
magnification. This response is quantified as the in logarithmic change in the
galaxy number count for a small change in magnitude (in all bands) due to
magnification,

$s\equiv d\log_{10}N/dm.$ (5.1)

For a magnitude-limited sample, $s$ is simply the “slope” of the (logarithmic)
number count as a function of the limiting magnitude. While our selection is
not a magnitude-limited selection, we nonetheless adopt the term “number count
slope” for $s$. We determine the value of $s$ using finite differences, by
shifting all magnitudes by a small amount, $\delta m=\pm 0.01$, and re-
applying the selection. However, there are two subtleties specific to our LRG
samples that prevent us from simply using Equation 5.1 for computing $s$.

First, the LRG selections include fiber-magnitude cuts such as Eq. 3.3a, which
is effectively a cut on surface brightness. If a galaxy is magnified, the
observed (total) magnitude changes by $\delta m$, but the fiber-magnitude does
not change by the same amount. This is because, for an extended object (i.e.,
a resolved galaxy), the fiber-flux fraction (the fraction of flux within the
fiber diameter) decreases as the size of the galaxy increases. Therefore, to
properly model the response of the number density of galaxies to lensing
magnification, one needs to know how the fiber-flux (or, equivalently, the
fiber-flux fraction) of each galaxy changes when it is magnified or
demagnified. We measure the fiber-flux fraction as a function of the shape
parameters for each morphology type, compute the fractional (fiber-)flux
change when the half-light radius is changed by a small amount, and use it to
compute $\delta m_{\mathrm{fiber}}$ for a given magnification-induced $\delta
m$. See appendix C for details of how $\delta m_{\mathrm{fiber}}$ is computed.

The other subtlety is that the redshift binning is done using photo-$z$’s.
Galaxy colors do not change with magnification, but the random forest-based
photo-$z$’s use magnitudes and galaxy sizes as features, which do respond to
magnification. To account for the change in photo-$z$’s, we recompute the
photo-$z$’s with the shifted magnitudes and sizes. To reduce random noise from
the random forest realizations, we use the same random seed for computing the
magnified and unmagnified photo-$z$’s.

Now that we have the $\delta m_{\mathrm{fiber}}$ value and the “shifted”
photo-$z$’s for each galaxy for magnitude shifts of $\delta m=\pm 0.01$, we
reapply the LRG selection and the photo-$z$ binning. The resulting value of
the number count slope $s$ from finite difference for each subsample is listed
in tables 5 and 6 for the Main and Extended samples, respectively. We list the
values for the North+South combined sample, and for North and South
separately. (We do not list the values for DECaLS and DES separately because
their differences are small and well within the statistical uncertainties.) To
demonstrate the effects of the fiber-flux cut and photo-$z$ binning, we also
list $s$ values if we let the fiber-magnitude change by the same amount as the
total magnitude, or if we use the “unshifted” photo-$z$’s for the photo-$z$
re-binning. The slope would be overestimated by ${\sim}\,13\%$ for the
unbinned Main LRG sample if the fiber-flux effects are not accounted for, or
${\sim}\,30\%$ for the highest redshift bin (which is also the faintest bin
and most subject to the fiber-flux cut). Shifts in the photo-$z$’s also have a
similarly significant effect on $s$. The actual impact from the magnification
term is even larger than these fractional changes in $s$ since the magnitude
kernel scales with $s-0.4$ (e.g., see equation 3.11 of [32]).

Bin | North | South | Combined | $dm_{\mathrm{fiber}}=dm$ | Same photo-$z$
---|---|---|---|---|---
all | $1.021\pm 0.012$ | $1.001\pm 0.008$ | $\boldsymbol{1.008\pm 0.007}$ | $1.136\pm 0.007$ | $1.008\pm 0.007$
1 | $1.002\pm 0.033$ | $0.958\pm 0.022$ | $\boldsymbol{0.972\pm 0.018}$ | $0.979\pm 0.018$ | $0.997\pm 0.018$
2 | $1.055\pm 0.025$ | $1.039\pm 0.017$ | $\boldsymbol{1.044\pm 0.014}$ | $1.073\pm 0.014$ | $1.007\pm 0.014$
3 | $0.964\pm 0.024$ | $0.978\pm 0.016$ | $\boldsymbol{0.974\pm 0.013}$ | $1.089\pm 0.013$ | $0.862\pm 0.013$
4 | $1.015\pm 0.025$ | $0.976\pm 0.016$ | $\boldsymbol{0.988\pm 0.014}$ | $1.284\pm 0.014$ | $1.148\pm 0.014$
Table 5:  The magnification “number count slope” value $s$ for the Main LRG sample, and its Poisson error from the finite difference calculation with $\delta m=\pm 0.01$. The “all” row is for the full DESI LRG sample (including objects that are not in any of the redshift bins). The “North”, “South” and “Combined” columns are our best estimates that correct for the impact of fiber-flux and photo-$z$’s. To show how large these effects are, the last two columns list the incorrect estimates (for north and south combined) that do not correct for either of these effects; these values are for illustration only and should not be used. We recommend using the values in the “Combined” column (in boldface) for the North+South combined sample. | North | South | Combined | $dm_{\mathrm{fiber}}=dm$ | Same photo-$z$
---|---|---|---|---|---
all | $0.752\pm 0.007$ | $0.748\pm 0.005$ | $\boldsymbol{0.750\pm 0.004}$ | $0.846\pm 0.004$ | $0.750\pm 0.004$
1 | $0.805\pm 0.022$ | $0.776\pm 0.015$ | $\boldsymbol{0.785\pm 0.012}$ | $0.787\pm 0.012$ | $0.839\pm 0.012$
2 | $0.862\pm 0.017$ | $0.832\pm 0.011$ | $\boldsymbol{0.841\pm 0.009}$ | $0.863\pm 0.009$ | $0.790\pm 0.009$
3 | $0.655\pm 0.014$ | $0.677\pm 0.010$ | $\boldsymbol{0.670\pm 0.008}$ | $0.750\pm 0.008$ | $0.556\pm 0.008$
4 | $0.681\pm 0.014$ | $0.683\pm 0.010$ | $\boldsymbol{0.682\pm 0.008}$ | $0.868\pm 0.008$ | $0.812\pm 0.008$
Table 6:  As table 5, but for the Extended LRG sample.

##  6 Angular clustering and sample characterization

The angular power spectra and angular correlation functions for our samples
are shown in figures 13 and 14. In all cases we detect the clustering at very
high significance. In the angular power spectra (figure 13) we see that the
Main sample has slightly higher large-scale bias than the Extended sample (the
low $\ell$ blue points are slightly above the red ones) and significantly
higher shot-noise (the blue points at high $\ell$ are well above the red
points). This is expected as the Extended sample tends to be less luminous
overall and has a higher number density. Assuming a Planck cosmology [33, 34]
the large-scale bias of the Main sample ranges from 1.8-2.3 with increasing
redshift. The bias of the Extended sample is approximately 10% lower. The
angular correlation functions (figure 14) tell a similar story, though the
difference in shot noise is not evident in $w(\theta)$.

While we have not attempted to fit a halo occupancy distribution (HOD) to
these specific samples in this paper, for the Main LRGs as a whole, fits to
the small-scale correlation function [35] find a satellite fraction of $11\pm
1\%$ and a mean halo mass of $\log_{10}M_{h}=13.40\pm 0.02$ at $0.4<z<0.6$
(roughly applicable to the lowest redshift bin) and a satellite fraction of
$14\pm 1\%$ and $\log_{10}M_{h}=13.24\pm 0.02$ at $0.6<z<0.8$ (roughly
applicable to the higher redshift bins).

The combination of high and relatively constant number density with redshift
in well-defined, spectroscopically calibrated redshift bins (figure 3) and
high bias (figure 13) makes these samples ideally suited for cross-correlation
science. An earlier version of the Main LRG tomographic sample [1] was used in
cross-correlation with CMB lensing measured by Planck [36] to make a high-SNR
measurement of $\sigma_{8}$ as a function of redshift (tomography) in the four
redshift bins described here. Combining all redshift bins together, [1] found
a value of $S_{8}=\sigma_{8}\sqrt{\Omega_{m}/0.3}=0.73\pm 0.03$, or a $\approx
4\%$ measurement of the matter fluctuations at low redshift.

Moving forward, the rapid increase in CMB lensing map noise will allow for a
considerable improvement in constraints compared to current analyses using
Planck CMB lensing. Assuming 13,000 sq deg of overlap between the CMB maps
from Chile-based CMB experiments and the LRG, we expect the cross-correlation
constraints of [1] to improve by a factor $\approx$ 1.4, 2 and 2.5 with ACT,
Simons Observatory and CMB-S4 [37] respectively555when used in combination
with Planck CMB lensing maps and assuming $\ell_{\rm max}=400$ throughout.
Larger improvements are expected with improved modeling if $\ell_{\rm max}$
can be increased, and when combining with the CMB lensing auto power
spectrum., leading to percent-level constraints on the amplitude of
fluctuations at low redshift and shedding light on dark energy [38] and
neutrino masses [39], testing our understanding of gravity and weighing in on
the “low $S_{8}$” discrepancy [40].

Similarly, these samples will allow for much improved constraints on the gas
properties of the halos hosting the LRG galaxies through the thermal and
kinematic Sunyaev-Zel’dovich effects (tSZ and kSZ respectively). Using the
assumptions and techniques outlined in [41], we forecast that for the tSZ
effect, which measures the integrated thermal pressure in the host halos, we
will achieve a combined SNR $\approx 50$, 85 and 140 with ACT, Simons
Observatory and CMB-S4 respectively (although care will need to be exercised
to distinguish the tSZ signal from the dust emission associated with the halos
themselves). This is thanks to the large number density of the LRG samples,
which will also allow for the study of the redshift dependence of the signal,
together with improvements in the depth of CMB temperature maps. Moreover, the
gas density around the LRG host halos, measured through kSZ, can be detected
with SNR $\approx 35$, 60 and 100 in cross-correlation with ACT, Simons
Observatory and CMB-S4 respectively when DESI spectroscopy is available on the
overlap region (here assumed to be $\approx$ 9,000 sq deg between Chile-based
CMB experiments and DESI spectroscopy). The combination of kSZ, tSZ and
lensing will reveal the full thermodynamic properties of the halo to
unprecedented precision and help us directly calibrate the baryon effects on
the matter distribution, one of the main systematic uncertainties in weak
lensing.

Furthermore, the spectroscopically calibrated samples described here will
provide an interesting alternative to the photometric clustering samples used
in many combined galaxy weak lensing and clustering analyses, e.g. [42]. The
samples defined here have full overlap with the DES footprint, and cross-
correlations with the third and fourth redshift bins of the DES
Metacalibration sample [43] yield a SNR of $\approx 50$ to $\ell=600$ [44].
The overlap with the Rubin Observatory LSST Wide-Fast-Deep (WFD) survey will
be approximately 10,000 sq deg, and 14,000 sq deg with Euclid, and so we
expect this sample will continue to be useful for galaxy lensing cross-
correlations for the foreseeable future.

Figure 13: Angular power spectra of the Main LRG subsamples and the Extended
LRG subsamples. The large-scale clustering of the Extended samples is only
slightly lower than that of the Main sample (due to the lower bias, see text),
but the small-scale power is much reduced due to the large reduction in shot
noise.

Figure 14: Angular correlation functions of the Main LRG subsamples and the
Extended LRG subsamples. For all samples the small-scale clustering of the
Main sample exceeds that of the Extended sample, though the large-scale
clustering of the Extended samples is only slightly lower than that of the
Main sample (due to the lower bias, see text).

##  7 Data products

The data and catalogs are publicly available at
https://data.desi.lbl.gov/public/papers/c3/lrg_xcorr_2023/, where README files
explain the data format. The data products include:

  * •

Main and Extended LRG catalogs that include the tomographic bin indices, veto
masks, imaging systematics weights, and photo-$z$’s.

  * •

Overdensity maps and masks of the Main and Extended LRG subsamples at
NSIDE=2048 resolution.

  * •

Lower resolution (NSIDE=256) maps of density and imaging systematics
properties described in section 4.

  * •

Coefficients for the linear regression imaging systematics weights for each
tomographic bin.

  * •

LRG veto mask values for the randoms (row-by-row matched to the already
released randoms
catalogs666https://data.desi.lbl.gov/public/edr/target/catalogs/dr9/0.49.0/randoms/resolve/).

  * •

Redshift distributions in figures 2 and 12.

  * •

Angular clustering measurements in figures 13 and 14.

We also make public the new set of photo-$z$’s (which are used in this work)
for all DR9 objects; they are available from the Legacy Surveys website:
https://www.legacysurvey.org/dr9/files/#photo-z-sweeps-9-1-photo-z-sweep-
brickmin-brickmax-pz-fits.

Data points in the figures are also available at
https://zenodo.org/record/8319955.

##  8 Conclusions

We presented two photometric LRG samples in tomographic bins with well-
characterized redshift distributions from spectroscopy. The first sample is
identical to the DESI LRGs, and the second sample has more extended selection
cuts that yield 2-3 times the DESI LRG density. The photometric redshifts used
for the tomographic binning are trained using DESI redshifts in addition to
redshifts from other surveys, and the photo-$z$’s for all objects in LS DR9
(which includes but are not limited to the LRG samples) are publicly
available. Unlike typical photometric galaxy samples that have large
uncertainties in their redshift distributions, the LRG samples have the unique
advantage of having DESI spectroscopic redshifts with high completeness over
large areas that make $N(z)$ uncertainties negligible, and spectroscopy also
confirms the very low ($0.3\%$) stellar contamination rate.

We examined the trends in the surface density with imaging/foreground
systematics, and we find that while significant trends exist, they can mostly
be removed with simple weighting based on linear regression. However we find
that due to the different depths and seeing between the DES region and the
remaining area, the samples in these two regions may have slightly different
physical properties (such as bias, mass distribution and redshift
distribution), as discussed in section 4, especially for the highest redshift
bins. Depending on the analysis being performed, the galaxies in the two
footprints may need to be treated as separate samples with different bias
parameters, shot noise and redshift distribution (or at least consistency of
the results obtained with the different samples should be checked).

For lensing and clustering analyses it is important to account for
magnification bias, and for this purpose we compute the effective “number
count slope” that properly accounts for the effects of the surface brightness
cut in the selection and the photo-$z$ binning.

The sample covers a large fraction of the extragalactic sky and thus is ideal
for cross-correlation with other data sets. It overlaps with the entirety of
the existing weak lensing surveys DES and HSC [45], and has 13,000 sq deg of
overlap with the ACT CMB survey, 10,000 sq deg with the planned Rubin
Observatory LSST WFD survey, and 14,000 sq deg with Euclid, thus enabling
transformative joint-survey science.

## Acknowledgments

We would like to thank Alex Krolewski and Ashley Ross for helpful discussions
during the preparation of this manuscript. R.Z. and S.F. are supported by the
Director, Office of Science, Office of High Energy Physics of the U.S.
Department of Energy under Contract No. DE-AC02-05CH11231. M.W. is supported
by the DOE and the NSF. N.S. is supported by the Office of Science Graduate
Student Research (SCGSR) program administered by the Oak Ridge Institute for
Science and Education for the DOE under contract number DE-SC0014664. This
research has made use of NASA’s Astrophysics Data System and the arXiv
preprint server.

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

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

Any opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views
of the U. S. National Science Foundation, the U. S. Department of Energy, or
any of the listed funding agencies.

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

##  Appendix A Comparison with the LRG sample in Ref. [1]

An earlier version of the Main LRG sample was used in the companion paper [1].
It has a few notable differences compared to the updated sample presented in
this work: 1) Ref. [1] used an older version of photo-$z$’s for tomographic
binning. 2) Ref. [1] used a smaller subset of the early DESI data for
estimating the redshift distributions. 3) At $\mathrm{Dec}<-29.25^{\circ}$,
the updated samples are based on photometry with corrected zero point offsets.
4) When requiring 2+ exposures in the $grz$ bands, we switched from the
tractor-based NOBS value to the pixel-based PIXEL_NOBS value; this results in
0.5% fewer objects compared to the sample in [1]. 5) The imaging systematics
weights in [1] included WISE $W1$ depth as an input, but we have since learned
that there is a discrepancy in the WISE $W1$ depth value between the LRGs and
the randoms which could bias the weight values; for this reason we dropped W1
depth from the inputs for the imaging weights in this work. Moreover, the
differences between the DES region and other regions were not understood in
[1], and the entire footprint was treated as a single galaxy sample per
redshift bin in the analysis.

Figure 15 compares the angular power spectrum of the Main LRG subsamples with
the older LRG subsamples in [1]. The two samples mostly agree within $2\%$,
although on average the new sample has higher $C_{\ell}$. The slightly higher
$C_{\ell}$ is presumably due to the narrower redshift bins of the updated
sample (mainly due to the inclusion of quasars in the photo-$z$ training that
reduced their photo-$z$ errors) and the zero point correction at
$\mathrm{Dec}<-29.25^{\circ}$. The shifts are nearly 1-sigma and a reanalysis
using updated CMB lensing maps and newer models is in progress. We will
present the results in a future publication.

Figure 15: Top panel: comparison of the angular power spectrum between the
Main LRG subsamples in this paper (filled circles) and the older LRG
subsamples used in [1] (crosses). Bottom panel: the $C_{\ell}$ ratio between
the two samples.

##  Appendix B Photometric redshifts

Data from the following surveys were used for photo-$z$ training in [23] and
is reused for the new photo-$z$’s presented here: 2dFLenS [46], AGES [47],
COSMOS2015 photo-$z$’s [48], DEEP2 [49] and DEEP3 [50], GAMA[51], OzDES [52]
(updated to DR2), SDSS Main Galaxy Sample [53] and LRG sample [54], BOSS [55,
56] (updated to SDSS DR16 [57]), VIPERS [58], VVDS [59] and WiggleZ [60].
Quality cuts on these datasets are described in [23].

A major update in the new photo-$z$’s is the inclusion of a large number of
additional spectroscopic redshifts for photo-$z$ training, some of which only
became available recently: C3R2 DR2 [61]; eBOSS LRG [62] and ELG [63]
redshifts from the eBOSS LSS catalogs (instead of the SDSS specObj catalog
which is based on a different redshifting algorithm); SDSS DR16 quasar catalog
[64]; and DESI Survey Validation (SV1) and 1% Survey (SV3). The DESI data used
for photo-$z$ training includes BGS [65], LRG [10] and QSO [66] redshifts from
SV1 and SV3 and ELG [67] redshifts from SV1. We also include redshifts from a
special (secondary) DESI program in COSMOS that observed a magnitude-limited
sample of galaxies with the same $z$-band fiber-magnitude limit as the DESI
LRGs and another magnitude-limited sample of $z>0.7$ galaxies that extends 0.8
magnitudes fainter; this program and the associated data will be described in
future work. Except for this DESI special program, all the DESI spectroscopic
redshifts used in the photo-$z$ training are publicly available in the DESI
Early Data Release, and they are also included in the photo-$z$ catalogs.

The photo-$z$’s are computed with the random forest regression method
implemented in SCIKIT-LEARN [68]. The following features are used for the
random forest: $r$-band magnitude and fiber-magnitude, $g-r$, $r-z$, $z-W1$
and $W1-W2$ colors, half-light radius, aspect ratio (ratio between semiminor
and semimajor axes), and a shape parameter that quantifies if a galaxy is
better fitted by an exponential profile or a de Vaucouleurs profile (see
section 3.1 of [23]). Note that the $r$-band fiber-magnitude was not used in
the earlier versions of the photo-$z$’s. All the magnitudes and colors are
extinction corrected using the Galactic transmission values from LS DR9.

Photo-$z$’s for galaxies at very low redshifts ($z\lesssim 0.05$) are often
biased high due to the lack of training data (which results from the small
volume) at such low redshifts. To mitigate this, we up-weight the low-redshift
galaxies by applying the following weights as a function of redshift:
$w=1/(z+0.01)^{2}+1$ and clipped to constant values at $z<0.0056$ and
$z>0.06$. There are similar biases at the high-redshift ($z\gtrsim 1$) end
(where the photo-$z$’s are biased low), but unlike in [23], we do not up-
weight galaxies at the high-redshift end due to issues with up-weighting them
when the new training data is added.

The photo-$z$’s are computed with 10-fold cross-validation. Specifically, the
training data is randomly divided into 10 subsets, and the photo-$z$’s of each
subset is computed using the training data of the combined 9 other subsets.
Objects that are not in the training data are randomly assigned to one of the
ten training data combinations. This avoids over-fitting for objects in the
training data and produces photo-$z$’s with consistent error properties
regardless of whether an object is in the training data. The cross-validation
also simplifies the assessment of the photo-$z$ performance.

As [23], we do not provide star-galaxy separation estimates. Users of the
photo-$z$’s might need to apply cuts to reject stars, e.g. by requiring a
non-“PSF” morphological classification or by applying color cuts such as those
applied in the DESI LRG selection.

Table 7 lists the training datasets and their photo-$z$ performance. To
demonstrate the photo-$z$ performance for non-LRG samples, we show in figure
16 photo-$z$ vs spec-$z$ for the DESI SV3 BGS sample (which has $<2\%$
photo-$z$ scatter) and the SDSS QSO sample. More photo-$z$ vs spec-$z$ plots
for all photo-$z$ training datasets can be found on the Legacy Surveys
website.

Survey | # objects | $\sigma_{\mathrm{NMAD}}$ |  $\sigma_{\mathrm{NMAD}}$ ($z_{\mathrm{mag}}<21$) |  $\eta$ (%) |  $\eta$ ($z_{\mathrm{mag}}<21$) (%)
---|---|---|---|---|---
2dFLenS | 28573 (0) | 0.014 (-) | 0.014 (-) | 1.4 (-) | 1.3 (-)
AGES | 4432 (17816) | 0.022 (0.023) | 0.022 (0.022) | 4.0 ( 3.3) | 3.1 ( 2.3)
BOSS | 967556 (383179) | 0.014 (0.015) | 0.014 (0.015) | 1.0 ( 0.8) | 0.9 ( 0.7)
C3R2 | 2551 (174) | 0.101 (0.159) | 0.026 (0.046) | 38.1 (52.3) | 5.0 (12.5)
COSMOS2015 | 64426 (0) | 0.072 (-) | 0.032 (-) | 25.4 (-) | 5.5 (-)
DEEP2 Fields 2,3,4 | 21188 (14835) | 0.069 (0.079) | 0.029 (0.032) | 21.3 (25.5) | 3.5 ( 4.8)
DEEP2+3 Field 1 | 0 (13480) | \- (0.086) | \- (0.032) | \- (32.2) | \- ( 5.0)
eBOSS-ELG | 184078 (8780) | 0.033 (0.041) | 0.030 (0.036) | 4.9 ( 7.9) | 3.2 ( 4.9)
eBOSS-LRG | 107677 (109072) | 0.020 (0.023) | 0.020 (0.023) | 0.5 ( 0.6) | 0.5 ( 0.5)
GAMA | 127642 (0) | 0.017 (-) | 0.017 (-) | 1.2 (-) | 1.1 (-)
OzDES | 13062 (894) | 0.023 (0.026) | 0.020 (0.022) | 5.1 ( 7.5) | 2.2 ( 2.4)
SDSS | 561448 (276299) | 0.010 (0.010) | 0.010 (0.010) | 0.5 ( 0.5) | 0.4 ( 0.4)
SDSS-QSO | 373930 (283553) | 0.076 (0.080) | 0.072 (0.076) | 25.6 (26.2) | 23.5 (24.1)
VIPERS | 48262 (0) | 0.031 (-) | 0.023 (-) | 4.7 (-) | 1.6 (-)
VVDS | 6705 (0) | 0.050 (-) | 0.029 (-) | 18.9 (-) | 4.9 (-)
WiggleZ | 145850 (1629) | 0.053 (0.071) | 0.038 (0.052) | 18.5 (24.4) | 10.1 (12.9)
DESI COSMOS | 33231 (0) | 0.033 (-) | 0.031 (-) | 5.5 (-) | 4.8 (-)
DESI SV1 BGS | 48509 (34688) | 0.021 (0.023) | 0.021 (0.023) | 2.0 ( 2.2) | 2.0 ( 2.1)
DESI SV1 ELG | 30176 (17735) | 0.095 (0.118) | 0.041 (0.055) | 34.7 (41.2) | 14.4 (18.7)
DESI SV1 LRG | 16865 (13783) | 0.028 (0.032) | 0.025 (0.027) | 3.3 ( 4.1) | 2.7 ( 3.0)
DESI SV1 QSO | 12357 (7836) | 0.103 (0.106) | 0.080 (0.083) | 36.9 (37.6) | 26.6 (27.4)
DESI SV3 BGS | 127709 (113055) | 0.019 (0.020) | 0.019 (0.020) | 1.3 ( 1.4) | 1.3 ( 1.4)
DESI SV3 LRG | 59855 (55390) | 0.025 (0.026) | 0.024 (0.025) | 1.9 ( 2.1) | 1.6 ( 1.8)
DESI SV3 QSO | 15498 (14852) | 0.093 (0.091) | 0.078 (0.075) | 32.1 (31.4) | 25.6 (24.4)

Table 7:  The number of objects, photo-$z$ scatter $\sigma_{\mathrm{NMAD}}$
and outlier fraction $\eta$ (defined in section 2.3) for each training
dataset. We also include the photo-$z$ scatter and outlier fraction for the
brighter subset of objects that have $z_{\mathrm{mag}}<21$. The numbers
without parentheses are for the South, and with parentheses for the North. The
photo-$z$’s are based on 10-fold cross-validation. The number of objects
includes duplicates with other surveys (which are removed when the training
datasets are combined).

Figure 16: Photo-$z$ vs spec-$z$ for DESI SV3 BGS sample (left panel) and SDSS
DR16 Quasar sample (right panel).

##  Appendix C Modeling the change in fiber-magnitude for a magnified galaxy

Here we describe how we obtain the change in fiber-magnitude $\delta
m_{\mathrm{fiber}}$ for a given change in magnitude $\delta m$ arising from
magnification. The $\delta m_{\mathrm{fiber}}$ value is necessary for properly
computing the magnification number count slope.

The DR9 imaging catalog has 5 types of morphology models: point source, round
exponential (REX), exponential, de Vaucouleurs and Sersic. Table 8 lists the
fraction of LRG targets in each type. For point sources, the fraction of flux
within the fiber does not change with magnification, and therefore have
$\delta m_{\mathrm{fiber}}=\delta m_{\mathrm{total}}$. For extended sources,
$\delta m_{\mathrm{fiber}}$ can be calculated either by numerically
integrating the model flux within the fiber radius for the magnified galaxy,
or it can be derived from the catalog as long as the galaxy shape parameters
are well sampled (which is true for the LS catalog that contains billions of
sources). We take the latter approach.

We first obtain the fiber-flux to total flux ratio
$f_{\mathrm{fiber}}/f_{\mathrm{total}}$ as a function of half light radius and
aspect ratio. Since both $f_{\mathrm{fiber}}$ and $f_{\mathrm{total}}$ values
are available for all sources in the tractor catalog, we obtain
$f_{\mathrm{fiber}}/f_{\mathrm{total}}$ using the tractor catalog and
interpolate between the shape parameters. If a galaxy is magnified, the
observed total flux increases by a small fraction of
$\epsilon_{\mathrm{total}}$, and the fiber-flux increases by a different
fraction $\epsilon_{\mathrm{fiber}}$. (Since $\delta m$ and $\epsilon$ are
equivalent, hereafter we use $\epsilon$ for simplicity.) Given
$f_{\mathrm{fiber}}/f_{\mathrm{total}}$ as a function of the shape parameters,
we can compute $\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ via
finite difference. Below we describe how
$f_{\mathrm{fiber}}/f_{\mathrm{total}}$ and
$\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ are obtained for each
morphology model.

Type | All | Faintest 0.01 mag
---|---|---
Point source | 2.2% | 5.0%
Round exponential | 29.1% | 52.8%
Exponential | 9.8% | 13.6%
de Vaucouleurs | 42.9% | 27.5%
Sersic | 16.0% | 1.0%
Table 8:  Morphological type composition of all Main LRG targets. Since our
sensitivity to magnification is mostly determined by the faintest objects
(although brighter sources also matter due to the photo-$z$ binning), we also
list the composition of the LRGs within 0.01 magnitude of the $z$-band fiber-
magnitude cut. We use all LRGs when computing the number count slope via
finite difference.

Round exponential galaxies, which constitute most of the LRG targets near the
fiber-flux cut, have only one shape parameter, the half-light radius. We
measure the mean $f_{\mathrm{fiber}}/f_{\mathrm{total}}$ in bins of half-light
radius, and interpolate with a cubic spline. We then use the interpolated
function to obtain $\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ with
finite difference. The measured
$\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ is noisy at radius above
2 arcsec, so we use the Savitzky–Golay filter to obtain a smoothed function.
Figure 17 shows $f_{\mathrm{fiber}}/f_{\mathrm{total}}$ and the smoothed
$\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ as a function of half-
light radius.

Figure 17: The fiber-flux to total flux ratio
($f_{\mathrm{fiber}}/f_{\mathrm{total}}$, blue dashed curve) and the ratio
between the fractional changes of the two fluxes
($\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$, red solid curve) as a
function of half-light radius, for round exponential galaxies. The
$\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ values are used in
calculating the “magnified” fiber-fluxes. The distribution of the half-light
radii for round exponential LRGs within 0.01 magnitude of the $z$-band fiber-
magnitude cut is shown in the gray histogram.

Exponential and de Vaucouleurs galaxies have two shape parameters, half-light
radius and aspect ratio (the ratio of the major axis to the minor axis). The
modeling is similar to round exponential galaxies, except that the binning and
interpolation are done in 2-D instead of 1-D. Figure 18 shows
$f_{\mathrm{fiber}}/f_{\mathrm{total}}$ and the smoothed
$\epsilon_{\mathrm{fiber}}/\epsilon_{\mathrm{total}}$ as a function of half-
light radius and the aspect ratio for de Vaucouleurs galaxies.

Figure 18: Similar to figure 17, but for de Vaucouleurs galaxies with an
additional shape parameter, the aspect ratio.

Sersic galaxies have an additional parameter, the Sersic index. Since only
$1\%$ of the LRG targets near the fiber-flux cut are Sersic, instead of
attempting to create a 3-parameter model, we simply approximate the Sersic
galaxies with either exponential or de Vaucouleurs profile, depending on the
Sersic index $n$: exponential for $n<2.5$ and de Vaucouleurs for $n\geq 2.5$.

## References

  * [1] M. White et al., Cosmological constraints from the tomographic cross-correlation of DESI Luminous Red Galaxies and Planck CMB lensing, JCAP 02 (2022), no. 02 007, [arXiv:2111.09898].
  * [2] DES Collaboration, T. Abbott et al., The Dark Energy Survey: more than dark energy – an overview, Mon. Not. Roy. Astron. Soc. 460 (2016), no. 2 1270–1299, [arXiv:1601.00329].
  * [3] DESI Collaboration, A. Aghamousa, J. Aguilar, S. Ahlen, S. Alam, L. E. Allen, C. Allende Prieto, J. Annis, S. Bailey, C. Balland, and et al., The DESI Experiment Part I: Science,Targeting, and Survey Design, ArXiv e-prints (Oct., 2016) [arXiv:1611.00036].
  * [4] DESI Collaboration, A. Aghamousa, J. Aguilar, S. Ahlen, S. Alam, L. E. Allen, C. Allende Prieto, J. Annis, S. Bailey, C. Balland, and et al., The DESI Experiment Part II: Instrument Design, ArXiv e-prints (Oct., 2016) [arXiv:1611.00037].
  * [5] LSST Dark Energy Science Collaboration, D. Alonso et al., The LSST Dark Energy Science Collaboration (DESC) Science Requirements Document, arXiv:1809.01669.
  * [6] L. Amendola, S. Appleby, A. Avgoustidis, D. Bacon, T. Baker, M. Baldi, N. Bartolo, A. Blanchard, C. Bonvin, S. Borgani, E. Branchini, C. Burrage, S. Camera, C. Carbone, L. Casarini, M. Cropper, C. de Rham, J. P. Dietrich, C. Di Porto, R. Durrer, A. Ealet, P. G. Ferreira, F. Finelli, J. García-Bellido, T. Giannantonio, L. Guzzo, A. Heavens, L. Heisenberg, C. Heymans, H. Hoekstra, L. Hollenstein, R. Holmes, Z. Hwang, K. Jahnke, T. D. Kitching, T. Koivisto, M. Kunz, G. La Vacca, E. Linder, M. March, V. Marra, C. Martins, E. Majerotto, D. Markovic, D. Marsh, F. Marulli, R. Massey, Y. Mellier, F. Montanari, D. F. Mota, N. J. Nunes, W. Percival, V. Pettorino, C. Porciani, C. Quercellini, J. Read, M. Rinaldi, D. Sapone, I. Sawicki, R. Scaramella, C. Skordis, F. Simpson, A. Taylor, S. Thomas, R. Trotta, L. Verde, F. Vernizzi, A. Vollmer, Y. Wang, J. Weller, and T. Zlosnik, Cosmology and fundamental physics with the Euclid satellite, Living Reviews in Relativity 21 (Apr., 2018) 2, [arXiv:1606.00180].
  * [7] J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, Optical design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera, Applied Optics 46 (June, 2007) 3444.
  * [8] J. E. Carlstrom et al., The 10 Meter South Pole Telescope, Publ. Astron. Soc. Pac. 123 (2011) 568–581, [arXiv:0907.4445].
  * [9] P. Ade, J. Aguirre, Z. Ahmed, S. Aiola, A. Ali, D. Alonso, M. A. Alvarez, K. Arnold, P. Ashton, J. Austermann, H. Awan, C. Baccigalupi, T. Baildon, D. Barron, N. Battaglia, R. Battye, E. Baxter, A. Bazarko, J. A. Beall, R. Bean, D. Beck, S. Beckman, B. Beringue, F. Bianchini, S. Boada, D. Boettger, J. R. Bond, J. Borrill, M. L. Brown, S. M. Bruno, S. Bryan, E. Calabrese, V. Calafut, P. Calisse, J. Carron, A. Challinor, G. Chesmore, Y. Chinone, J. Chluba, H.-M. S. Cho, S. Choi, G. Coppi, N. F. Cothard, K. Coughlin, D. Crichton, K. D. Crowley, K. T. Crowley, A. Cukierman, J. M. D’Ewart, R. Dünner, T. De Haan, M. Devlin, S. Dicker, J. Didier, M. Dobbs, B. Dober, C. J. Duell, S. Duff, A. Duivenvoorden, J. Dunkley, J. Dusatko, J. Errard, G. Fabbian, S. Feeney, S. Ferraro, P. Fluxà, K. Freese, J. C. Frisch, A. Frolov, G. Fuller, B. Fuzia, N. Galitzki, P. A. Gallardo, J. T. G. Ghersi, J. Gao, E. Gawiser, M. Gerbino, V. Gluscevic, N. Goeckner-Wald, J. Golec, S. Gordon, M. Gralla, D. Green, A. Grigorian, J. Groh, C. Groppi, Y. Guan, J. E. Gudmundsson, D. Han, P. Hargrave, M. Hasegawa, M. Hasselfield, M. Hattori, V. Haynes, M. Hazumi, Y. He, E. Healy, S. W. Henderson, C. Hervias-Caimapo, C. A. Hill, J. C. Hill, G. Hilton, M. Hilton, A. D. Hincks, G. Hinshaw, R. Hložek, S. Ho, S.-P. P. Ho, L. Howe, Z. Huang, J. Hubmayr, K. Huffenberger, J. P. Hughes, A. Ijjas, M. Ikape, K. Irwin, A. H. Jaffe, B. Jain, O. Jeong, D. Kaneko, E. D. Karpel, N. Katayama, B. Keating, S. S. Kernasovskiy, R. Keskitalo, T. Kisner, K. Kiuchi, J. Klein, K. Knowles, B. Koopman, A. Kosowsky, N. Krachmalnicoff, S. E. Kuenstner, C.-L. Kuo, A. Kusaka, J. Lashner, A. Lee, E. Lee, D. Leon, J. S.-Y. Leung, A. Lewis, Y. Li, Z. Li, M. Limon, E. Linder, C. Lopez-Caraballo, T. Louis, L. Lowry, M. Lungu, M. Madhavacheril, D. Mak, F. Maldonado, H. Mani, B. Mates, F. Matsuda, L. Maurin, P. Mauskopf, A. May, N. McCallum, C. McKenney, J. McMahon, P. D. Meerburg, J. Meyers, A. Miller, M. Mirmelstein, K. Moodley, M. Munchmeyer, C. Munson, S. Naess, F. Nati, M. Navaroli, L. Newburgh, H. N. Nguyen, M. Niemack, H. Nishino, J. Orlowski-Scherer, L. Page, B. Partridge, J. Peloton, F. Perrotta, L. Piccirillo, G. Pisano, D. Poletti, R. Puddu, G. Puglisi, C. Raum, C. L. Reichardt, M. Remazeilles, Y. Rephaeli, D. Riechers, F. Rojas, A. Roy, S. Sadeh, Y. Sakurai, M. Salatino, M. S. Rao, E. Schaan, M. Schmittfull, N. Sehgal, J. Seibert, U. Seljak, B. Sherwin, M. Shimon, C. Sierra, J. Sievers, P. Sikhosana, M. Silva-Feaver, S. M. Simon, A. Sinclair, P. Siritanasak, K. Smith, S. R. Smith, D. Spergel, S. T. Staggs, G. Stein, J. R. Stevens, R. Stompor, A. Suzuki, O. Tajima, S. Takakura, G. Teply, D. B. Thomas, B. Thorne, R. Thornton, H. Trac, C. Tsai, C. Tucker, J. Ullom, S. Vagnozzi, A. V. Engelen, J. V. Lanen, D. D. V. Winkle, E. M. Vavagiakis, C. Vergès, M. Vissers, K. Wagoner, S. Walker, J. Ward, B. Westbrook, N. Whitehorn, J. Williams, J. Williams, E. J. Wollack, Z. Xu, B. Yu, C. Yu, F. Zago, H. Zhang, N. Zhu, and The Simons Observatory collaboration, The Simons Observatory: Science goals and forecasts, Journal of Cosmology and Astroparticle Physics 2019 (Feb., 2019) 056–056.
  * [10] R. Zhou, B. Dey, J. A. Newman, D. J. Eisenstein, K. Dawson, S. Bailey, A. Berti, J. Guy, T.-W. Lan, H. Zou, J. Aguilar, S. Ahlen, S. Alam, D. Brooks, A. de la Macorra, A. Dey, G. Dhungana, K. Fanning, A. Font-Ribera, S. G. A. Gontcho, K. Honscheid, M. Ishak, T. Kisner, A. Kovács, A. Kremin, M. Landriau, M. E. Levi, C. Magneville, M. Manera, P. Martini, A. M. Meisner, R. Miquel, J. Moustakas, A. D. Myers, J. Nie, N. Palanque-Delabrouille, W. J. Percival, C. Poppett, F. Prada, A. Raichoor, A. J. Ross, E. Schlafly, D. Schlegel, M. Schubnell, G. Tarlé, B. A. Weaver, R. H. Wechsler, C. Yèche, and Z. Zhou, Target Selection and Validation of DESI Luminous Red Galaxies, The Astronomical Journal 165 (Feb., 2023) 58, [arXiv:2208.08515].
  * [11] Q. Hang, S. Alam, J. A. Peacock, and Y.-C. Cai, Galaxy clustering in the DESI Legacy Survey and its imprint on the CMB, MNRAS 501 (Feb., 2021) 1481–1498, [arXiv:2010.00466].
  * [12] Q. Hang, S. Alam, Y.-C. Cai, and J. A. Peacock, Stacked CMB lensing and ISW signals around superstructures in the DESI Legacy Survey, MNRAS 507 (Oct., 2021) 510–523, [arXiv:2105.11936].
  * [13] E. Kitanidis and M. White, Cross-correlation of Planck CMB lensing with DESI-like LRGs, MNRAS 501 (Mar., 2021) 6181–6198, [arXiv:2010.04698].
  * [14] E. L. Wright, P. R. M. Eisenhardt, A. K. Mainzer, M. E. Ressler, R. M. Cutri, T. Jarrett, J. D. Kirkpatrick, D. Padgett, R. S. McMillan, M. Skrutskie, S. A. Stanford, M. Cohen, R. G. Walker, J. C. Mather, D. Leisawitz, T. N. Gautier, III, I. McLean, D. Benford, C. J. Lonsdale, A. Blain, B. Mendez, W. R. Irace, V. Duval, F. Liu, D. Royer, I. Heinrichsen, J. Howard, M. Shannon, M. Kendall, A. L. Walsh, M. Larsen, J. G. Cardon, S. Schick, M. Schwalm, M. Abid, B. Fabinsky, L. Naes, and C.-W. Tsai, The Wide-field Infrared Survey Explorer (WISE): Mission Description and Initial On-orbit Performance, AJ 140 (Dec., 2010) 1868–1881, [arXiv:1008.0031].
  * [15] A. Dey, D. J. Schlegel, D. Lang, R. Blum, K. Burleigh, X. Fan, J. R. Findlay, D. Finkbeiner, D. Herrera, S. Juneau, M. Landriau, M. Levi, I. McGreer, A. Meisner, A. D. Myers, J. Moustakas, P. Nugent, A. Patej, E. F. Schlafly, A. R. Walker, F. Valdes, B. A. Weaver, C. Yèche, H. Zou, X. Zhou, B. Abareshi, T. M. C. Abbott, B. Abolfathi, C. Aguilera, S. Alam, L. Allen, A. Alvarez, J. Annis, B. Ansarinejad, M. Aubert, J. Beechert, E. F. Bell, S. Y. BenZvi, F. Beutler, R. M. Bielby, A. S. Bolton, C. Briceño, E. J. Buckley-Geer, K. Butler, A. Calamida, R. G. Carlberg, P. Carter, R. Casas, F. J. Castander, Y. Choi, J. Comparat, E. Cukanovaite, T. Delubac, K. DeVries, S. Dey, G. Dhungana, M. Dickinson, Z. Ding, J. B. Donaldson, Y. Duan, C. J. Duckworth, S. Eftekharzadeh, D. J. Eisenstein, T. Etourneau, P. A. Fagrelius, J. Farihi, M. Fitzpatrick, A. Font-Ribera, L. Fulmer, B. T. Gänsicke, E. Gaztanaga, K. George, D. W. Gerdes, S. G. A Gontcho, C. Gorgoni, G. Green, J. Guy, D. Harmer, M. Hernandez, K. Honscheid, L. W. Huang, D. J. James, B. T. Jannuzi, L. Jiang, R. Joyce, A. Karcher, S. Karkar, R. Kehoe, J.-P. Kneib, A. Kueter-Young, T.-W. Lan, T. R. Lauer, L. L. Guillou, A. L. Van Suu, J. H. Lee, M. Lesser, L. P. Levasseur, T. S. Li, J. L. Mann, R. Marshall, C. E. Martínez-Vázquez, P. Martini, H. du Mas des Bourboux, S. McManus, T. G. Meier, B. Ménard, N. Metcalfe, A. Muñoz-Gutiérrez, J. Najita, K. Napier, G. Narayan, J. A. Newman, J. Nie, B. Nord, D. J. Norman, K. A. G. Olsen, A. Paat, N. Palanque-Delabrouille, X. Peng, C. L. Poppett, M. R. Poremba, A. Prakash, D. Rabinowitz, A. Raichoor, M. Rezaie, A. N. Robertson, N. A. Roe, A. J. Ross, N. P. Ross, G. Rudnick, S. Safonova, A. Saha, F. J. Sánchez, E. Savary, H. Schweiker, A. Scott, H.-J. Seo, H. Shan, D. R. Silva, Z. Slepian, C. Soto, D. Sprayberry, R. Staten, C. M. Stillman, R. J. Stupak, D. L. Summers, S. S. Tie, H. Tirado, M. Vargas-Magaña, A. K. Vivas, R. H. Wechsler, D. Williams, J. Yang, Q. Yang, T. Yapici, D. Zaritsky, A. Zenteno, K. Zhang, T. Zhang, R. Zhou, and Z. Zhou, Overview of the DESI Legacy Imaging Surveys, The Astronomical Journal 157 (Apr., 2019) 168.
  * [16] H. Zou, X. Zhou, X. Fan, T. Zhang, Z. Zhou, J. Nie, X. Peng, I. McGreer, L. Jiang, A. Dey, D. Fan, B. He, Z. Jiang, D. Lang, M. Lesser, J. Ma, S. Mao, D. Schlegel, and J. Wang, Project Overview of the Beijing–Arizona Sky Survey, Publications of the Astronomical Society of the Pacific 129 (June, 2017) 064101.
  * [17] D. Lang, D. W. Hogg, and D. Mykytyn, “The Tractor: Probabilistic astronomical source detection and measurement.” Astrophysics Source Code Library, Apr., 2016.
  * [18] R. Zhou, A. Dey, D. Lang, J. Moustakas, E. F. Schlafly, and D. J. Schlegel, Comparing the Photometric Calibration of DESI Imaging and Gaia Synthetic Photometry, Research Notes of the AAS 7 (May, 2023) 105, [arXiv:2305.16630].
  * [19] K. C. Chambers, E. A. Magnier, N. Metcalfe, H. A. Flewelling, M. E. Huber, C. Z. Waters, L. Denneau, P. W. Draper, D. Farrow, D. P. Finkbeiner, C. Holmberg, J. Koppenhoefer, P. A. Price, A. Rest, R. P. Saglia, E. F. Schlafly, S. J. Smartt, W. Sweeney, R. J. Wainscoat, W. S. Burgett, S. Chastel, T. Grav, J. N. Heasley, K. W. Hodapp, R. Jedicke, N. Kaiser, R.-P. Kudritzki, G. A. Luppino, R. H. Lupton, D. G. Monet, J. S. Morgan, P. M. Onaka, B. Shiao, C. W. Stubbs, J. L. Tonry, R. White, E. Bañados, E. F. Bell, R. Bender, E. J. Bernard, M. Boegner, F. Boffi, M. T. Botticella, A. Calamida, S. Casertano, W.-P. Chen, X. Chen, S. Cole, N. Deacon, C. Frenk, A. Fitzsimmons, S. Gezari, V. Gibbs, C. Goessl, T. Goggia, R. Gourgue, B. Goldman, P. Grant, E. K. Grebel, N. C. Hambly, G. Hasinger, A. F. Heavens, T. M. Heckman, R. Henderson, T. Henning, M. Holman, U. Hopp, W.-H. Ip, S. Isani, M. Jackson, C. D. Keyes, A. M. Koekemoer, R. Kotak, D. Le, D. Liska, K. S. Long, J. R. Lucey, M. Liu, N. F. Martin, G. Masci, B. McLean, E. Mindel, P. Misra, E. Morganson, D. N. A. Murphy, A. Obaika, G. Narayan, M. A. Nieto-Santisteban, P. Norberg, J. A. Peacock, E. A. Pier, M. Postman, N. Primak, C. Rae, A. Rai, A. Riess, A. Riffeser, H. W. Rix, S. Röser, R. Russel, L. Rutz, E. Schilbach, A. S. B. Schultz, D. Scolnic, L. Strolger, A. Szalay, S. Seitz, E. Small, K. W. Smith, D. R. Soderblom, P. Taylor, R. Thomson, A. N. Taylor, A. R. Thakar, J. Thiel, D. Thilker, D. Unger, Y. Urata, J. Valenti, J. Wagner, T. Walder, F. Walter, S. P. Watters, S. Werner, W. M. Wood-Vasey, and R. Wyse, The Pan-STARRS1 Surveys, arXiv:1612.05560 [astro-ph] (Dec., 2016) [arXiv:1612.05560].
  * [20] A. Zonca, L. Singer, D. Lenz, M. Reinecke, C. Rosset, E. Hivon, and K. Gorski, healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in python, Journal of Open Source Software 4 (Mar., 2019) 1298.
  * [21] D. Collaboration, A. G. Adame, J. Aguilar, S. Ahlen, S. Alam, G. Aldering, D. M. Alexander, R. Alfarsy, C. A. Prieto, M. Alvarez, O. Alves, and et al., Validation of the Scientific Program for the Dark Energy Spectroscopic Instrument, ArXiv e-prints (Apr., 2023) [arXiv:2306.06307].
  * [22] D. Collaboration, A. G. Adame, J. Aguilar, S. Ahlen, S. Alam, G. Aldering, D. M. Alexander, R. Alfarsy, C. A. Prieto, M. Alvarez, O. Alves, and et al., The Early Data Release of the Dark Energy Spectroscopic Instrument, ArXiv e-prints (June, 2023) [arXiv:2306.06308].
  * [23] R. Zhou, J. A. Newman, Y.-Y. Mao, A. Meisner, J. Moustakas, A. D. Myers, A. Prakash, A. R. Zentner, D. Brooks, Y. Duan, M. Landriau, M. E. Levi, F. Prada, and G. Tarle, The Clustering of DESI-like Luminous Red Galaxies Using Photometric Redshifts, Monthly Notices of the Royal Astronomical Society (Dec., 2020) staa3764, [arXiv:2001.06018].
  * [24] A. Krolewski, S. Ferraro, E. F. Schlafly, and M. White, unWISE tomography of Planck CMB lensing, JCAP 05 (2020) 047, [arXiv:1909.07412].
  * [25] D. J. Schlegel, D. P. Finkbeiner, and M. Davis, Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds, The Astrophysical Journal 500 (June, 1998) 525–553.
  * [26] A. D. Myers, J. Moustakas, S. Bailey, B. A. Weaver, A. P. Cooper, J. E. Forero-Romero, B. Abolfathi, D. M. Alexander, D. Brooks, E. Chaussidon, C.-H. Chuang, K. Dawson, A. Dey, B. Dey, G. Dhungana, P. Doel, K. Fanning, E. Gaztañaga, S. G. A. Gontcho, A. X. Gonzalez-Morales, C. Hahn, H. K. Herrera-Alcantar, K. Honscheid, M. Ishak, T. Karim, D. Kirkby, T. Kisner, S. E. Koposov, A. Kremin, T.-W. Lan, M. Landriau, D. Lang, M. E. Levi, C. Magneville, L. Napolitano, P. Martini, A. Meisner, J. A. Newman, N. Palanque-Delabrouille, W. Percival, C. Poppett, F. Prada, A. Raichoor, A. J. Ross, E. F. Schlafly, D. Schlegel, M. Schubnell, T. Tan, G. Tarle, M. J. Wilson, C. Yèche, R. Zhou, Z. Zhou, and H. Zou, The Target-selection Pipeline for the Dark Energy Spectroscopic Instrument, The Astronomical Journal 165 (Feb., 2023) 50, [arXiv:2208.08518].
  * [27] Y.-K. Chiang and B. Ménard, Extragalactic Imprints in Galactic Dust Maps, The Astrophysical Journal 870 (Jan., 2019) 120.
  * [28] S. Alam et al., Desi first generation mocks paper, in preparation (2022).
  * [29] J. Moon, D. Valcin, M. Rashkovetskyi, C. Saulder, J. N. Aguilar, S. Ahlen, S. Alam, S. Bailey, C. Baltay, R. Blum, D. Brooks, E. Burtin, E. Chaussidon, K. Dawson, A. de la Macorra, A. de Mattia, G. Dhungana, D. Eisenstein, B. Flaugher, A. Font-Ribera, C. Garcia-Quintero, J. Guy, M. M. S. Hanif, K. Honscheid, M. Ishak, R. Kehoe, S. Kim, T. Kisner, A. Kremin, M. Landriau, L. L. Guillou, M. Levi, P. Martini, P. McDonald, A. Meisner, R. Miquel, J. Moustakas, A. Myers, S. Nadathur, R. Neveux, J. A. Newman, J. Nie, N. Padmanabhan, N. Palanque-Delabrouille, W. Percival, A. P. Fernández, C. Poppett, F. Prada, A. J. Ross, G. Rossi, H.-J. Seo, G. Tarlé, M. V. Magana, A. Variu, B. A. Weaver, M. J. White, S. Yuan, C. Zhao, R. Zhou, Z. Zhou, and H. Zou, First Detection of the BAO Signal from Early DESI Data, Apr., 2023.
  * [30] N. A. Maksimova, L. H. Garrison, D. J. Eisenstein, B. Hadzhiyska, S. Bose, and T. P. Satterthwaite, AbacusSummit: A Massive Set of High-Accuracy, High-Resolution $N$-Body Simulations, Monthly Notices of the Royal Astronomical Society 508 (Oct., 2021) 4017–4037, [arXiv:2110.11398].
  * [31] L. H. Garrison, D. J. Eisenstein, D. Ferrer, N. A. Maksimova, and P. A. Pinto, The $\texttt{}Abacus{}$ Cosmological $N$-body Code, Monthly Notices of the Royal Astronomical Society 508 (Sept., 2021) 575–596, [arXiv:2110.11392].
  * [32] A. Krolewski, S. Ferraro, and M. White, Cosmological constraints from unWISE and Planck CMB lensing tomography, Journal of Cosmology and Astroparticle Physics 2021 (Dec., 2021) 028, [arXiv:2105.03421].
  * [33] Planck Collaboration, N. Aghanim, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, R. Battye, K. Benabed, J. P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. F. Cardoso, J. Carron, B. Casaponsa, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J. M. Delouis, F. X. Désert, E. Di Valentino, C. Dickinson, J. M. Diego, S. Donzelli, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, Y. Fantaye, J. Fergusson, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Hand ley, F. K. Hansen, G. Helou, D. Herranz, S. R. Hildebrandt, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, L. Knox, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. M. Lamarre, M. Langer, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, J. P. Leahy, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mand olesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, M. Martinelli, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. D. Meerburg, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. Millea, S. Mitra, M. A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, S. Mottet, M. Münchmeyer, P. Natoli, H. U. Nørgaard-Nielsen, C. A. Oxborrow, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, T. J. Pearson, M. Peel, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, C. Renault, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, M. Shiraishi, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Terenzi, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, L. Vibert, P. Vielva, F. Villa, N. Vittorio, B. D. Wand elt, I. K. Wehus, M. White, S. D. M. White, A. Zacchei, and A. Zonca, Planck 2018 results. I. Overview and the cosmological legacy of Planck, A&A 641 (Sept., 2020) A1, [arXiv:1807.06205].
  * [34] Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, R. Battye, K. Benabed, J. P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, J. Chluba, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J. M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, M. Farhang, J. Fergusson, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, S. R. Hildebrandt, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, L. Knox, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, P. Lemos, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, M. Martinelli, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. Millea, S. Mitra, M. A. Miville-Deschênes, D. Molinari, L. Montier, G. Morgante, A. Moss, P. Natoli, H. U. Nørgaard-Nielsen, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, L. Valenziano, J. Valiviita, B. Van Tent, L. Vibert, P. Vielva, F. Villa, N. Vittorio, B. D. Wand elt, I. K. Wehus, M. White, S. D. M. White, A. Zacchei, and A. Zonca, Planck 2018 results. VI. Cosmological parameters, A&A 641 (Sept., 2020) A6, [arXiv:1807.06209].
  * [35] S. Yuan et al., The DESI One-Percent Survey: Exploring the Halo Occupation Distribution of Luminous Red Galaxies and Quasi-Stellar Objects with AbacusSummit, ArXiv e-prints (6, 2023) [arXiv:2306.06314].
  * [36] Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, E. Calabrese, J. F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, L. Knox, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, A. Melchiorri, A. Mennella, M. Migliaccio, M. A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, C. Sirignano, R. Sunyaev, A. S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, M. White, S. D. M. White, A. Zacchei, and A. Zonca, Planck 2018 results. VIII. Gravitational lensing, A&A 641 (Sept., 2020) A8, [arXiv:1807.06210].
  * [37] K. Abazajian, G. Addison, P. Adshead, Z. Ahmed, S. W. Allen, D. Alonso, M. Alvarez, A. Anderson, K. S. Arnold, C. Baccigalupi, K. Bailey, D. Barkats, D. Barron, P. S. Barry, J. G. Bartlett, R. B. Thakur, N. Battaglia, E. Baxter, R. Bean, C. Bebek, A. N. Bender, B. A. Benson, E. Berger, S. Bhimani, C. A. Bischoff, L. Bleem, S. Bocquet, K. Boddy, M. Bonato, J. R. Bond, J. Borrill, F. R. Bouchet, M. L. Brown, S. Bryan, B. Burkhart, V. Buza, K. Byrum, E. Calabrese, V. Calafut, R. Caldwell, J. E. Carlstrom, J. Carron, T. Cecil, A. Challinor, C. L. Chang, Y. Chinone, H.-M. S. Cho, A. Cooray, T. M. Crawford, A. Crites, A. Cukierman, F.-Y. Cyr-Racine, T. de Haan, G. de Zotti, J. Delabrouille, M. Demarteau, M. Devlin, E. Di Valentino, M. Dobbs, S. Duff, A. Duivenvoorden, C. Dvorkin, W. Edwards, J. Eimer, J. Errard, T. Essinger-Hileman, G. Fabbian, C. Feng, S. Ferraro, J. P. Filippini, R. Flauger, B. Flaugher, A. A. Fraisse, A. Frolov, N. Galitzki, S. Galli, K. Ganga, M. Gerbino, M. Gilchriese, V. Gluscevic, D. Green, D. Grin, E. Grohs, R. Gualtieri, V. Guarino, J. E. Gudmundsson, S. Habib, G. Haller, M. Halpern, N. W. Halverson, S. Hanany, K. Harrington, M. Hasegawa, M. Hasselfield, M. Hazumi, K. Heitmann, S. Henderson, J. W. Henning, J. C. Hill, R. Hlozek, G. Holder, W. Holzapfel, J. Hubmayr, K. M. Huffenberger, M. Huffer, H. Hui, K. Irwin, B. R. Johnson, D. Johnstone, W. C. Jones, K. Karkare, N. Katayama, J. Kerby, S. Kernovsky, R. Keskitalo, T. Kisner, L. Knox, A. Kosowsky, J. Kovac, E. D. Kovetz, S. Kuhlmann, C.-l. Kuo, N. Kurita, A. Kusaka, A. Lahteenmaki, C. R. Lawrence, A. T. Lee, A. Lewis, D. Li, E. Linder, M. Loverde, A. Lowitz, M. S. Madhavacheril, A. Mantz, F. Matsuda, P. Mauskopf, J. McMahon, M. McQuinn, P. D. Meerburg, J.-B. Melin, J. Meyers, M. Millea, J. Mohr, L. Moncelsi, T. Mroczkowski, S. Mukherjee, M. Münchmeyer, D. Nagai, J. Nagy, T. Namikawa, F. Nati, T. Natoli, M. Negrello, L. Newburgh, M. D. Niemack, H. Nishino, M. Nordby, V. Novosad, P. O’Connor, G. Obied, S. Padin, S. Pandey, B. Partridge, E. Pierpaoli, L. Pogosian, C. Pryke, G. Puglisi, B. Racine, S. Raghunathan, A. Rahlin, S. Rajagopalan, M. Raveri, M. Reichanadter, C. L. Reichardt, M. Remazeilles, G. Rocha, N. A. Roe, A. Roy, J. Ruhl, M. Salatino, B. Saliwanchik, E. Schaan, A. Schillaci, M. M. Schmittfull, D. Scott, N. Sehgal, S. Shandera, C. Sheehy, B. D. Sherwin, E. Shirokoff, S. M. Simon, A. Slosar, R. Somerville, D. Spergel, S. T. Staggs, A. Stark, R. Stompor, K. T. Story, C. Stoughton, A. Suzuki, O. Tajima, G. P. Teply, K. Thompson, P. Timbie, M. Tomasi, J. I. Treu, M. Tristram, G. Tucker, C. Umiltà, A. van Engelen, J. D. Vieira, A. G. Vieregg, M. Vogelsberger, G. Wang, S. Watson, M. White, N. Whitehorn, E. J. Wollack, W. L. K. Wu, Z. Xu, S. Yasini, J. Yeck, K. W. Yoon, E. Young, and A. Zonca, CMB-S4 Science Case, Reference Design, and Project Plan, July, 2019.
  * [38] B. Yu, S. Ferraro, Z. R. Knight, L. Knox, and B. D. Sherwin, The physical origin of dark energy constraints from rubin observatory and CMB-S4 lensing tomography, Mon. Not. Roy. Astron. Soc. 513 (2022), no. 2 1887–1894, [arXiv:2108.02801].
  * [39] B. Yu, R. Z. Knight, B. D. Sherwin, S. Ferraro, L. Knox, and M. Schmittfull, Towards Neutrino Mass from Cosmology without Optical Depth Information, ArXiv e-prints (9, 2018) [arXiv:1809.02120].
  * [40] E. Abdalla et al., Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, JHEAp 34 (2022) 49–211, [arXiv:2203.06142].
  * [41] N. Battaglia, S. Ferraro, E. Schaan, and D. Spergel, Future constraints on halo thermodynamics from combined Sunyaev-Zel’dovich measurements, JCAP 11 (2017) 040, [arXiv:1705.05881].
  * [42] D. Collaboration, T. M. C. Abbott, M. Aguena, A. Alarcon, S. Allam, O. Alves, A. Amon, F. Andrade-Oliveira, J. Annis, S. Avila, D. Bacon, E. Baxter, K. Bechtol, M. R. Becker, G. M. Bernstein, S. Bhargava, S. Birrer, J. Blazek, A. Brandao-Souza, S. L. Bridle, D. Brooks, E. Buckley-Geer, D. L. Burke, H. Camacho, A. Campos, A. C. Rosell, M. C. Kind, J. Carretero, F. J. Castander, R. Cawthon, C. Chang, A. Chen, R. Chen, A. Choi, C. Conselice, J. Cordero, M. Costanzi, M. Crocce, L. N. da Costa, M. E. d. S. Pereira, C. Davis, T. M. Davis, J. De Vicente, J. DeRose, S. Desai, E. Di Valentino, H. T. Diehl, J. P. Dietrich, S. Dodelson, P. Doel, C. Doux, A. Drlica-Wagner, K. Eckert, T. F. Eifler, F. Elsner, J. Elvin-Poole, S. Everett, A. E. Evrard, X. Fang, A. Farahi, E. Fernandez, I. Ferrero, A. Ferté, P. Fosalba, O. Friedrich, J. Frieman, J. García-Bellido, M. Gatti, E. Gaztanaga, D. W. Gerdes, T. Giannantonio, G. Giannini, D. Gruen, R. A. Gruendl, J. Gschwend, G. Gutierrez, I. Harrison, W. G. Hartley, K. Herner, S. R. Hinton, D. L. Hollowood, K. Honscheid, B. Hoyle, E. M. Huff, D. Huterer, B. Jain, D. J. James, M. Jarvis, N. Jeffrey, T. Jeltema, A. Kovacs, E. Krause, R. Kron, K. Kuehn, N. Kuropatkin, O. Lahav, P.-F. Leget, P. Lemos, A. R. Liddle, C. Lidman, M. Lima, H. Lin, N. MacCrann, M. A. G. Maia, J. L. Marshall, P. Martini, J. McCullough, P. Melchior, J. Mena-Fernández, F. Menanteau, R. Miquel, J. J. Mohr, R. Morgan, J. Muir, J. Myles, S. Nadathur, A. Navarro-Alsina, R. C. Nichol, R. L. C. Ogando, Y. Omori, A. Palmese, S. Pandey, Y. Park, F. Paz-Chinchón, D. Petravick, A. Pieres, A. A. P. Malagón, A. Porredon, J. Prat, M. Raveri, M. Rodriguez-Monroy, R. P. Rollins, A. K. Romer, A. Roodman, R. Rosenfeld, A. J. Ross, E. S. Rykoff, S. Samuroff, C. Sánchez, E. Sanchez, J. Sanchez, D. S. Cid, V. Scarpine, M. Schubnell, D. Scolnic, L. F. Secco, S. Serrano, I. Sevilla-Noarbe, E. Sheldon, T. Shin, M. Smith, M. Soares-Santos, E. Suchyta, M. E. C. Swanson, M. Tabbutt, G. Tarle, D. Thomas, C. To, A. Troja, M. A. Troxel, D. L. Tucker, I. Tutusaus, T. N. Varga, A. R. Walker, N. Weaverdyck, R. Wechsler, J. Weller, B. Yanny, B. Yin, Y. Zhang, and J. Zuntz, Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing, Physical Review D 105 (Jan., 2022) 023520, [arXiv:2105.13549].
  * [43] M. Gatti, E. Sheldon, A. Amon, M. Becker, M. Troxel, A. Choi, C. Doux, N. MacCrann, A. Navarro-Alsina, I. Harrison, D. Gruen, G. Bernstein, M. Jarvis, L. F. Secco, A. Ferté, T. Shin, J. McCullough, R. P. Rollins, R. Chen, C. Chang, S. Pandey, I. Tutusaus, J. Prat, J. Elvin-Poole, C. Sanchez, A. A. Plazas, A. Roodman, J. Zuntz, T. M. C. Abbott, M. Aguena, S. Allam, J. Annis, S. Avila, D. Bacon, E. Bertin, S. Bhargava, D. Brooks, D. L. Burke, A. Carnero Rosell, M. Carrasco Kind, J. Carretero, F. J. Castander, C. Conselice, M. Costanzi, M. Crocce, L. N. da Costa, T. M. Davis, J. De Vicente, S. Desai, H. T. Diehl, J. P. Dietrich, P. Doel, A. Drlica-Wagner, K. Eckert, S. Everett, I. Ferrero, J. Frieman, J. García-Bellido, D. W. Gerdes, T. Giannantonio, R. A. Gruendl, J. Gschwend, G. Gutierrez, W. G. Hartley, S. R. Hinton, D. L. Hollowood, K. Honscheid, B. Hoyle, E. M. Huff, D. Huterer, B. Jain, D. J. James, T. Jeltema, E. Krause, R. Kron, N. Kuropatkin, M. Lima, M. A. G. Maia, J. L. Marshall, R. Miquel, R. Morgan, J. Myles, A. Palmese, F. Paz-Chinchón, E. S. Rykoff, S. Samuroff, E. Sanchez, V. Scarpine, M. Schubnell, S. Serrano, I. Sevilla-Noarbe, M. Smith, M. Soares-Santos, E. Suchyta, M. E. C. Swanson, G. Tarle, D. Thomas, C. To, D. L. Tucker, T. N. Varga, R. H. Wechsler, J. Weller, W. Wester, and R. D. Wilkinson, Dark energy survey year 3 results: weak lensing shape catalogue, MNRAS 504 (July, 2021) 4312–4336, [arXiv:2011.03408].
  * [44] J. Chen, Shi-Fan; DeRose et al., Cosmological constraints from the cross-correlation of desi lrgs and des y3 shear, in preparation (2023).
  * [45] H. Aihara, N. Arimoto, R. Armstrong, S. Arnouts, N. A. Bahcall, S. Bickerton, J. Bosch, K. Bundy, P. L. Capak, J. H. H. Chan, M. Chiba, J. Coupon, E. Egami, M. Enoki, F. Finet, H. Fujimori, S. Fujimoto, H. Furusawa, J. Furusawa, T. Goto, A. Goulding, J. P. Greco, J. E. Greene, J. E. Gunn, T. Hamana, Y. Harikane, Y. Hashimoto, T. Hattori, M. Hayashi, Y. Hayashi, K. G. Hełminiak, R. Higuchi, C. Hikage, P. T. P. Ho, B.-C. Hsieh, K. Huang, S. Huang, H. Ikeda, M. Imanishi, A. K. Inoue, K. Iwasawa, I. Iwata, A. T. Jaelani, H.-Y. Jian, Y. Kamata, H. Karoji, N. Kashikawa, N. Katayama, S. Kawanomoto, I. Kayo, J. Koda, M. Koike, T. Kojima, Y. Komiyama, A. Konno, S. Koshida, Y. Koyama, H. Kusakabe, A. Leauthaud, C.-H. Lee, L. Lin, Y.-T. Lin, R. H. Lupton, R. Mandelbaum, Y. Matsuoka, E. Medezinski, S. Mineo, S. Miyama, H. Miyatake, S. Miyazaki, R. Momose, A. More, S. More, Y. Moritani, T. J. Moriya, T. Morokuma, S. Mukae, R. Murata, H. Murayama, T. Nagao, F. Nakata, M. Niida, H. Niikura, A. J. Nishizawa, Y. Obuchi, M. Oguri, Y. Oishi, N. Okabe, Y. Okura, Y. Ono, M. Onodera, M. Onoue, K. Osato, M. Ouchi, P. A. Price, T.-S. Pyo, M. Sako, S. Okamoto, M. Sawicki, T. Shibuya, K. Shimasaku, A. Shimono, M. Shirasaki, J. D. Silverman, M. Simet, J. Speagle, D. N. Spergel, M. A. Strauss, Y. Sugahara, N. Sugiyama, Y. Suto, S. H. Suyu, N. Suzuki, P. J. Tait, T. Takata, M. Takada, N. Tamura, M. M. Tanaka, M. Tanaka, M. Tanaka, Y. Tanaka, T. Terai, Y. Terashima, Y. Toba, J. Toshikawa, E. L. Turner, T. Uchida, H. Uchiyama, K. Umetsu, F. Uraguchi, Y. Urata, T. Usuda, Y. Utsumi, S.-Y. Wang, W.-H. Wang, K. C. Wong, K. Yabe, Y. Yamada, H. Yamanoi, N. Yasuda, S. Yeh, A. Yonehara, and S. Yuma, The Hyper Suprime-Cam SSP Survey: Overview and Survey Design, Publications of the Astronomical Society of Japan 70 (Jan., 2018) S4, [arXiv:1704.05858].
  * [46] C. Blake, A. Amon, M. Childress, T. Erben, K. Glazebrook, J. Harnois-Deraps, C. Heymans, H. Hildebrandt, S. R. Hinton, S. Janssens, A. Johnson, S. Joudaki, D. Klaes, K. Kuijken, C. Lidman, F. A. Marin, D. Parkinson, G. B. Poole, and C. Wolf, The 2-degree Field Lensing Survey: Design and clustering measurements, Monthly Notices of the Royal Astronomical Society 462 (Nov., 2016) 4240–4265, [arXiv:1608.02668].
  * [47] C. S. Kochanek, D. J. Eisenstein, R. J. Cool, N. Caldwell, R. J. Assef, B. T. Jannuzi, C. Jones, S. S. Murray, W. R. Forman, A. Dey, M. J. I. Brown, P. Eisenhardt, A. H. Gonzalez, P. Green, and D. Stern, AGES: The AGN and Galaxy Evolution Survey, The Astrophysical Journal Supplement Series 200 (May, 2012) 8, [arXiv:1110.4371].
  * [48] C. Laigle, H. J. McCracken, O. Ilbert, B. C. Hsieh, I. Davidzon, P. Capak, G. Hasinger, J. D. Silverman, C. Pichon, J. Coupon, H. Aussel, D. L. Borgne, K. Caputi, P. Cassata, Y.-Y. Chang, F. Civano, J. Dunlop, J. Fynbo, J. S. kartaltepe, A. Koekemoer, O. L. Fevre, E. L. Floc’h, A. Leauthaud, S. Lilly, L. Lin, S. Marchesi, B. Milvang-Jensen, M. Salvato, D. B. Sanders, N. Scoville, V. Smolcic, M. Stockmann, Y. Taniguchi, L. Tasca, S. Toft, M. Vaccari, and J. Zabl, The COSMOS2015 Catalog: Exploring the 1$<$z$<$6 Universe with half a million galaxies, The Astrophysical Journal Supplement Series 224 (June, 2016) 24, [arXiv:1604.02350].
  * [49] J. A. Newman, M. C. Cooper, M. Davis, S. M. Faber, A. L. Coil, P. Guhathakurta, D. C. Koo, A. C. Phillips, C. Conroy, A. A. Dutton, D. P. Finkbeiner, B. F. Gerke, D. J. Rosario, B. J. Weiner, C. N. A. Willmer, R. Yan, J. J. Harker, S. A. Kassin, N. P. Konidaris, K. Lai, D. S. Madgwick, K. G. Noeske, G. D. Wirth, A. J. Connolly, N. Kaiser, E. N. Kirby, B. C. Lemaux, L. Lin, J. M. Lotz, G. A. Luppino, C. Marinoni, D. J. Matthews, A. Metevier, and R. P. Schiavon, The DEEP2 Galaxy Redshift Survey: Design, Observations, Data Reduction, and Redshifts, The Astrophysical Journal Supplement Series 208 (Aug., 2013) 5, [arXiv:1203.3192].
  * [50] R. Zhou, M. C. Cooper, J. A. Newman, M. L. N. Ashby, J. Aird, C. J. Conselice, M. Davis, A. A. Dutton, S. M. Faber, J. J. Fang, G. G. Fazio, P. Guhathakurta, D. Kocevski, D. C. Koo, K. Nandra, A. C. Phillips, D. J. Rosario, E. F. Schlafly, J. R. Trump, B. Weiner, C. N. A. Willmer, and R. Yan, Deep ugrizY imaging and DEEP2/3 spectroscopy: A photometric redshift testbed for LSST and public release of data from the DEEP3 Galaxy Redshift Survey, Monthly Notices of the Royal Astronomical Society 488 (Oct., 2019) 4565–4584.
  * [51] I. K. Baldry, J. Liske, M. J. I. Brown, A. S. G. Robotham, S. P. Driver, L. Dunne, M. Alpaslan, S. Brough, M. E. Cluver, E. Eardley, D. J. Farrow, C. Heymans, H. Hildebrandt, A. M. Hopkins, L. S. Kelvin, J. Loveday, A. J. Moffett, P. Norberg, M. S. Owers, E. N. Taylor, A. H. Wright, S. P. Bamford, J. Bland-Hawthorn, N. Bourne, M. N. Bremer, M. Colless, C. J. Conselice, S. M. Croom, L. J. M. Davies, C. Foster, M. W. Grootes, B. W. Holwerda, D. H. Jones, P. R. Kafle, K. Kuijken, M. A. Lara-Lopez, A. R. Lopez-Sanchez, M. J. Meyer, S. Phillipps, W. J. Sutherland, E. van Kampen, and S. M. Wilkins, Galaxy And Mass Assembly (GAMA): The G02 field, Herschel-ATLAS target selection and Data Release 3, Monthly Notices of the Royal Astronomical Society 474 (Mar., 2018) 3875–3888, [arXiv:1711.09139].
  * [52] C. Lidman, B. E. Tucker, T. M. Davis, S. A. Uddin, J. Asorey, K. Bolejko, D. Brout, J. Calcino, D. Carollo, A. Carr, M. Childress, J. K. Hoormann, R. J. Foley, L. Galbany, K. Glazebrook, S. R. Hinton, R. Kessler, A. G. Kim, A. King, A. Kremin, K. Kuehn, D. Lagattuta, G. F. Lewis, E. Macaulay, U. Malik, M. March, P. Martini, A. Möller, D. Mudd, R. C. Nichol, F. Panther, D. Parkinson, M. Pursiainen, M. Sako, E. Swann, R. Scalzo, D. Scolnic, R. Sharp, M. Smith, N. E. Sommer, M. Sullivan, S. Webb, P. Wiseman, Z. Yu, F. Yuan, B. Zhang, T. M. C. Abbott, M. Aguena, S. Allam, J. Annis, S. Avila, E. Bertin, S. Bhargava, D. Brooks, A. C. Rosell, M. C. Kind, J. Carretero, F. J. Castander, M. Costanzi, L. N. da Costa, J. De Vicente, P. Doel, T. F. Eifler, S. Everett, P. Fosalba, J. Frieman, J. García-Bellido, E. Gaztanaga, D. Gruen, R. A. Gruendl, J. Gschwend, G. Gutierrez, W. G. Hartley, D. L. Hollowood, K. Honscheid, D. J. James, N. Kuropatkin, T. S. Li, M. Lima, H. Lin, M. A. G. Maia, J. L. Marshall, P. Melchior, F. Menanteau, R. Miquel, A. Palmese, F. Paz-Chinchón, A. A. Plazas, A. Roodman, E. S. Rykoff, E. Sanchez, B. Santiago, V. Scarpine, M. Schubnell, S. Serrano, I. Sevilla-Noarbe, E. Suchyta, M. E. C. Swanson, G. Tarle, D. L. Tucker, T. N. Varga, A. R. Walker, W. Wester, and R. D. Wilkinson, OzDES multi-object fibre spectroscopy for the Dark Energy Survey: Results and second data release, Monthly Notices of the Royal Astronomical Society 496 (July, 2020) 19–35, [arXiv:2006.00449].
  * [53] M. A. Strauss, D. H. Weinberg, R. H. Lupton, V. K. Narayanan, J. Annis, Mariangela Bernardi, M. Blanton, S. Burles, A. J. Connolly, J. Dalcanton, M. Doi, Daniel Eisenstein, J. A. Frieman, M. Fukugita, J. E. Gunn, Ž. Ivezić, S. Kent, R. S. J. Kim, G. R. Knapp, R. G. Kron, J. A. Munn, H. J. Newberg, R. C. Nichol, Sadanori Okamura, T. R. Quinn, M. W. Richmond, D. J. Schlegel, K. Shimasaku, Mark SubbaRao, A. S. Szalay, D. V. Berk, M. S. Vogeley, B. Yanny, N. Yasuda, D. G. York, and I. Zehavi, Spectroscopic Target Selection in the Sloan Digital Sky Survey: The Main Galaxy Sample, The Astronomical Journal 124 (2002), no. 3 1810.
  * [54] D. J. Eisenstein, J. Annis, J. E. Gunn, A. S. Szalay, A. J. Connolly, R. C. Nichol, N. A. Bahcall, M. Bernardi, S. Burles, F. J. Castander, M. Fukugita, D. W. Hogg, Ž. Ivezić, G. R. Knapp, R. H. Lupton, V. Narayanan, M. Postman, D. E. Reichart, M. Richmond, D. P. Schneider, D. J. Schlegel, M. A. Strauss, M. SubbaRao, D. L. Tucker, D. Vanden Berk, M. S. Vogeley, D. H. Weinberg, and B. Yanny, Spectroscopic Target Selection for the Sloan Digital Sky Survey: The Luminous Red Galaxy Sample, The Astronomical Journal 122 (Nov., 2001) 2267–2280.
  * [55] K. S. Dawson, D. J. Schlegel, C. P. Ahn, S. F. Anderson, E. Aubourg, S. Bailey, R. H. Barkhouser, J. E. Bautista, A. Beifiori, A. A. Berlind, V. Bhardwaj, D. Bizyaev, C. H. Blake, M. R. Blanton, M. Blomqvist, A. S. Bolton, A. Borde, J. Bovy, W. N. Brandt, H. Brewington, J. Brinkmann, P. J. Brown, J. R. Brownstein, K. Bundy, N. G. Busca, W. Carithers, A. R. Carnero, M. A. Carr, Y. Chen, J. Comparat, N. Connolly, F. Cope, R. A. C. Croft, A. J. Cuesta, L. N. da Costa, J. R. A. Davenport, T. Delubac, R. de Putter, S. Dhital, A. Ealet, G. L. Ebelke, D. J. Eisenstein, S. Escoffier, X. Fan, N. F. Ak, H. Finley, A. Font-Ribera, R. Génova-Santos, J. E. Gunn, H. Guo, D. Haggard, P. B. Hall, J.-C. Hamilton, B. Harris, D. W. Harris, S. Ho, D. W. Hogg, D. Holder, K. Honscheid, J. Huehnerhoff, B. Jordan, W. P. Jordan, G. Kauffmann, E. A. Kazin, D. Kirkby, M. A. Klaene, J.-P. Kneib, J.-M. L. Goff, K.-G. Lee, D. C. Long, C. P. Loomis, B. Lundgren, R. H. Lupton, M. A. G. Maia, M. Makler, E. Malanushenko, V. Malanushenko, R. Mandelbaum, M. Manera, C. Maraston, D. Margala, K. L. Masters, C. K. McBride, P. McDonald, I. D. McGreer, R. McMahon, O. Mena, J. Miralda-Escudé, A. D. Montero-Dorta, F. Montesano, D. Muna, A. D. Myers, T. Naugle, R. C. Nichol, P. Noterdaeme, S. E. Nuza, M. D. Olmstead, A. Oravetz, D. J. Oravetz, R. Owen, N. Padmanabhan, N. Palanque-Delabrouille, K. Pan, J. K. Parejko, I. Pâris, W. J. Percival, I. Pérez-Fournon, I. Pérez-Ràfols, P. Petitjean, R. Pfaffenberger, J. Pforr, M. M. Pieri, F. Prada, A. M. Price-Whelan, M. J. Raddick, R. Rebolo, J. Rich, G. T. Richards, C. M. Rockosi, N. A. Roe, A. J. Ross, N. P. Ross, G. Rossi, J. A. Rubiño-Martin, L. Samushia, A. G. Sánchez, C. Sayres, S. J. Schmidt, D. P. Schneider, C. G. Scóccola, H.-J. Seo, A. Shelden, E. Sheldon, Y. Shen, Y. Shu, A. Slosar, S. A. Smee, S. A. Snedden, F. Stauffer, O. Steele, M. A. Strauss, A. Streblyanska, N. Suzuki, M. E. C. Swanson, T. Tal, M. Tanaka, D. Thomas, J. L. Tinker, R. Tojeiro, C. A. Tremonti, M. V. Magana, L. Verde, M. Viel, D. A. Wake, M. Watson, B. A. Weaver, D. H. Weinberg, B. J. Weiner, A. A. West, M. White, W. M. Wood-Vasey, C. Yeche, I. Zehavi, G.-B. Zhao, and Z. Zheng, The Baryon Oscillation Spectroscopic Survey of SDSS-III, The Astronomical Journal 145 (Jan., 2013) 10, [arXiv:1208.0022].
  * [56] K. S. Dawson, J.-P. Kneib, W. J. Percival, S. Alam, F. D. Albareti, S. F. Anderson, E. Armengaud, E. Aubourg, S. Bailey, J. E. Bautista, A. A. Berlind, M. A. Bershady, F. Beutler, D. Bizyaev, M. R. Blanton, M. Blomqvist, A. S. Bolton, J. Bovy, W. N. Brandt, J. Brinkmann, J. R. Brownstein, E. Burtin, N. G. Busca, Z. Cai, C.-H. Chuang, N. Clerc, J. Comparat, F. Cope, R. A. C. Croft, I. Cruz-Gonzalez, L. N. da Costa, M.-C. Cousinou, J. Darling, A. de la Macorra, S. de la Torre, T. Delubac, H. d. M. des Bourboux, T. Dwelly, A. Ealet, D. J. Eisenstein, M. Eracleous, S. Escoffier, X. Fan, A. Finoguenov, A. Font-Ribera, P. Frinchaboy, P. Gaulme, A. Georgakakis, P. Green, H. Guo, J. Guy, S. Ho, D. Holder, J. Huehnerhoff, T. Hutchinson, Y. Jing, E. Jullo, V. Kamble, K. Kinemuchi, D. Kirkby, F.-S. Kitaura, M. A. Klaene, R. R. Laher, D. Lang, P. Laurent, J.-M. L. Goff, C. Li, Y. Liang, M. Lima, Q. Lin, W. Lin, Y.-T. Lin, D. C. Long, B. Lundgren, N. MacDonald, M. A. G. Maia, E. Malanushenko, V. Malanushenko, V. Mariappan, C. K. McBride, I. D. McGreer, B. Menard, A. Merloni, A. Meza, A. D. Montero-Dorta, D. Muna, A. D. Myers, K. Nandra, T. Naugle, J. A. Newman, P. Noterdaeme, P. Nugent, R. Ogando, M. D. Olmstead, A. Oravetz, D. J. Oravetz, N. Padmanabhan, N. Palanque-Delabrouille, K. Pan, J. K. Parejko, I. Paris, J. A. Peacock, P. Petitjean, M. M. Pieri, A. Pisani, F. Prada, A. Prakash, A. Raichoor, B. Reid, J. Rich, J. Ridl, S. Rodriguez-Torres, A. C. Rosell, A. J. Ross, G. Rossi, J. Ruan, M. Salvato, C. Sayres, D. P. Schneider, D. J. Schlegel, U. Seljak, H.-J. Seo, B. Sesar, S. Shandera, Y. Shu, A. Slosar, F. Sobreira, A. Streblyanska, N. Suzuki, C. Tao, D. Taylor, J. L. Tinker, R. Tojeiro, M. Vargas-Magana, Y. Wang, B. A. Weaver, D. H. Weinberg, M. White, W. M. Wood-Vasey, C. Yeche, Z. Zhai, C. Zhao, G.-b. Zhao, Z. Zheng, G. B. Zhu, and H. Zou, The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data, The Astronomical Journal 151 (Feb., 2016) 44, [arXiv:1508.04473].
  * [57] R. Ahumada, C. A. Prieto, A. Almeida, F. Anders, S. F. Anderson, B. H. Andrews, B. Anguiano, R. Arcodia, E. Armengaud, M. Aubert, S. Avila, V. Avila-Reese, C. Badenes, C. Balland, K. Barger, J. K. Barrera-Ballesteros, S. Basu, J. Bautista, R. L. Beaton, T. C. Beers, B. I. T. Benavides, C. F. Bender, M. Bernardi, M. Bershady, F. Beutler, C. M. Bidin, J. Bird, D. Bizyaev, G. A. Blanc, M. R. Blanton, M. Boquien, J. Borissova, J. Bovy, W. N. Brandt, J. Brinkmann, J. R. Brownstein, K. Bundy, M. Bureau, A. Burgasser, E. Burtin, M. Cano-Diaz, R. Capasso, M. Cappellari, R. Carrera, S. Chabanier, W. Chaplin, M. Chapman, B. Cherinka, C. Chiappini, P. D. Choi, S. D. Chojnowski, H. Chung, N. Clerc, D. Coffey, J. M. Comerford, J. Comparat, L. da Costa, M.-C. Cousinou, K. Covey, J. D. Crane, K. Cunha, G. d. S. Ilha, Y. S. Dai, S. B. Damsted, J. Darling, J. W. Davidson Jr., R. Davies, K. Dawson, N. De, A. de la Macorra, N. De Lee, A. B. d. A. Queiroz, A. D. Machado, S. de la Torre, F. Dell’Agli, H. d. M. des Bourboux, A. M. Diamond-Stanic, S. Dillon, J. Donor, N. Drory, C. Duckworth, T. Dwelly, G. Ebelke, S. Eftekharzadeh, A. D. Eigenbrot, Y. P. Elsworth, M. Eracleous, G. Erfanianfar, S. Escoffier, X. Fan, E. Farr, J. G. Fernandez-Trincado, D. Feuillet, A. Finoguenov, P. Fofie, A. Fraser-McKelvie, P. M. Frinchaboy, S. Fromenteau, H. Fu, L. Galbany, R. A. Garcia, D. A. Garcia-Hernandez, L. A. G. Oehmichen, J. Ge, M. A. G. Maia, D. Geisler, J. Gelfand, J. Goddy, J.-M. L. Goff, V. Gonzalez-Perez, K. Grabowski, P. Green, C. J. Grier, H. Guo, J. Guy, P. Harding, S. Hasselquist, A. J. Hawken, C. R. Hayes, F. Hearty, S. Hekker, D. W. Hogg, J. Holtzman, D. Horta, J. Hou, B.-C. Hsieh, D. Huber, J. A. S. Hunt, J. I. Chitham, J. Imig, M. Jaber, C. E. J. Angel, J. A. Johnson, A. M. Jones, H. Jonsson, E. Jullo, Y. Kim, K. Kinemuchi, C. C. Kirkpatrick IV, G. W. Kite, M. Klaene, J.-P. Kneib, J. A. Kollmeier, H. Kong, M. Kounkel, D. Krishnarao, I. Lacerna, T.-W. Lan, R. R. Lane, D. R. Law, H. W. Leung, H. Lewis, C. Li, J. Lian, L. Lin, D. Long, P. Longa-Pena, B. Lundgren, B. W. Lyke, J. T. Mackereth, C. L. MacLeod, S. R. Majewski, A. Manchado, C. Maraston, P. Martini, T. Masseron, K. L. Masters, S. Mathur, R. M. McDermid, A. Merloni, M. Merrifield, S. Meszaros, A. Miglio, D. Minniti, R. Minsley, T. Miyaji, F. G. Mohammad, B. Mosser, E.-M. Mueller, D. Muna, A. Munoz-Gutierrez, A. D. Myers, S. Nadathur, P. Nair, K. Nandra, J. C. do Nascimento, R. J. Nevin, J. A. Newman, D. L. Nidever, C. Nitschelm, P. Noterdaeme, J. E. O’Connell, M. D. Olmstead, D. Oravetz, A. Oravetz, Y. Osorio, Z. J. Pace, N. Padilla, N. Palanque-Delabrouille, P. A. Palicio, H.-A. Pan, K. Pan, J. Parker, R. Paviot, S. Peirani, K. P. Ramrez, S. Penny, W. J. Percival, I. Perez-Fournon, I. Perez-Rafols, P. Petitjean, M. M. Pieri, M. Pinsonneault, V. J. Poovelil, J. T. Povick, A. Prakash, A. M. Price-Whelan, M. J. Raddick, A. Raichoor, A. Ray, S. B. Rembold, M. Rezaie, R. A. Riffel, R. Riffel, H.-W. Rix, A. C. Robin, A. Roman-Lopes, C. Roman-Zuniga, B. Rose, A. J. Ross, G. Rossi, K. Rowlands, K. H. R. Rubin, M. Salvato, A. G. Sanchez, L. Sanchez-Menguiano, J. R. Sanchez-Gallego, C. Sayres, A. Schaefer, R. P. Schiavon, J. S. Schimoia, E. Schlafly, D. Schlegel, D. P. Schneider, M. Schultheis, A. Schwope, H.-J. Seo, A. Serenelli, A. Shafieloo, S. J. Shamsi, Z. Shao, S. Shen, M. Shetrone, R. Shirley, V. S. Aguirre, J. D. Simon, M. F. Skrutskie, A. Slosar, R. Smethurst, J. Sobeck, B. C. Sodi, D. Souto, D. V. Stark, K. G. Stassun, M. Steinmetz, D. Stello, J. Stermer, T. Storchi-Bergmann, A. Streblyanska, G. S. Stringfellow, A. Stutz, G. Suarez, J. Sun, M. Taghizadeh-Popp, M. S. Talbot, J. Tayar, A. R. Thakar, R. Theriault, D. Thomas, Z. C. Thomas, J. Tinker, R. Tojeiro, H. H. Toledo, C. A. Tremonti, N. W. Troup, S. Tuttle, E. Unda-Sanzana, M. Valentini, J. Vargas-Gonzalez, M. Vargas-Magana, J. A. Vazquez-Mata, M. Vivek, D. Wake, Y. Wang, B. A. Weaver, A.-M. Weijmans, V. Wild, J. C. Wilson, R. F. Wilson, N. Wolthuis, W. M. Wood-Vasey, R. Yan, M. Yang, C. Yeche, O. Zamora, P. Zarrouk, G. Zasowski, K. Zhang, C. Zhao, G. Zhao, Z. Zheng, Z. Zheng, G. Zhu, and H. Zou, The Sixteenth Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra, May, 2020.
  * [58] M. Scodeggio, L. Guzzo, B. Garilli, B. R. Granett, M. Bolzonella, S. de la Torre, U. Abbas, C. Adami, S. Arnouts, D. Bottini, A. Cappi, J. Coupon, O. Cucciati, I. Davidzon, P. Franzetti, A. Fritz, A. Iovino, J. Krywult, V. L. Brun, O. L. Févre, D. Maccagni, K. Malek, A. Marchetti, F. Marulli, M. Polletta, A. Pollo, L. A. M. Tasca, R. Tojeiro, D. Vergani, A. Zanichelli, J. Bel, E. Branchini, G. De Lucia, O. Ilbert, H. J. McCracken, T. Moutard, J. A. Peacock, G. Zamorani, A. Burden, M. Fumana, E. Jullo, C. Marinoni, Y. Mellier, L. Moscardini, and W. J. Percival, The VIMOS Public Extragalactic Redshift Survey (VIPERS). Full spectroscopic data and auxiliary information release (PDR-2), Astronomy & Astrophysics 609 (Jan., 2018) A84, [arXiv:1611.07048].
  * [59] O. Le Fevre, P. Cassata, O. Cucciati, B. Garilli, O. Ilbert, V. L. Brun, D. Maccagni, C. Moreau, M. Scodeggio, L. Tresse, G. Zamorani, C. Adami, S. Arnouts, S. Bardelli, M. Bolzonella, M. Bondi, A. Bongiorno, D. Bottini, A. Cappi, S. Charlot, P. Ciliegi, T. Contini, S. de la Torre, S. Foucaud, P. Franzetti, I. Gavignaud, L. Guzzo, A. Iovino, B. Lemaux, H. J. McCracken, B. Marano, C. Marinoni, A. Mazure, Y. Mellier, R. Merighi, P. Merluzzi, S. Paltani, R. Pello, A. Pollo, L. Pozzetti, R. Scaramella, D. Vergani, G. Vettolani, A. Zanichelli, and E. Zucca, The VIMOS VLT Deep Survey final data release: A spectroscopic sample of 35016 galaxies and AGN out to z~6.7 selected with 17.5$<$=i_{}AB{}$<$=24.7, Astronomy & Astrophysics 559 (Nov., 2013) A14, [arXiv:1307.0545].
  * [60] D. Parkinson, S. Riemer-Sørensen, C. Blake, G. B. Poole, T. M. Davis, S. Brough, M. Colless, C. Contreras, W. Couch, S. Croom, D. Croton, M. J. Drinkwater, K. Forster, D. Gilbank, M. Gladders, K. Glazebrook, B. Jelliffe, R. J. Jurek, I.-h. Li, B. Madore, D. C. Martin, K. Pimbblet, M. Pracy, R. Sharp, E. Wisnioski, D. Woods, T. K. Wyder, and H. K. C. Yee, The WiggleZ Dark Energy Survey: Final data release and cosmological results, Physical Review D 86 (Nov., 2012) [arXiv:1210.2130].
  * [61] D. C. Masters, D. K. Stern, J. G. Cohen, P. L. Capak, S. A. Stanford, N. Hernitschek, A. Galametz, I. Davidzon, J. D. Rhodes, D. Sanders, B. Mobasher, F. Castander, K. Pruett, and S. Fotopoulou, The Complete Calibration of the Color-Redshift Relation (C3R2) Survey: Analysis and Data Release 2, The Astrophysical Journal 877 (May, 2019) 81, [arXiv:1904.06394].
  * [62] A. J. Ross, J. Bautista, R. Tojeiro, S. Alam, S. Bailey, E. Burtin, J. Comparat, K. S. Dawson, A. de Mattia, H. d. M. des Bourboux, H. Gil-Marín, J. Hou, H. Kong, B. W. Lyke, F. G. Mohammad, J. Moustakas, E.-M. Mueller, A. D. Myers, W. J. Percival, A. Raichoor, M. Rezaie, H.-J. Seo, A. Smith, J. L. Tinker, P. Zarrouk, C. Zhao, G.-B. Zhao, D. Bizyaev, J. Brinkmann, J. R. Brownstein, A. C. Rosell, S. Chabanier, P. D. Choi, C.-H. Chuang, I. Cruz-Gonzalez, A. de la Macorra, S. de la Torre, S. Escoffier, S. Fromenteau, A. Higley, E. Jullo, J.-P. Kneib, J. N. McLane, A. Muñoz-Gutiérrez, R. Neveux, J. A. Newman, C. Nitschelm, N. Palanque-Delabrouille, R. Paviot, A. R. Pullen, G. Rossi, V. Ruhlmann-Kleider, D. P. Schneider, M. V. Magaña, M. Vivek, and Y. Zhang, The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogs for Cosmological Analysis, Monthly Notices of the Royal Astronomical Society 498 (Sept., 2020) 2354–2371, [arXiv:2007.09000].
  * [63] A. Raichoor, A. de Mattia, A. J. Ross, C. Zhao, S. Alam, S. Avila, J. Bautista, J. Brinkmann, J. R. Brownstein, E. Burtin, M. J. Chapman, C.-H. Chuang, J. Comparat, K. S. Dawson, A. Dey, H. du Mas des Bourboux, J. Elvin-Poole, V. Gonzalez-Perez, C. Gorgoni, J.-P. Kneib, H. Kong, D. Lang, J. Moustakas, A. D. Myers, E.-M. Müller, S. Nadathur, J. A. Newman, W. J. Percival, M. Rezaie, G. Rossi, V. Ruhlmann-Kleider, D. J. Schlegel, D. P. Schneider, H.-J. Seo, A. Tamone, J. L. Tinker, R. Tojeiro, M. Vivek, C. Yèche, and G.-B. Zhao, The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale structure catalogues and measurement of the isotropic BAO between redshift 0.6 and 1.1 for the Emission Line Galaxy Sample, Monthly Notices of the Royal Astronomical Society 500 (Dec., 2020) 3254–3274, [arXiv:2007.09007].
  * [64] B. W. Lyke, A. N. Higley, J. N. McLane, D. P. Schurhammer, A. D. Myers, A. J. Ross, K. Dawson, S. Chabanier, P. Martini, N. G. Busca, H. d. M. des Bourboux, M. Salvato, A. Streblyanska, P. Zarrouk, E. Burtin, S. F. Anderson, J. Bautista, D. Bizyaev, W. N. Brandt, J. Brinkmann, J. R. Brownstein, J. Comparat, P. Green, A. de la Macorra, A. M. Gutiérrez, J. Hou, J. A. Newman, N. Palanque-Delabrouille, I. Pâris, W. J. Percival, P. Petitjean, J. Rich, G. Rossi, D. P. Schneider, A. Smith, M. Vivek, and B. A. Weaver, The Sloan Digital Sky Survey Quasar Catalog: Sixteenth Data Release, The Astrophysical Journal Supplement Series 250 (Aug., 2020) 8, [arXiv:2007.09001].