11institutetext: INAF - Osservatorio Astronomico di Brera, via Brera 28,
I-20121 Milano, Italy 22institutetext: INAF – Osservatorio Astronomico di
Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 33institutetext:
INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131
Napoli, Italy 44institutetext: Dipartimento di Fisica “E.R. Caianiello”,
Università degli studi di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano
(SA) 55institutetext: INAF – Osservatorio di Astrofisica e Scienza dello
Spazio, Via P. Gobetti 93/3, I-40129 Bologna, Italy 66institutetext: Instituto
de Astronomía y Ciencias Planetarias de Atacama (INCT), Universidad de
Atacama, Copayapu 485, Copiapó, Chile 77institutetext: INAF - Osservatorio
Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy
88institutetext: Centro de Astrobiología (CSIC-INTA), Ctra de Ajalvir km 4,
Torrejón de Ardoz, E-28850, Madrid, Spain 99institutetext: Università degli
studi di Milano-Bicocca, Piazza della scienza, I-20125 Milano, Italy
1010institutetext: Isaac Newton Group of Telescopes, ING, 38700 La Palma (S.C.
Tenerife), Spain 1111institutetext: Instituto de Astrofísica de Canarias, IAC,
Vía Láctea s/n, E-38205, La Laguna (S.C. Tenerife), Spain 1212institutetext:
Departamento de Astrofísica, Universidad de La Laguna, E-38206, La Laguna
(S.C. Tenerife), Spain 1313institutetext: School of Physics and Astronomy,
University of Birmingham, Birmingham, B15 2TT, UK 1414institutetext: INAF -
IASF Milano, via Bassini 15, I-20133 Milano, Italy 1515institutetext:
Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, vicolo
dell’Osservatorio 3, I-35122, Padova, Italy 1616institutetext: Dept. Physics,
University of Oxford, Keble Road, Oxford OX1 3RH, U.K. 1717institutetext: RAL,
Space, Science and Technology Facilities Council, Harwell, Didcot OX11 0QX,
U.K. 1818institutetext: Instituto de Astrofísica de Andalucía (CSIC), P.O. Box
3004, E-18080, Granada, Spain 1919institutetext: Kapteyn Astronomical
Institute, Rijksuniversiteit Groningen, Landleven 12, 9747 AD Groningen, the
Netherlands 2020institutetext: SRON - Netherlands Institute for Space
Research, Landleven 12, 9747 AD Groningen, the Netherlands 2121institutetext:
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3
0HA, U.K. 2222institutetext: Departamento de Física de la Tierra y
Astrofísica, Universidad Complutense de Madrid, E-28040 Madrid, Spain
2323institutetext: Instituto de Física de Partículas y del Cosmos (IPARCOS),
Universidad Complutense de Madrid, E-28040 Madrid, Spain 2424institutetext:
Università di Bologna - Department of Physics and Astronomy, via Gobetti 93/2,
I-40129, Bologna, Italy

# WEAVE-StePS. A stellar population survey using WEAVE at WHT

A. Iovino<EMAIL_ADDRESS>B. M. Poggianti 22 A. Mercurio 33 4 4 M.
Longhetti 11 M. Bolzonella 55 G. Busarello 33 M. Gullieuszik 22 F. La Barbera
33 P. Merluzzi 33 L. Morelli 66 1 1 C. Tortora 33 D. Vergani 55 S. Zibetti 77
C. P. Haines 66 1 1 L. Costantin 88 F. R. Ditrani 11 9 9 L. Pozzetti 55 J.
Angthopo 11 M. Balcells 1010 11 11 12 12 S. Bardelli 55 C. R. Benn 1010 M.
Bianconi 1313 L. P. Cassarà 1414 E. M. Corsini 151522 O. Cucciati 55 G. Dalton
1616 17 17 A. Ferré-Mateu 1111 12 12 M. Fossati 99 1 1 A. Gallazzi 77 R.
García-Benito 1818 B. Granett 11 R. M. González Delgado 1818 A. Ikhsanova 1515
E. Iodice 33 S. Jin 161619192020 J. H. Knapen 1111 12 12 S. McGee 1313 A.
Moretti 22 D. N. A. Murphy 2121 L. Peralta de Arriba 2121 8 8 A. Pizzella 1515
2 2 P. Sánchez-Blázquez 2222 23 23 C. Spiniello 1616 3 3 M. Talia 2424 5 5 S.
C. Trager 1919 A. Vazdekis 1111 12 12 B. Vulcani 22 E. Zucca 55

(Received November 3, 2022; accepted January 18, 2023)

###### Abstract

Context. The upcoming new generation of optical spectrographs on four-meter-
class telescopes will provide valuable opportunities for forthcoming galaxy
surveys through their huge multiplexing capabilities, excellent spectral
resolution, and unprecedented wavelength coverage.

Aims. WEAVE is a new wide-field spectroscopic facility mounted on the 4.2 m
William Herschel Telescope in La Palma. WEAVE-StePS is one of the five
extragalactic surveys that will use WEAVE during its first five years of
operations. It will observe galaxies using WEAVE MOS ($\sim$ 950 fibres
distributed across a field of view of $\sim$ 3 square degrees on the sky) in
low-resolution mode ($R\sim$ 5000, spanning the wavelength range $3660-9590$
Å).

Methods. WEAVE-StePS will obtain high-quality spectra ($S/N\sim 10\,\AA^{-1}$
at $R\sim$ 5000) for a magnitude-limited ($I_{AB}=20.5$) sample of $\sim
25,000$ galaxies, the majority selected at $z\geq 0.3$. The survey goal is to
provide precise spectral measurements in the crucial interval that bridges the
gap between LEGA-C and SDSS data. The wide area coverage of $\sim$ 25 square
degrees will enable us to observe galaxies in a variety of environments. The
ancillary data available in each of the observed fields (including X-ray
coverage, multi-narrow-band photometry and spectroscopic redshift information)
will provide an environmental characterisation for each observed galaxy.

Results. This paper presents the science case of WEAVE-StePS, the fields to be
observed, the parent catalogues used to define the target sample, and the
observing strategy that was chosen after a forecast of the expected
performance of the instrument for our typical targets.

Conclusions. WEAVE-StePS will go back further in cosmic time than SDSS,
extending its reach to encompass more than $\sim 6$ Gyr. This is nearly half
of the age of the Universe. The spectral and redshift range covered by WEAVE-
StePS will open a new observational window by continuously tracing the
evolutionary path of galaxies in the largely unexplored intermediate-redshift
range.

###### Key Words.:

galaxies: general - galaxies: formation - galaxies: evolution - galaxies:
statistics \- galaxies: star formation - galaxies: stellar content

##  1 Introduction

One of the unfulfilled goals of astrophysics is to understand the physical
processes that cause the formation and evolution of luminous structures to
deviate so markedly from the assembly history of dark matter (DM) haloes. The
large-scale structure evolution of the Universe is theoretically understood
and well reproduced by simulations on scales larger than $\sim 1$ Mpc. At
these scales, the behaviour of the main agents that shape large-scale
structure growth (gravity and dark energy) is relatively well known. At
smaller scales, the stellar mass growth of galaxies within DM haloes, and thus
the complex mechanisms that ae known as gastrophysics (Bond, 1993), depend on
highly nonlinear processes (star formation, energetic feedback, and mergers,
to mention a few) whose working details are still largely unknown (Kuhlen et
al., 2012; Bullock & Boylan-Kolchin, 2017).

Advanced theoretical models are needed to shed light on the mechanisms that
regulate the connection between galaxies and their DM haloes and, in turn, on
the connection with the surrounding large-scale structures. Still, the
complexity of the problem is such that observations are essential to
empirically constrain both theories and simulations of galaxy assembly history
(Wechsler & Tinker, 2018).

In the past decades, the study of galaxies in the local Universe has greatly
enriched our knowledge and understanding of galaxy evolution. Theoretical and
empirical approaches are now anchored at $z\sim 0$ by the large, uniform, and
complete spectroscopic data of the Sloan Digital Sky Survey (SDSS; York et
al., 2000). Observations of colours, morphology, spectral type, and star
formation of galaxies show a striking bimodality in the galaxy population,
where blue star-forming late-type galaxies are separated from red quiescent
early-type galaxies (Kauffmann et al., 2003; Blanton et al., 2003; Baldry et
al., 2004).

The stellar mass of a galaxy is a powerful and reliable proxy for its total
mass, and it is a fundamental quantity for predicting the position of each
galaxy in the observed bimodal distribution. However, especially at lower
galaxy stellar masses, the role of the environment in defining galaxy
properties, and thus their position in the observed bimodal distribution,
cannot be neglected (Kauffmann et al., 2004; Baldry et al., 2006; Blanton &
Moustakas, 2009; Bamford et al., 2009).

The bimodality is also visible in spatially resolved observations of local
galaxies (Zibetti et al., 2017; López Fernández et al., 2018), suggesting that
its local and structural origin might lie within the galaxies. This bimodal
distribution in galaxy properties persists at higher redshifts, where only the
relative fraction of the two populations in the bimodality peaks changes,
while the role played by the environment becomes progressively less important
(Peng et al., 2010; Bolzonella et al., 2010; Iovino et al., 2010; Haines et
al., 2017).

Parallel information on the global cosmic star formation history (SFH)
provides an integrated view of galaxy evolution: there is firm evidence for a
first phase of an increasing cosmic star formation rate (SFR) density in the
Universe, reaching a peak at $z\sim 2$, roughly 3.5 Gyr after the Big Bang,
followed by a second phase in which the cosmic SFR density declines steadily
to the present-day value (Madau & Dickinson, 2014). Although largely
independent of the complex evolutionary phases of each galaxy, this
observational constraint provides a boundary that the cumulative galaxy SFHs
need to satisfy.

Many works have explored the fossil record information encoded in the spectra
of local Universe galaxies, providing important constraints on the formation
histories of galaxies of different masses, the archaeological reconstruction.
However, retrieving information on the early phases of the SFHs from nearby
galaxies has intrinsic limits: most local galaxies are too old for the
differences in their early SFHs to be resolved because stellar spectra in the
age range $>5$ Gyr are very similar (see Gallazzi et al., 2005).

Galaxy spectra contain the luminosity-weighted output from billions of stars
and the surrounding interstellar medium (ISM) and thus encode essential
information on the physical properties of stellar populations and the gas
content within each galaxy. In turn, the most powerful way of probing galaxy
evolution (see Conroy, 2013, for a review) and of exploring the physical
mechanisms that stop or rekindle star formation is tracing galaxy masses,
stellar ages, chemical abundances, and the stellar initial mass function
(IMF).

An alternative approach consists of making a census of galaxies at
increasingly earlier redshifts, which is called the look-back approach. By
comparing snapshots of galaxy samples taken at different cosmic epochs, we can
trace the evolution of galaxies as a population back in time. However, it is
difficult to directly link the galaxies observed in the local Universe with
their progenitors at higher redshifts because we are fundamentally ignorant of
the actual progenitors of present-day galaxies of different types.

The challenge for new observational studies is thus to combine the
archaeological and the look-back approaches to provide precise measurements of
a variety of physical parameters of galaxies, continuously and homogeneously
sampled as a function of cosmic time and for a statistically robust sample of
galaxies in different environments. The goal is to capture the richness
(including the inherently stochastic nature) of the various processes involved
in galaxy evolution, and to determine the different mechanisms (both internal
and external) capable of modulating or shutting down star formation activity
in galaxies and thus give rise to the observed galaxy bimodality in its many
facets and its evolution.

So far, the only notable survey designed to obtain high-quality high-
resolution spectra in the relatively distant Universe is the Large Early
Galaxy Census survey (LEGA-C), whose data are limited to the redshift window
$0.6\leq z\leq 1.0$ and to a sample of $\sim$ 3200 galaxies within the COSMOS
field. The LEGA-C spectra have a median signal-to-noise ratio ($S/N$) of
$\sim$20 $\AA^{-1}$ and a resolution $R\sim 2500$. They cover the observed
wavelength range [6000 - 8800] $\AA$, corresponding to a rest-frame wavelength
range [3750 - 5500]/[3000 - 4400] $\AA$ at $z\sim 0.6/1.0$, respectively (see
van der Wel et al., 2016; Straatman et al., 2018; van der Wel et al., 2021).
The LEGA-C observations have shown the full power of high-resolution continuum
spectroscopy with a high signal-to-noise ratio as a tool for constraining
galaxy formation models (Bezanson et al., 2018; Wu et al., 2018, 2020; Chauke
et al., 2018, 2019).

However, fundamental questions remain open. The LEGA-C observations suggest
that even the evolution of the most massive and supposedly passive galaxies
does not always progress in a state of permanent quiescence after their
initial star formation burst, as previously thought. Some of these galaxies
may experience new star formation episodes between $z\sim 0.8$ and $z\sim 0$
(Chauke et al., 2018; Wu et al., 2021). Defining the mechanisms that give rise
to this unexpected rekindling of star formation activity will provide
important constraints on the evolutionary path of galaxies.

Figure 1: Comparison of typical SDSS ($z\sim 0.1$, solid coloured lines) and
VIPERS ($z\sim 0.5$, dash-dotted lines) spectra of four early-type galaxies of
different stellar masses as indicated in the plot. VIPERS spectra are offset
vertically by 10 units for clarity. The $S/N$ values of all these spectra are
close to the median value for galaxies of that mass in the corresponding
survey. The black curves show model spectra of a single stellar population
with solar metallicities and ages in the range of 2.5-10 Gyr (from bottom to
top), obtained using the MILES spectral library (Vazdekis et al., 2010) and
chosen to reproduce the data. Key spectral indices used for estimating the
stellar ages or metallicities are indicated with their names, and the grey
bands refer to the width of the Lick wavebands. The low $S/N$ and low
resolution ($\sim$ 16 Å FWHM, $R\sim 210$) of the VIPERS spectra smooth out
(or fill in) the key spectral absorption features, preventing reliable
measurements of the Lick indices for individual galaxies. The higher-
resolution SDSS spectra retain the details of these absorption features.

Surprisingly, the intermediate-$z$ window $0.3\leq z\leq 0.7$ remains largely
unexplored by surveys of the quality required to adopt the archaeological
look-back approach, limiting our ability to retrace the evolutionary path of
galaxies without discontinuities over the $\sim 8$ Gyr since $z\sim 1$. Until
recently, only a few works have analysed ages and metallicities from high
$S/N$ spectra of intermediate-redshift galaxies, most of them focusing on
quiescent galaxies in clusters (e.g. Kelson et al. (2000); Sánchez-Blázquez et
al. (2009); Jørgensen & Chiboucas (2013); Ferré-Mateu et al. (2014); Werle et
al. (2022), but see Gallazzi et al. (2014) for an analysis of both quiescent
and star-forming field galaxies). Despite the small sample sizes (a few tens
to one hundred galaxies), these works have highlighted the importance of
tracing the physical properties of galaxies at different redshifts and in
different environments.

The WHT Enhanced Area Velocity Explorer (WEAVE), a new optical spectrograph
mounted at the $4.2$m William Herschel Telescope (WHT) in La Palma, offers the
possibility of filling this gap in our knowledge. Some of the unique
capabilities of WEAVE are its wide field of view ($\sim 3$ square degrees on
the sky), its high multiplexing capabilities ($\sim 950$ fibres per pointing
when used in MOS, i.e. multi-object spectrograph mode, with a minimum
separation of fibres on the sky of $\sim 60\arcsec$), and its wide spectral
coverage, $\sim 3700$ to $\sim 9600\AA$ when used in its low-resolution mode
at $R\sim$ 5000 (Balcells et al., 2010; Dalton et al., 2012, 2014, 2016b). The
WEAVE LR mode provides an FWHM $\sim 1\AA$ at 5000 $\AA$, spanning values that
vary from 0.9 $\AA$ in the blue arm and up to 1.5 $\AA$ in the red arm. This
roughly corresponds to 3 pixels throughout the entIre covered wavelength
range.

The WEAVE-Stellar Population Survey (WEAVE-StePS in short) is one of the eight
surveys (five of which are extragalactic) that will be performed by the WEAVE
spectroscopic facility, using a total of approximately 1150 nights over five
years of WHT time (see Jin et al., 2022, for more details on the planning of
WEAVE operations). WEAVE-StePS will use $\sim 3\%$ of this total budget of
nights and aims to take full advantage of the WEAVE capabilities to obtain
high-quality ($S/N\sim$ 10 $\AA^{-1}$ at $R\sim$ 5000) spectra of $\sim
25,000$ galaxies, the vast majority in the redshift range $0.3\leq z\leq 0.7$.
The goal is to provide precise spectral measurements in the crucial redshift
interval that bridges the gap between LEGA-C and SDSS data, thus rising to the
challenge of characterising galaxy evolution in this intermediate-redshift
range by obtaining data with a quality that is comparable to SDSS and LEGA-C
data.

In this paper, we describe WEAVE-StePS in detail. The paper is organised as
follows. In Sect. 2 we illustrate that the characteristics of the WEAVE
spectrograph can provide a statistical galaxy sample of unique quality,
enabling us to address significant questions about galaxy evolution. In Sect.
3 we detail the choices that define WEAVE-StePS, the apparent magnitude and
photometric redshift selection, and the specific fields that will be targeted
by our survey. In Sect. 4 we discuss the WEAVE-StePS observational strategy,
including the expected $S/N$ distribution for the galaxy sample observed by
WEAVE-StePS. Finally, in Sect. 5 we briefly summarize the main points that
define WEAVE-StePS.

We adopt $H_{0}=69.6$ km s-1 Mpc-1, $\Omega_{M}=0.286$, and
$\Omega_{\Lambda}=0.714$ as fiducial cosmological parameters throughout our
paper (Bennett et al., 2014). All magnitudes are quoted in the AB system (Oke,
1974).

##  2 Main Science Goals of WEAVE-StePS

Three crucial ingredients are needed to shed light on the physical mechanisms
that cause the different evolutionary routes of galaxies throughout cosmic
time.

Figure 2: Observability of the main spectral indices as a function of redshift
($0.05<z<1.0$) in the wavelength range covered by the WEAVE spectrograph in
its low-resolution mode. The visibility of other emission/absorption lines is
easily extrapolated from adjacent indices. The blue (red) region indicates the
wavelength range covered by the blue (red) arm of the WEAVE spectrograph, and
the overlap region covered by both arms is shaded in violet. The two narrower
vertical grey bands are CCD gaps in the blue and red arm of the WEAVE
spectrograph. They indicate the redshift ranges in which some of the features
will not be available in observations. The empty region shows the redshift
range in which the large majority of StePS targets will be observed ($z\geq
0.3$). The bottom panel shows an OH sky lines spectrum for reference.

The first ingredient is a large and well-defined sample of target galaxies,
chosen to encompass a range of galaxy properties (stellar masses,
morphologies, and colours, to mention the main properties) in a wide range of
redshifts beyond the local Universe and located in a variety of environments.

The second ingredient is high-quality photometric data for each target galaxy
(the wider the wavelength range covered, the better). High-quality imaging
enables the retrieval of morphological parameters for each galaxy. The
photometric information in many bands enables the estimation of accurate
photometric redshifts for each target galaxy (typical error in redshift
${\delta}_{z}\sim 0.03\times(1+z)$). With spectral energy distribution (SED)
fitting techniques, rest-frame physical properties are retrieved: galaxy
stellar masses, rest-frame magnitudes/colours, and, although with large
uncertainties, first-order estimates of galaxy star formation rates, ages, and
metallicities.

More accurate redshift information (e.g. those obtained from narrow-band
filter photometry or from redshift surveys, with a typical velocity error
ranging from ${\delta}_{v}\sim 100-1000$ km/s) is a valuable addition: it
allows a more robust estimate of quantities from SED fitting. Furthermore, if
the number density of galaxies with accurate redshift information is high
enough in the considered volume, each galaxy can be assigned its precise
location within the cosmic web, adding the environment variable to the
analysis.

The third and crucial ingredient is high-quality spectroscopic data for each
target galaxy, meaning spectra with an adequate $S/N$ and spectral resolution
over a sizeable rest-frame wavelength range, to obtain key physical
information such as the age, metallicity, and abundance ratios of each galaxy
stellar populations and ISM, and the kinematics for its stellar and gaseous
components.

Many large (N${}_{\rm gal}\geq$ 10000) surveys of distant galaxies ($z\geq
0.3$) satisfy the first two requirements. To mention a few, theses are the AGN
and Galaxy Evolution Survey (AGES, Kochanek et al., 2012), the Smithsonian
Hectospec Lensing Survey (SHELS, Geller et al., 2014), the Galaxy and Mass
Assembly survey (GAMA, Driver et al., 2012), or the Baryon Oscillation
Spectroscopic Survey (BOSS, Dawson et al., 2013) at the lower redshift end and
the DEEP Extragalactic Evolutionary Probe 2 (DEEP2, Newman et al., 2013), the
VIMOS Public Extragalactic Redshift Survey (VIPERS, Guzzo et al., 2014),
zCOSMOS (Lilly et al., 2009), and the VIMOS-VLT Deep Survey (VVDS, Le Fèvre et
al., 2015) at higher redshifts. The spectral quality of these surveys (both
their typical low $S/N$ values and low resolution, $R\sim 500-1000$) makes
them very efficient at measuring redshifts, but it is insufficient for
retrieving galaxy stellar population and gas properties.

Overcoming the limits of low $S/N$ spectroscopy by stacking spectra of a large
number of galaxies selected in homogeneous bins (e.g. stellar mass, redshift,
and velocity dispersion) is not a fully satisfying solution: it may provide
the correct (light-weighted) average properties in a given bin, but misses the
information about the scatter around this average and the higher moments of
the distribution. Determining these moments is important for quantifying the
number of stochastic events involved in galaxy evolution processes and the
timescales of transitional phases.

Only deep and high-resolution ($R\gtrsim 2000$) spectroscopy can provide
reliable measurements of the high number of absorption features in the stellar
continuum and the emission features superimposed on it, unlocking the variety
of physical information that galaxy spectra can provide. Figure 1, which
directly compares VIPERS and SDSS spectral data, makes a clear case for this
point. The low $S/N$ and low-resolution VIPERS spectra ($\sim$ 16 Å FWHM)
smooth out (or fill in) the key spectral absorption features, preventing
reliable measurements of the Lick indices for individual galaxies. Even the
power of emission-line diagnostics in these spectra is severely limited to the
strongest-lined galaxies, which are just the tip of the iceberg of the star-
forming population.

Using SDSS spectra, Gallazzi et al. (2005) have argued that an $S/N\sim$ 20
$\AA^{-1}$ is the threshold for reliable age and metallicity estimates based
on absorption features. More recent results have shown that stellar ages,
metallicities, velocity dispersions, and dust extinction can be accurately
recovered without significant systematic offsets down to $S/N\sim$ 10
$\AA^{-1}$, albeit with significant uncertainties (Choi et al., 2014; Magris
et al., 2015; Citro et al., 2016).

The WEAVE spectrograph will provide adequate spectral resolution ($R\sim$ 5000
in its low-resolution, LR, mode and $S/N$ for relatively bright targets while
offering another important advantage: its wide spectral range coverage,
spanning the region $3660-9590\AA$. The blue spectral range observed by WEAVE
will map the UV rest-frame down to $\sim 2900$ Å for galaxies at $z\sim 0.3$,
extending to $\sim 2200$ Å for galaxies at $z\geq 0.7$. This spectral window
provides information on hot stellar components of galaxies, such as the young
stars that trace the most recent tail of galaxy star formation histories. This
is a novelty of the WEAVE observations, as LEGA-C data, covering the observed
wavelength range [6000 - 8800] $\AA$, start to probe the rest-frame region
below $\sim$ 3200 $\AA$ only for the highest-redshift galaxies.

As shown in Fig. 2, this wide wavelength range up to redshift $z\sim 1$ yields
a large number of absorption and emission features that are useful tracers of
physical properties of the stellar and ionised-gas components. WEAVE spectra
can provide homogeneous measurements of gas metallicity, and they can
distinguish between AGN, LINER, and star-formation-powered emission using the
same set of lines over a wide redshift range. The [OIII]$\lambda$5007 emission
line and the Hβ line are both within the wavelength range of WEAVE up to z
$\sim 0.9$, while $\rm H\alpha$ is available up to $z\sim 0.4$ and can be used
for different line-ratio diagnostics detection of AGN (Kewley et al., 2006;
Lamareille, 2010; Juneau et al., 2011, and references therein). Similarly, the
[OII]$\lambda$3727 line is available as a star formation indicator and can be
calibrated using $\rm H\alpha$ up to $z\sim 0.4$. Metallicity indicators for
refining the SFR estimate are available up to $z=0.7$, for example
[OIII]5007/$H_{\beta}$, [OIII]5007/[OII]3727 and, when available,
[NeIII]3870/[OII]3727 (Nagao et al., 2006; Kewley & Ellison, 2008; Speagle et
al., 2014).

The potential of WEAVE-like spectra for galaxy evolution studies has been
investigated in detail in Costantin et al. (2019) and in Ditrani et al. (2023,
in prep), using simulations that mimic WEAVE-expected performances for the
full variety of spectral galaxy types that WEAVE-StePS will observe. Adopting
Bayesian analysis, as developed in Gallazzi et al. (2014), coupled with the
extended galaxy model library of Zibetti et al. (2017), Costantin et al.
(2019) have shown that with the full suite of indices available to WEAVE, even
with an $S/N$ as low as $\sim$ 10 ${\AA}^{-1}$ in the observed I band, it is
possible to be sensitive to secondary episodes of star formation younger than
$\sim 0.2$ Gyr in addition to a bulk stellar population older than $\sim$ 5
Gyr, which is the expected age for the stellar population of massive galaxies
that WEAVE-StePS will target. It will thus be possible to recover evidence of
past rejuvenation episodes in old galaxies, or conversely, to identify
galaxies containing truly long-term passive old stellar populations. In a
parallel paper and using the same method, Ditrani et al. (2023, in prep) have
shown that unbiased stellar metallicity estimates can be obtained in WEAVE-
like spectra at an $S/N$ as low as $\sim$ 10 ${\AA}^{-1}$ in the observed I
band. For these typical $S/N$ values, the uncertainties in the retrieved
metallicity are high when the spectra are dominated by young stars ($\sim 0.3$
dex for galaxies with $r$-band-weighted ages younger than 1 Gyr), but they
decrease significantly for the older galaxy population (down to $\sim 0.2$ dex
for galaxies with $r$-band-weighted ages older than 6 Gyr). Before we describe
our survey planning in detail, we concisely list the principal physical
information we intend to obtain for WEAVE-StePS galaxies:

  * •

The age(s) of the stellar component. WEAVE-StePS high-quality data will
provide reliable estimates of stellar population ages. The distribution of
stellar population ages will provide constraints on the stellar mass growth of
galaxies across cosmic time from $z\sim 1$ to today, a redshift range that
will be available by combining the information provided by WEAVE-StePS with
LEGA-C and SDSS data.

  * •

The star formation activity timescale. The definition of the typical timescale
for the decrease in star formation activity in galaxies and the parallel
quenching phenomena will benefit from a detailed estimate of the stellar
population ages of galaxies. WEAVE-StePS spectra will also enable us to
estimate the presence of rejuvenating events and, conversely, will provide the
demographic of truly passive old galaxies (see Costantin et al., 2019).

  * •

The metal abundances in stars and gas. We will use WEAVE-StePS spectra to
measure individual chemical abundances in galaxy spectra (see e.g. La Barbera
et al., 2017; Gallazzi et al., 2021) and investigate the mass–metallicity
relations for the gaseous and stellar components of observed galaxies, as well
as the fundamental metallicity relation (Mannucci et al., 2010). This is an
interesting indicator of galaxy evolution. It reflects gas cycling through
stars and any gas exchange (inflows or outflows) between the galaxy and its
environment (see Maiolino & Mannucci, 2019, for a comprehensive review).

  * •

The presence/absence of AGN activity. The wide wavelength range covered by
WEAVE-StePS spectra will allow us to use a common set of lines as AGN/LINER
activity indicators to distinguish between AGN, LINER, and star-formation-
powered emission. The AGN fraction demographic will shed light on the role of
AGN in galaxy evolution (Heckman & Best, 2014).

  * •

The presence of inflows and outflows. The phenomena of inflows and outflows of
gas play an important role in regulating the growth of galaxies as powerful
agents to accrete/remove gas from the galaxy (Rubin et al., 2012; Harrison et
al., 2018). The [OIII]5007 emission line, which is used to detect and study
AGN outflows (Woo et al., 2016), is within the wavelength range of WEAVE up to
z $\sim$ 0.9. The adopted R $\sim$ 5000 spectral resolution, corresponding to
a FWHM $\sim 50$ km/s, will enable WEAVE-StePS to detect the different
kinematic components expected in these objects. This in turn will enable the
separation of narrow ($\sim$ 100 km/s) and broad (¿300 km/s) components that
are generally present in AGN outflows.

  * •

The stellar and dynamical mass of galaxies. An accurate estimate of stellar
and dynamical masses is crucial to link the evolution of galaxies with their
DM halo (Tortora et al., 2018). WEAVE spectra will enable estimates of galaxy
velocity dispersion with a statistical accuracy below $\sim 15\%$ and with
deviations smaller than $\sim 30\%$ (La Barbera et al., 2010). WEAVE-StePS
will be the first survey to provide a large sample of galaxies in the
intermediate-redshift range with accurate estimates of stellar velocity
dispersions and dynamical and stellar masses. We will also be able to
constrain the stellar IMF using gravity-sensitive features (see e.g. La
Barbera et al., 2013; Spiniello et al., 2015) and its impact on stellar mass
estimates at intermediate redshifts.

  * •

Green valley, or transition, galaxies. We expect to observe a sizeable sample
of transition/green-valley galaxies (see Figure 3). These galaxies are located
in the wide region separating blue and red galaxies. They have abandoned
intense star formation activity and are on their way to reaching a passive
status. They contribute to the bending and broadening of the star-forming main
sequence observed at the high galaxy mass ranges we target (Popesso et al.,
2019) and can help to shed light on the mechanisms that quench star formation
in galaxies (Angthopo et al., 2021).

Figure 3: Expected redshift and colors distribution of WEAVE-StePS galaxies.
Left panel: Redshift distribution of a magnitude-limited sample of galaxies
down to $I_{AB}\sim 20.5$. The y-axis shows the expected surface density of
galaxies per square degree and per 0.1 redshift interval. The mean values
(thick line) and their field-to-field variance (shaded region) were obtained
in random positions within the CFHTLS-W1 and CFHTLS-W4 photometric catalogues
(Ilbert et al., 2006; Hudelot et al., 2012). These numbers were obtained by
removing all regions masked because of lower-quality photometry. Right panel:
Expected two-colour distribution of our target sample on the rest-frame
colour-colour $(NUV-r)$ and $(r-J)$ plane, as obtained using the WEAVE-StePS
sample definition and the UltraVISTA catalogue in the COSMOS field (McCracken
et al., 2012; Ilbert et al., 2013). This colour-colour plot is an efficient
way to distinguish between quiescent and star-forming galaxies, avoiding a mix
between dusty star-forming galaxies and quiescent galaxies, as extinction
moves star-forming galaxies along a diagonal direction parallel to the slanted
line in the plot (see Ilbert et al., 2010, for more details).

The large sample of galaxies that WEAVE-StePS plans to observe (roughly 25000;
see Section 4) will provide an opportunity for detecting and selecting
rare/peculiar targets. An interesting set of objects that may serendipitously
enter our observations is that of strongly lensed galaxies, which are detected
through their emission lines that are overlaid on the observed foreground
galaxy spectra; see Warren et al. (1996) for a prototypical such case, and
more recently, Bolton et al. (2006) and Talbot et al. (2021). Our target
sample will include many massive galaxies at $\sim 0.5$, which are ideal
lenses considering their mass and location in redshift. We can therefore
expect a few lensed galaxies to enter our sample whenever foreground (lens)
and background (lensed) galaxies are well aligned.

Last but not least, WEAVE-StePS will undoubtedly be a legacy survey. Regular
public data releases are planned for WEAVE data, with an expected yearly
cadence of public data releases, following the first public data release two
years after the start of survey operations (Jin et al., 2022). The spectra of
thousands of WEAVE-StePS galaxies and their associated measurements (e.g.
emission lines and the equivalent widths of stellar absorption features) will
be valuable for the identification and characterisation of galaxy populations
in large sky surveys. As an example, the spectra and equivalent widths of
emission lines such as $\rm H\alpha$, $H_{\beta}$, [NII]6585, [OIII]5007, and
[OII]3727 can be input to machine-learning algorithms applied to narrow-band
photometric surveys such as J-PAS (Benitez et al., 2014). This information
will make it possible to infer the emission-line properties of objects through
their observed narrow-band colours, enabling unbiased samples of QSO, AGN and
star-forming galaxies to be identified up to z$\sim$1 (Martínez-Solaeche et
al., 2021, 2022).

##  3 Survey plan of WEAVE-StePS

This section details the constraints that define the WEAVE-StePS galaxy sample
and explore its redshift, colour, and stellar mass distributions. We then
present the WEAVE-StePS target fields: their position, area coverage, and
available ancillary data (both photometric and spectroscopic), and we discuss
the quality of the astrometry for our input catalogues and that of the
available photometric redshifts. Finally, we conclude the section by
discussing the yearly visibility of each of the chosen fields.

###  3.1 Sample selection: Magnitude and redshift constraints

One of the main characteristics of the WEAVE spectrograph is its high
multiplexing capability. The sample of galaxies to be observed is expected to
have a surface density that fully exploits this characteristic while covering
a magnitude range that enables obtaining high $S/N$ spectra at $R\sim$ 5000
with a 4m class telescope.

The two simple constraints that define the WEAVE-StePS target galaxy sample
are:

  * •

target total observed magnitude $I_{AB}\leq 20.5$, and

  * •

target redshift $z\geq 0.3$.

As we show in Section 4, this magnitude limit is well within the capabilities
of WEAVE to produce spectra at $S/N\sim 10\,\AA^{-1}$ for the majority of the
targeted sample. In the following, we explore the distribution in redshift and
the physical properties of the sample of galaxies defined using these two
simple constraints, taking advantage of public catalogues available in three
of the four fields that we will target (see Section 3.2), namely the two
CFHTLS fields CFHTLS-W1 and CFHTLS-W4, and the COSMOS field.

To assess the number density of the sample of galaxies defined by the two
WEAVE-StePS constraints, we used the publicly available photometric catalogues
(including photometric redshifts) in the two wide areas of the CFHTLS-W1 and
CFHTLS-W4 fields (Ilbert et al., 2006; Hudelot et al., 2012), excluding
galaxies that are located in poor-quality/masked regions. The resulting
redshift distribution of target galaxies, including its field-to-field
variance (i.e. the $rms$ of the counts obtained at different random sky
positions within the two fields) is shown in the left panel of Fig. 3.

Roughly $\sim$60% of the magnitude-selected targets are located at $z\geq$0.3,
and only $\sim 2.5\%$ are located at $z\geq$0.7. The actual cumulative numbers
are $\sim 2500\pm 250$ galaxies per square degree when no redshift pre-
selection is applied, and $\sim 1500\pm 170$ galaxies per square degree when
the subset of galaxies at $z\geq$ 0.3 is considered.

The constraint in redshift ($z\geq$ 0.3, photometric or spectroscopic whenever
available) combined with the bright magnitude selection focuses the interest
of WEAVE-StePS on the intermediate-redshift range between LEGA-C and SDSS:
$0.3<z<0.7$, with only a tail of the sample, roughly $4\%$, located at
$z\geq$0.7. Only in the COSMOS field will we relax the redshift limit to
$z\geq$ 0.1 the (see Section 3.2 for more details).

The two constraints in $I_{AB}$ magnitude and redshift imply that a total of
$\sim$ 5000 galaxies are available for targeting within each WEAVE FoV
pointing ($\sim$ 8000 if no redshift cut-off is chosen). This density of
targets is very well suited to the multiplexing capabilities of WEAVE,
enabling multiple passes on the same sky position (see Section 4). It is worth
noting that these numbers represent a conservative lower limit for target
surface densities that is obtained by removing lower-quality masked regions in
any of the bands that are used to compute photometric redshifts, regions
surrounding stars, and general problematic areas.

To explore the physical properties of the galaxies selected by WEAVE-StePS in
even more detail, we take advantage of the COSMOS field. This field covers a
smaller area, but with a much larger set of ancillary data. The publicly
available UltraVISTA catalogue provides high-quality photometric redshifts,
rest-frame magnitudes, and galaxy stellar masses that were obtained using the
code LePhare and a library of synthetic spectra generated using the Stellar
Population Synthesis (SPS) model of Bruzual and Charlot (Bruzual & Charlot,
2003) and a Chabrier IMF (Chabrier, 2003) for each galaxy in the COSMOS field
down to $\sim$ 24 in the $K_{sAB}$ band. The right panel of Fig. 3 shows the
rest-frame $(NUV-r)$ vs $(r-J)$ colour-colour diagram for galaxies selected
using WEAVE-StePS criteria in the UltraVISTA catalogue. This diagram is
commonly used to distinguish between red/passive and blue/active galaxies
(Ilbert et al., 2013). It clearly illustrates that the galaxies targeted by
WEAVE-StePS have an approximately equal percentage of red/blue galaxies
($41\%$ ($59\%$ respectively). The WEAVE-StePS selection criteria will sample
the broad variety of galaxy types within the galaxy population, from blue
star-forming to transition galaxies, and finally, to red and passive ones.

For both the red and the blue galaxy populations, Fig. 4 shows the estimated
colour-dependent completeness limit in stellar mass. To obtain this, we used
the galaxy stellar masses estimates provided in the UltraVISTA catalogue and a
procedure similar to that described by Pozzetti et al. (2010). We first
calculated the stellar mass that each target galaxy would have at its redshift
if its apparent magnitude were the limiting magnitude of the survey
$I_{AB}=20.5$, and then we used these limiting stellar masses to define the
stellar mass value below which $90\%$ of galaxies lie. We calculated this
separately for the blue and red samples, obtaining the completeness values
shown in Fig. 4, that is, an average typical stellar mass limit equal to
log(${\cal M/M}_{\sun}$)$\sim 10.4/11.0/11.3$ at z $\sim$ 0.3/0.5/0.7. Thus we
sample the high stellar mass tail of the galaxy population at all explored
redshifts.

These galaxies contribute significantly to the fraction of baryonic mass
locked in stars, and their evolution is still far from complete at the
redshifts targeted by WEAVE-StePS. The idea of massive galaxies as systems
that formed all their stars early in time and are passively evolving since
then has been challenged in the past few years: recent results have shown that
the ages of massive galaxies (${\cal M}>10^{11}{\cal M}_{\sun}$) at $z\sim
0.8$ are inconsistent with those of their local counterparts (Wu et al., 2018;
Spilker et al., 2018; Chauke et al., 2018) when a passive evolution of the
whole massive galaxy population is assumed. This result is also indicated by
the apparent slowing down of the $D4000$ value evolution of massive passive
galaxies after $z\sim 0.5$ (Haines et al. 2023, _in prep._). Our sample of
massive galaxies at intermediate redshifts will provide observational
constraints to shed light on this topic.

###  3.2 Sample selection: Choice of target fields

The WEAVE spectrograph is fibre-fed. Each MOS science fibre has an 85 $\mu$m
core, which subtends $1\aas@@fstack{\prime\prime}3$ on the sky, and an
expected positioning accuracy $\sim 0\aas@@fstack{\prime\prime}2$ rms (Hughes
et al., 2020). The target coordinates provided to the spectrograph must be
accurate and precise down to similar levels. They should be defined on the
Gaia reference frame of EDR3 (Gaia Collaboration et al., 2021), the same as
was adopted by the general WEAVE survey planning. Thus the availability of
quality astrometry is a crucial prerequisite when defining the target fields
for WEAVE-StePS.

Figure 4:  90$\%$ colour-dependent completeness limit in stellar mass for blue
and red galaxies as a function of redshift (blue and red lines). We used data
and stellar masses (Chabrier IMF) from the UltraVISTA catalogue in the COSMOS
field (McCracken et al., 2012; Ilbert et al., 2013), and the blue and red
galaxies were defined using a simple colour-colour rest-frame $NUV-R-J$ plot.
The shaded area indicates the $z\leq 0.3$ redshift range.

As discussed in Sect. 2, the choice of target fields should be further driven
by the availability of high-quality ancillary data, both photometric (the
wider the wavelength range covered, the better) and spectroscopic. The
presence of high-quality ancillary photometric data over a wide wavelength
range will improve the quality of the photometric redshift information
available for each target, an important parameter to consider as we have
adopted a redshift cut-off in our survey design (see Sect. 3). The
availability of a sizeable percentage of targets with spectroscopic redshift
information is a further important bonus, as it enables us both to test and
improve the quality of photometric redshifts and to refine environment
characterisation for the targeted galaxies. Last but not least, the fields to
be observed should be distributed evenly in $RA$ to permit observations with
WEAVE throughout the year and be located in $Dec$ positions such that each
field is positioned at relatively low air masses for a sizeable number of
hours in the nights when it is available for observations.

Our selection takes advantage of the recently released Hyper-Supreme-Cam
Subaru Strategic Program (HSC-SSP) data (Aihara et al., 2018a). These data
cover several fields that are all well accessible from the WHT, as the Subaru
and William Herschel telescopes are at latitudes that differ by only $\sim$ 10
degrees. Each HSC-SSP field is observed in five broadband filters modelled on
the SDSS filter set ($g,r,i,z,y$) at various depths (wide, deep, and
ultradeep, depending on the sky position) and offers the important advantage
of using the PanSTARRS1 DR2 catalogue as primary calibration source (Schlafly
et al., 2012; Magnier et al., 2013; Chambers et al., 2016), a catalogue
astrometrically calibrated against Gaia DR1 (Gaia Collaboration et al., 2016b,
a). The wide fields of HSC-SSP reach a $5\sigma$ I-band magnitude depth of
$\leavevmode\nobreak\ 26.2$ for point sources and a corresponding $5\sigma$
I-band limiting magnitude within apertures of two arcseconds in diameter that
are shallower by $\sim 0.3$ mag. This depth is well beyond our selection
needs.

We used the available HSC-SSP PDR2 data (Aihara et al., 2019), incremental
version $2$, as available when we produced our target catalogues 111See
https://hsc-release.mtk.nao.ac.jp/doc/index.php/sample-page/pdr2/ for a full
description. Any subsequent changes in later releases (see also Aihara et al.,
2022, for a detailed list of new observations and improvements introduced in
the third data release) were considered negligible for our purposes. From here
onwards, when we quote HSC-SSP data, we mean DR2 data of incremental version
$2$ . These data include target catalogues in the different bands, a list of
masked regions, and photometric redshifts for each target.

Table 1: List of fields covered by WEAVE-StePS Name | RA(J2000) | Dec(J2000)
---|---|---
COSMOS | 10 00 30 | +02 12 21
ELAIS-N1 | 16 11 00 | +54 59 17
CFHTLS-W4 | 22 15 00 | +01 36 00
CFHTLS-W1 | 02 24 00 |  $-$05 06 00

In the following, we detail the available ancillary information for each of
the four fields that WEAVE-StePS will target. The information is listed in
Table 1. All magnitudes in our catalogues are corrected for galactic
extinction and were computed using the newer estimates of Galactic dust
extinction from Schlafly et al. (2012) and the mean extinction curve of the
diffuse interstellar medium with $R_{V}$=3.1 from Fitzpatrick (1999).

####  3.2.1 COSMOS field

The COSMOS field is the first obvious choice as a WEAVE-StePS target field
(see Table 1 for its coordinates). COSMOS is still the largest of the classic
extragalactic fields imaged by the HST: a $\sim 1.7$ square-degree mosaic with
ACS in the F814W band (Scoville et al., 2007). This enables excellent
structural parameter estimates and morphological classifications (Sargent et
al., 2007; Scarlata et al., 2007; Kartaltepe et al., 2015). Forthcoming JWST
observations are planned for the area. This field is covered by HSC-SSP data,
with four extended-COSMOS pointings to deep depth, and a fifth pointing to
ultradeep depth (Aihara et al., 2018b). These HSC data further enrich the
ample dataset available for this field, which outside the optical data range
includes two UV bands from the Galaxy Evolution Explorer (GALEX; Morrissey et
al. (2005); Bianchi et al. (2011, 2017)), deep u-band imaging from the
Canada–France–Hawaii Telescope (CLAUDS; see Sawicki et al., 2019), YJHK
broadband data from the VIRCAM instrument on the VISTA telescope, and the four
IRAC/Spitzer channels (see Laigle et al., 2016; Weaver et al., 2022, for a
complete list and depths of the available photometric data). This field has
also been the target of various spectroscopic campaigns, most notably zCOSMOS
(Lilly et al., 2007), the PRIsm MUlti-Object Survey (PRIMUS Coil et al.,
2011), and recently, the LEGA-C survey (van der Wel et al., 2016). In
particular, the LEGA-C survey spectra will provide an important control sample
for the galaxies in common with WEAVE-StePS. Part of the area covered by
WEAVE-StePS in COSMOS is covered by deep XMM and Chandra pointings (Hasinger
et al., 2007; Cappelluti et al., 2009; Elvis et al., 2009). The COSMOS field
is observable in the first trimester of the year and is the only one for which
we decided to extend our target selection to lower redshifts (down to
$z\gtrsim 0.1$) to explore the trends that the main WEAVE-StePS sample will
observe to higher redshifts down to lower masses.

####  3.2.2 ELAIS-N1 field

The second WEAVE-StePS field is ELAIS-N1 (see Table 1 for its centre), another
well-known extragalactic field. This field was originally chosen for deep
extragalactic observations with the Infrared Space Observatory (ISO) because
the infrared background is low (Oliver et al., 2000). Since then, a variety of
other photometric data has been added. The ELAIS-N1 field is covered by HSC-
SSP four deep pointings, totalling $\sim 6.5$ square degrees. Ancillary data
include deep CFHT Telescope U band data (CLAUDS; see Sawicki et al., 2019), JK
Near InfraRed (NIR) broadband UKIDSS-DSX data (Lawrence et al., 2007;
Swinbank, 2013), Spitzer IRAC+MIPS data, and Herschel PACS+SPIRE data (see
Małek et al., 2018; Shirley et al., 2021, for a summary of the available bands
and their depths). It is worth noting that ELAIS-N1 is the deepest LOFAR two-
metre sky survey field (Sabater et al., 2021). The number of spectroscopic
redshifts in this field is somewhat limited and mostly consists of data from
SDSS-DR16 (Ahumada et al., 2020), which has been complemented with the
compilation of Vaccari (2022). ELAIS-N1 can be observed in the second
trimester of the year.

####  3.2.3 CFHTLS-W4 and CFHTLS-W1 fields

The third and fourth fields are two areas within the CFHTLS-W4 and CFHTLS-W1
wide fields (Hudelot et al., 2012), both covered by HSC-SSP Wide data, and
centred on the sky regions covered by spectroscopic VLT-VIMOS data. The
ancillary photometric data for both CFHTLS-W4 and CFHTLS-W1 include the u-band
photometry from the CFHTLS T07 data release (Hudelot et al., 2012), YJHK NIR
broadband UKIDSS-LAS data (Lawrence et al., 2007, 2012), and the VIPERS Multi-
Lambda Survey, which for part of the fields provides ready-to-use matched
photometry from the GALEX Deep Imaging Survey, and NIR photometry in Ks band
obtained at WIRCam (Moutard et al., 2016). Galaxies in both fields possess
morphological parameter estimates, both from the CFHTLenS collaboration
(Miller et al., 2013) and from the VIPERS collaboration (Krywult et al.,
2017). The availability of morphological parameters, even though it is of
lower quality than those provided by HST data in the COSMOS field, will be
crucial to obtain reliable dynamical masses.

The CFHTLS-W4 field can be observed in the third trimester of the year, and
the centre chosen for WEAVE-StePS is listed in Table 1. The centre choice is
such that this field largely overlaps the VIPERS-W4 spectroscopic data and
therefore includes VIPERS observations at $z\geq 0.5$ (Guzzo et al., 2014;
Scodeggio et al., 2018). There is partial overlap with spectroscopic data from
the VVDS-Wide survey (Garilli et al., 2008) and from Stripe 82 of the SDSS
Legacy Survey (Annis et al., 2014).

Figure 5: Astrometric and photometric redshift quality of HSC-SSP data in the
four WEAVE-StePS fields. Left panel: Histogram of the coordinate cross-match
statistics obtained for $\sim 2000$ matched AGNs, obtained by comparing their
GAIA EDR3 and HSC-SSP DR2 coordinates (see text for more details). The median
value is the green line at a separation of $0\aas@@fstack{\prime\prime}015$,
and the dashed line is the $95\%$ percentile limit, corresponding to a
separation on the sky of $\sim$ $0\aas@@fstack{\prime\prime}03$. Right panel:
Completeness and purity of our target selection, estimated using zCOSMOS and
VVDS-Wide/Deep spectroscopic data. The top panel shows the COSMOS field, and
the bottom panel shows the CFHTLS-W1 and CFHTLS-W2 fields, covered by HSC deep
and ultradeep and HSC wide data, respectively. The histogram outlined in black
shows the spectroscopic redshift of all galaxies with a magnitude
$I_{AB}<20.5$. The cyan histogram shows the distribution in spec-z of galaxies
whose spectroscopic and photometric redshifts, computed using the DEmP
algorithm (Hsieh & Yee, 2014), are above the 0.3 value redshift cut-off. The
orange histogram is the spectroscopic redshift distribution of the subset of
galaxies whose photometric redshift is above 0.3 when the corresponding
spectroscopic redshift is below this value, as shown by the x-axis. The
corresponding values for completeness and contamination of the sample selected
using DEmP photometric redshifts are $94/88\%$ and $1/8\%,$ respectively (see
text for more details).

The CFHTLS-W1 wide field is well suited for observations in the fourth
trimester of the year (see its centre in Table 1). The area we will target
within the CFHTLS-W1 wide field was chosen to overlap the spectroscopic
information coming from the GAMA-02 field (Baldry et al., 2018), the VIPERS-W1
field (Guzzo et al., 2014; Scodeggio et al., 2018), and partly the VIMOS VLT
Deep Survey (VVDS; Le Fèvre et al., 2013). In addition to Wide HSC-SSP
photometry, the area we chose is partially covered by the data of the original
Spitzer Extragalactic Representative Volume Survey, SERVS (Mauduit et al.,
2012), which has now been extended (Lacy et al., 2021), and by the XMM-LSS
survey and the wider XMM-XXL North Survey (Pierre et al., 2011, 2016; Chen et
al., 2018). Further photometric coverage includes the deep CFHT Telescope
U-band data (CLAUDS; see Sawicki et al., 2019) and data from the VIDEO survey
(Jarvis et al., 2013) where available.

In all of these four fields, we retrieved the available 3.4, 4.6, 12, and 22
${\mu}$m data from the WISE all-sky survey (Wright et al., 2010; Schlafly et
al., 2019) from the literature.

###  3.3 Sample selection: Astrometry, photometric redshifts quality and field
visibility

A fibre-fed spectrograph such as WEAVE needs excellent astrometric quality of
the input target catalogues. We checked the quality of HSC-SSP astrometry in
the WEAVE-StePS fields against the reference system of the GAIA EDR3 data
release (Gaia Collaboration et al., 2021), which is adopted by all the WEAVE
surveys.

In the GAIA EDR3 catalogue, the Gaia celestial reference frame (CRF) is
defined by a table containing $\sim 1.6$ million AGNs, which are used to
define the Gaia CRF, and they are themselves aligned using Very Long Baseline
Array (VLBA) astrometric precision coordinates with the international
celestial reference frame (ICRF; Lindegren et al., 2021; Gaia Collaboration et
al., 2022).

For each of the four WEAVE-StePS fields (see Section 3.2), we cross-correlated
the positions of the CRF AGN table and the HSC-SSP catalogues for sources in
the magnitude range $18.0\leq I_{AB}\leq 22.0$. These limits avoid the
brightest objects, which are probably saturated and thus have problematic
centring, while stopping at reasonable magnitude limits for fainter targets.

Figure 6: Number of hours per night at an airmass below 1.3 for each of the
planned WEAVE-StePS fields (as labelled) throughout the year.

The distribution of the projected separations between the positions for the
$\sim 2000$ cross-matched AGNs are presented in the left panel of Fig. 5, and
the results are satisfactory for our goals: $95\%$ of the cross-matched AGNs
are at separations on the sky smaller than $0\aas@@fstack{\prime\prime}03$,
which is well within the expected accuracy in fibre positioning ($\sim
0\aas@@fstack{\prime\prime}2$ rms; see Hughes et al., 2020).

The WEAVE-StePS target selection uses a redshift cut-off, and accurate
spectroscopic redshifts are available only for a subset of the sources in the
WEAVE-StePS fields. Therefore, the success of target selection relies on the
accuracy of photometric redshift in our fields.

The DR2 of HSC-SSP provides two photometric redshift values for each source
that are computed with two different algorithms (Tanaka et al., 2018;
Nishizawa et al., 2020). The first algorithm, DEmP, is based on an empirical
quadratic polynomial photometric redshift fitting code (Hsieh & Yee, 2014),
and the second algorithm, MIZUKI, is based on template fitting (for more
details, see Tanaka et al., 2018).

We decided to use DEmP for our selection because it performs better
($\sigma_{z}/(1+z)\leq 0.03)$ at the brighter magnitudes we are interested in
(down to $I_{AB}\leq 20.5$; see Table 1 and the second panel from the top of
Figure 3 in Nishizawa et al. (2020)).

As an independent test of how well DEmP performs for target selection, we used
spectroscopic redshifts available in the COSMOS, CFHTLS-W4, and CFHTLS-W1
fields. In the COSMOS field, the zCOSMOS survey is available (Lilly et al.,
2007, 2009). This redshift survey defined its targets using only a
$I_{AB}<22.5$ magnitude limit. In the fields CFHTLS-W4 and CFHTLS-W1, the
VVDS-Wide and Deep surveys are available, with targets defined using only a
$I_{AB}<22.5/24.0$ magnitude limit selection, respectively (see Le Fèvre et
al., 2005; Garilli et al., 2008; Le Fèvre et al., 2013). The deeper magnitude
used to select spectroscopic targets for these surveys and the absence of any
further colour/redshift limit enables us to extract spectroscopic redshifts
for a complete subsample at $I_{AB}<20.5$ for each of these fields to verify
the purity and completeness of the photometric redshift selection based on
DEmP.

The results of this test, using a total of 2110 galaxies with spectroscopic
redshifts (252, 810, and 1048 in the W1, W4, and COSMOS fields, respectively),
are shown in the right panel of Fig. 5 for the COSMOS field and the two CFHTLS
fields separately. The COSMOS field, being covered by Deep and UltraDeep HSC
data, has higher-quality photometric redshifts and thus displays excellent
values of completeness, roughly $\sim 94\%$, and a negligible contamination of
$\sim 1\%$, when adopting DEmP for photometric redshifts selection. Similar
values are expected for the ELAIS-N1 field, which is similarly covered by Deep
HSC data. The values do not change dramatically when the same analysis is
performed for the two CFHTLS fields, which are mostly covered by HSC Wide
photometric data. The value for completeness decreases to 88$\%$, and that of
contamination rises to 8$\%$.

These values will further improve when the actual target selection is
finalised, see sect. 3.1, as a non-negligible percentage of targets in our
fields already possess a reliable spectroscopic redshift estimate (roughly
$\sim 25\%$; see the numbers in Table 2).

Finally, in Fig. 6 we show the number of hours available at airmass lower than
$1.3$ as a function of the time of year (i.e. at zenith distance smaller than
$40$ degrees, the adopted constraint for our planned observations) for each
WEAVE-StePS field. During all months, there are always at least 2 hours of
observability for at least one of our fields. Even the field CFHTLS-W1, which
is located furthest south (see Table 1), will be visible from WHT for about
three months with more than 2 hours per night at an airmass value lower than
$1.3$.

##  4 Survey strategy: Field tiling and planned exposure times

Table 2: List of WEAVE-StePS pointing centres for each field. Columns 1, 2, and 3 list the field name and RA and Dec of its centre. Column 4 lists the number of potential WEAVE-StePS targets within each pointing, NTargets , and in parentheses, the number of targets in common (i.e. in the overlapping area) with the adjacent pointings. Column 5 lists for each pointing the number of targets with good-quality spectroscopic redshift from the literature, N${}^{\rm Targets}_{\rm spec-z}$ , and in parentheses, the number of spectroscopic redshifts common to the adjacent pointing(s).  Tile Name | RA(J2000) | Dec(J2000) | NTargets | N${}^{\rm Targets}_{\rm spec-z}$
---|---|---|---|---
COSMOS_01 | 10 00 27.84 | +02 12 21.60 | 8827 | 3892
ELAIS-N1_01 | 16 11 00.72 | +54 17 31.20 | 6619 (1300) | 821 (206)
ELAIS-N1_02 | 16 11 00.72 | +55 41 49.20 | 6210 (1300) | 589 (206)
Total number of distinct targets in ELAIS-N1 | 11529 | 1204
CFHTLS-W4_01 | 22 10 50.16 | +01 37 12.00 | 5351 (2363) | 1090 (531)
CFHTLS-W4_02 | 22 14 50.40 | +01 37 12.00 | 5822 (2363, 2137) | 1275 (531, 489)
CFHTLS-W4_03 | 22 18 50.40 | +01 31 12.00 | 5989 (2137) | 1049 (489)
Total number of distinct targets in CFHTLS-W4 | 12662 | 2394
CFHTLS-W1_01 | 02 17 36.00 |  $-$05 15 00.00 | 5662 (2303) | 1676 (706)
CFHTLS-W1_02 | 02 21 36.96 |  $-$05 15 00.00 | 6050 (2303, 2531) | 1758 (706, 769)
CFHTLS-W1_03 | 02 25 37.92 |  $-$05 09 00.00 | 6244 (2531, 2394) | 1886 (769, 712)
CFHTLS-W1_04 | 02 29 38.40 |  $-$05 09 00.00 | 6354 (2394) | 1791 (712)
Total number of distinct targets in CFHTLS-W1 | 17082 | 4924
Total number of distinct targets in all fields | 50100 | 12414
Figure 7: Pointing layout of each field targeted by WEAVE-StePS. The orange
points are the potential WEAVE-StePS targets, and the red points are the
subset with available good-quality spectroscopic redshifts. The asterisks
indicate the position of bright stars from GAIA catalogue: blue for those
brighter than 7.5mag in the GAIA G band, and cyan for those in the GAIA G-band
magnitude range 7.5-8.5. See text for more details.

The tiling strategy adopted within each WEAVE-StePS field is driven by the
goal to reach the most overlap with spectroscopic data, if available (or with
good-quality HSC deep/ultra-deep photometry in the case of ELAIS-N1, where
spectroscopic data are scarce). Another point we considered is the need to
avoid regions in which bright stars (brighter than seventh magnitude) may
hamper the quality of our data, both for the input catalogues, which will
present large masked areas, and for the WEAVE spectroscopic data, which might
be contaminated by stray light from internal reflections.

The centres of each of the WEAVE-StePS pointings within each field are listed
in Table 2. The table shows for each pointing the total number of targets,
those with good-quality spectroscopic redshifts, and, in parentheses, those in
common with adjacent pointings. The definition of good-quality spectroscopic
redshifts is based on the information provided by the spectroscopic surveys
available in each field. The relevant information for the main spectroscopic
surveys that enter our compilation is the following. For SDSS spectroscopic
redshifts, we used the three flags values ZWARNING=0, PLATEQUALITY$\neq$
”bad”, and SPECPRIMARY=1. For GAMA redshifts, we used only spectral
information flagged IS_BEST and $nQ>2$. Finally, for VVDS, VIPERS, and
zCOSMOS, we used only redshift values with spectroscopic redshift quality flag
$\geq 2$. For each field (except for the COSMOS unique pointing), the final
row lists the number of distinct targets within the total field area and the
subset with available good-quality spectroscopic redshifts. The pointing
layout in each field is shown in Fig. 7, where the orange points are the
potential WEAVE-StePS targets, and the red points are the subset with
available good-quality spectroscopic redshifts. The asterisks indicate the
position of bright stars from GAIA catalogue: blue for those brighter than
7.5mag in the GAIA G band, and cyan for those in the GAIA G-band magnitude
range 7.5-8.5. Multiple pointings located within the same field overlap
slightcause of the one-degree radius FoV of WEAVE.

The total area covered by our survey is $\sim 25$ square degrees. The
corresponding large volume covered will enable us to trace a wide range of
environments at each redshift, from voids to groups and clusters, beating down
cosmic variance.

In the COSMOS field alone, as discussed in Sect.3.2.1, will we extend our
target selection to lower redshifts (down to $z\gtrsim 0.1$). This explains
the higher number of galaxy targets within the COSMOS unique pointing in Table
2. For all of the other pointings, we adopted the general WEAVE-StePS
selection in redshift.

To complete the definition of our survey strategy, we quantified the exposure
times needed to obtain spectra with the $S/N$ values expected to achieve our
science goals ($S/N\sim 10{\AA}^{-1}$, see Sect. 2). A simple exposure-time
calculator was provided to the WEAVE team and was made available on the WEAVE
web pages 222see
https://ingconfluence.ing.iac.es/confluence/display/WEAV/Exposure+Time+Calculator.
A more complex operation rehearsal within the WEAVE project was also
performed, which used the WEAVE simulator for thorough end-to-end testing of
the data-processing system (see Dalton et al., 2016a; Jin et al., 2022). Both
methods need realistic in-fibre spectral fluxes and sky-brightness values as
input and provide similar outputs. In the following, we present the results
obtained by operation rehearsal.

Figure 8: Distribution of the two morphological parameters Sérsic index and
effective radius $R_{50}$ for WEAVE-StePS targets. The points were obtained
from galaxies in the COSMOS field, where structural parameters for each
potential target are available from HST data (Sargent et al., 2007; Scarlata
et al., 2007).

In the COSMOS field, available HST images provide accurate information on the
structural parameters (Sargent et al., 2007; Scarlata et al., 2007) for each
galaxy selected using WEAVE-StePS criteria, and the distribution of Sérsic
index and effective radius $R_{50}$ is shown in Fig. 8. These two parameter
values were therefore used to estimate the expected in-fibre magnitude for
each potential target in this field, that is, the flux loss due to the
structural parameters of the source, considering only a single-component fit.
This is a good first-order approximation for our tests. By comparing the
effective radius $R_{50}$ values with the 1$\aas@@fstack{\prime\prime}$3 WEAVE
fibre diameter on the sky, it is clear that a significant percentage of the
observed galaxies will suffer from non-negligible light loss due to the finite
fibre size. We then considered a slightly pessimistic seeing of
$1\aas@@fstack{\prime\prime}30$ for our simulated observations (the median
seeing in La Palma varies at the zenith from $0\aas@@fstack{\prime\prime}80$
in the period April–November to $1\aas@@fstack{\prime\prime}07$ in the period
December–March
333https://www.ing.iac.es//Astronomy/observing/conditions/#seeing), obtaining
for each target the further flux loss due to the effect of seeing.

We used the colour information provided by the UltraVISTA catalogue (McCracken
et al., 2012; Ilbert et al., 2013) to define the most appropriate E-MILES
spectral template (Vazdekis et al., 2016) for each target galaxy. This is to
be used in the simulations so as to have the correct spectral flux
distribution. Finally, we adopted a sky surface brightness in the V band of
$\sim 21.6$ mag arcsec-2 for our simulations, which agrees with the typical
value we expect for our fields if they are observed at an airmass limit of
$\sim 1.3$.

Figure 9: Normalized distribution of the expected $S/N$ $\AA^{-1}$ in the
observed [4000-5000] and [7000-8000] ${\AA}$ wavelength ranges (left and
right), assuming the stacking of 21 exposures of $20$ minutes each (including
overheads) for a total exposure time of $7$ hours. The estimate was obtained
using the results of the latest operation rehearsal performed within the WEAVE
project. Median and quartile values are shown by the vertical lines. The inset
plots in each panel show the relation between the $B_{AB}/I_{AB}$ magnitudes
and observed $S/N$ $\AA^{-1}$ in the defined wavelength range. For each
observed galaxy, lighter points show total magnitudes and darker points show
magnitudes within the fibre, see text for more details. See text for more
details.

Based on a realistic distribution of $S/N$ $\AA^{-1}$ for a representative
subset of our targets, roughly $\sim 800$ in number, we then determined the
optimal choice in exposure time to obtain the I-band target goal of $S/N\sim
10$ $\AA^{-1}$.

The left and right panels of Fig. 9 show the normalized distribution of the
expected $S/N$ $\AA^{-1}$ in the observed [4000-5000] and [7000-8000] ${\AA}$
wavelength ranges, respectively, assuming the stacking of 21 exposures of $20$
minutes each (including overheads), for a total exposure time of $7$ hours.

Planning an exposure time of $\sim 7$ hours for each WEAVE-StePS pointing
should thus enable us to reach the required $S/N\sim 10{\AA}^{-1}$ in the
observed I band for the majority of the observed galaxies, even in the
slightly pessimistic observing conditions we considered. The median $S/N$
$\AA^{-1}$ in the observed I band is $\sim 11.3$, with lower/upper quartile
values of $\sim 8.8$/$\sim 16.2$. This means that fewer than $\sim 25\%$ of
the observed spectra will be at an $S/N$ that is significantly below our
fiducial value of $10{\AA}^{-1}$ in the observed I band. These spectra will be
analysed using stacking techniques within homogeneous bins of galaxy
properties (stellar mass, redshift, velocity dispersion, etc.). The
corresponding $S/N$ values in the blue arm are significantly lower, as
expected. However, as discussed in Costantin et al. (2019) and Ditrani et al.
(2023, in prep.), these values are sufficient for our analysis.

According to the allocation of fibre-hours foreseen for WEAVE-StePS within the
general WEAVE survey, and assuming 7 hours of exposure time for each pointing,
we can expect to observe a total of 35 WEAVE-StePS pointings.

To compute the total number of galaxies observed by WEAVE-StePS at the end of
the five-year survey campaign, we need a rough estimate of the number of
galaxies that is observed at each pointing.

Out of the $\sim 950$ fibres available per pointing in MOS mode, $\sim 100$
sky-fibres will be allocated to observe empty-sky regions. These fibres will
be used to perform an accurate sky subtraction. A further $\sim 10$ fibres are
devoted to observations of white dwarf stars as part of the WEAVE calibration
plan and of a dedicated WEAVE survey.

For an a posteriori sanity check of the quality of the sky subtraction, we
plan to allocate $\sim 30$ fibres to empty sky regions in each pointing, the
undeclared sky-fibres. A further $\sim 20$ fibres will be reserved for known
star calibrators that are available within each field to verify the flux
calibration. These additional calibrators were selected from the GAIA EDR3
database and were matched with the SDSS-DR16 spectroscopic and photometric
catalogues. The majority are type A or F stars with Gaia BP/RP magnitudes in
the range $14-19$, and high-quality spectra are available from SDSS
($S/N\gtrsim 30$ in $r-$band).

We finally need to consider the overall fibre allocation inefficiencies (e.g.
parked and broken fibres) and the possibility of some residual contamination
of our input sample by stars and/or lower-redshift galaxies. A realistic
estimate of the mean WEAVE-StePS targets observed in each pointing is thus
$\sim 700$, which agrees well with the results of tests using the code
Configure (Terrett et al., 2014; Hughes et al., 2022). This software will be
used to position fibres during actual survey operations. As a result, we
expect that a total of $\sim 25,000$ galaxies are observed by WEAVE-StePS by
the end of the five-year survey campaign.

Given the distribution of expected $S/N$ $\AA^{-1}$ for our targets as shown
in Fig. 8, such a large sample implies that WEAVE-StePS will produce a
significant number of galaxy spectra ($\sim 3500$) at $S/N\geq 20$, which is
comparable to the values quoted for the LEGA-C survey (Straatman et al.,
2018), whose spectra are at a slightly lower resolution of $R\sim 2500$ in a
narrower observed spectral wavelength range [6000 - 8800] $\AA$. Last but not
least, and as already mentioned, the large total area covered by our survey
will enable us to observe a wide range of environments at each redshift,
reducing the impact of cosmic large-scale structure variance.

We note from Table 2 that the number of distinct passes we may perform in each
pointing, given the total number of targets available per pointing, varies
from a maximum of $\sim$7-8, as in the case of COSMOS, down to a minimum of
$\sim 3$ as in the case of CFHTLS-W1/CFHTLS-W4, where each chosen area
overlaps non-negligibly with adjacent areas. ELAIS-N1 is an intermediate case
for which we may easily consider positioning about four passes per each
pointing. The WEAVE-StePS planning will therefore easily fit in the general
WEAVE survey planning, with a roughly homogeneous distribution of our targeted
areas during the different months of the year.

##  5 Summary and conclusions

The WEAVE spectrograph mounted on the WHT has unprecedented multiplex
capabilities in MOS mode over a wide field of view (950 fibres over $\sim$3
square degrees). These characteristics, in combination with its wide spectral
coverage (3700 to 9600 Å) in the low-resolution mode ($R\sim$ 5000, a factor
of $\sim$ 10 improvement of typical literature values), will enable
astronomers to carry out surveys that have not been feasible so far. In this
paper, we presented the WEAVE-StePS survey, one of the five extragalactic
surveys that will be carried out with WEAVE and whose observations are
expected to start in the first trimester of 2023. We have outlined the main
scientific objectives of StePS, the detailed survey design and strategy, and
the expected spectral and sample characteristics.

WEAVE-StePS will collect $\sim$ 25000 spectra of galaxies. The vast majority
of them is located in the intermediate-redshift range between LEGA-C and SDSS:
0.3$\leq z\leq$ 0.7. This will characterise in detail the properties and
stellar histories of a large sample of galaxies during this cosmic period for
the first time. Only $\sim 4\%$ of the targeted sample will be at $z\geq$0.7,
and the lower redshift cut-off will be lowered to $z\geq$ 0.1 in the COSMOS
field alone. The planned long exposure times (7 hours), combined with the
WEAVE throughput, will enable WEAVE-StePS to gather high-quality spectra
($S/N\geq 10\,\AA^{-1}$ in the I band for the majority of the spectra, with a
resolution $R\sim$ 5000) and to accurately measure for individual galaxies the
star formation rates, histories, and timescales, gas and stellar
metallicities, stellar and dynamical masses, gas inflows and outflows, and
AGN/LINER emission. The $\sim 25$ square degrees of the area covered by WEAVE-
StePS in four of the most well-studied extragalactic fields (COSMOS, ELAIS-N1,
CFHTLS-W4, and CFHTLS-W1, all with extensive ancillary data) will include all
types of galaxy environments, from voids to filaments, galaxy groups, and
clusters, thus providing the opportunity to study galaxy evolution at these
epochs for different environmental conditions and in a wide range of dark
matter halo masses.

WEAVE-StePS will go back in cosmic time beyond SDSS and will fill the crucial
redshift interval that bridges the gap between LEGA-C and SDSS data, enabling
us to continuously retrace the evolutionary path of galaxies over the $\sim 8$
Gyr since $z\sim 1$.

###### Acknowledgements.

Funding for the WEAVE facility has been provided by UKRI STFC, the University
of Oxford, NOVA, NWO, Instituto de Astrofísica de Canarias (IAC), the Isaac
Newton Group partners (STFC, NWO, and Spain, led by the IAC), INAF, CNRS-INSU,
the Observatoire de Paris, Région Île-de-France, CONCYT through INAOE, Konkoly
Observatory (CSFK), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Lund
University, the Leibniz Institute for Astrophysics Potsdam (AIP), the Swedish
Research Council, the European Commission, and the University of Pennsylvania.
The WEAVE Survey Consortium consists of the ING, its three partners,
represented by UKRI STFC, NWO, and the IAC, NOVA, INAF, GEPI, INAOE, and
individual WEAVE Participants. Please see the relevant footnotes for the WEAVE
website444https://ingconfluence.ing.iac.es/confluence//display/WEAV/The+WEAVE+Project
and for the full list of granting agencies and grants supporting
WEAVE555https://ingconfluence.ing.iac.es/confluence/display/WEAV/WEAVE+Acknowledgements.
This work makes use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular, the institutions
participating in the Gaia Multilateral Agreement. This work makes use of data
from the VIMOS VLT Deep Survey, the VIPERS-MLS database and the HST-COSMOS
database, operated by CeSAM/Laboratoire d’Astrophysique de Marseille, France.
This work makes use of observations obtained with MegaPrime/MegaCam, a joint
project of CFHT and CEA/IRFU, at the Canada-France-Hawaii Telescope (CFHT)
which is operated by the National Research Council (NRC) of Canada, the
Institut National des Science de l’Univers of the Centre National de la
Recherche Scientifique (CNRS) of France, and the University of Hawaii. This
work makes use of data products produced at Terapix available at the Canadian
Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy
Survey, a collaborative project of NRC and CNRS. R.G.B. and R.G.D. acknowledge
financial support from the grants CEX2021-001131-S funded by
MCIN/AEI/10.13039/501100011033, SEV-2017-0709, and to PID2019-109067-GB100.
A.F.M. acknowledges financial support from grant CEX2019-000920-S from the
Spanish Ministry of Science and Innovation. M.Bi. acknowledges support from
STFC grant numbers ST/N021702/1 C.S. is supported by a ’Hintze Fellow’ at the
Oxford Centre for Astrophysical Surveys, which is funded through generous
support from the Hintze Family Charitable Foundation. G.B., M.Bo., F.R.D.,
A.I., F.L.B., M.L., P.M., B.P. C.T. D.V. and S.Z. acknowledge financial
support from INAF funds, program 1.05.01.86.16 - Mainstream 2019. L.C.
acknowledges financial support from Comunidad de Madrid under Atracción de
Talento grant 2018-T2/TIC-11612. J.A. acknowledges financial support from
INAF-WEAVE funds, program 1.05.03.04.05 and INAF-OABrera funds, program
1.05.01.01. J.H.K. acknowledges financial support from the State Research
Agency (AEI-MCINN) of the Spanish Ministry of Science and Innovation under the
grant ”The structure and evolution of galaxies and their central regions” with
reference PID2019-105602GB-I00/10.13039/501100011033, and from the ACIISI,
Consejería de Economía, Conocimiento y Empleo del Gobierno de Canarias and the
European Regional Development Fund (ERDF) under grant with reference
PROID2021010044. A special thanks to Daniela Bettoni for her suggestions and
comments and to the anonymous referee for his/her useful comments.

## References

  * Ahumada et al. (2020) Ahumada, R., Prieto, C. A., Almeida, A., et al. 2020, ApJS, 249, 3
  * Aihara et al. (2019) Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, PASJ, 71, 114
  * Aihara et al. (2022) Aihara, H., AlSayyad, Y., Ando, M., et al. 2022, PASJ, 74, 247
  * Aihara et al. (2018a) Aihara, H., Arimoto, N., Armstrong, R., et al. 2018a, PASJ, 70, S4
  * Aihara et al. (2018b) Aihara, H., Armstrong, R., Bickerton, S., et al. 2018b, PASJ, 70, S8
  * Angthopo et al. (2021) Angthopo, J., Negri, A., Ferreras, I., et al. 2021, MNRAS, 502, 3685
  * Annis et al. (2014) Annis, J., Soares-Santos, M., Strauss, M. A., et al. 2014, ApJ, 794, 120
  * Balcells et al. (2010) Balcells, M., Benn, C. R., Carter, D., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 77357G
  * Baldry et al. (2006) Baldry, I. K., Balogh, M. L., Bower, R. G., et al. 2006, MNRAS, 373, 469
  * Baldry et al. (2004) Baldry, I. K., Glazebrook, K., Brinkmann, J., et al. 2004, ApJ, 600, 681
  * Baldry et al. (2018) Baldry, I. K., Liske, J., Brown, M. J. I., et al. 2018, MNRAS, 474, 3875
  * Bamford et al. (2009) Bamford, S. P., Nichol, R. C., Baldry, I. K., et al. 2009, MNRAS, 393, 1324
  * Benitez et al. (2014) Benitez, N., Dupke, R., Moles, M., et al. 2014, arXiv e-prints, arXiv:1403.5237
  * Bennett et al. (2014) Bennett, C. L., Larson, D., Weiland, J. L., & Hinshaw, G. 2014, ApJ, 794, 135
  * Bezanson et al. (2018) Bezanson, R., van der Wel, A., Pacifici, C., et al. 2018, ApJ, 858, 60
  * Bianchi et al. (2011) Bianchi, L., Herald, J., Efremova, B., et al. 2011, Ap&SS, 335, 161
  * Bianchi et al. (2017) Bianchi, L., Shiao, B., & Thilker, D. 2017, ApJS, 230, 24
  * Blanton et al. (2003) Blanton, M. R., Hogg, D. W., Bahcall, N. A., et al. 2003, ApJ, 594, 186
  * Blanton & Moustakas (2009) Blanton, M. R. & Moustakas, J. 2009, ARA&A, 47, 159
  * Bolton et al. (2006) Bolton, A. S., Burles, S., Koopmans, L. V. E., Treu, T., & Moustakas, L. A. 2006, ApJ, 638, 703
  * Bolzonella et al. (2010) Bolzonella, M., Kovač, K., Pozzetti, L., et al. 2010, A&A, 524, A76
  * Bond (1993) Bond, J. R. 1993, in Astrophysics and Space Science Library, Vol. 188, The Environment and Evolution of Galaxies, ed. J. M. Shull & H. A. Thronson, 3
  * Bruzual & Charlot (2003) Bruzual, G. & Charlot, S. 2003, MNRAS, 344, 1000
  * Bullock & Boylan-Kolchin (2017) Bullock, J. S. & Boylan-Kolchin, M. 2017, ARA&A, 55, 343
  * Cappelluti et al. (2009) Cappelluti, N., Brusa, M., Hasinger, G., et al. 2009, A&A, 497, 635
  * Chabrier (2003) Chabrier, G. 2003, ApJ, 586, 4379
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chauke et al. (2018) Chauke, P., van der Wel, A., Pacifici, C., et al. 2018, ApJ, 861, 13
  * Chauke et al. (2019) Chauke, P., van der Wel, A., Pacifici, C., et al. 2019, ApJ, 877, 48
  * Chen et al. (2018) Chen, C. T. J., Brandt, W. N., Luo, B., et al. 2018, MNRAS, 478, 2132
  * Choi et al. (2014) Choi, J., Conroy, C., Moustakas, J., et al. 2014, ApJ, 792, 95
  * Citro et al. (2016) Citro, A., Pozzetti, L., Moresco, M., & Cimatti, A. 2016, A&A, 592, A19
  * Coil et al. (2011) Coil, A. L., Blanton, M. R., Burles, S. M., et al. 2011, ApJ, 741, 8
  * Conroy (2013) Conroy, C. 2013, ARA&A, 51, 393
  * Costantin et al. (2019) Costantin, L., Iovino, A., Zibetti, S., et al. 2019, A&A, 632, A9
  * Dalton et al. (2016a) Dalton, G., Ham, S. J., Trager, S., et al. 2016a, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9913, Proc. SPIE, 99132X
  * Dalton et al. (2016b) Dalton, G., Trager, S., Abrams, D. C., et al. 2016b, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, ed. C. J. Evans, L. Simard, & H. Takami, 99081G
  * Dalton et al. (2014) Dalton, G., Trager, S., Abrams, D. C., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9147, Ground-based and Airborne Instrumentation for Astronomy V, ed. S. K. Ramsay, I. S. McLean, & H. Takami, 91470L
  * Dalton et al. (2012) Dalton, G., Trager, S. C., Abrams, D. C., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8446, Ground-based and Airborne Instrumentation for Astronomy IV, 84460P
  * Dawson et al. (2013) Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2013, AJ, 145, 10
  * Driver et al. (2012) Driver, S. P., Robotham, A. S. G., Kelvin, L., et al. 2012, MNRAS, 427, 3244
  * Elvis et al. (2009) Elvis, M., Civano, F., Vignali, C., et al. 2009, ApJS, 184, 158
  * Ferré-Mateu et al. (2014) Ferré-Mateu, A., Sánchez-Blázquez, P., Vazdekis, A., & de la Rosa, I. G. 2014, ApJ, 797, 136
  * Fitzpatrick (1999) Fitzpatrick, E. L. 1999, PASP, 111, 63
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1
  * Gaia Collaboration et al. (2016a) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2016a, A&A, 595, A2
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Klioner, S. A., Lindegren, L., et al. 2022, arXiv e-prints, arXiv:2204.12574
  * Gaia Collaboration et al. (2016b) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016b, A&A, 595, A1
  * Gallazzi et al. (2014) Gallazzi, A., Bell, E. F., Zibetti, S., Brinchmann, J., & Kelson, D. D. 2014, ApJ, 788, 72
  * Gallazzi et al. (2005) Gallazzi, A., Charlot, S., Brinchmann, J., White, S. D. M., & Tremonti, C. A. 2005, MNRAS, 362, 41
  * Gallazzi et al. (2021) Gallazzi, A. R., Pasquali, A., Zibetti, S., & Barbera, F. L. 2021, MNRAS, 502, 4457
  * Garilli et al. (2008) Garilli, B., Le Fèvre, O., Guzzo, L., et al. 2008, A&A, 486, 683
  * Geller et al. (2014) Geller, M. J., Hwang, H. S., Fabricant, D. G., et al. 2014, ApJS, 213, 35
  * Guzzo et al. (2014) Guzzo, L., Scodeggio, M., Garilli, B., et al. 2014, A&A, 566, A108
  * Haines et al. (2017) Haines, C. P., Iovino, A., Krywult, J., et al. 2017, A&A, 605, A4
  * Harrison et al. (2018) Harrison, C. M., Costa, T., Tadhunter, C. N., et al. 2018, Nature Astronomy, 2, 198
  * Hasinger et al. (2007) Hasinger, G., Cappelluti, N., Brunner, H., et al. 2007, ApJS, 172, 29
  * Heckman & Best (2014) Heckman, T. M. & Best, P. N. 2014, ARA&A, 52, 589
  * Hsieh & Yee (2014) Hsieh, B. C. & Yee, H. K. C. 2014, ApJ, 792, 102
  * Hudelot et al. (2012) Hudelot, P., Cuillandre, J. C., Withington, K., et al. 2012, VizieR Online Data Catalog, II/317
  * Hughes et al. (2022) Hughes, S., Dalton, G., Smith, D., et al. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12184, Ground-based and Airborne Instrumentation for Astronomy IX, ed. C. J. Evans, J. J. Bryant, & K. Motohara, 121846I
  * Hughes et al. (2020) Hughes, S., Schallig, E., Lewis, I. J., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 11447, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 114477R
  * Ilbert et al. (2006) Ilbert, O., Arnouts, S., McCracken, H. J., et al. 2006, A&A, 457, 841
  * Ilbert et al. (2013) Ilbert, O., McCracken, H. J., Le Fèvre, O., et al. 2013, A&A, 556, A55
  * Ilbert et al. (2010) Ilbert, O., Salvato, M., Le Floc’h, E., et al. 2010, ApJ, 709, 644
  * Iovino et al. (2010) Iovino, A., Cucciati, O., Scodeggio, M., et al. 2010, A&A, 509, A40
  * Jarvis et al. (2013) Jarvis, M. J., Bonfield, D. G., Bruce, V. A., et al. 2013, MNRAS, 428, 1281
  * Jin et al. (2022) Jin, S., Trager, S. C., Dalton, G. B., et al. 2022, arXiv e-prints, arXiv:2212.03981
  * Jørgensen & Chiboucas (2013) Jørgensen, I. & Chiboucas, K. 2013, AJ, 145, 77
  * Juneau et al. (2011) Juneau, S., Dickinson, M., Alexander, D. M., & Salim, S. 2011, ApJ, 736, 104
  * Kartaltepe et al. (2015) Kartaltepe, J. S., Mozena, M., Kocevski, D., et al. 2015, ApJS, 221, 11
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 33
  * Kauffmann et al. (2004) Kauffmann, G., White, S. D. M., Heckman, T. M., et al. 2004, MNRAS, 353, 713
  * Kelson et al. (2000) Kelson, D. D., Illingworth, G. D., van Dokkum, P. G., & Franx, M. 2000, ApJ, 531, 184
  * Kewley & Ellison (2008) Kewley, L. J. & Ellison, S. L. 2008, ApJ, 681, 1183
  * Kewley et al. (2006) Kewley, L. J., Groves, B., Kauffmann, G., & Heckman, T. 2006, MNRAS, 372, 961
  * Kochanek et al. (2012) Kochanek, C. S., Eisenstein, D. J., Cool, R. J., et al. 2012, ApJS, 200, 8
  * Krywult et al. (2017) Krywult, J., Tasca, L. A. M., Pollo, A., et al. 2017, A&A, 598, A120
  * Kuhlen et al. (2012) Kuhlen, M., Vogelsberger, M., & Angulo, R. 2012, Physics of the Dark Universe, 1, 50
  * La Barbera et al. (2010) La Barbera, F., de Carvalho, R. R., de La Rosa, I. G., et al. 2010, MNRAS, 408, 1313
  * La Barbera et al. (2013) La Barbera, F., Ferreras, I., Vazdekis, A., et al. 2013, MNRAS, 433, 3017
  * La Barbera et al. (2017) La Barbera, F., Vazdekis, A., Ferreras, I., et al. 2017, MNRAS, 464, 3597
  * Lacy et al. (2021) Lacy, M., Surace, J. A., Farrah, D., et al. 2021, MNRAS, 501, 892
  * Laigle et al. (2016) Laigle, C., McCracken, H. J., Ilbert, O., et al. 2016, ApJS, 224, 24
  * Lamareille (2010) Lamareille, F. 2010, A&A, 509, A53
  * Lawrence et al. (2007) Lawrence, A., Warren, S. J., Almaini, O., et al. 2007, MNRAS, 379, 1599
  * Lawrence et al. (2012) Lawrence, A., Warren, S. J., Almaini, O., et al. 2012, VizieR Online Data Catalog, II/314
  * Le Fèvre et al. (2013) Le Fèvre, O., Cassata, P., Cucciati, O., et al. 2013, A&A, 559, A14
  * Le Fèvre et al. (2015) Le Fèvre, O., Tasca, L. A. M., Cassata, P., et al. 2015, A&A, 576, A79
  * Le Fèvre et al. (2005) Le Fèvre, O., Vettolani, G., Garilli, B., et al. 2005, A&A, 439, 845
  * Lilly et al. (2009) Lilly, S. J., Le Brun, V., Maier, C., et al. 2009, ApJS, 184, 218
  * Lilly et al. (2007) Lilly, S. J., Le Fèvre, O., Renzini, A., et al. 2007, ApJS, 172, 70
  * Lindegren et al. (2021) Lindegren, L., Klioner, S. A., Hernández, J., et al. 2021, A&A, 649, A2
  * López Fernández et al. (2018) López Fernández, R., González Delgado, R. M., Pérez, E., et al. 2018, A&A, 615, A27
  * Madau & Dickinson (2014) Madau, P. & Dickinson, M. 2014, ARA&A, 52, 415
  * Magnier et al. (2013) Magnier, E. A., Schlafly, E., Finkbeiner, D., et al. 2013, ApJS, 205, 20
  * Magris et al. (2015) Magris, G., Mateu P., J., Mateu, C., et al. 2015, PASP, 127, 16
  * Maiolino & Mannucci (2019) Maiolino, R. & Mannucci, F. 2019, A&A Rev., 27, 3
  * Małek et al. (2018) Małek, K., Buat, V., Roehlly, Y., et al. 2018, A&A, 620, A50
  * Mannucci et al. (2010) Mannucci, F., Cresci, G., Maiolino, R., Marconi, A., & Gnerucci, A. 2010, MNRAS, 408, 2115
  * Martínez-Solaeche et al. (2021) Martínez-Solaeche, G., González Delgado, R. M., García-Benito, R., et al. 2021, A&A, 647, A158
  * Martínez-Solaeche et al. (2022) Martínez-Solaeche, G., González Delgado, R. M., García-Benito, R., et al. 2022, A&A, 661, A99
  * Mauduit et al. (2012) Mauduit, J. C., Lacy, M., Farrah, D., et al. 2012, PASP, 124, 714
  * McCracken et al. (2012) McCracken, H. J., Milvang-Jensen, B., Dunlop, J., et al. 2012, A&A, 544, A156
  * Miller et al. (2013) Miller, L., Heymans, C., Kitching, T. D., et al. 2013, MNRAS, 429, 2858
  * Morrissey et al. (2005) Morrissey, P., Schiminovich, D., Barlow, T. A., et al. 2005, ApJ, 619, L7
  * Moutard et al. (2016) Moutard, T., Arnouts, S., Ilbert, O., et al. 2016, A&A, 590, A102
  * Nagao et al. (2006) Nagao, T., Maiolino, R., & Marconi, A. 2006, A&A, 459, 85
  * Newman et al. (2013) Newman, J. A., Cooper, M. C., Davis, M., et al. 2013, ApJS, 208, 5
  * Nishizawa et al. (2020) Nishizawa, A. J., Hsieh, B.-C., Tanaka, M., & Takata, T. 2020, arXiv e-prints, arXiv:2003.01511
  * Oke (1974) Oke, J. B. 1974, ApJS, 27, 21
  * Oliver et al. (2000) Oliver, S., Rowan-Robinson, M., Alexander, D. M., et al. 2000, MNRAS, 316, 749
  * Peng et al. (2010) Peng, Y.-j., Lilly, S. J., Kovač, K., et al. 2010, ApJ, 721, 193
  * Pierre et al. (2016) Pierre, M., Pacaud, F., Adami, C., et al. 2016, A&A, 592, A1
  * Pierre et al. (2011) Pierre, M., Pacaud, F., Juin, J. B., et al. 2011, MNRAS, 414, 1732
  * Popesso et al. (2019) Popesso, P., Concas, A., Morselli, L., et al. 2019, MNRAS, 483, 3213
  * Pozzetti et al. (2010) Pozzetti, L., Bolzonella, M., Zucca, E., et al. 2010, A&A, 523, A13
  * Rubin et al. (2012) Rubin, K. H. R., Prochaska, J. X., Koo, D. C., & Phillips, A. C. 2012, ApJ, 747, L26
  * Sabater et al. (2021) Sabater, J., Best, P. N., Tasse, C., et al. 2021, A&A, 648, A2
  * Sánchez-Blázquez et al. (2009) Sánchez-Blázquez, P., Jablonka, P., Noll, S., et al. 2009, A&A, 499, 47
  * Sargent et al. (2007) Sargent, M. T., Carollo, C. M., Lilly, S. J., et al. 2007, ApJS, 172, 434
  * Sawicki et al. (2019) Sawicki, M., Arnouts, S., Huang, J., et al. 2019, MNRAS, 489, 5202
  * Scarlata et al. (2007) Scarlata, C., Carollo, C. M., Lilly, S., et al. 2007, ApJS, 172, 406
  * Schlafly et al. (2012) Schlafly, E. F., Finkbeiner, D. P., Jurić, M., et al. 2012, ApJ, 756, 158
  * Schlafly et al. (2019) Schlafly, E. F., Meisner, A. M., & Green, G. M. 2019, ApJS, 240, 30
  * Scodeggio et al. (2018) Scodeggio, M., Guzzo, L., Garilli, B., et al. 2018, A&A, 609, A84
  * Scoville et al. (2007) Scoville, N., Aussel, H., Brusa, M., et al. 2007, ApJS, 172, 1
  * Shirley et al. (2021) Shirley, R., Duncan, K., Campos Varillas, M. C., et al. 2021, MNRAS, 507, 129
  * Speagle et al. (2014) Speagle, J. S., Steinhardt, C. L., Capak, P. L., & Silverman, J. D. 2014, ApJS, 214, 15
  * Spilker et al. (2018) Spilker, J., Bezanson, R., Barišić, I., et al. 2018, ApJ, 860, 103
  * Spiniello et al. (2015) Spiniello, C., Trager, S. C., & Koopmans, L. V. E. 2015, ApJ, 803, 87
  * Straatman et al. (2018) Straatman, C. M. S., van der Wel, A., Bezanson, R., et al. 2018, ApJS, 239, 27
  * Swinbank (2013) Swinbank, A. M. 2013, in Astrophysics and Space Science Proceedings, Vol. 37, Thirty Years of Astronomical Discovery with UKIRT, 299
  * Talbot et al. (2021) Talbot, M. S., Brownstein, J. R., Dawson, K. S., Kneib, J.-P., & Bautista, J. 2021, MNRAS, 502, 4617
  * Tanaka et al. (2018) Tanaka, M., Coupon, J., Hsieh, B.-C., et al. 2018, PASJ, 70, S9
  * Terrett et al. (2014) Terrett, D. L., Lewis, I. J., Dalton, G., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9152, Software and Cyberinfrastructure for Astronomy III, ed. G. Chiozzi & N. M. Radziwill, 91520P
  * Tortora et al. (2018) Tortora, C., Napolitano, N. R., Roy, N., et al. 2018, MNRAS, 473, 969
  * Vaccari (2022) Vaccari, M. 2022, in Zenodo dataset, Vol. 63, 6368348
  * van der Wel et al. (2021) van der Wel, A., Bezanson, R., D’Eugenio, F., et al. 2021, ApJS, 256, 44
  * van der Wel et al. (2016) van der Wel, A., Noeske, K., Bezanson, R., et al. 2016, ApJS, 223, 29
  * Vazdekis et al. (2016) Vazdekis, A., Koleva, M., Ricciardelli, E., Röck, B., & Falcón-Barroso, J. 2016, MNRAS, 463, 3409
  * Vazdekis et al. (2010) Vazdekis, A., Sánchez-Blázquez, P., Falcón-Barroso, J., et al. 2010, MNRAS, 404, 1639
  * Warren et al. (1996) Warren, S. J., Hewett, P. C., Lewis, G. F., et al. 1996, MNRAS, 278, 139
  * Weaver et al. (2022) Weaver, J. R., Kauffmann, O. B., Ilbert, O., et al. 2022, ApJS, 258, 11
  * Wechsler & Tinker (2018) Wechsler, R. H. & Tinker, J. L. 2018, ARA&A, 56, 435
  * Werle et al. (2022) Werle, A., Poggianti, B., Moretti, A., et al. 2022, ApJ, 930, 43
  * Woo et al. (2016) Woo, J.-H., Bae, H.-J., Son, D., & Karouzos, M. 2016, ApJ, 817, 108
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * Wu et al. (2021) Wu, P.-F., Nelson, D., van der Wel, A., et al. 2021, AJ, 162, 201
  * Wu et al. (2020) Wu, P.-F., van der Wel, A., Bezanson, R., et al. 2020, ApJ, 888, 77
  * Wu et al. (2018) Wu, P.-F., van der Wel, A., Gallazzi, A., et al. 2018, ApJ, 855, 85
  * York et al. (2000) York, D. G., Adelman, J., Anderson, John E., J., et al. 2000, AJ, 120, 1579
  * Zibetti et al. (2017) Zibetti, S., Gallazzi, A. R., Ascasibar, Y., et al. 2017, MNRAS, 468, 1902